TEST BANK for College Physics A Strategic Approach 4th Edition by Randall Knight, Brian Jones & Stua by StudyGuide

TABLE OF CONTENTS Chapter 1 Representing Motion Chapter 2 Motion in One Dimension Chapter 3 Vectors and Motion in Two Dimensions Chapter 4 Forces and Newton's Laws of Motion Chapter 5 Applying Newton's Laws Chapter 6 Gravity Chapter 7 Rotational Motion Chapter 8 Equilibrium ad Elasticity Chapter 9 Momentum Chapter 10 Energy and Work Chapter 11 Using Energy Chapter 12 Thermal Properties of Matter Chapter 13 Fluids Chapter 14 Oscillations Chapter 15 Traveling Waves and Sound Chapter 16 Superposition and Standing Waves Chapter 17 Wave Optics Chapter 18 Ray Optics Chapter 19 Optical Instruments Chapter 20 Electric Fields and Forces Chapter 21 Electric Potential Chapter 22 Current and Resistance Chapter 23 Circuits 23.1 Conceptual Questions Chapter 24 Magnetic Fields and Forces Chapter 25 EM Induction and EM Waves Chapter 26 AC Electricity Chapter 27 Relativity Chapter 28 Quantum Physics Chapter 29 Atoms and Molecules Chapter 30 Nuclear

College Physics: A Strategic Approach, 4e (Knight) Chapter 1 Representing Motion 1.1 Conceptual Questions 1) In the product A ∙ B ∙ C, A has 5 significant figures, B has 2 significant figures, and C has 3 significant figures. How many significant figures does the product have? A) 2 B) 3 C) 4 D) 5 E) 10 Answer: A Var: 1 2) In the quotient

, A has 5 significant figures, B has 2 significant figures, and C has 3

significant figures. How many significant figures does the quotient have? A) 2 B) 3 C) 4 D) 0 E) 1 Answer: A Var: 1 3) In the sum A + B + C, A is accurate to 5 decimal places, B is accurate to 2 decimal places, and C is accurate to 3 decimal places. What is the correct number of decimal places in the sum? A) 2 B) 3 C) 4 D) 5 E) 10 Answer: A Var: 1 4) In the difference A - B - C, A is accurate to 5 decimal places, B is accurate to 2 decimal places, and C is accurate to 3 decimal places. What is the correct number of decimal places in the difference? A) 2 B) 3 C) 4 D) 5 E) 0 Answer: A Var: 1 1 Copyright © 2019 Pearson Education, Inc.

5) How many significant figures are in the number 0.0037010? A) four B) five C) six D) seven E) eight Answer: B Var: 1 6) How many significant figures are in the number 0.010? A) four B) three C) two D) one Answer: C Var: 1 7) How many significant figures are in the number 120.070? A) six B) five C) four D) three Answer: A Var: 1 8) The number of significant figures in 10001 is A) two. B) three. C) five. D) six. Answer: C Var: 6 9) The number of significant figures in 0.01500 is A) two. B) three. C) four. D) five. Answer: C Var: 5

10) The number of significant figures in 0.040 is A) one. B) two. C) three. D) four. Answer: B Var: 6 11) Which of the following numbers has 4 significant figures; which has 5 significant figures? (a) 3001 (b) 0.00370 (c) 4774.00 (d) 29.290 Answer: (a) has 4 significant figures; (d) has 5 significant figures Var: 1 12) In a parallel universe, the quantity π has the value 3.14049… . Express π in that universe to (a) four significant figures (b) five significant figures. Answer: (a) 3.140 (b) 3.1405 Var: 1 13) The metric system is preferred over the British system in science for the following main reason. A) The metric system is more precise than the British system. B) Metric quantities can be defined more accurately than the quantities in the British system. C) Metric quantities are natural whereas British quantities are invented. D) Conversions between metric quantities are especially easy because they are all related by factors of ten. Answer: D Var: 1 14) A reasonable estimate for the mass of a typical female college student is A) 20 kg. B) 50 kg. C) 150 kg. D) 200 kg. Answer: B Var: 1 15) A reasonable estimate for the height of an ordinary adult male is A) 50 cm. B) 70 cm. C) 200 cm. D) 300 cm. Answer: C Var: 1 3 Copyright © 2019 Pearson Education, Inc.

16) A reasonable estimate for the mass of a typical new-born baby is A) 1 kg. B) 3 kg. C) 10 kg. D) 20 kg. Answer: B Var: 1 17) A reasonable estimate for the height of the walls in an ordinary American home is A) 10 m. B) 8 m. C) 2.5 m. D) 1.5 m. Answer: C Var: 1 18) A reasonable estimate for the duration of a typical physics lecture is A) 600 s. B) 1000 s. C) 3500 s. D) 10,000 s. Answer: C Var: 1 19) A reasonable estimate for the mass of an ordinary passenger car is A) 100 kg B) 1000 kg C) 5000 kg D) 10,000 kg Answer: B Var: 1

1.2 Problems 1) What is the product of 12.56 and 2.12 expressed to the correct number of significant figures? A) 27 B) 26.6 C) 26.23 D) 26.627 Answer: B Var: 3 2) What is the quotient of 2.43 ÷ 4.561 expressed to the correct number of significant figures? A) 5.3278 × B) 5.328 × C) 5.33 × D) 5.3 × Answer: C Var: 3 3) What is

expressed to the correct number of significant figures?

A) 0.91 B) 0.911 C) 0.9108 D) 0.9 Answer: A Var: 50+ 4) What is 0.2052/3, to the correct number of significant figures? A) 0.348 B) 0.35 C) 0.3 D) 0.3477 Answer: A Var: 50+ 5) Add and significant figures. A) 4.64 × 107 mg B) 4.64 × 104 mg C) 4.64 × 105 mg D) 4.64 × 106 mg Answer: A Var: 50+

and express your answer in milligrams (mg) to the correct number of

6) What is

expressed to the correct number of significant figures?

Answer: 1.22 Var: 1 7) The length and width of a rectangle are 1.125 m and 0.606 m, respectively. Multiplying, your calculator gives the product as 0.68175. Rounding properly to the correct number of significant figures, the area of the rectangle should be written as A) 0.68 m2 B) 0.682 m2 C) 0.6818 m2 D) 0.68175 m2 Answer: B Var: 1 8) What is the sum of 2.67 + 1.976 + 2.1 expressed to the correct number of significant figures? A) 6.7 B) 6.75 C) 6.746 D) 6.7460 Answer: A Var: 3 9) Express the sum of 420.77, 13.821, and 2317.8 to the correct number of significant figures. Answer: 2752.4 Var: 1 10) What is the difference between 103.5 and 102.24 expressed to the correct number of significant figures? A) 1.3 B) 1.26 C) 1.260 D) 1.2600 Answer: A Var: 3 11) What is the sum of 1.53 + 2.786 + 3.3 expressed to the correct number of significant figures? A) 7 B) 7.6 C) 7.62 D) 7.616 E) 7.6160 Answer: B Var: 3

12) Express the result of the following calculation to the proper number of significant figures: 50.19 - 7966 × 10-3. Answer: 42.22 Var: 1 13) What is the result, expressed to the proper number of significant figures, of adding 23.4 to 91.237 and then subtracting 23.4? A) 91.237 B) 91.2 C) 91.3 D) 91.0 E) 91 Answer: B Var: 1 14) Express the result of the following calculation, in scientific notation, to the proper number of significant figures:

+ 19

Answer: 5.9 × 104 Var: 1 15) Add the following lengths, each obtained from a different measuring instrument, and round the answer to the proper number of significant figures: 20.02 m, 5.91 m, 0.0097 m, and 2.467 m. Answer: 28.41 m Var: 1 16) The last page of a book is numbered 764. The book is 3.0 cm thick, not including its covers. What is the average thickness (in centimeters) of a page in the book, rounded to the proper number of significant figures? A) 0.0039 cm B) 0.072 cm C) 0.0079 cm D) 0.00393 cm E) 0.00785 cm Answer: C Var: 1 17) The length and width of a rectangle are 1.125 m and 0.606 m, respectively. You calculate the rectangle's perimeter by adding these numbers and multiplying by two. Your calculator's display reads 3.462. To the correct number of significant figures, the perimeter should be written as A) 3.5 m. B) 3.46 m. C) 3.462 m. D) 3.4620 m. Answer: C Var: 1 7 Copyright © 2019 Pearson Education, Inc.

18) A rectangular garden measures 15 m long and 13.70 m wide. What is the length of a diagonal from one corner of the garden to the other? A) 18 m B) 19 m C) 20 m D) 4.1 × 102 m Answer: C Var: 1 19) If a circle has a radius of 1.109 m, what is its area expressed to the correct number of significant figures? A) 3.86 m2 B) 3.863 m2 C) 3.864 m2 D) 3.8638 m2 E) 3.86379 m2 Answer: C Var: 1 20) A train travels at a constant speed of 60.4 mi/h for 101.5 min. What distance does the train cover expressed to the correct number of significant figures? A) 100 mi B) 102 mi C) 102.2 mi D) 102.18 mi E) 102.181 mi Answer: B Var: 1 21) A dog has three puppies. Spot weighs 12 ounces. Rascal weighs 9.5 ounces. Socks weighs 10.2 ounces. What is the total weight of the litter expressed to the correct number of significant figures? A) 31.7 ounces B) 31 ounces C) 32 ounces D) 30 ounces E) 31.70 ounces Answer: C Var: 1

22) A traveler has about $536 in his checking account, about $2107 in his savings account and exactly $7.62 in his wallet. To the greatest precision warranted, how much money does this shopper have? A) $2651 B) $2,650 C) $2,650.6 D) $2,650.62 E) $2,650.620 Answer: A Var: 1 23) To get to her physics class, Alice walks 0.25 mi to the bus stop. She takes the bus 1.2 mi to the train station. She takes the train 13 mi and walks the remaining 0.17 mi to her class. How far is her commute expressed to the correct number of significant figures? A) 14.6 mi B) 10 mi C) 15 mi D) 14.62 mi E) 14.620 mi Answer: C Var: 1 24) What is 56 +

written with the correct number of significant figures?

A) 62.8 B) 62.812 C) 62.81 D) 63 E) 62.8123846 Answer: D Var: 1 25) Using a digital balance the mass of a certain piece of wood is read as 12.946 g. Thinking in terms of accuracy and significant figures, what value would you record on your data sheet if the balance is accurate to one-tenth of a gram? A) 12.9 g B) 12.95 g C) 13 g D) 13.0 g Answer: A Var: 1

26) Which of the following numbers is the smallest? A) 15 × 10-3 B) 0.15 × 100 C) 0.00015 × 103 D) 0.00000015 × 106 Answer: A Var: 1 27) Which one of the following numbers is equivalent to the number 0.0001776? A) 1.776 × 10-4 B) 17.76 × 10-3 C) 1776 × 10-5 D) 177.6 × 10-7 Answer: A Var: 1 28) Write out the number 8.42 × 10-5 in full with a decimal point and correct number of zeros. A) 0.00000842 B) 0.0000842 C) 0.000842 D) 0.00842 Answer: B Var: 5 29) What is the result of the calculation (0.410 + 0.021) × (2.20 × 103)? A) 880 B) 946 C) 948 D) 950 Answer: C Var: 1 30) Express (2.2 × 106)-1/2 in scientific notation. A) 6.7 × 10-4 B) 1.5 × 103 C) 1.5 × 10-5 D) 1.5 × 104 Answer: A Var: 40

31) Express the number 13.5 gigameters in meters without using scientific notation. A) 135,000 m B) 135,000,000 m C) 135,000,000,000 m D) 13,500,000,000 m Answer: D Var: 1 32) A volume of 100 mL is equivalent to which one of the following volumes? A) 1 kL B) 10-6 μL C) 0.1 L D) 0.01 ML Answer: C Var: 1 33) The volume of a 10-mL test tube is equivalent to which one of the following quantities? A) 0.01 L B) 0.001 kL C) 0.1 L D) 1 × 10-6 L E) 0.001 ML Answer: A Var: 1 34) The number 0.00325 × 10-8 cm can be expressed in millimeters as A) 3.25 × 10-12 mm. B) 3.25 × 10-11 mm. C) 3.25 × 10-10 mm. D) 3.25 × 10-9 mm. Answer: C Var: 1 35) An area of 1.00 × 102 cm2 is how many square meters? A) 1.00 m2 B) 1.00 × 102 m2 C) 1.00 × 10-2 m2 D) 1.00 × 104 m2 E) 1.00 × 10-3 m2 Answer: C Var: 1

36) The prefix yotta (Y) signifies a multiple of 1024. How many yottameters are there in a gigameter? Answer: 10-15 ym Var: 1 37) Express the sum 1.00 kg + 1531 g + 2.54 × 104 mg in kilograms with the correct number of significant figures. A) 2.56 kg B) 27.9 kg C) 2.53 kg D) 2.79 kg Answer: A Var: 1 38) The quantity 0.00325 × 10-8 cm is equivalent to A) 3.25 × 10-12 mm B) 3.25 × 10-11 mm C) 3.25 × 10-10 mm D) 3.25 × 10-9 mm E) 3.25 × 10-8 mm Answer: C Var: 1 39) A weight lifter can bench press A) 1.71 × 108 mg B) 1.71 × 109 mg C) 1.71 × 107 mg D) 1.71 × 106 mg Answer: A Var: 50+

How many milligrams is this?

40) How many nanoseconds does it take for a computer to perform one calculation if it performs calculations per second? A) 15 ns B) 67 ns C) 11 ns D) 65 ns Answer: A Var: 50+

41) A certain disk can store 600 megabytes of information. If an average word requires 9.0 bytes of storage, how many words can be stored on one disk? A) 6.7 × 107 words B) 5.4 × 109 words C) 2.1 × 107 words D) 2.0 × 109 words Answer: A Var: 9 42) The wavelength of the light from a certain laser is What is this wavelength in nanometers? (1 nm = 10-9m) A) 6.6 × 102 nm B) 6.6 × 103 nm C) 6.6 × 101 nm D) 6.6 × 104 nm Answer: A Var: 50+

where

43) If you are 5'10'' tall, what is your height in meters? (2.54 cm = 1.00 in.) A) 1.5 m B) 1.6 m C) 1.7 m D) 1.8 m Answer: D Var: 1 44) Given that 1.00 in. = 2.54 cm and 1.00 yd = 36.0 in., how many meters are in 7.00 yd? A) 6.40 m B) 36.3 m C) 640 m D) 1.78 × 103 m Answer: A Var: 1 45) Hydraulicists often express rainfall in acre-feet. This is the amount of water required to cover an area of one acre to a depth of one foot. There are 640.0 acres in a square mile, and 5280 feet in one mile. How many cubic feet are there in one acre-foot? Answer: 43,560 ft3 Var: 1

46) Express 50 mi/h in units of meters per second. (1 mi = 1609 m) A) 49 m/s B) 2.2 m/s C) 22 m/s D) 45 m/s Answer: C Var: 1 47) Given that 1.00 in. = 2.54 cm, how many square centimeters are in 1.00 square inch? A) 1.59 B) 2.54 C) 5.08 D) 6.45 Answer: D Var: 1 48) A plot of land contains ft2 and 2.54 cm = 1.00 in.) A) 2.3 × 104 m2 B) 7.1 × 103 m2 C) 7.0 × 104 m2 D) 5.0 × 104 m2 Answer: A Var: 50+

How many square meters does it contain? (1.0 acre = 43,560

49) The density of water is 1.00 g/cm3. What is its density in kg/m3? Answer: 1.00 ×103 kg/m3 Var: 1 50) A light-year (ly) is the distance that light travels in one year. The speed of light is 3.00 × 108 m/s. How many miles are there in 1.00 ly? (1.00 mi = 1.609 km and one year is 365.25 days.) A) 2.87 × 1013 mi B) 9.46 × 1015 mi C) 5.88 × 1015 mi D) 9.46 × 1012 mi E) 5.88 × 1012 mi Answer: E Var: 1

51) A speed of 60 mi/h is closest to which of the following? (2.54 cm = 1.00 in.) A) 60 m/s B) 20 m/s C) 30 km/h D) 120 m/s E) 30 m/s Answer: E Var: 1 52) Which of the following speeds is greatest? (2.54 cm = 1.00 in.) A) 10 km/h B) 10 m/s C) 10 ft/s D) 10 mi/h E) 10 yd/s Answer: B Var: 1 53) A person on a diet loses A) 2.6 × 103 μg/s B) 1.6 × 105 μg/s C) 44 μg/s D) 6.4 × 104 μg/s Answer: A Var: 11

in a week. How many micrograms per second (μg/s) are lost?

54) There are 640 acres in a square mile, 5280 ft in one mile, and 3.28 ft in one meter. How many acres are there in a hectare, which is a square one hundred meters on each side? Answer: 2.47 acres Var: 1 55) There are 2.00 dry pints to 1.00 dry quart, 8.00 dry quarts to 1.00 peck, 4.00 pecks to 1.00 bushel. An organic farmer wants to pick enough berries to fill 40,000 pint containers. How many bushels of berries does the farmer need? Answer: 625 bushels Var: 1 56) A typical ruby-throated hummingbird is 8 cm long. Express its length in millimeters and micrometers (µm). A) 80 mm; 800 µm B) 80 mm; 80,000 µm C) 800 mm; 0.008 µm D) 800 mm; 0.8 µm E) 0.8 mm; 8000 µm Answer: B Var: 1 15 Copyright © 2019 Pearson Education, Inc.

57) A jogger has a mass of 50 kg. Express her mass in grams and micrograms (µg). A) 50,000 g; 5 ×106 µg B) 500,000 g; 500 × 106 µg C) 500,000 g; 5000 µg D) 50,000 g; 5 × 1010 µg E) 50,000 g; 50,000 µg Answer: D Var: 1 58) A jar of peanut butter costs $3.29. Express its price in dekadollars and decidollars. A) 0.329 dekadollars; 0.329 decidollars B) 32.9 dekadollars; 0.329 decidollars C) 329 dekadollars; 32.9 decidollars D) 0.329 dekadollars; 32.9 decidollars E) 32.9 dekadollars; 329 decidollars Answer: D Var: 1 59) The following conversion equivalents are given: 1.00 gal = 231 1.0 ft = 12 in 1.0 min = 60 s If a pipe delivers water at the rate of 95 gal/min, its rate of flow in ft3/s is closest to A) 0.21 ft3/s. B) 0.19 ft3/s. C) 0.17 ft3/s. D) 0.15 ft3/s. E) 0.14 ft3/s. Answer: A Var: 50+ 60) The following conversion equivalents are given: 1.0 m = 100 cm 1.0 in = 2.54 cm 1.0 ft = 12 in If a bin has a volume of 1.5 m3, the volume of the bin, in ft3, is closest to A) 35 ft3 B) 41 ft3 C) 47 ft3 D) 53 ft3 E) 59 ft3 Answer: D Var: 1

61) The following conversion equivalents are given: 1.0 mile = 5280 ft 1.0 ft = 12 in 1 m = 39.37 in 1.0 hour = 60 min 1.0 min = 60 s If a deer runs at 4.7 mi/h, its speed, in meters per second, is closest to A) 2.1 m/s. B) 1.7 m/s. C) 1.9 m/s. D) 2.3 m/s. E) 2.5 m/s. Answer: A Var: 50+ 62) A speed of 65 miles per hour is the same as which of the following? (1.00 ft = 30.48 cm) A) 24 m/s B) 29 m/s C) 32 m/s D) 37 m/s E) 42 m/s Answer: B Var: 1 63) The following conversion equivalents are given: 1.0 kg = 1000 g 1.0 l = 1000 1.0 l = 0.0353 The density of a certain liquid is 0.83 g/ . The density of this liquid, expressed in kg/ft3, is closest to A) 24 kg/ft3. B) 19 kg/ft3. C) 21 kg/ft3. D) 26 kg/ft3. E) 28 kg/ft3. Answer: A Var: 50+ 64) Your car gets 34.7 mi/gal on a vacation trip in the U.S. If you were figuring your mileage in Europe, how many km/L did it get? (3.79 L = 1.00 gal; 1.00 mi = 1.61 km) A) 14.7 km/L B) 9.16 km/L C) 55.9 km/L D) 32.4 km/L Answer: A Var: 50+

65) An oak tree was planted take leap days into account.) A) 6.9 × 108 B) 1.2 × 107 C) 2.9 × 107 D) 2.8 × 108 Answer: A Var: 12

ago. How many seconds does this correspond to? (Do not

66) At a certain time, the average size of a transistor in a microprocessor was 250 nanometers. A human hair has a diameter of 70 microns (micrometers). How many transistors fit across a human hair? A) 280 B) 28 C) 2800 D) 2.8 E) 0.28 Answer: A Var: 1 67) The king's chamber of the great pyramid in Egypt is 10.43 m long, 5.21 m wide, and 5.82 m high. What is the volume of the chamber in cubic feet, expressed to the correct number of significant figures? (1.00 in. = 2.54 cm) A) 316 ft3 B) 3,720 ft3 C) 6,530 ft3 D) 11,200 ft3 E) 13,200 ft3 Answer: D Var: 1 68) Rover eats 0.50 pound of dry dog food per day. How many 5.0-kg sacks of dog food does his owner need to buy in a year? (1.0 kg weighs 2.2 lb) A) 17 B) 25 C) 52 D) 80 E) 81 Answer: A Var: 1

69) The peak of Mt. Everest, at 10,900 m, is the highest point above sea level in the world. What is its elevation in miles? (1.00 m = 3.281 ft) A) 17.6 mi B) 0.630 mi C) 6.77 mi D) 6.20 mi E) 67.1 mi Answer: C Var: 1 70) The Hope Diamond weighs 44.5 carats, and there are 200 mg per carat. What is the mass of the Hope Diamond in kilograms? A) 0.000890 kg B) 0.00890 kg C) 0.0890 kg D) 0.890 kg E) 8.90 kg Answer: B Var: 1 71) The column of Trajan, erected in Rome in 106-113 A.D., is 125 feet tall. What is its height in centimeters? (2.54 cm = 1.00 in.) A) 1,510 cm B) 591 cm C) 2,520 cm D) 3,810 cm E) 38,100 cm Answer: D Var: 1 72) There are 640 acres in a square mile, and 5280 feet in 1.00 mile. What is the length in feet (to the nearest foot) of the side of a square having an area of 1.00 acre? A) 660 feet B) 209 feet C) 165 feet D) 412 feet E) 435 feet Answer: B Var: 1

73) An American football field, including end zones, is 360 feet long and 160 feet wide. If you needed to describe it for someone in Europe using the metric system, which one of the following quantities would be closest to its area in square meters? (2.54 cm = 1.00 in.) A) 4,920 m2 B) 5,350 m2 C) 88.0 m2 D) 12,100 m2 E) 13,200 m2 Answer: B Var: 1 74) Leonardo da Vinci's Mona Lisa is 21 in. wide and 30.25 in. tall. What is the area of the painting in square centimeters? (1.00 m = 39.37 in.) A) 4,100 cm2 B) 1,600 cm2 C) 660 cm2 D) 3,300 cm2 E) 2,400 cm2 Answer: A Var: 1 75) A cylindrical drinking glass has a diameter of 2.5 in. and is 5.5 in. tall. What is the volume of the drinking glass in cubic centimeters? (2.54 cm = 1.00 in.) A) 170 cubic cm B) 440 cubic cm C) 350 cubic cm D) 710 cubic cm E) 530 cubic cm Answer: B Var: 1 76) A football field is 120 yd long and 50 yd wide. What is the area of the football field, in square meters, given that 1.0 yd = 91.44 cm? A) 2.4 × 103 m2 B) 3.7 × 103 m2 C) 4.2 × 103 m2 D) 5.0 × 103 m2 Answer: D Var: 1

77) Wall posters are usually sold curled up in cylindrical cardboard tubes. If the length of the tube is 84.5 cm, and the inside diameter of the tube is 2.40 cm, what is the area of the poster expressed to the correct number of significant figures? (Assume the poster is just as long as the tube and does not overlap itself.) A) 202.8 cm2 B) 637.1 cm2 C) 203 cm2 D) 319 cm2 E) 637 cm2 Answer: E Var: 1 78) A spherical fruit has a radius of 3.23 cm. What is the volume of the fruit in cubic meters? A) 1.41 × 10-4 m3 B) 1.41 m3 C) 4.23 × 10-4 m3 D) 4.23 m3 Answer: A Var: 1 79) A thick-walled metal pipe of length 20.0 cm has an inside diameter of 2.00 cm and an outside diameter of 2.40 cm. What is the total surface area of the pipe, counting the ends, in square centimeters? A) 276 cm2 B) 277 cm2 C) 278 cm2 D) 279 cm2 Answer: D Var: 1 80) The radius of the earth is 3963 mi. Which one of the following numbers is closest to the surface area of the earth? (1.0 mi = 1609 m) A) 4.9 × 107 m2 B) 1.3 × 1014 m2 C) 2.6 × 1014 m2 D) 5.1 × 1014 m2 Answer: D Var: 1

81) A large school district has 300 school buses. If each school bus is used 3.0 hours each day, the average speed of the school buses is 15 mi/h, and the fuel economy of the buses is 10 mi/gal. How much does it cost to run these buses for 22 school days if gasoline costs $4.10 a gallon? A) $60,000 B) $120,000 C) $180,000 D) $240,000 Answer: B Var: 1 82) A 2.00-qt bottle of soda is on sale for $1.29. What should be the price of a 2.00-L bottle of the same soda to yield the same value? (1.00 qt = 0.947 L) Answer: $1.36 Var: 1 83) In a country where the unit of currency is the Passi, kerosene costs 130 Passi per liter, and one dollar buys 227 Passi. What is the cost of kerosene in dollars per gallon? (1.00 gal = 3.79 L) Answer: $2.17 per gallon Var: 1 84) The tank of a certain car holds 16 gallons of gasoline. (1.00 gal = 3.785 L) (a) How many liters of gasoline does this tank hold? (b) How many kilometers can the car travel on one tank if it gets 25 miles per gallon? Answer: (a) 61 L (b) 640 km Var: 1 85) The mass of Mars, 6.40 × 1023 kg, is about one-tenth that of Earth, and its radius, 3395 km, is about half that of Earth. What is the mean density (mass divided by volume) of Mars in kilograms per cubic meter? A) 9.76 × 102 kg/m3 B) 1.95 × 103 kg/m3 C) 3.90 × 103 kg/m3 D) 7.81 × 103 kg/m3 Answer: C Var: 1 86) The average density of blood is 1.06 × 103 kg/m3. If you donate a pint of blood to the Red Cross, how many grams of blood have you donated? (2.00 pt = 1.00 qt, 1.00 L = 1000 cm3, 1.00 qt = 0.947 L, and density is mass per unit volume.) A) 502 g B) 0.502 g C) 5020 g D) 5.02 × 105 g E) 5.02 g Answer: A Var: 1 22 Copyright © 2019 Pearson Education, Inc.

87) Concrete is sold by the cubic yard. What is the mass, in kilograms, of 1.00 cubic yard of concrete that is 5.00 times as dense as water? (1.00 m = 1.094 yd, a cubic meter of water has a mass of 1,000 kg, and density is mass per unit volume.) A) 764 kg B) 6550 kg C) 2420 kg D) 8730 kg E) 3820 kg Answer: E Var: 1 88) A porch roof that slopes upward at 45° measures 3.0 m × 5.0 m. It is covered with a slab of insulating material that is 2.0 cm thick. If the density of the insulation is 15 kg/m3, what is the weight of the insulation, in pounds, on the roof? (1.00 kg weighs 2.2 lb and density is mass per unit volume.) A) 4.5 lb B) 9.0 lb C) 20 lb D) 990 lb E) 9.9 lb Answer: E Var: 1 89) Estimate how many pennies would you have to stack to reach from the floor to an average 8ft ceiling. A) 2 × 103 B) 2 × 102 C) 2 × 104 D) 2 × 105 E) 2 x 106 Answer: A Var: 1 90) Estimate the number of times the earth will rotate on its axis during a human's lifetime. A) 3 × 104 B) 3 × 105 C) 3 × 106 D) 3 × 107 E) 3 × 108 Answer: A Var: 1

91) Estimate the thickness, in meters, of an ordinary sheet of paper. A) 10-4 m B) 10-5 m C) 10-6 m D) 10-7 m E) 10-8 m Answer: A Var: 1 92) Which of the following is the most reasonable estimate of the number of characters (typed letters or numbers) in a 609-page book? Assume an average of 194 words per page and a reasonable average number of letters per word. A) 5 × 105 char B) 5 × 107 char C) 5 × 106 char D) 5 × 104 char Answer: A Var: 50+ 93) A marathon race is 26 mi and 385 yd long. Estimate how many strides would be required to run a marathon. Assume a reasonable value for the average number of feet/stride. A) 4.5 × 104 strides B) 4.5 × 103 strides C) 4.5 × 105 strides D) 4.5 × 106 strides Answer: A Var: 1 94) Estimate the number of times an average person's heart beats in a lifetime. Assume the average heart rate is and a life span of 75 years. A) 3 × 109 beats B) 3 × 108 beats C) 3 × 1010 beats D) 3 × 107 beats Answer: A Var: 50+

College Physics: A Strategic Approach, 4e (Knight) Chapter 2 Motion in One Dimension 2.1 Conceptual Questions 1) Consider a deer that runs from point A to point B. The distance the deer runs can be greater than the magnitude of its displacement, but the magnitude of the displacement can never be greater than the distance it runs. A) True B) False Answer: A Var: 1 2) Which of the following quantities has units of a displacement? (There could be more than one correct choice.) A) 32 ft/s2 vertically downward B) 40 km southwest C) 9.8 m/s2 D) -120 m/s E) 186,000 mi Answer: B, E Var: 1 3) Suppose that an object travels from one point in space to another. Make a comparison between the magnitude of the displacement and the distance traveled by this object. A) The displacement is either greater than or equal to the distance traveled. B) The displacement is always equal to the distance traveled. C) The displacement is either less than or equal to the distance traveled. D) The displacement can be either greater than, smaller than, or equal to the distance traveled. Answer: C Var: 1 4) Consider a car that travels between points A and B. The car's average speed can be greater than the magnitude of its average velocity, but the magnitude of its average velocity can never be greater than its average speed. A) True B) False Answer: A Var: 1

5) Which of the following quantities has units of a velocity? (There could be more than one correct choice.) A) 40 km southwest B) -120 m/s C) 9.8 m/s2 downward D) 186,000 mi E) 9.8 m/s downward Answer: B, E Var: 1 6) When is the average velocity of an object equal to the instantaneous velocity? A) only when the velocity is increasing at a constant rate B) only when the velocity is decreasing at a constant rate C) when the velocity is constant D) always E) never Answer: C Var: 1 7) You drive 6.0 km at 50 km/h and then another 6.0 km at 90 km/h. Your average speed over the 12 km drive will be A) greater than 70 km/h. B) equal to 70 km/h. C) less than 70 km/h. D) exactly 38 km/h. E) It cannot be determined from the information given because we must also know directions traveled. Answer: C Var: 1 8) If the velocity of an object is zero at some point, then its acceleration must also be zero at that point. A) True B) False Answer: B Var: 1 9) Which of the following situations is impossible? A) An object has velocity directed east and acceleration directed west. B) An object has velocity directed east and acceleration directed east. C) An object has zero velocity but non-zero acceleration. D) An object has constant non-zero acceleration and changing velocity. E) An object has constant non-zero velocity and changing acceleration. Answer: E Var: 1

10) If the acceleration of an object is zero, then that object cannot be moving. A) True B) False Answer: B Var: 1 11) If the velocity of an object is zero, then that object cannot be accelerating. A) True B) False Answer: B Var: 1 12) Suppose that a car traveling to the west begins to slow down as it approaches a traffic light. Which of the following statements about its acceleration is correct? A) The acceleration is toward the east. B) Since the car is slowing down, its acceleration must be negative. C) The acceleration is zero. D) The acceleration is toward the west. Answer: A Var: 1 13) An auto manufacturer advertises that their car can go "from zero to sixty in eight seconds." This is a description of what characteristic of the car's motion? A) average speed B) instantaneous speed C) average acceleration D) instantaneous acceleration E) displacement Answer: C Var: 1 14) An object moving in the +x direction experiences an acceleration of +2.0 m/s2. This means the object A) travels 2.0 m in every second. B) is traveling at 2.0 m/s. C) is decreasing its velocity by 2.0 m/s every second. D) is increasing its velocity by 2.0 m/s every second. Answer: D Var: 1

15) Suppose that a car traveling to the east (+x direction) begins to slow down as it approaches a traffic light. Which statement concerning its acceleration must be correct? A) Its acceleration is in the +x direction. B) Its acceleration is in the -x direction. C) Its acceleration is zero. D) Its acceleration is decreasing in magnitude as the car slows down. Answer: B Var: 1 16) Suppose that a car traveling to the west (-x direction) begins to slow down as it approaches a traffic light. Which statement concerning its acceleration must be correct? A) Its acceleration is positive. B) Its acceleration is negative. C) Its acceleration is zero. D) Its acceleration is decreasing in magnitude as the car slows down. Answer: A Var: 1 17) Suppose that an object is moving with a constant velocity. Which statement concerning its acceleration must be correct? A) The acceleration is constantly increasing. B) The acceleration is constantly decreasing. C) The acceleration is a constant non-zero value. D) The acceleration is equal to zero. Answer: D Var: 1 18) If the velocity of an object is zero at one instant, what is true about the acceleration of that object? (There could be more than one correct choice.) A) The acceleration could be positive. B) The acceleration could be negative. C) The acceleration could be zero. D) The acceleration must be zero. Answer: A, B, C Var: 1 19) Under what condition is average velocity equal to the average of the object's initial and final velocity? A) This can only occur if there is no acceleration. B) The acceleration is constant. C) This can occur only when the velocity is zero. D) The acceleration must be constantly increasing. E) The acceleration must be constantly decreasing. Answer: B Var: 1

20) A racing car accelerates uniformly from rest along a straight track. This track has markers spaced at equal distances along it from the start, as shown in the figure. The car reaches a speed of 140 km/h as it passes marker 2.

Where on the track was the car when it was traveling at half this speed, that is at 70 km/h? A) Before marker 1 B) At marker 1 C) Between marker 1 and marker 2 Answer: A Var: 1 21) When a ball is thrown straight up with no air resistance, the acceleration at its highest point A) is upward B) is downward C) is zero D) reverses from upward to downward E) reverses from downward to upward Answer: B Var: 1 22) A rock from a volcanic eruption is launched straight up into the air with no appreciable air resistance. Which one of the following statements about this rock while it is in the air is correct? A) On the way up, its acceleration is downward and its velocity is upward, and at the highest point both its velocity and acceleration are zero. B) On the way down, both its velocity and acceleration are downward, and at the highest point both its velocity and acceleration are zero. C) Throughout the motion, the acceleration is downward, and the velocity is always in the same direction as the acceleration. D) The acceleration is downward at all points in the motion. E) The acceleration is downward at all points in the motion except that is zero at the highest point. Answer: D Var: 1 23) Suppose a ball is thrown straight up and experiences no appreciable air resistance. What is its acceleration just before it reaches its highest point? A) zero B) slightly less than g C) exactly g D) slightly greater than g Answer: C Var: 1 5 Copyright © 2019 Pearson Education, Inc.

24) A ball is thrown straight up, reaches a maximum height, then falls to its initial height. Which of the following statements about the direction of the velocity and acceleration of the ball as it is going up is correct? A) Both its velocity and its acceleration point upward. B) Its velocity points upward and its acceleration points downward. C) Its velocity points downward and its acceleration points upward. D) Both its velocity and its acceleration points downward. Answer: B Var: 1 25) A ball is thrown downward in the absence of air resistance. After it has been released, which statement(s) concerning its acceleration is correct? (There could be more than one correct choice.) A) Its acceleration is constantly increasing. B) Its acceleration is constant. C) Its acceleration is constantly decreasing. D) Its acceleration is zero. E) Its acceleration is greater than g. Answer: B Var: 1 26) A 10-kg rock and a 20-kg rock are thrown upward with the same initial speed v0 and experience no significant air resistance. If the 10-kg rock reaches a maximum height h, what maximum height will the 20-kg ball reach? A) h/4 B) h/2 C) h D) 2h E) 4h Answer: C Var: 1 27) A 10-kg rock and 20-kg rock are dropped from the same height and experience no significant air resistance. If it takes the 20-kg rock a time T to reach the ground, what time will it take the 10-kg rock to reach the ground? A) 4T B) 2T C) T D) T/2 E) T/4 Answer: C Var: 1

28) A 10-kg rock and a 20-kg rock are dropped at the same time and experience no significant air resistance. If the 10-kg rock falls with acceleration a, what is the acceleration of the 20-kg rock? A) 4a B) 2a C) a D) a/2 E) a/4 Answer: C Var: 1 29) Two objects are dropped from a bridge, an interval of 1.0 s apart. Air resistance is negligible. During the time that both objects continue to fall, their separation A) increases. B) decreases. C) stays constant. D) increases at first, but then stays constant. E) decreases at first, but then stays constant. Answer: A Var: 1 30) From the edge of a roof top you toss a green ball upwards with initial speed v0 and a blue ball downwards with the same initial speed. Air resistance is negligible. When they reach the ground below A) the green ball will be moving faster than the blue ball. B) the blue ball will be moving faster than the green ball. C) the two balls will have the same speed. Answer: C Var: 1 31) Ball A is dropped from the top of a building. One second later, ball B is dropped from the same building. Neglect air resistance. As time progresses, the difference in their speeds A) increases. B) remains constant. C) decreases. D) cannot be determined from the information given. Answer: B Var: 1 32) Two objects are thrown from the top of a tall building. One is thrown up, and the other is thrown down, both with the same initial speed. What are their speeds when they hit the street? Neglect air resistance. A) The one thrown up is traveling faster. B) The one thrown down is traveling faster. C) They are traveling at the same speed. D) It is impossible to tell because the height of the building is not given. Answer: C Var: 1 7 Copyright © 2019 Pearson Education, Inc.

33) Brick A is dropped from the top of a building. Brick B is thrown straight down from the same building, and neither one experiences appreciable air resistance. Which statement about their accelerations is correct? A) The acceleration of A is greater than the acceleration of B. B) The acceleration of B is greater than the acceleration of A. C) The two bricks have exactly the same acceleration. D) Neither brick has any acceleration once it is released. Answer: C Var: 1 34) An object is moving with constant non-zero velocity in the +x direction. The position versus time graph of this object is A) a horizontal straight line. B) a vertical straight line. C) a straight line making an angle with the time axis. D) a parabolic curve. Answer: C Var: 1 35) An object is moving with constant non-zero acceleration in the +x direction. The position versus time graph of this object is A) a horizontal straight line. B) a vertical straight line. C) a straight line making an angle with the time axis. D) a parabolic curve. Answer: D Var: 1 36) An object is moving with constant non-zero velocity in the +x direction. The velocity versus time graph of this object is A) a horizontal straight line. B) a vertical straight line. C) a straight line making an angle with the time axis. D) a parabolic curve. Answer: A Var: 1 37) An object is moving with constant non-zero acceleration in the +x direction. The velocity versus time graph of this object is A) a horizontal straight line. B) a vertical straight line. C) a straight line making an angle with the time axis. D) a parabolic curve. Answer: C Var: 1 8 Copyright © 2019 Pearson Education, Inc.

38) The slope of a position versus time graph gives A) the distance traveled. B) velocity. C) acceleration. D) displacement. Answer: B Var: 1 39) The slope of a velocity versus time graph gives A) the distance traveled. B) velocity. C) acceleration. D) displacement. Answer: C Var: 1 40) If the position versus time graph of an object is a horizontal line, the object is A) moving with constant non-zero speed. B) moving with constant non-zero acceleration. C) at rest. D) moving with increasing speed. Answer: C Var: 1 41) If the velocity versus time graph of an object is a horizontal line, the object is A) moving with zero acceleration. B) moving with constant non-zero acceleration. C) at rest. D) moving with increasing speed. Answer: A Var: 1 42) If the velocity versus time graph of an object is a straight line making an angle of +30° (counter clockwise) with the time axis, the object is A) moving with constant non-zero speed. B) moving with constant non-zero acceleration. C) at rest. D) moving with increasing acceleration. Answer: B Var: 1

43) The motions of a car and a truck along a straight road are represented by the velocity-time graphs in the figure. The two vehicles are initially alongside each other at time t = 0.

At time T, what is true of the distances traveled by the vehicles since time t = 0? A) They will have traveled the same distance. B) The truck will not have moved. C) The car will have travelled further than the truck. D) The truck will have travelled further than the car. Answer: D Var: 1

44) Which of the following graphs represent an object at rest? (There could be more than one correct choice.)

A) graph a B) graph b C) graph c D) graph d E) graph e Answer: A Var: 1

45) Which of the following graphs represent an object having zero acceleration?

A) only graph a B) only graph b C) graphs a and b D) graphs b and c E) graphs c and d Answer: C Var: 1 46) The figure shows a graph of the position x of two cars, C and D, as a function of time t.

According to this graph, which statements about these cars must be true? (There could be more than one correct choice.) A) The magnitude of the acceleration of car C is greater than the magnitude of the acceleration of car D. B) The magnitude of the acceleration of car C is less than the magnitude of the acceleration of car D. C) At time t = 10 s, both cars have the same velocity. D) Both cars have the same acceleration. E) The cars meet at time t = 10 s. Answer: D, E Var: 1

47) The graph in the figure shows the position of an object as a function of time. The letters H-L represent particular moments of time.

(a) At which moment in time is the speed of the object the greatest? (b) At which moment in time is the speed of the object equal to zero? Answer: (a) J (b) I Var: 1

48) A child standing on a bridge throws a rock straight down. The rock leaves the child's hand at time t = 0 s. If we take upward as the positive direction, which of the graphs shown below best represents the velocity of the stone as a function of time?

Answer: C Var: 1

49) A child standing on a bridge throws a rock straight down. The rock leaves the child's hand at time t = 0 s. If we take upward as the positive direction, which of the graphs shown below best represents the acceleration of the stone as a function of time?

Answer: B Var: 1 50) The motion of a particle is described in the velocity vs. time graph shown in the figure.

Over the nine-second interval shown, we can say that the speed of the particle A) only increases. B) only decreases. C) increases and then decreases. D) decreases and then increases. E) remains constant. Answer: D Var: 1 15 Copyright © 2019 Pearson Education, Inc.

51) The graph in the figure shows the position of a particle as it travels along the x-axis.

At what value of t is the speed of the particle equal to 0 m/s? A) 0 s B) 1 s C) 2 s D) 3 s E) 4 s Answer: D Var: 1 52) The area under a curve in a velocity versus time graph gives A) acceleration. B) velocity. C) displacement. D) position. Answer: C Var: 1

2.2 Problems 1) If, in the figure, you start from the Bakery, travel to the Cafe, and then to the Art Gallery (a) what distance you have traveled? (b) what is your displacement?

Answer: (a) 10.5 km Var: 1

(b) 2.50 km south

2) An object moves 15.0 m north and then 11.0 m south. Find both the distance it has traveled and the magnitude of its displacement. A) 4.0 m, 26.0 m B) 26.0 m, 4.0 m C) 26.0 m, 26.0 m D) 4.0 m, 4.0 m Answer: B Var: 1 3) What must be your average speed in order to travel 350 km in 5.15 h? A) 66.0 km/h B) 67.0 km/h C) 68.0 km/h D) 69.0 km/h Answer: C Var: 1 4) A runner ran the marathon (approximately 42.0 km) in 2 hours and 57 min. What was the average speed of the runner in m/s? A) 14,200 m/s B) 124 m/s C) 3.95 m/s D) 14.2 m/s Answer: C Var: 1 5) A light-year is the distance that light travels in one year. The speed of light is 3.00 × 108 m/s. How many miles are there in one light-year? (1 mi = 1609 m, 1 y = 365 d) A) 9.46 × 1012 mi B) 9.46 × 1015 mi C) 5.88 × 1012 mi D) 5.88 × 1015 mi Answer: C Var: 1 17 Copyright © 2019 Pearson Education, Inc.

6) If you are driving 72 km/h along a straight road and you look to the side for 4.0 s, how far do you travel during this inattentive period? A) 18 m B) 20 m C) 40 m D) 80 m Answer: D Var: 4 7) If you run a complete loop around an outdoor track of length 400 m in 100 s, find your (a) average velocity and (b) average speed. Answer: (a) 0 m/s (b) 4 m/s Var: 1 8) A polar bear starts at the North Pole. It travels 1.0 km south, then 1.0 km east, and then 1.0 km north to return to its starting point. This trip takes 45 min. What was the bear's average speed? A) 0.00 km/h B) 0.067 km/h C) 4.0 km/h D) 5.3 km/h Answer: C Var: 1 9) A polar bear starts at the North Pole. It travels 1.0 km south, then 1.0 km east, and then 1.0 km north to return to its starting point. This trip takes 45 min. What was the bear's average velocity? A) 0.00 km/h B) 0.067 km/h C) 4.0 km/h D) 5.3 km/h Answer: A Var: 1 10) You are driving home on a weekend from school at 55 mi/h for 110 miles. It then starts to snow and you slow to 35 mi/h. You arrive home after driving 4 hours and 15 minutes. How far is your hometown from school? A) 180 mi B) 190 mi C) 200 mi D) 210 mi Answer: B Var: 1

11) A motorist travels 160 km at 80 km/h and 160 km at 100 km/h. What is the average speed of the motorist for this trip? A) 84 km/h B) 89 km/h C) 90 km/h D) 91 km/h Answer: B Var: 1 12) A motorist travels for 3.0 h at 80 km/h and 2.0 h at 100 km/h. What is her average speed for the trip? A) 85 km/h B) 88 km/h C) 90 km/h D) 92 km/h Answer: B Var: 1 13) An airplane travels at 300 mi/h south for 2.00 h and then at 250 mi/h north for 750 miles. What is the average speed for the trip? A) 260 mi/h B) 270 mi/h C) 275 mi/h D) 280 mi/h Answer: B Var: 1 14) A race car circles 10 times around a circular 8.0-km track in 20 min. Using SI units (a) what is its average speed for the ten laps? (b) what is its average velocity for the ten laps? Answer: (a) 67 m/s (b) 0 m/s Var: 1 15) A bat, flying toward the east at 2.0 m/s, emits a shriek that is reflected back to it from a wall that is 20.0 m in front of the bat at the instant the shriek is emitted. Sound travels at 340 m/s in the air. How many milliseconds after emitting the shriek does the bat hear the reflected echo from the wall? Answer: 117 ms Var: 1

16) If, in the figure, you start from the Bakery, travel to the Cafe, and then to the Art Gallery in 2.00 hours, what is your (a) average speed? (b) average velocity?

Answer: (a) 5.25 km/h Var: 1

(b) 1.25 km/h south

17) A runner runs around a track consisting of two parallel lines 96 m long connected at the ends by two semicircles with a radius of 49 m. She completes one lap in 100 seconds. What is her average velocity? A) 2.5 m/s B) 5.0 m/s C) 10 m/s D) 0 m/s E) 1.3 m/s Answer: D Var: 1 18) A runner runs around a track consisting of two parallel lines 96 m long connected at the ends by two semicircles with a radius of 49 m. She completes one lap in 100 seconds. What is her average speed? A) 2.5 m/s B) 5.0 m/s C) 10 m/s D) 0 m/s E) 1.3 m/s Answer: B Var: 1 19) You leave on a trip in order to attend a meeting that will start after you begin your trip. Along the way you plan to stop for dinner. If the fastest you can safely drive is 65 mi/h, what is the longest time you can spend over dinner and still arrive just in time for the meeting? A) 2.4 h B) 2.6 h C) 1.9 h D) You can't stop at all. Answer: A Var: 50+

20) A motorist makes a trip of 180 miles. For the first 90 miles she drives at a constant speed of 30 mph. At what constant speed must she drive the remaining distance if her average speed for the total trip is to be 40 mph? A) 45 mph B) 50 mph C) 52.5 mph D) 55 mph E) 60 mph Answer: E Var: 1 21) Human reaction times are worsened by alcohol. How much further (in feet) would a drunk driver's car travel before he hits the brakes than a sober driver's car? Assume that both are initially traveling at 50.0 mi/h and their cars have the same acceleration while slowing down, and that the sober driver takes 0.33 s to hit the brakes in a crisis, while the drunk driver takes 1.0 s to do so. (5280 ft = 1 mi) Answer: 49 ft Var: 1 22) Arthur and Betty start walking toward each other when they are 100 m apart. Arthur has a speed of 3.0 m/s and Betty has a speed of 2.0 m/s. How long does it take for them to meet? Answer: 20 seconds Var: 1 23) The position x(t) of a particle as a function of time t is given by the equation x(t) = (3.5 m/s)t - (5.0 m/s2)t2. What is the average velocity of the particle between t = 0.30 s and t = 0.40 s? Answer: 0.00 m/s Var: 1 24) A water rocket can reach a speed of 75 m/s in 0.050 seconds from launch. What is its average acceleration? Answer: 1500 m/s2 Var: 1 25) An airplane increases its speed at the average rate of 15 m/s2. How much time does it take to increase its speed from 100 m/s to 160 m/s? A) 17 s B) 0.058 s C) 4.0 s D) 0.25 s Answer: C Var: 1

26) The captain orders his starship to accelerate from rest at a rate of "1 g" (1 g = 9.8 m/s2). How many days does it take the starship to reach 10% the speed of light? (Light travels at 3.0 × 108 m/s.) Answer: 35 days Var: 1 27) A car is traveling north at After 12 s its velocity is Find the magnitude and direction of the car's average acceleration. A) 0.30 m/s2, south B) 2.7 m/s2, south C) 0.30 m/s2, north D) 2.7 m/s2, north Answer: A Var: 50+

in the same direction.

28) A racquetball strikes a wall with a speed of 30 m/s and rebounds in the opposite direction with a speed of 26 m/s. The collision takes 20 ms. What is the average acceleration of the ball during the collision with the wall? A) 0 m/s2 B) 200 m/s2 C) 2800 m/s2 D) 1500 m/s2 E) 1300 m/s2 Answer: C Var: 1 29) The velocity v(t) of a particle as a function of time is given by v(t) = (2.3 m/s) + (4.1 m/s2)t (6.2 m/s3)t2. What is the average acceleration of the particle between t = 1.0 s and t = 2.0 s? A) -13 m/s2 B) -15 m/s2 C) 13 m/s2 D) 15 m/s2 E) 0 m/s2 Answer: B Var: 1 30) If a car accelerates at a uniform 4.0 m/s2, how long will it take to reach a speed of 80 km/hr, starting from rest? Answer: 5.6 s Var: 1

31) A car that is initially moving at 7.50 m/s begins to accelerate forward uniformly at 0.550 m/s2. (a) How long after beginning to accelerate does it take the car to move 3.50 km? (b) How fast is the car moving just as it has traveled 3.50 km? Answer: (a) 1.00 × 102 s (b) 62.5 m/s Var: 1 32) An auto accelerates forward from 7.0 m/s at a uniform 0.71 m/s2. It travels a distance of 1.033 km while accelerating. (a) How fast is the auto moving just as it is traveled the 1.033 km? (b) How many seconds did it take to travel the 1.033 km? Answer: (a) 39 m/s (b) 45 s Var: 1 33) In a ballistics test, a bullet moving horizontally with a speed of 500 m/s strikes a sandbag and penetrates a distance of 10.0 cm. (a) What is the magnitude of the average acceleration of the bullet in the sandbag? (b) How many milliseconds does it take the bullet to come to rest in the sandbag? Answer: (a) 1.25 × 106 m/s2 (b) 0.400 ms Var: 1 34) A certain test car can go from rest to 32.0 m/s in 3.88 s. The same car can come to a full stop from that speed in 4.14 s. What is the ratio of the magnitude of the starting acceleration to the stopping acceleration? A) 0.937 B) 1.07 C) 0.878 D) 1.14 Answer: B Var: 1 35) A car initially traveling at 60 km/h accelerates at a constant rate of 2.0 m/s2. How much time is required for the car to reach a speed of 90 km/h? A) 15 s B) 30 s C) 45 s D) 4.2 s Answer: D Var: 1

36) A cart starts from rest and accelerates uniformly at 4.0 m/s2 for 5.0 s. It next maintains the velocity it has reached for 10 s. Then it slows down at a steady rate of 2.0 m/s2 for 4.0 s. What is the final speed of the car? A) 20 m/s B) 16 m/s C) 12 m/s D) 10 m/s Answer: C Var: 1 37) A car travels at 15 m/s for 10 s. It then speeds up with a constant acceleration of 2.0 m/s2 for 15 s. At the end of this time, what is its velocity? A) 15 m/s B) 30 m/s C) 45 m/s D) 375 m/s Answer: C Var: 1 38) A cart with an initial velocity of 5.0 m/s to the right experiences a constant acceleration of 2.0 m/s2 to the right. What is the cart's displacement during the first 6.0 s of this motion? A) 10 m B) 55 m C) 66 m D) 80 m Answer: C Var: 1 39) A jet plane is launched from a catapult on an aircraft carrier. In 2.0 s it reaches a speed of 42 m/s at the end of the catapult. Assuming the acceleration is constant, how far did it travel during those 2.0 s? A) 16 m B) 24 m C) 42 m D) 84 m Answer: C Var: 1

40) A car starting from rest accelerates at a constant 2.0 m/s2 for 10 s. It then travels with constant speed it has achieved for another 10 s. Then it finally slows to a stop with constant acceleration of magnitude 2.0 m/s2. How far does it travel after starting? A) 200 m B) 300 m C) 400 m D) 500 m Answer: C Var: 1 41) A car increases its forward velocity uniformly from 40 m/s to 80 m/s while traveling a distance of 200 m. What is its acceleration during this time? A) 8.0 m/s2 B) 9.6 m/s2 C) 12 m/s2 D) 24 m/s2 Answer: C Var: 1 42) An object starts from rest and undergoes uniform acceleration. During the first second it travels 5.0 m. How far will it travel during the third second? A) 5.0 m B) 15 m C) 25 m D) 45 m Answer: C Var: 2 43) An object is moving in a straight line with constant acceleration. Initially it is traveling at 16 m/s. Three seconds later it is traveling at 10 m/s. How far does it move during this time? A) 30 m B) 39 m C) 48 m D) 57 m Answer: B Var: 4 44) A car starts from rest and accelerates uniformly at 3.0 m/s2 toward the north. A second car starts from rest 6.0 s later at the same point and accelerates uniformly at 5.0 m/s2 toward the north. How long after the second car starts does it overtake the first car? A) 12 s B) 19 s C) 21 s D) 24 s Answer: C Var: 1 25 Copyright © 2019 Pearson Education, Inc.

45) A car with good tires on a dry road can decelerate (slow down) at a steady rate of about 5.0 m/s2 when braking. If a car is initially traveling at 55 mi/h (a) how much time does it take the car to stop? (b) what is its stopping distance? Answer: (a) 4.9 s (b) 60 m Var: 1 46) At the instant a traffic light turns green, a car that has been waiting at the intersection starts ahead with a constant acceleration of 2.00 m/s2. At that moment a truck traveling with a constant velocity of 15.0 m/s overtakes and passes the car. (a) Calculate the time necessary for the car to reach the truck. (b) Calculate the distance beyond the traffic light that the car will pass the truck. (c) Determine the speed of the car when it passes the truck. Answer: (a) 15.0 s (b) 225 m (c) 30.0 m/s Var: 1 47) Starting from rest, a dragster travels a straight 1/4 mi racetrack in 6.70 s with constant acceleration. What is its velocity when it crosses the finish line? A) 269 mi/h B) 188 mi/h C) 296 mi/h D) 135 mi/h Answer: A Var: 40 48) A bicyclist starts a timed race at In order to win, he must average Assuming constant acceleration from the start, how fast must he be traveling at the end of the race? A) 36 mi/h B) 30 mi/h C) 24 mi/h D) 42 mi/h Answer: A Var: 21 49) A car accelerates from while accelerating? A) 69 m B) 207 m C) 41 m D) 117 m Answer: A Var: 50+

at a constant rate of

How far does it travel

50) An airplane needs to reach a forward velocity of to take off. On a runway, what is the minimum uniform acceleration necessary for the plane to take flight if it starts from rest? A) 0.79 m/s2 B) 0.87 m/s2 C) 0.95 m/s2 D) 1.0 m/s2 Answer: A Var: 50+ 51) Assuming equal rates of uniform acceleration in both cases, how much further would you travel if braking from to rest than from ? A) 4 times farther B) 3.2 times farther C) 4.8 times farther D) 5.2 times farther Answer: A Var: 50+ 52) Acceleration is sometimes expressed in multiples of g, where is the acceleration of an object due to the earth's gravity. In a car crash, the car's forward velocity may go from to in How many g's are experienced, on average, by the driver? A) 20 g B) 14 g C) 24 g D) 26 g Answer: A Var: 11 53) A baseball is hit with a bat and, as a result, its direction is completely reversed and its speed is doubled. If the actual contact with the bat lasts 0.45 s, what is the ratio of the magnitude of the average acceleration of the ball to its original speed? A) 6.7 s-1 B) 4.4 s-1 C) 2.2 s-1 D) 0.15 s-1 Answer: A Var: 1

54) A train starts from rest and accelerates uniformly until it has traveled 5.6 km and acquired a forward velocity of The train then moves at a constant velocity of for 420 s. The train then slows down uniformly at until it is brought to a halt. The acceleration during the first 5.6 km of travel is closest to which of the following? A) 0.16 m/ B) 0.14 m/ C) 0.17 m/ D) 0.19 m/ E) 0.20 m/ Answer: A Var: 50+ 55) A train starts from rest and accelerates uniformly until it has traveled 2.1 km and acquired a forward velocity of The train then moves at a constant velocity of for 400 s. The train then slows down uniformly at until it is brought to a halt. The distance traveled by the train while slowing down is closest to A) 4.4 km. B) 4.2 km. C) 4.0 km. D) 3.8 km. E) 3.6 km. Answer: A Var: 50+ 56) A soccer ball is released from rest at the top of a grassy incline. After 6.4 seconds the ball has rolled 91 m with constant acceleration, and 1.0 s later it reaches the bottom of the incline. (a) What was the ball's acceleration? (b) How long was the incline? Answer: *a) 4.4 m/ (b) 120 m Var: 50+ 57) A car starts from rest and accelerates at a steady 6.00 m/s2. How far does it travel in the first 3.00 s? A) 9.00 m B) 18.0 m C) 27.0 m D) 36.0 m E) 54.0 m Answer: C Var: 1

58) A car is moving with a constant acceleration. At time t = 5.0 s its velocity is 8.0 m/s in the forward direction, and at time t = 8.0 s its velocity is 12.0 m/s forward. What is the distance traveled in that interval of time? A) 10 m B) 20 m C) 30 m D) 40 m E) 50 m Answer: C Var: 1 59) An airplane starts from rest and accelerates at a constant 10.8 m/s2. What is its speed at the end of a 400 m-long runway? A) 37.0 m/s B) 93.0 m/s C) 65.7 m/s D) 4320 m/s E) 186 m/s Answer: B Var: 1 60) A car is moving with a speed of 32.0 m/s. The driver sees an accident ahead and slams on the brakes, causing the car to slow down with a uniform acceleration of magnitude 3.50 m/s2. How far does the car travel after the driver put on the brakes until it comes to a stop? A) 4.57 m B) 9.14 m C) 112 m D) 146 m E) 292 m Answer: D Var: 1 61) A car is traveling with a constant speed when the driver suddenly applies the brakes, causing the car to slow down with a constant acceleration of magnitude 3.50 m/s2. If the car comes to a stop in a distance of 30.0 m, what was the car's original speed? A) 10.2 m/s B) 14.5 m/s C) 105 m/s D) 210 m/s E) 315 m/s Answer: B Var: 1

62) A car is traveling with a constant speed of 30.0 m/s when the driver suddenly applies the brakes, causing the car to slow down with a constant acceleration. The car comes to a stop in a distance of 120 m. What was the acceleration of the car as it slowed down? A) 3.75 m/s2 B) 4.00 m/s2 C) 4.25 m/s2 D) 4.50 m/s2 E) 4.75 m/s2 Answer: A Var: 1 63) A car is traveling at 26.0 m/s when the driver suddenly applies the brakes, causing the car to slow down with constant acceleration. The car comes to a stop in a distance of 120 m. How fast was the car moving when it was 60.0 m past the point where the brakes were applied? A) 22.5 m/s B) 18.4 m/s C) 15.0 m/s D) 12.1 m/s E) 9.20 m/s Answer: B Var: 5 64) Car A is traveling at 22.0 m/s and car B at 29.0 m/s. Car A is 300 m behind car B when the driver of car A accelerates his car with a uniform forward acceleration of 2.40 m/ . How long after car A begins to accelerate does it take car A to overtake car B? A) 5.50 s B) 12.6 s C) 19.0 s D) 316 s E) Car A never overtakes car B. Answer: C Var: 5 65) A stone is thrown with an initial upward velocity of 7.0 m/s and experiences negligible air resistance. If we take upward as the positive direction, what is the velocity of the stone after 0.50 s? A) 2.1 m/s B) 4.9 m/s C) -2.1 m/s D) -4.9 m/s E) 0.00 m/s Answer: A Var: 1

66) An astronaut on a strange new planet having no atmosphere finds that she can jump up to a maximum height of 27 m when her initial upward speed is 6.0 m/s. What is the magnitude of the acceleration due to gravity on the planet? Answer: 0.67 m/s2 Var: 1 67) A laser is thrown upward with a speed of 12 m/s on the surface of planet X where the acceleration due to gravity is 1.5 m/s2 and there is no atmosphere. What is the maximum height reached by the laser? A) 8.0 m B) 18 m C) 48 m D) 144 m Answer: C Var: 4 68) A laser is thrown upward with a speed of 12 m/s on the surface of planet X where the acceleration due to gravity is 1.5 m/s2 and there is no atmosphere. How long does it take for the laser to reach the maximum height? A) 8.0 s B) 11 s C) 14 s D) 16 s Answer: A Var: 4 69) An instrument is thrown upward with a speed of 15 m/s on the surface of planet X where the acceleration due to gravity is 2.5 m/s2 and there is no atmosphere. How long does it take for the instrument to return to where it was thrown? A) 6.0 s B) 8.0 s C) 10 s D) 12 s Answer: D Var: 4 70) A hammer is thrown upward with a speed of 14 m/s on the surface of planet X where the acceleration due to gravity is 3.5 m/s2 and there is no atmosphere. What is the speed of the hammer after 8.0 s? A) 7.0 m/s B) 14 m/s C) 21 m/s D) 64 m/s Answer: B Var: 2 31 Copyright © 2019 Pearson Education, Inc.

71) Human reaction time is usually greater than 0.10 s. If your friend holds a ruler between your fingers and releases it without warning, how far can you expect the ruler to fall before you catch it, assuming negligible air resistance? A) At least 3.0 cm B) At least 4.9 cm C) At least 6.8 cm D) At least 9.8 cm Answer: B Var: 1 72) A ball is thrown upward at a velocity of 19.6 m/s. What is its velocity after 3.0 s, assuming negligible air resistance? A) 9.8 m/s upward B) 9.8 m/s downward C) 0 m/s D) 19.6 m/s downward Answer: B Var: 1 73) A bullet shot straight up returns to its starting point in 10 s. What is the initial speed of the bullet, assuming negligible air resistance? A) 9.8 m/s B) 25 m/s C) 49 m/s D) 98 m/s Answer: C Var: 1 74) A ball is thrown straight up with a speed of 36 m/s. How long does it take to return to its starting point, assuming negligible air resistance? A) 3.7 s B) 7.3 s C) 11 s D) 15 s Answer: B Var: 1 75) A ball is thrown downward from the top of a building with an initial speed of 25 m/s. It strikes the ground after 2.0 s. How high is the building, assuming negligible air resistance? A) 20 m B) 30 m C) 50 m D) 70 m Answer: D Var: 1

76) A ball is thrown straight up with a speed of 30 m/s, and air resistance is negligible. (a) How long does it take the ball to reach the maximum height? (b) What is the maximum height reached by the ball? (c) What is its speed after 4.2 s? Answer: (a) 3.1 s (b) 46 m (c) 11 m/s Var: 1 77) A foul ball is hit straight up into the air with a speed of 30 m/s, and air resistance is negligible. (a) Calculate the time required for the ball to rise to its maximum height. (b) Calculate the maximum height reached by the ball above the point where it hit the bat. (c) Determine the times at which the ball passes a point 25 m above the point where it was hit by the bat. (d) Explain why there are two answers to part (c). Answer: (a) 3.1 s (b) 46 m (c) 1.0 s and 5.1 s (d) One value for the ball traveling upward; one value for the ball traveling downward. Var: 1 78) A ball is projected upward at time t = 0 s, from a point on a flat roof 10 m above the ground. The ball rises and then falls with insignificant air resistance, missing the roof, and strikes the ground. The initial velocity of the ball is Consider all quantities as positive in the upward direction. At time the vertical velocity of the ball is closest to A) 0 m/s. B) +175 m/s. C) +12 m/s. D) -175 m/s. E) -12 m/s. Answer: A Var: 50+ 79) A ball is projected upward at time t = 0 s, from a point on a flat roof 90 m above the ground. The ball rises and then falls with insignificant air resistance, missing the roof, and strikes the ground. The initial velocity of the ball is Consider all quantities as positive in the upward direction. The vertical velocity of the ball when it is above the ground is closest to A) -81 m/s. B) -64 m/s. C) -48 m/s. D) -32 m/s. E) -97 m/s. Answer: A Var: 50+

80) A test rocket at ground level is fired straight up from rest with a net upward acceleration of 20 m/s2. After 4.0 s, the motor turns off but the rocket continues to coast upward with insignificant air resistance. What maximum elevation does the rocket reach? A) 160 m B) 330 m C) 320 m D) 410 m E) 490 m Answer: E Var: 1 81) A toy rocket is launched vertically from ground level at time t = 0.00 s. The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to 64 m and acquired an upward velocity of The rocket continues to rise with insignificant air resistance in unpowered flight, reaches maximum height, and falls back to the ground. The time interval during which the rocket engine provided the upward acceleration, is closest to A) 2.1 s. B) 2.3 s. C) 1.9 s. D) 1.7 s. E) 1.5 s. Answer: A Var: 50+ 82) A toy rocket is launched vertically from ground level at time t = 0.00 s. The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to 81 m and acquired an upward velocity of The rocket continues to rise with insignificant air resistance in unpowered flight, reaches maximum height, and falls back to the ground. The upward acceleration of the rocket during the burn phase is closest to A) 9.9 m/ . B) 9.6 m/ . C) 9.3 m/ . D) 9.0 m/ . E) 8.7 m/ . Answer: A Var: 50+

83) A toy rocket is launched vertically from ground level at time t = 0 s. The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to 49.0 m and acquired an upward velocity of The rocket continues to rise with insignificant air resistance in unpowered flight, reaches maximum height, and falls back to the ground. The maximum height reached by the rocket is closest to A) 233 m. B) 221 m. C) 209 m. D) 244 m. E) 256 m. Answer: A Var: 50+ 84) A rock is projected upward from the surface of the Moon, at time t = 0 s, with an upward velocity of 30.0 m/s. The acceleration due to gravity at the surface of the Moon is 1.62 m/s2, and the Moon has no atmosphere. The height of the rock when it is descending with a speed of 20.0 m/s is closest to A) 115 m. B) 125 m. C) 135 m. D) 145 m. E) 154 m. Answer: E Var: 1 85) A ball is thrown straight upward from ground level with a speed of passes before the ball strikes the ground if we disregard air resistance? A) 3.7 s B) 1.8 s C) 1.1 s D) 0.6 s Answer: A Var: 31

How much time

86) A rock is thrown directly upward from the edge of a flat roof of a building that is 56.3 meters tall. The rock misses the building on its way down, and is observed to strike the ground 4.00 seconds after being thrown. Take the acceleration due to gravity to have magnitude and neglect any effects of air resistance. With what speed was the rock thrown? Answer: 5.53 m/s Var: 50+ 87) A package is dropped from a helicopter that is moving upward at If it takes before the package strikes the ground, how high above the ground was the package when it was released? Neglect air resistance. Answer: 190 m Var: 25 35 Copyright © 2019 Pearson Education, Inc.

88) At the same moment, one rock is dropped and one is thrown downward with an initial velocity of from the top of a building that is tall. How much earlier does the thrown rock strike the ground? Neglect air resistance. Answer: 2.4 s Var: 21 89) An object is dropped from a bridge. A second object is thrown downwards 1.0 s later. They both reach the water 20 m below at the same instant. What was the initial speed of the second object? Neglect air resistance. A) 4.9 m/s B) 15 m/s C) 9.9 m/s D) 20 m/s E) 21 m/s Answer: B Var: 1 90) To determine the height of a bridge above the water, a person drops a stone and measures the time it takes for it to hit the water. If the time is 2.3 s, what is the height of the bridge? Neglect air resistance. A) 10 m B) 14 m C) 26 m D) 32 m E) 52 m Answer: C Var: 1 91) To determine the height of a bridge above the water, a person drops a stone and measures the time it takes for it to hit the water. If the height of the bridge is 41 m, how long will it take for the stone to hit the water? Neglect air resistance. A) 2.3 s B) 2.6 s C) 2.9 s D) 3.2 s E) 3.6 s Answer: C Var: 1

92) An astronaut stands by the rim of a crater on the Moon, where the acceleration of gravity is 1.62 m/s2 and there is no air. To determine the depth of the crater, she drops a rock and measures the time it takes for it to hit the bottom. If the time is 6.3 s, what is the depth of the crater? A) 10 m B) 14 m C) 26 m D) 32 m E) 38 m Answer: D Var: 1 93) An astronaut stands by the rim of a crater on the Moon, where the acceleration of gravity is 1.62 m/s2 and there is no air. To determine the depth of the crater, she drops a rock and measures the time it takes for it to hit the bottom. If the depth of the crater is 120 m, how long does it take for the rock to fall to the bottom of the crater? A) 3.04 s B) 12.2 s C) 29.3 s D) 32.1 s E) 37.5 s Answer: B Var: 1 94) An object is thrown upwards with a speed of 16 m/s. How long does it take it to reach a height of 7.0 m on the way up? Neglect air resistance. A) 0.52 s B) 1.2 s C) 2.4 s D) 3.1 s E) 4.2 s Answer: A Var: 5 95) An object is thrown upwards with a speed of 13 m/s. How long does it take to reach a height of 4.0 m above the projection point while descending? Neglect air resistance. A) 0.42 s B) 1.2 s C) 2.3 s D) 3.1 s E) 4.2 s Answer: C Var: 5

96) To determine the height of a flagpole, Abby throws a ball straight up and times it. She sees that the ball goes by the top of the pole after 0.50 s and then reaches the top of the pole again after a total elapsed time of 4.1 s. How high is the pole above the point where the ball was launched? Neglect air resistance. A) 10 m B) 13 m C) 16 m D) 18 m E) 26 m Answer: A Var: 1 97) Abby throws a ball straight up and times it. She sees that the ball goes by the top of a flagpole after 0.50 s and reaches the level of the top of the pole after a total elapsed time of 4.1 s. What was the speed of the ball at launch? Neglect air resistance. A) 11 m/s B) 23 m/s C) 34 m/s D) 45 m/s E) 48 m/s Answer: B Var: 1 98) Abby throws a ball straight up and times it. She sees that the ball goes by the top of a flagpole after 0.50 s and reaches the level of the top of the pole after a total elapsed time of 4.1 s. What was the speed of the ball at as it passed the top of the flagpole? Neglect air resistance. A) 6.4 m/s B) 16 m/s C) 18 m/s D) 29 m/s E) 33 m/s Answer: C Var: 1 99) A car is able to stop in a distance d. Assuming the same braking force (and therefore the same acceleration), what distance does this car require to stop when it is traveling twice as fast? A) d B) 2d C) d D) 4d E) 2 d Answer: D Var: 1

100) Assuming equal rates of acceleration in both cases, how much longer would it take a car to stop if braking from 56 mi/h than from 28 mi/h? A) 8 times as long B) 4 times as long C) 2 times as long D) 1.4 times as long E) the same in both cases Answer: C Var: 1 101) Two identical objects A and B fall from rest from different heights to the ground. If object B takes twice as long as object A to reach the ground, what is the ratio of the heights from which A and B fell? Neglect air resistance. A) hA/hB = 1/ B) hA/hB = 1/2 C) hA/hB = 1/4 D) hA/hB = 1/8 Answer: C Var: 1 102) Two cars are traveling at the same speed and hit the brakes at the same time. Car A decelerates (decreases its velocity) at twice the rate of car B. If car B takes time T to stop, how long does it take car A to stop? A) 4T B) 2T C) T D) T /2 E) T/4 Answer: D Var: 1 103) Two cars are traveling at the same speed and hit the brakes at the same time. Car A decelerates (decreases its velocity) at twice the rate of car B. If car A travels a distance D before stopping, how far does car B travel before stopping? A) 4D B) 2D C) D D) D/2 E) D/4 Answer: B Var: 1

104) Car A is traveling at twice the speed of car B. They both hit the brakes at the same time and decrease their velocities at the same rate. If car B travels a distance D before stopping, how far does car A travel before stopping? A) 4D B) 2D C) D D) D/2 E) D/4 Answer: A Var: 1 105) A car moving initially with speed v0 slows down with an acceleration of magnitude a and comes to a full stop after traveling a distance d. What was the speed of the car when it had traveled half that distance, d/2? A) v0/2 B) v0/4 C) v0/ D) v0/8 Answer: C Var: 1 106) Two athletes jump straight up. John has twice the initial speed of Harry. Compared to Harry, John stays in the air A) 0.50 times as long as Harry. B) the same time as Harry. C) twice as long as Harry. D) three times as long as Harry. E) four times as long as Harry. Answer: C Var: 1 107) In the absence of air resistance, a ball is thrown vertically upward with initial speed v. An identical ball is thrown upward with initial speed 2v. If the first ball reaches a maximum height h, what maximum height will the second ball reach? A) 8h B) 4h C) 2h D) h E) h Answer: B Var: 1

108) The graph in the figure represents the velocity of a particle as it travels along the x-axis. What is the average acceleration of the particle between t = 2.0 s and t = 4.0 s?

Answer: 1.5 m/s2 Var: 1 109) The graph in the figure shows the position of a particle as a function of time as it travels along the x-axis. (a) What is the average speed of the particle between t = 2.0 s and t = 4.0 s? (b) What is the average velocity of the particle between t = 2.0 s and t = 4.0 s?

Answer: (a) 1.0 m/s Var: 1

(b) 0 m/s

110) The graph in the figure shows the position of a particle as a function of time as it travels along the x-axis. (a) What is the magnitude of the average velocity of the particle between t = 1.0 s and t = 4.0 s? (b) What is the average speed of the particle between t = 1.0 s and t = 4.0 s?

Answer: (a) 0.67 m/s Var: 1

(b) 1.3 m/s

111) The graph in the figure shows the position of a particle as it travels along the x-axis. What is the magnitude of the instantaneous velocity of the particle when t = 1.0 s?

Answer: 3.0 m/s Var: 1

112) The graph in the figure shows the position of a particle as it travels along the x-axis. What is the magnitude of the average velocity of the particle between t = 1.0 s and t = 4.0 s?

A) 0.25 m/s B) 0.50 m/s C) 0.67 m/s D) 1.0 m/s E) 1.3 m/s Answer: C Var: 1 113) The graph in the figure shows the position of a particle as it travels along the x-axis. What is the magnitude of the average speed of the particle between t = 1.0 s and t = 4.0 s?

A) 1.0 m/s B) 1.3 m/s C) 0.67 m/s D) 0.50 m/s E) 0.25 m/s Answer: B Var: 1

114) The graph in the figure shows the velocity of a particle as it travels along the x-axis. What is the magnitude of the average acceleration of the particle between t = 1.0 s and t = 4.0 s?

A) 0.33 m/s2 B) 1.7 m/s2 C) 2.0 m/s2 D) 2.5 m/s2 E) 3.0 m/s2 Answer: B Var: 1 115) The graph in the figure shows the velocity of a particle as it travels along the x-axis. (a) In what direction (+x or -x) is the acceleration at t = 0.5 s? (b) In what direction (+x or -x) is the acceleration at t = 3.0 s? (c) What is the average acceleration of the particle between t = 2.0 s and t = 4.0 s? (d) At what value of t is the instantaneous acceleration equal to 0 m/s2?

Answer: (a) -x Var: 1

(b) +x

(d) 1.0 s

116) The figure shows a graph of the position of a moving object as a function of time. What is the velocity of the object at each of the following times? (a) At t = 1.0 s (b) At t = 2.5 s (c) At t = 4.0 s (d) At t = 5.5 s

Answer: (a) 10 m/s Var: 1

(b) 20 m/s

(d) -40 m/s

117) The figure shows a graph of the position of a moving object as a function of time. (a) What is the average velocity of the object from t = 0 s to t = 4.0 s? (b) What is the average velocity of the object from t = 0 s to t = 6.0 s?

Answer: (a) 10 m/s Var: 1

(b) 0 m/s

118) The figure shows a graph of the velocity of an object as a function of time. What is the acceleration of the object at the following times? (a) At 1.0 s (b) At 3.0 s

Answer: (a) 10 m/s2 Var: 1

(b) 0 m/s2

119) The figure shows a graph of the velocity of an object as a function of time. What is the average acceleration of the object over the following time intervals? (a) From t = 0 s to t = 5.0 s (b) From t = 0 s to t = 8.0 s

Answer: (a) 2.0 m/s2 Var: 1

(b) -2.5 m/s2

120) The figure shows the velocity-versus-time graph for a basketball player traveling up and down the court in a straight-line path. Find the displacement of the player (a) during the first two seconds. (b) between t = 4 s and t = 8 s.

Answer: (a) 4 m Var: 1

(b) 8 m

121) The figure shows a graph of the velocity of an object as a function of time. What is the displacement of the object from 0 s to 6.0 s?

A) 20 m B) 40 m C) 60 m D) 80 m E) 100 m Answer: D Var: 1 122) The figure shows a graph of the velocity of an object as a function of time. What is the displacement of the object from 0 s to 8.0 s?

A) 20 m B) 40 m C) 60 m D) 80 m E) 100 m Answer: C Var: 1

College Physics: A Strategic Approach, 4e (Knight) Chapter 3 Vectors and Motion in Two Dimensions 3.1 Conceptual Questions 1) If a vector pointing upward has a positive magnitude, a vector pointing downward has a negative magnitude. A) True B) False Answer: B Var: 1 2) Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. If these two vectors are added together, the magnitude of the sum A) is equal to 2.0 m. B) could be as small as 2.0 m or as large as 12 m. C) is equal to 12 m. D) is equal to 8.6 m. Answer: B Var: 1 3) Two vectors, of magnitudes 20 mm and 50 mm, are added together. Which one of the following is a possible value for the magnitude of the resultant? A) 10 mm B) 20 mm C) 40 mm D) 80 mm Answer: C Var: 1 4) The magnitude of the resultant of two vectors cannot be less than the magnitude of either of those two vectors. A) True B) False Answer: B Var: 1 5) A student adds two displacement vectors that have the magnitudes of 12.0 m and 5.0 m. What is the range of possible answers for the magnitude of the resultant vector? Answer: Between 7.0 m and 17.0 m Var: 1

6) If + = and their magnitudes are given by A + B = C, then the vectors oriented A) perpendicular relative to one other. B) parallel to each other (in the same direction). C) antiparallel to each other (in opposite directions). D) It is impossible to know from the given information. Answer: B Var: 1 7) If - = 0, then the vectors direction. A) True B) False Answer: A Var: 1

and

are

have equal magnitudes and are directed in the same

8) If three vectors add to zero, they must all have equal magnitudes. A) True B) False Answer: B Var: 1 9) The sum of two vectors of fixed magnitudes has the greatest magnitude when the angle between these two vectors is A) 90° B) 180° C) 60° D) 0° E) 270° Answer: D Var: 1 10) The sum of two vectors of fixed magnitudes has its minimum magnitude when the angle between these vectors is A) 0° B) 90° C) 270° D) 180° E) 360° Answer: D Var: 1

11) Vectors and obey the equation + = 0. These vectors satisfy which one of the following statements? A) Vectors and are at right angles to each other. B) Vectors and point in the same direction. C) Vectors and have the same magnitudes. D) The magnitude of is the negative of the magnitude of . Answer: C Var: 1 12) Consider two vectors by

and

shown in the figure. The difference

is best illustrated

and

shown in the figure. The difference

is best illustrated

A) choice (a) B) choice (b) C) choice (c) D) choice (d) Answer: C Var: 1 13) Consider two vectors by

A) choice (a) B) choice (b) C) choice (c) D) choice (d) Answer: B Var: 1

14) Refer to the figure, which shows four vectors , (a) Vector as expressed in terms of vectors and A) + . B) - . C) - . (b) Vector as expressed in terms of vectors and A) + . B) - . C) - .

, , and . is given by

is given by

Answer: (a) B (b) A Var: 1 15) If a vector's components are all negative, then the magnitude of the vector is negative. A) True B) False Answer: B Var: 1 16) The magnitude of a vector can never be less than the magnitude of any of its components. A) True B) False Answer: A Var: 1 17) The magnitude of a vector an only zero if all of its components are zero. A) True B) False Answer: A Var: 1

18) If a vector has components Ax < 0, and Ay > 0, then the angle that this vector makes with the positive x-axis must be in the range A) 0° to 90° B) 90° to 180° C) 180° to 270° D) 270° to 360° E) It cannot be determined without additional information. Answer: B Var: 1 19) If a vector has components Ax < 0, and Ay < 0, then the angle that this vector makes with the positive x-axis must be in the range A) 0° to 90° B) 90° to 180° C) 180° to 270° D) 270° to 360° E) cannot be determined without additional information Answer: C Var: 1 20) If a vector has components Ax > 0, and Ay < 0, then the angle that this vector makes with the positive x-axis must be in the range A) 0° to 90° B) 90° to 180° C) 180° to 270° D) 270° to 360° E) cannot be determined without additional information Answer: D Var: 1 21) The eastward component of vector is equal to the westward component of vector and their northward components are equal. Which one of the following statements must be correct for these two vectors? A) Vector is parallel to vector . B) Vector is antiparallel (in the opposite direction) to vector . C) Vector must be perpendicular to vector . D) The magnitude of vector E) The angle between vector Answer: D Var: 1

must be equal to the magnitude of vector and vector must be 90°.

22) Vector is along the +x-axis and vector is along the +y-axis. Which one of the following statements is correct with respect to these vectors? A) The x component of vector is equal to the x component of vector . B) The y component of vector is equal to the y component of vector . C) The x component of vector is equal to the y component of vector . D) The y component of vector is equal to the x component of vector . Answer: D Var: 1 23) Shown below are the velocity and acceleration vectors for an object in several different types of motion. In which case is the object slowing down and turning to its right?

Answer: B Var: 1 24) A boulder rolls off of a very high cliff and experiences no significant air resistance. While it is falling, its trajectory is never truly vertical. A) True B) False Answer: A Var: 1

25) For general projectile motion with no air resistance, the horizontal component of a projectile's velocity A) remains zero. B) remains a non-zero constant. C) continuously increases. D) continuously decreases. E) first decreases and then increases. Answer: B Var: 1 26) For general projectile motion with no air resistance, the horizontal component of a projectile's acceleration A) is always zero. B) remains a non-zero constant. C) continuously increases. D) continuously decreases. E) first decreases and then increases. Answer: A Var: 1 27) For general projectile motion with no air resistance, the vertical component of a projectile's acceleration A) is always zero. B) remains a non-zero constant. C) continuously increases. D) continuously decreases. E) first decreases and then increases. Answer: B Var: 1 28) Which of the following statements are true about an object in two-dimensional projectile motion with no air resistance? (There could be more than one correct choice.) A) The speed of the object is constant but its velocity is not constant. B) The acceleration of the object is +g when the object is rising and -g when it is falling. C) The acceleration of the object is zero at its highest point. D) The speed of the object is zero at its highest point. E) The horizontal acceleration is always zero and the vertical acceleration is always a non-zero constant downward. Answer: E Var: 1

29) A ball is thrown horizontally from the top of a tower at the same instant that a stone is dropped vertically. Which object is traveling faster when it hits the level ground below if neither of them experiences any air resistance? A) It is impossible to tell because we do not know their masses. B) the stone C) the ball D) Both are traveling at the same speed. Answer: C Var: 1 30) In an air-free chamber, a pebble is thrown horizontally, and at the same instant a second pebble is dropped from the same height. Compare the times of fall of the two pebbles. A) The thrown pebble hits first. B) The dropped pebble hits first. C) They hit at the same time. D) We cannot tell without knowing which pebble is heavier. Answer: C Var: 1 31) A pilot drops a package from a plane flying horizontally at a constant speed. Neglecting air resistance, when the package hits the ground the horizontal location of the plane will A) be behind the package. B) be directly over the package. C) be in front of the package. D) depend on the speed of the plane when the package was released. Answer: B Var: 1 32) James and John dive from an overhang into the lake below. James simply drops straight down from the edge. John takes a running start and jumps with an initial horizontal velocity of 25 m/s. If there is no air resistance, when they reach the lake below A) the splashdown speed of James is larger than that of John. B) the splashdown speed of John is larger than that of James. C) they will both have the same splashdown speed. D) the splashdown speed of James must be 9.8 m/s larger than that of John. E) the splashdown speed of John must be 25 m/s larger than that of James. Answer: B Var: 1

33) James and John dive from an overhang into the lake below. James simply drops straight down from the edge. John takes a running start and jumps with an initial horizontal velocity of 25 m/s. Compare the time it takes each to reach the lake below if there is no air resistance. A) James reaches the surface of the lake first. B) John reaches the surface of the lake first. C) James and John will reach the surface of the lake at the same time. D) Cannot be determined without knowing the mass of both James and John. E) Cannot be determined without knowing the weight of both James and John. Answer: C Var: 1 34) A player kicks a soccer ball in a high arc toward the opponent's goal. At the highest point in its trajectory A) both the velocity and the acceleration of the soccer ball are zero. B) neither the ball's velocity nor its acceleration are zero. C) the ball's acceleration is zero but its velocity is not zero. D) the ball's acceleration points upward. E) the ball's velocity points downward. Answer: B Var: 1 35) Mary and Debra stand on a snow-covered roof. They both throw snowballs with the same initial speed, but in different directions. Mary throws her snowball downward, at 30° below the horizontal; Debra throws her snowball upward, at 30° above the horizontal. Which of the following statements are true about just as the snowballs reach the ground below? (There could be more than one correct choice.) A) Debra's snowball will have a higher speed than Mary's snowball. B) Mary's snowball will have a higher speed than Debra's snowball. C) Both snowballs will hit the ground with the same speed. D) Both snowballs hit the ground at the same time. E) Mary's snowball reaches the ground before Debra's snowball. Answer: C, E Var: 1 36) Mary and Debra stand on a snow-covered roof. They both throw snowballs with the same initial speed, but in different directions. Mary throws her snowball downward, at 30° below the horizontal; Debra throws her snowball upward, at 30° above the horizontal. Which of the following statements are true about just before the snowballs reach the ground below? (There could be more than one correct choice.) A) Debra's snowball will stay in the air longer than Mary's snowball. B) Mary's snowball will stay in the air longer than Debra's snowball. C) Both snowballs will take the same amount of time to hit the ground. D) Debra's snowball has exactly the same acceleration as Mary's snowball. E) Mary's snowball has a greater downward acceleration than Debra's snowball. Answer: A, D Var: 1 9 Copyright © 2019 Pearson Education, Inc.

37) A rock is thrown from the upper edge of a tall cliff at some angle above the horizontal. It reaches its highest point and starts falling down. Which of the following statements about the rock's motion are true just before it hits the ground? (There could be more than one correct choice.) A) Its horizontal velocity component is zero. B) Its velocity is vertical. C) Its vertical velocity component is the same as it was just as it was launched. D) Its horizontal velocity component is the same as it was just as it was launched. E) Its speed is the same as it was just as it was launched. Answer: D Var: 1 38) Shown below are the velocity and acceleration vectors for an object in several different types of motion. In which case is the object's velocity changing while its speed is not changing?

Answer: D Var: 1 39) If a satellite moves with constant speed in a perfectly circular orbit around the earth, what is the direction of the acceleration of the satellite? A) in the forward direction B) in the backward direction C) outward away from the earth D) inward toward the earth E) The acceleration is zero because the speed is constant. Answer: D Var: 1

40) An object moves in a circular path at a constant speed. Compare the direction of the object's velocity and acceleration vectors. A) Both vectors point in the same direction. B) The vectors point in opposite directions. C) The vectors are perpendicular to each other. D) The acceleration is zero but the velocity is constant. Answer: C Var: 1 41) The Moon is accelerated toward the earth, so it is gradually getting closer to the earth. A) True B) False C) The moon is not accelerated toward the earth. Answer: B Var: 1 42) You are trying to cross a river that flows toward the south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat A) directly toward the west. B) directly toward the north. C) in a general southwesterly direction. D) in a general northwesterly direction. Answer: D Var: 1 3.2 Problems 1) A velocity vector has components 36 m/s westward and 22 m/s northward. What are the magnitude and direction of this vector? Answer: 42 m/s at 31° north of west Var: 1 2) The x component of vector is closest to A) 9.9 units B) 7.9 units C) 8.9 units D) 11 units E) 12 units Answer: D Var: 1

is 8.7 units, and its y component is -6.5 units. The magnitude of

3) When rolled down a mountainside at 7.0 m/s, the horizontal component of its velocity vector was 1.8 m/s. What was the angle of the mountain surface above the horizontal? A) 75° B) 57 ° C) 33° D) 15° Answer: A Var: 47 4) When Jeff ran up a hill at 7.0 m/s, the horizontal component of his velocity vector was 5.1 m/s. What was the vertical component of Jeff's velocity? A) 4.8 m/s B) 4.3 m/s C) 3.8 m/s D) 3.4 m/s Answer: A Var: 50+ 5) The x component of vector is 5.3 units, and its y component is -2.3 units. The angle that vector makes with the +x-axis is closest to A) 340° B) 160° C) 250° D) 110° E) 23° Answer: A Var: 1 6) A vector in the xy-plane has an x component of -7.50 units. What must be the y component of this vector so that its magnitude is 10.0 units. (Note: There are two possible answers.) Answer: +6.6 units and -6.6 units Var: 1

7) A displacement vector is 34.0 m in length and is directed 60.0° east of north. Selecting from the choices in the table below, what are the components of this vector? Northward choice component 1 29.4 m 2 18.2 m 3 22.4 m 4 17.0 m 5 25.2 m A) choice 1 B) choice 2 C) choice 3 D) choice 4 E) choice 5 Answer: D Var: 1

Eastward component 17.0 m 28.1 m 11.5 m 29.4 m 18.2 m

8) A player throws a football 50.0 m at 61.0° north of west. What is the westward component of the displacement of the football? A) 64.7m B) 55.0 m C) 0.00 m D) 74.0 m E) 24.2 m Answer: E Var: 1 9) A vector

has components Ax = 12.0 m and Ay = 5.00 m.

(a) What is the angle that vector makes with the +x-axis? (b) What is the magnitude of vector ? Answer: (a) 22.6° (b) 13.0 m Var: 1 10) The x and y components of a vector in a horizontal plane are 4.00 m and 3.00 m, respectively. (a) What is the magnitude of this vector? (b) What angle does this vector make with the positive +y-axis. Answer: (a) 5.00 m (b) 53.1° Var: 1

11) A boy jumps with a velocity of magnitude 20.0 m/s at an angle of 25.0° above the horizontal. What is the horizontal component of the boy's velocity? A) 18.1 m/s B) 15.6 m/s C) 8.45 m/s D) 12.6 m/s E) 9.33 m/s Answer: A Var: 1 12) The magnitude of is 5.5 m, and this vector lies in the second quadrant and makes an angle of 34 ° with the +y-axis. The components of are closest to: A) = -3.1 m, = 4.6 m. B) = 3.1 m, = -4.6 m. C) = 4.6 m, = -3.1 m. D) = -4.6 m, = 3.1 m. E) = -4.6 m, = -3.1 m. Answer: A Var: 50+ 13) The components of vectors = -9.2 = -6.1

and

are given as follows:

= -4.5 = 4.3

The angle (less than 180°) between vectors A) 77°. B) 103°. C) 10°. D) 170°. E) 84°. Answer: A Var: 50+

and

is closest to

14) A car travels 20 km west and then 20 km south. What is the magnitude of its displacement vector? A) 0 km B) 20 km C) 28 km D) 40 km Answer: C Var: 1

15) You walk to the north, then turn 60° to your right and walk another you from where you originally started? A) 68 m B) 39 m C) 75 m D) 35 m Answer: A Var: 31

How far are

16) You walk 53 m to the north, then you turn 60° to your right and walk another Determine the direction of your displacement vector. Express your answer as an angle relative to east. A) 63° N of E B) 50° N of E C) 57° N of E D) 69° N of E Answer: A Var: 50+ 17) The components of vectors Ax = 7.6 Bx = -5.1 Ay = -9.2 By = -6.8

and

are given as follows:

What is the magnitude of the vector difference A) 13 B) 3.5 C) 16 D) 170 E) 3.4 Answer: A Var: 1 18) If vector

has components Ax = -3.0 lb and Ay = -4.0 lb, and vector

3.0 lb and By = -8.0 lb, what is the magnitude of vector A) 13 lb B) 16 lb C) 140 lb D) 7.2 lb Answer: D Var: 1

has components Bx =

19) Vector has magnitude 2 units and is directed to the north. Vector and is directed to the south. Calculate the magnitude and direction of A) 7 units, north B) 7 units, south C) 3 units, north D) 3 units, south Answer: A Var: 39

has magnitude

20) Two perpendicular vectors, and , are added together giving vector . If the magnitudes of both vectors and are doubled without changing their directions, the magnitude of vector will A) increase by a factor of 8. B) increase by a factor of 4. C) increase by a factor of 2. D) increase by a factor of . E) not change. Answer: C Var: 1 21) Three ropes are tied in a knot as shown in the figure. One student pulls on rope A with 1.0 pound of force, and another student pulls on rope B with 7.0 pounds of force. How hard and in what direction must you pull on rope C to balance the first two pulls? Give the direction by specifying the angle (clockwise or counterclockwise) of the pull with the direction of rope A.

Answer: 6.6 lb at 68° clockwise from rope A Var: 1

22) The figure shows two vectors vector is given by = - .

and

, along with their magnitudes and directions. The

(a) What is the magnitude of vector ? (b) What angle does vector make with the +x-axis? Answer: (a) 6.6 (b) 170° Var: 1 23) Displacement vector is 5.5 cm long and points along the +x-axis. Displacement vector is 7.5 cm long and points at +30° to the -x-axis. (a) Determine the x and y components of vector . (b) Determine the x and y components of vector . (c) Determine the x and y components of the resultant of these two vectors. (d) Determine the magnitude and direction of the resultant of these two vectors. Answer: (a) Ax = 5.5 cm, Ay = 0 cm (b) Bx = -6.5 cm, By = 3.8 cm (c) Rx = -1.0 cm, Ry = 3.8 cm (d) 3.9 cm at 75° above the -x axis Var: 1 24) Displacement vector is 75 cm long and points at 30° above the +x-axis. Displacement vector is 25 cm long and points along the -x-axis. Displacement vector is 40 cm long and points at 45° below the -x-axis. (a) Determine the x and y components of vector . (b) Determine the x and y components of vector . (c) Determine the x and y components of vector . (d) Determine the x and y components of the resultant of these three vectors. (e) Determine the magnitude and direction of the resultant of these three vectors. Answer: (a) Ax = 65 cm, Ay = 38 cm (b) Bx = -25 cm, By = 0 cm (c) Cx = -28 cm, Cy = -28 cm (d) Rx = 12 cm, Ry = 9 cm (e) 15 cm at 38° above the +x-axis Var: 1

25) Vector = 4.00 m points eastward and vector vector + is given by A) 5.00 m at an angle of 36.9° south of east. B) 5.00 m at an angle of 53.1° south of east. C) 5.00 m at an angle of 71.6° south of east. D) 5.00 m at an angle of 18.4° south of east. E) 5.00 m at an angle of 26.6° south of east. Answer: A Var: 1

= 3.00 m points southward. The resultant

26) Vector has a magnitude of 6.0 m and points 30° north of east. Vector has a magnitude of 4.0 m and points 30° east of north. The resultant vector + is given by A) 0.70 m at an angle of 42° north of east. B) 14 m at an angle of 42° north of east. C) 1.1 m at an angle of 42° north of east. D) 9.7 m at an angle of 42° north of east. E) 2.0 m at an angle of 42° north of east. Answer: D Var: 1 27) Vector has a magnitude of 6.0 m and points 30° north of east. Vector has a magnitude of 4.0 m and points 30° west of north. The resultant vector + is given by A) 9.8 m at an angle of 64° east of north. B) 9.8 m at an angle of 26° north of east. C) 7.2 m at an angle of 26° east of north. D) 3.3 m at an angle of 26° north of east. E) 3.3 m at an angle of 64° east of north. Answer: C Var: 1 28) Vector has a magnitude of 6.0 m and points 30° north of east. Vector has a magnitude of 4.0 m and points 30° west of south. The resultant vector + is given by A) 2.7 m at an angle of 8.3° south of east. B) 2.7 m at an angle of 8.3° east of south. C) 3.2 m at an angle of 8.3° east of south. D) 3.2 m at an angle of 8.3° south of east. E) 2.3 m at an angle of 8.3° south of east. Answer: D Var: 1

29) Vector has a magnitude of 6.0 m and points 30° south of east. Vector has a magnitude of 4.0 m and points 30° west of south. The resultant vector + is given by A) 7.2 m at an angle of 64° south of east. B) 3.3 m at an angle of 64° south of east. C) 9.8 m at an angle of 26° south of east. D) 9.8 m at an angle of 64° south of east. E) 3.3 m at an angle of 26° south of east. Answer: A Var: 1 30) Vector has a magnitude of 4.0 m and points 30° south of east. Vector has a magnitude of 2.0 m and points 30° north of west. The resultant vector + is given by A) 10.0 m at an angle 30° south of east. B) 10.0 m at an angle 60° east of south. C) 2.0 m at an angle 60° south of east. D) 2.0 m at an angle 30° south of east. E) 1.0 m at an angle 30° east of south. Answer: D Var: 5 31) Vector has a magnitude of 7.0 m and points 30° east of north. Vector has a magnitude of 5.0 m and points 30° west of south. The resultant vector + is given by A) 10.0 m at an angle 60° north of east. B) 10.0 m at an angle 30° east of north. C) 2.0 m at an angle 30° north of east. D) 2.0 m at an angle 60° north of east. E) 1.0 m at an angle 60° east of north Answer: D Var: 5 32) Vector has a magnitude of 6.0 m and points 30° east of south. Vector has a magnitude of 4.0 m and points 30° west of north. The resultant vector + is given by A) 2.0 m at an angle of 30° north of west. B) 2.0 m at an angle of 30° east of south. C) 10.0 m at an angle of 60° north of west. D) 10.0 m at an angle of 60° east of south. E) 1.0 m at an angle of 60° north of west. Answer: B Var: 1

33) Vector has a magnitude of 8.0 m and points east, vector has a magnitude of 6.0 m and points north, and vector has a magnitude of 5.0 m and points west. The resultant vector + + is given by A) 2.0 m at an angle 63° north of east. B) 2.0 m at an angle 63° east of north. C) 6.7 m at an angle 63° east of north. D) 6.7 m at an angle 63° north of east. E) 3.8 m at an angle 67° north of east Answer: D Var: 5 34) The figure shows three vectors and their magnitudes and relative directions. The magnitude of the resultant of the three vectors is closest to

A) 19 B) 16 C) 13 D) 10 E) 7.0 Answer: C Var: 1 35) Find the magnitude and direction of the resultant of the three force vectors, , , and , shown in the figure. These vectors have the following magnitudes: A = 5.0 lb, B = 7.9 lb, and C = 8.0 lb. Express the direction of the resultant by specifying the angle it makes with the +x-axis, with counterclockwise angles taken to be positive.

Answer: 1.6 lb, 312° Var: 1

36) Two boys, Joe and Sam, who are searching for buried treasure start underneath the same tree. Joe walks 12 m east and then 12 m north, while Sam walks 15 m west and then 10 m south. Both boys then stop. Find the magnitude and direction of the vector from Sam to Joe. Express the direction of this vector by specifying the angle it makes with the west-to-east direction. Answer: 35 m at 39° north of east Var: 1 37) An airplane undergoes the following displacements, all at the same altitude: First, it flies in a direction 30.0° east of north. Next, it flies due south. Finally, it flies 30.0° north of west. Use components to determine how far the airplane ends up from its starting point. A) 71.5 km B) 73.0 km C) 74.4 km D) 70.1 km E) 68.7 km Answer: A Var: 50+ 38) Two forces are acting on an object as shown in the figure. Assume that all the quantities shown are accurate to three significant figures.

(a) What is the magnitude of the resultant force on the object? (b) What is the direction of the resultant force? Answer: (a) 185 N (b) 77.8° above the +x-axis Var: 1

39) Three forces, 1, 2, and 3, each of magnitude 70 N, all act on an object as shown in the figure. The magnitude of the resultant force acting on the object is

A) 35 N. B) 70 N. C) 140 N. D) 210 N. E) 0 N. Answer: E Var: 1 40) Three forces, 1, 2, and 3, all act on an object, as shown in the figure. The magnitudes of the forces are: F1 = 80.0 N, F2 = 60.0 N, and F3 = 40.0 N. The resultant force acting on the object is given by

A) 180 N at an angle of 60.0° with respect to +x-axis. B) 60.0 N at an angle of 90.0° with respect to +x-axis. C) 20.0 N at an angle of 34.3° with respect to +x-axis. D) 35.5 N at an angle of 34.3° with respect to +x-axis. E) 40.0 N at an angle of 60.0° with respect to +x-axis. Answer: D Var: 1

41) Four vectors, , , , and , are shown in the figure. The sum of these four vectors is a vector having magnitude and direction

A) 4.0 cm, along +x-axis. B) 4.0 cm, along -x-axis. C) 4.0 cm, along +y-axis. D) 4.0 cm, along -y-axis. E) 4.0 cm, 45° above +x-axis. Answer: D Var: 1 42) Vector has a magnitude of 8.0 m and points 30° north of east; vector has a magnitude of 6.0 m and points 30° west of north; and vector has a magnitude of 5.0 m and points 30° west of south. The resultant vector + + is given by A) 2.7 m at an angle 74° north of east. B) 5.9 m at an angle 74° north of east. C) 4.8 m at an angle 74° east of north. D) 5.1 m at an angle 74° north of east. E) 2.1 m at an angle 66° east of north. Answer: D Var: 5

43) The figure shows three vectors, , , and , having magnitudes 7.0 cm, 6.0 cm, and 4.0 cm, respectively. Find the x and y components of the resultant of these three vectors.

Answer: -11 cm (x component), -4.5 cm (y component) Var: 1 44) The figure shows four vectors, , , , and , having magnitudes 10.0 m, 8.00 m, 6.00 m, and 2.00 m, respectively. Find the magnitude of the sum of these four vectors.

Answer: 14.4 m Var: 1

45) The figure shows four vectors, , , , and , having magnitudes 12.0 m, 10.0 m, 8.0 m, and 4.0 m, respectively. The sum of these four vectors is

A) 16.4 m at an angle 77.8° with respect to +x-axis. B) 16.4 m at an angle 12.3° with respect to +x-axis. C) 19.5 m at an angle 77.8° with respect to +x-axis. D) 19.5 m at an angle 12.3° with respect to +x-axis. E) 8.20 m at an angle 77.8° with respect to +x-axis. Answer: A Var: 5 46) The figure shows four vectors, , , , and . Vectors and each have a magnitude of 7.0 cm, and vectors and each have a magnitude of 4.0 cm. Find the x and y components of the sum of these four vectors.

Answer: 0.00 cm (x component), 4.2 cm (y component) Var: 1

47) The figure shows four vectors, , , , and . Vectors and both have a magnitude of 7.0 cm, and vectors and both have a magnitude of 4.0 cm. Find the magnitude and direction of the sum of these four vectors.

Answer: 4.2 cm along the +y-axis Var: 1 48) The figure shows three vectors, , , and , along with their magnitudes. Determine the magnitude and direction of the vector given by - - .

Answer: 85 m at 5.4° above the +x-axis Var: 1 49) The figure shows three vectors, , , and , along with their magnitudes. Determine the magnitude and direction of the vector given by + - .

Answer: 100 m at 31° above the +x-axis Var: 1

50) Three vectors, , , and , have the components shown in the table. What is the magnitude of the resultant of these three vectors? x component y component 3.50 m

-4.50 m

2.00 m

0.00 m

-5.50 m

2.50 m

A) 5.50 m B) 13.0 m C) 11.1 m D) 7.00 m E) 2.00 m Answer: E Var: 1 51) Three vectors, , , and , have the components shown in the table. What angle does the resultant of these three vectors make with the +x-axis? x component y component -3.5 m

4.5 m

0.00 m

-6.5 m

5.5 m

-2.5 m

A) 24° above the +x-axis B) 24° below the +x-axis C) 66° above the +x-axis D) 66° below the +x-axis Answer: D Var: 1 52) A runner runs on a circular path of radius 10 m. What is the magnitude of the displacement of the jogger if he runs (a) half-way around the track? (b) all the way around the track? Answer: (a) 20 m (b) 0 m Var: 1 53) A player hits a tennis ball into the air with an initial velocity of 32 m/s at 35° from the vertical. How fast is the ball moving at the highest point in its trajectory if air resistance is negligible? Answer: 18 m/s Var: 1 27 Copyright © 2019 Pearson Education, Inc.

54) A ball is thrown with an initial velocity of 20 m/s at an angle of 60° above the horizontal. If we can neglect air resistance, what is the horizontal component of its instantaneous velocity at the exact top of its trajectory? A) 10 m/s B) 17 m/s C) 20 m/s D) zero Answer: A Var: 2 55) A ball is thrown at an original speed of 8.0 m/s at an angle of 35° above the horizontal. If there is no air resistance, what is the speed of the ball when it returns to the same horizontal level? A) 4.0 m/s B) 8.0 m/s C) 16 m/s D) 9.8 m/s Answer: B Var: 1 56) A stone is thrown horizontally with an initial speed of 10 m/s from the edge of a cliff. A stopwatch measures the stone's trajectory time from the top of the cliff to the bottom to be 4.3 s. What is the height of the cliff if air resistance is negligibly small? A) 22 m B) 43 m C) 77 m D) 91 m Answer: D Var: 1 57) A girl throws a rock horizontally, with a velocity of 10 m/s, from a bridge. It falls 20 m to the water below. How far does the rock travel horizontally before striking the water, assuming negligible air resistance? A) 14 m B) 16 m C) 20 m D) 24 m Answer: C Var: 1

58) A ball thrown horizontally from a point 24 m above the ground, strikes the ground after traveling horizontally a distance of 18 m. With what speed was it thrown, assuming negligible air resistance? A) 6.1 m/s B) 7.4 m/s C) 8.1 m/s D) 8.9 m/s Answer: C Var: 1 59) As shown in the figure, a heavy rock is shot upward from the edge of a vertical cliff. It leaves the edge of the cliff with an initial velocity of 15 m/s directed at 25° from the vertical and experiences no appreciable air resistance as it travels. How high is the cliff?

Answer: 68 m Var: 1 60) The acceleration due to gravity on the Moon is only one-sixth of that on Earth, and the Moon has no atmosphere. If you hit a baseball on the Moon with the same effort (and therefore at the speed and angle) as on Earth, how far would the ball would travel on the Moon compared to on Earth? Neglect air resistance on Earth. A) 1/6 as far as on Earth B) 36 times as far as on Earth C) the same distance as on Earth D) 6 times as far as on Earth E) as far as on Earth Answer: D Var: 1 61) A boy throws a rock with an initial velocity of at 30.0° above the horizontal. How long does it take for the rock to reach the maximum height of its trajectory if air resistance is negligibly small and g = 9.80 m/s2? A) 0.160 s B) 0.282 s C) 0.313 s D) 0.441 s Answer: A Var: 50+

62) A cat leaps to try to catch a bird. If the cat's jump was at 60° off the ground and its initial velocity was what is the highest point of its trajectory, neglecting air resistance? A) 0.29 m B) 0.58 m C) 10.96 m D) 0.19 m Answer: A Var: 50+ 63) A fisherman casts his bait toward the river at an angle of 25° above the horizontal. As the line unravels, he notices that the bait and hook reach a maximum height of What was the initial velocity he launched the bait with? Assume that the line exerts no appreciable drag force on the bait and hook and that air resistance is negligible. A) 18 m/s B) 7.9 m/s C) 7.6 m/s D) 6.3 m/s Answer: A Var: 30 64) A football kicker is attempting a field goal from out. The ball is kicked and just clears the lower bar with a time of flight of If the angle of the kick was 45°, what was the initial speed of the ball, assuming no air resistance? A) 21.5 m/s B) 19.7 m/s C) 2.2 m/s D) 39 m/s Answer: A Var: 50+ 65) You throw a rock horizontally off a cliff with a speed of 20 m/s and no significant air resistance. After 2.0 s, the magnitude of the velocity of the rock is closest to A) 28 m/s B) 20 m/s C) 40 m/s D) 37 m/s Answer: A Var: 1 66) A shell is launched with a velocity of 100 m/s at an angle of 30.0° above horizontal from a point on a cliff 50.0 m above a level plain below. How far from the base of the cliff does the shell strike the ground? There is no appreciable air resistance, and g = 9.80 m/s2 at the location of the cliff. Answer: 963 m Var: 1

67) At target practice, a rifle bullet is fired at an angle of 30° below the horizontal with an initial velocity of 800 m/s from the top of a cliff 80 m high. How far from the base of the cliff does it strike the level ground below if air resistance is negligible? Answer: 140 m Var: 1 68) A batter hits a home run in which the ball travels 110 m horizontally with no appreciable air resistance. If the ball left the bat at 50° above the horizontal just above ground level, how fast was it hit? Answer: 33 m/s Var: 1 69) A marble moving 1.48 m/s rolls off the top edge of a 125-cm high table in a room where there is no appreciable air resistance and the acceleration due to gravity is 9.80 m/s2. (a) How far from the base of the table will it strike the floor? (b) How long will it be in the air? Answer: (a) 75.0 cm (b) 0.505 s Var: 1 70) A hunter points a rifle horizontally and holds it 3.30 m above the ground. The bullet leaves the barrel at 325 m/s and experiences no significant air resistance. The acceleration due to gravity at this location is 9.80 m/s2. (a) How long does it take for the bullet to strike the ground? (b) How far horizontally does it travel? Answer: (a) 0.821 s (b) 267 m Var: 1 71) A girl throws a rock horizontally with a speed of 12 m/s from a bridge. It falls 2.28 s before hitting the water below. Neglect air resistance. (a) How high is the bridge from the water below? (b) How far horizontally does the rock travel before striking the water? Answer: (a) 25 m (b) 27 m Var: 1 72) A celebrating student throws a water balloon horizontally from a dormitory window that is 50 m above the ground. It hits the ground at a point 60 m from the building without appreciable air resistance. (a) What will be the horizontal component of the velocity of the balloon just before it hits the ground? (b) What will be the magnitude of the vertical velocity of the balloon just before it hits the ground? Answer: (a) 19 m/s (b) 31 m/s Var: 1

73) Enzo throws a rock horizontally with a speed of 12 m/s from a bridge. It falls for 2.28 s before reaching the water below with no appreciable air resistance. Just as the rock reaches the water, find (a) the horizontal component of its velocity. (b) the speed with which it is moving. Answer: (a) 12 m/s (b) 25 m/s Var: 1 74) A ball rolls over the edge of a platform with a horizontal velocity of magnitude v. The height of the platform is 1.6 m and the horizontal range of the ball from the base of the platform is 20 m. What is the magnitude of v if air resistance is negligibly small? Answer: 35 m/s Var: 1 75) A hockey puck slides off the edge of a platform with an initial velocity of 20 m/s horizontally. The height of the platform above the ground is 2.0 m. What is the magnitude of the velocity of the puck just before it touches the ground? You can neglect air resistance. A) 21 m/s B) 22 m/s C) 24 m/s D) 25 m/s E) 6.3 m/s Answer: A Var: 1 76) A hockey puck slides off the edge of a horizontal platform with an initial velocity of 20 m/s horizontally and experiences no significant air resistance. The height of the platform above the ground is 2.0 m. What is the magnitude of the vertical component of the velocity of the puck just before it hits the ground? A) 20 m/s B) 6.3 m/s C) 13 m/s D) 15 m/s E) 21 m/s Answer: B Var: 1

77) A hockey puck slides off the edge of a horizontal platform with an initial velocity of 28.0 m/shorizontally in a city where the acceleration due to gravity is 9.81 m/s2. The puck experiences no significant air resistance as it falls. The height of the platform above the ground is 2.00 m. What is the angle below the horizontal of the velocity of the puck just before it hits the ground? A) 77.2° B) 72.6° C) 12.8° D) 12.6° E) 31.8° Answer: D Var: 6 78) A plane flying horizontally at a speed of 50 m/s and at an elevation of 160 m drops a package, and 2.0 s later it drops a second package. How far apart will the two packages land on the ground if air resistance is negligible? A) 100 m B) 160 m C) 180 m D) 320 m Answer: A Var: 1 79) In a room where g = 9.81 m/s2, a hockey puck slides off the edge of a platform with an initial velocity of 28.0 m/s horizontally. The height of the platform above the ground is 2.00 m. What is the speed of the puck just before it hits the ground? The air resistance is negligibly small. A) 48.2 m/s B) 28.7 m/s C) 28.0 m/s D) 26.3 m/s E) 6.26 m/s Answer: B Var: 1 80) A ball rolls over the edge of a platform with only a horizontal velocity. The height of the platform is 1.6 m and the horizontal range of the ball from the base of the platform is 20 m. What is the horizontal velocity of the ball just before it touches the ground? Neglect air resistance. A) 35 m/s B) 9.8 m/s C) 20 m/s D) 4.9 m/s E) 70 m/s Answer: A Var: 1

81) A projectile is shot horizontally at 23.4 m/s from the roof of a building 55 m tall and experiences negligible air resistance. (a) Determine the time necessary for the projectile to reach the ground below. (b) Determine the distance from the base of the building that the projectile lands. (c) Determine the horizontal and vertical components of the velocity just before the projectile reaches the ground. Answer: (a) 3.4 s (b) 78 m (c) vhoriz = 23.4 m/s, vvert = 33 m/s downward Var: 1 82) A person throws a ball horizontally from the top of a building that is 24.0 m above the ground level. The ball lands 100 m down range from the base of the building. What was the initial velocity of the ball? Neglect air resistance and use g = 9.81 m/s2. A) 202 m/s B) 9.80 m/s C) 19.6 m/s D) 45.2 m/s E) 94.4° Answer: D Var: 6 83) A wind farm generator uses a two-bladed propeller mounted on a pylon at a height of 20 m, as shown in the figure. The width of the pylon is very narrow, and the length of each propeller blade is 12 m. A tip of the propeller breaks off just when the propeller is vertical. The fragment flies off horizontally, falls, and strikes the ground at point P with negligible air resistance. Just before the fragment broke off, the propeller was turning uniformly, taking 1.2 s for each rotation. How far is point P from the base of the pylon?

A) 120 m B) 130 m C) 140 m D) 150 m E) 160 m Answer: E Var: 1

84) A boy throws a ball with an initial velocity of 25 m/s at an angle of 30° above the horizontal. If air resistance is negligible, how high above the projection point is the ball after 2.0 s? A) 5.4 m B) 13 m C) 25 m D) 43 m E) 50 m Answer: A Var: 5 85) A projectile is fired from ground level with a speed of 150 m/s at an angle 30° above the horizontal on an airless planet where g = 10.0 m/s2. What is the horizontal component of its velocity after 4.0 s? A) 150 m/s B) 35 m/s C) 130 m/s D) 75 m/s E) 38 m/s Answer: C Var: 1 86) A high-speed dart is shot from ground level with a speed of 150 m/s at an angle 30° above the horizontal. What is the vertical component of its velocity after 4.0 s if air resistance is neglected? A) 150 m/s B) 36 m/s C) 130 m/s D) 75 m/s E) 38 m/s Answer: B Var: 1 87) A projectile leaves the ground at 150 m/s and reaches a maximum height of 0.57 km. If there was no air resistance, at what angle above the horizontal did it leave the ground? Answer: 45° Var: 1

88) A child is trying to throw a ball over a fence. She gives the ball an initial speed of 8.0 m/s at an angle of 40° above the horizontal. The ball leaves her hand 1.0 m above the ground and the fence is 2.0 m high. The ball just clears the fence while still traveling upwards and experiences no significant air resistance. How far is the child from the fence? A) 0.73 m B) 1.6 m C) 2.7 m D) 3.8 m E) 7.5 m Answer: B Var: 1 89) A boy kicks a football from ground level with an initial velocity of 20 m/s at an angle of 30° above the horizontal. What is the horizontal distance to the point where the football hits the ground if we neglect air resistance? A) 20 m B) 35 m C) 18 m D) 60 m E) 30.0 m Answer: B Var: 6 90) An athlete competing in the long jump leaves the ground with a speed of 9.14 m/s at an angle of 55° with the vertical. What is the length of the athlete's jump if air resistance is of no significance? A) 0.88 m B) 8.0 m C) 12 m D) 17 m E) 4.0 m Answer: B Var: 1 91) An athlete competing in the long jump leaves the ground with a speed of 9.14 m/s at an angle of 35° above the horizontal. How long does the athlete stay in the air, assuming no significant air resistance? A) 0.50 s B) 0.88 s C) 1.1 s D) 2.5 s E) 0.54 s Answer: C Var: 1

92) An athlete participates in an interplanetary discus throw competition during an Olympiad that takes place on a planet where the acceleration due to gravity is 9.7 m/s2. He throws the discus with an initial velocity of 20 m/s at an angle of 60° from the vertical. Neglecting air resistance and the height of the discus at the point of release, what is the range of the discus? A) 21 m B) 60 m C) 36 m D) 40 m E) 32 m Answer: C Var: 1 93) A child throws a ball with an initial speed of 8.0 m/s at an angle of 40° above the horizontal. The ball leaves her hand 1.0 m above the ground and experiences no appreciable air resistance as it moves. (a) How far from where the child is standing does the ball hit the ground? (b) How long is the ball in flight before it hits the ground? (c) What is the magnitude of the ball's velocity just before it hits the ground? Answer: (a) 7.5 m (b) 1.2 s (c) 9.1 m/s Var: 1 94) A child throws a ball with an initial speed of 8.0 m/s at an angle of 40° above the horizontal. The ball leaves her hand 1.0 m above the ground. At what angle below the horizontal does the ball approach the ground? A) 35° B) 42° C) 48° D) 40° E) 65° Answer: C Var: 1 95) The horizontal and vertical components of the initial velocity of a football are 16 m/s and 20 m/s respectively. If there is no air resistance, how long does it take the football to reach the top of its trajectory? A) 1.0 s B) 2.0 s C) 3.0 s D) 4.0 s E) 5.0 s Answer: B Var: 1

96) A projectile is fired at an angle above the horizontal at a location where g = 9.8 m/s2. The initial x and y components of its velocity are 86.6 m/s and 50 m/s respectively. At what angle was the projectile fired above the horizontal? A) 45° B) 60° C) 30° D) 90° E) 75° Answer: C Var: 1 97) A projectile is fired from ground level at an angle above the horizontal on an airless planet where g = 10.0 m/s2. The initial x and y components of its velocity are 86.6 m/s and 50.0 m/s respectively. How long after firing does it take before the projectile hits the level ground? A) 5.00 seconds B) 10.0 seconds C) 15.0 seconds D) 20.0 seconds Answer: B Var: 1 98) A projectile is fired from ground level with an initial speed of 55.6 m/s at an angle of 41.2° above the horizontal. Neglect air resistance, take upward as the positive direction, and use g = 9.8 m/s2. (a) Determine the time necessary for the projectile to reach its maximum height. (b) Determine the maximum height reached by the projectile. (c) Determine the horizontal and vertical components of the velocity vector at the maximum height. (d) Determine the horizontal and vertical components of the acceleration vector at the maximum height. Answer: (a) 3.7 s (b) 68 m (c) vhorizontal = 42 m/s, vvertical = 0 m/s (d) ahorizontal = 0 m/s2, avertical = -9.8 m/s2 Var: 1 99) At a location where g = 9.80 m/s2, a projectile returns to its original height after 4.08 seconds, during which time it travels 76.2 meters horizontally. If air resistance can be neglected, what was the projectile's initial speed? Answer: 27.4 m/s Var: 1 100) A rock is thrown from the roof of a building, with an initial velocity of 10 m/s at an angle of 30° above the horizontal. The rock is observed to strike the ground 43 m from the base of the building. What is the height of the building assuming no air resistance? Answer: 96 m Var: 1 38 Copyright © 2019 Pearson Education, Inc.

101) A 5.0-kg stone is thrown upward at 7.5 m/s at an angle of 51° above the horizontal from the upper edge of a cliff, and it hits the ground 1.5 s later with no air resistance. Find the magnitude of its velocity vector just as it reaches the ground. Answer: 10 m/s Var: 1 102) A projectile is thrown upward at 24° with the vertical and returns to the horizontal ground 12.5 s later with no air drag. (a) How fast was it thrown? (b) How far from its original position did it land? (c) How high above its original position did it go? Answer: (a) 67 m/s (b) 340 m (c) 190 m Var: 1 103) A projectile is fired from the edge of a cliff as shown in the figure. The initial velocity components are 940 m/s (horizontal) and 96 m/s (vertical). The projectile reaches maximum height at point P and then falls and strikes the ground at point Q. How high is point P above point Q, assuming no air resistance?

A) 470 m B) 490 m C) 45,000 m D) 940 m E) 90,000 m Answer: B Var: 1

104) As shown in the figure, a projectile is fired at time t = 0.00 s, from point 0 at the upper edge of a cliff, with initial velocity components of and The projectile rises and then falls into the sea at point P. The time of flight of the projectile is and air resistance 2 is negligible. At this location, g = 9.80 m/s . What is the horizontal distance D?

A) 2250 m B) 2520 m C) 2790 m D) 3060 m E) 3330 m Answer: A Var: 50+ 105) A projectile is launched with an initial velocity of 80 m/s at 30° above the horizontal. Neglecting air resistance, what is horizontal component of the projectile's acceleration? A) 80 m/s2 B) 40 m/s2 C) 9.8 m/s2 D) 0 m/s2 E) 69 m/s2 Answer: D Var: 1 106) A boy kicks a football with an initial velocity of 20 m/s at an angle of 25° above the horizontal. If we neglect air resistance, the magnitude of the acceleration of the ball while it is in flight is A) 25 m/s2. B) 18 m/s2. C) 9.8 m/s2. D) 8.5 m/s2. E) 0 m/s2. Answer: C Var: 1

107) A projectile is fired from ground level on a horizontal plain. If the initial speed of the projectile is now doubled, and we neglect air resistance, A) its range will be increased by . B) its range will double. C) its range will be decreased by a factor of two. D) its range will quadruple. E) its range will decrease by a factor of four. Answer: D Var: 1 108) A hobbyist launches a projectile from ground level on a horizontal plain. It reaches a maximum height of 72.3 m and lands 111 m from the launch point, with no appreciable air resistance. What was the angle of launch if g = 9.80 m/s2? A) 69.0° B) 67.4° C) 22.6° D) 44.8° Answer: A Var: 1 109) Sarah drives at a constant speed of 15 m/s around a circular horizontal curve of diameter 60 m. What are the magnitude and direction of her acceleration? Answer: 7.5 m/s2 toward the center of the circle Var: 1 110) You need to design a wheel for testing purposes such that its rim will have an acceleration of 1.5 g when the rim is moving at 37 m/s while spinning. What should be the diameter of this wheel? Answer: 190 m Var: 1 111) A child sits on a merry-go-round, 1.5 meters from the center. The merry-go-round is turning at a constant rate, and the child is observed to have a radial acceleration of 2.3 m/s2. How long does it take for the merry-go-round to make one revolution? Answer: 5.1 s Var: 1 112) A disk-shaped space station 125 m in diameter spins at a uniform rate about an axis through its center and perpendicular to the plane of the disk. If the acceleration of a point on the rim of the disk is to be equal to g, how long does it take for the station to make one revolution? Use g = 9.8 m/s2. Answer: 16 s Var: 1

113) An object moves with a constant speed of 30 m/s on a circular track of radius 150 m. What is the acceleration of the object? A) 0 m/s2 B) 0.17 m/s2 C) 5.0 m/s2 D) 6.0 m/s2 Answer: D Var: 3 114) A point on a wheel of radius 40 cm that is rotating at a constant 5.0 revolutions per second is located 0.20 m from the axis of rotation. What is the acceleration of that point due to the spin of the wheel? A) 0.050 m/s2 B) 1.4 m/s2 C) 48 m/s2 D) 200 m/s2 E) 0.00 m/s2 Answer: D Var: 1 115) You are driving at your acceleration? A) 36.0 m/s2 B) 1.20 m/s2 C) 20.8 m/s2 D) 0.833 m/s2 Answer: A Var: 50+

on a freeway curve of radius

What is the magnitude of

116) The maximum acceleration a pilot can stand without blacking out is about 7.0 g. In an endurance test for a jet plane's pilot, what is the maximum speed he can tolerate if he is spun in a horizontal circle of diameter 85 m? Answer: 54 m/s Var: 1 117) A race car traveling at a constant speed of 50 m/s drives around a circular track that is 500 m in diameter. What is the magnitude of the acceleration of the car? A) 0 m/s2 B) 1.0 m/s2 C) 10 m/s2 D) 0.63 m/s2 E) 2.2 m/s2 Answer: C Var: 1 42 Copyright © 2019 Pearson Education, Inc.

118) A jet plane flying 600 m/s experiences an acceleration of 4.0 g when pulling out of the circular section of a dive. What is the radius of curvature of this section of the dive? A) 1.2 km B) 5.8 km C) 0.64 km D) 9.2 km E) 7.0 km Answer: D Var: 1 119) The Moon is 3.84 × 108 m from Earth and takes 27.3 days to complete each orbit. What are the magnitude and direction of the acceleration of the Moon, assuming a circular orbit? Answer: 2.72 × 10-3 m/s2, toward Earth Var: 1 120) You are traveling at 55 mi/h along the +x-axis relative to a straight, level road and pass a car that is traveling at 45 mi/h. The relative velocity of your car to the other car is A) -10 mi/h. B) 10 mi/h. C) 65 mi/h. D) 35 mi/h. Answer: B Var: 2 121) Your motorboat can move at 30 km/h in still water. What is the minimum time it will take you to move 12 km downstream in a river flowing at 6.0 km/h? A) 20 min B) 22 min C) 24 min D) 30 min Answer: A Var: 1 122) An airplane with an airspeed of 140 km/h has a heading of 50° west of north in a wind that is blowing toward the east at 25 km/h. What is the groundspeed of the plane? Answer: 120 km/h Var: 1 123) A plane has an airspeed of 200 m/s northward, and is in a wind of 50.0 m/s to the west. The plane's speed relative to the ground is A) 150 m/s. B) 200 m/s. C) 206 m/s. D) 250 m/s. Answer: C Var: 1 43 Copyright © 2019 Pearson Education, Inc.

124) An airplane with an airspeed of 120 km/h has a heading of 30° east of north in a wind that is blowing toward the west at 30 km/h. What is the speed of the plane relative to the ground? A) 90 km/h B) 110 km/h C) 140 km/h D) 150 km/h Answer: B Var: 1 125) A plane moving 200 m/s horizontally fires a projectile with speed 50 m/s in a forward direction 30.0° below the horizontal. At that instant, what is the speed of the projectile with respect to a stationary observer on the ground? A) 245 m/s B) 250 m/s C) 268 m/s D) 293 m/s Answer: A Var: 1 126) Alicia intends to swim to a point straight across a 100 m wide river with a current that flows at 1.2 m/s. She can swim 2.5 m/s in still water. At what angle, measured from the upstream direction, must she swim upstream to achieve her goal? Answer: 61° Var: 1 127) On a calm day with no wind, you can run a 1500-m race at a velocity of 4.0 m/s. If you run the same race on a day when you have a constant headwind that slows your speed by 2.0 m/s, how much time would it take you to finish the race? A) 250 s B) 750 s C) 1125 s D) 9000 s Answer: B Var: 2 128) A pickup truck moves at 25 m/s toward the east. Ahmed is standing in the back and throws a baseball in what to him is the southwest direction at 28 m/s (with respect to the truck). A person at rest on the ground would see the ball moving how fast in what direction? Answer: 20 m/s at 15° east of south Var: 1 129) A submarine must travel how fast (with respect to the water) and be pointed in what direction such that it moves 10 m/s directly northward (relative to the earth) if the water moves westward at 5.0 m/s? Answer: 11 m/s at 63° north of east Var: 1 44 Copyright © 2019 Pearson Education, Inc.

130) An airplane is pointed at 45° north of east and is moving at 71 m/s with respect to the air. The jet stream (moving air) carries the plane at 30 m/s toward the east. What are the magnitude and direction of the velocity of the plane relative to the ground? Answer: 94 m/s at 32° north of east Var: 1 131) The driver of a motorboat that can move at 10 m/s in still water wishes to travel directly across a river in which the current flows at 5.0 m/s. (a) At what angle, measured from the upstream direction, should the driver head the boat? (b) How many minutes will it take to cross the river if it is 1.6 km wide at that point? Answer: (a) 60° (b) 3.1 min Var: 1 132) A 960-m wide river flows at 16 m/s as shown in the figure. Alice and John have a race in identical boats which each travel 20 m/s in still water. Alice leaves point A and steers so that she goes straight to point B directly across and then back to A. John leaves point A and steers up to point C (960 m upstream) and then returns to A. (a) Which person arrives back at point A first? (b) How much sooner than the loser does the winner arrive back at point A?

Answer: (a) Alice Var: 1

(b) Alice arrives 110 s before John

133) A plane has an eastward heading with an airspeed of 156 m/s. A 20.0 m/s wind is blowing southward at the same time as the plane is flying. The velocity of the plane relative to the ground is A) 157 m/s at an angle 7.31° south of east. B) 157 m/s at an angle 7.31° east of south. C) 155 m/s at an angle 7.36° south of east. D) 155 m/s at an angle 7.36° east of south. E) 157 m/s at an angle 7.36° south of east. Answer: A Var: 1

134) A plane has an airspeed of 142 m/s. A 30.0 m/s wind is blowing southward at the same time as the plane is flying. What must be the heading of the plane in order to move directly eastward relative to the ground? A) 78.1° north of east B) 11.9° north of east C) 77.8° north of east D) 12.2° north of east E) 55.3° north of east Answer: D Var: 1 135) A plane has an airspeed of 142 m/s. A 16 m/s wind is blowing southward at the same time as the plane is flying. If the velocity of the plane relative to the ground is directly eastward, what is the magnitude of that velocity? A) 130 m/s B) 16 m/s C) 160 m/s D) 141 m/s E) 48 m/s Answer: D Var: 1 136) An airplane flies between two points on the ground that are 500 km apart. The destination is directly north of the point of origin of the flight. The plane flies with an airspeed of 120 m/s. If a constant wind blows at 10 m/s toward the west during the flight, what direction must the plane fly relative to the air to arrive at the destination? A) 4.8° east of north B) 5.9° east of north C) 85° west of north D) 4.8° west of north E) 5.9° west of north Answer: A Var: 1 137) A swimmer heading directly across a river that is 200 m wide reaches the opposite bank in 6 min 40 s. During this swim, she is swept downstream 480 m. How fast can she swim in still water? A) 0.50 m/s B) 0.80 m/s C) 1.2 m/s D) 1.4 m/s E) 1.8 m/s Answer: A Var: 1

138) A swimmer heading directly across a river that is 200 m wide reaches the opposite bank in 6 min 40 s. During this swim, she is swept downstream 480 m. What is the speed of the current? A) 0.50 m/s B) 0.80 m/s C) 1.2 m/s D) 1.4 m/s E) 1.8 m/s Answer: C Var: 1 139) A boat, whose speed in still water is 1.75 m/s, must aim upstream at an angle of 26.3° (with respect to a line perpendicular to the shore) in order to travel directly across the stream. (a) What is the speed of the current? (b) What is the resultant speed of the boat with respect to the shore? Answer: (a) 0.775 m/s (b) 1.57 m/s Var: 1 140) A boat, whose speed in still water is 8.0 m/s, crosses a river with a current of 6.0 m/s. If the boat heads perpendicular to the current, what is the speed of the boat relative to an observer standing on the shore as it crosses the river? A) 5.3 m/s B) 6.0 m/s C) 8.0 m/s D) 10.0 m/s Answer: D Var: 1 141) A plane flies directly from city A to city B, which are separated by 2300 mi. From A to B, the plane flies into a 65 mi/h headwind. On the return trip from B to A, the wind velocity is unchanged. The trip from B to A takes less than the trip from A to B. What is the airspeed (assumed constant) of the plane relative to the air (that is, the airspeed)? A) 530 mi/h B) 400 mi/h C) 480 mi/h D) 610 mi/h Answer: A Var: 31

College Physics: A Strategic Approach, 4e (Knight) Chapter 4 Forces and Newton's Laws of Motion 4.1 Conceptual Questions 1) In a collision between a huge SUV and a small hybrid car, the SUV exerts a larger force on the hybrid than the hybrid exerts on the SUV. A) True B) False C) It depends on whether the collision is a head-on collision or a rear-end collision. Answer: B Var: 1 2) A box is placed on a table which rests on the floor. The box pushes on the table; the reaction force to the box's push on the table is the table's push on the floor. A) True B) False Answer: B Var: 1 3) In order to get an object moving, you must push harder on it than it pushes back on you. A) True B) False Answer: B Var: 1 4) A girl attaches a rock to a string, which she then swings counter-clockwise in a horizontal circle. The string breaks at point P in the figure, which shows a bird's-eye view (as seen from above). Which path (A-E) will the rock follow?

A) Path A B) Path B C) Path C D) Path D E) Path E Answer: B Var: 1

5) If you pound a feather with a hammer, which one feels a greater force? A) always the feather B) always the hammer C) The size of the force is always exactly the same on both of them. D) If the feather moves, then it felt the greater force. Otherwise the force was the same on both. Answer: C Var: 1 6) A satellite is in orbit around the earth. Which one feels the greater force? A) the satellite because the earth is so much more massive B) the earth because the satellite has so little mass C) Earth and the satellite feel exactly the same force. D) It depends on the distance of the satellite from Earth. Answer: C Var: 1 7) You pull on a crate with a rope. If the crate moves, the rope's pull on the crate must have been larger than the crate's pull on the rope, but if the crate does not move, both of these pulls must have been equal. A) True B) False Answer: B Var: 1 8) In order to lift a bucket of concrete, you must pull up harder on the bucket than the bucket pulls down on you. A) True B) False Answer: B Var: 1 9) If the rockets of a spaceship in outer space (far from all gravity) suddenly lose power and go off, the spaceship will gradually slow to a stop. A) True B) False Answer: B Var: 1

10) You are in a train traveling on a horizontal track and notice that a piece of luggage starts to slide directly toward the front of the train. From this observation, you can conclude that this train is A) speeding up. B) slowing down. C) changing direction. D) speeding up and changing direction. E) slowing down and changing direction. Answer: B Var: 1 11) While flying horizontally in an airplane, you notice that a string dangling from the overhead luggage compartment hangs at rest at 15° away from the vertical toward the front of the plane. Using this observation, you can conclude that the airplane is A) moving forward. B) moving backward. C) accelerating forward. D) accelerating backward. E) not accelerating because the string is at rest. Answer: D Var: 1 12) An elevator suspended by a vertical cable is moving downward but slowing down. The tension in the cable must be A) greater than the weight of the elevator. B) less than than the weight of the elevator. C) equal to the weight of the elevator. Answer: A Var: 1 13) A crate is sliding down an inclined ramp at a constant speed of 0.55 m/s. The vector sum of all the forces acting on this crate must point A) down the ramp. B) up the ramp. C) perpendicular to the ramp. D) vertically downward. E) None of the above choices is correct. Answer: E Var: 1 14) A bucket is being lowered by a very light rope with a constant downward velocity. The tension in the rope must be A) equal to the weight of the bucket. B) greater than the weight of the bucket. C) less than the weight of the bucket. Answer: A Var: 1 3 Copyright © 2019 Pearson Education, Inc.

15) Bill and his daughter Susan are both standing on identical skateboards (with really good frictionless ball bearings), initially at rest. Bill weighs three times as much as Susan. Bill pushes horizontally on Susan's back, causing Susan to start moving away from Bill. Just after Bill stops pushing, A) Susan and Bill are moving away from each other, and Susan's speed is three times that of Bill. B) Susan is moving away from Bill, and Bill is stationary. C) Susan and Bill are moving away from each other, with equal speeds. D) Susan and Bill are moving away from each other, and Susan's speed is one-third that of Bill. Answer: A Var: 1 16) You push on box G that is next to box H, causing both boxes to slide along the floor, as shown in the figure. The reaction force to your push is

A) the push of box G on box H. B) the push of box H on box G. C) the push of box G against you. D) the upward force of the floor n box G. E) the acceleration of box G. Answer: C Var: 1 17) A small car and a large SUV are at a stoplight. The car has a mass equal to half that of the SUV, and the SUV can produce a maximum accelerating force equal to twice that of the car. When the light turns green, both drivers push their accelerators to the floor at the same time. Which vehicle pulls ahead of the other vehicle after a few seconds? A) The car pulls ahead. B) The SUV pulls ahead. C) It is a tie. Answer: C Var: 1 18) An object is moving with constant non-zero velocity. Which of the following statements about it must be true? A) A constant force is being applied to it in the direction of motion. B) A constant force is being applied to it in the direction opposite of motion. C) A constant force is being applied to it perpendicular to the direction of motion. D) The net force on the object is zero. E) Its acceleration is in the same direction as it velocity. Answer: D Var: 1

19) A 20-ton truck collides with a 1500-lb car. Which of the following statements must be true? A) During the collision, the force on the truck is greater then the force on the car. B) During the collision, the force on the truck is equal to the force on the car. C) During the collision, the force on the truck is smaller than the force on the car. D) The truck did not slow down during the collision, but the car did. E) The car did not slow down during the collision, but the truck did. Answer: B Var: 1 20) A truck is using a hook to tow a car whose mass is one quarter that of the truck. If the force exerted by the truck on the car is 6000 N, then the force exerted by the car on the truck is A) 1500 N. B) 24000 N. C) 6000 N. D) 12000 N. E) We need to know if the car is accelerating to answer this question. Answer: C Var: 1 21) A golf club hits a golf ball with a force of 2400 N, sending the ball into the air. The force exerted on the club by the ball must be less than 2400 N or else the ball would not have moved forward. A) True B) False C) The answer depends on whether the golfer followed through with the swing. Answer: B Var: 1 22) The figure shows two boxes, with m1 > m2, that are on a level frictionless surface. We can apply a horizontal force either toward the right on m1 or toward the left on m2. The magnitude of the force that the boxes exert on each other is

A) zero newtons in either case. B) larger if is applied toward the right. C) larger if is applied toward the left. D) the same in either case. Answer: C Var: 1 5 Copyright © 2019 Pearson Education, Inc.

23) A horse pulls a cart with force . As a result of this force the cart accelerates with constant acceleration. The magnitude of the force that the cart exerts on the horse A) is zero newtons. B) equal to the magnitude of . C) less than the magnitude of . D) greater than the magnitude of . E) cannot be determined without knowing the mass of the horse. Answer: B Var: 1 24) An object of weight W is in freefall close to the surface of Earth. The magnitude of the force that the object exerts on Earth is A) greater than W. B) less than W. C) equal to W. D) zero. E) cannot be determined without knowing the relative masses of the object and the earth. Answer: C Var: 1 25) An object of mass m rests on a flat table. The earth pulls on this object with a force of magnitude mg. What is the reaction force to this pull? A) The table pushing up on the object with force mg. B) The object pushing down on the table with force mg. C) The table pushing down on the floor with force mg. D) The object pulling upward on the Earth with force mg. E) The table pulling upward on the Earth with force mg. Answer: D Var: 1 26) You are standing in a moving bus, facing forward, when you suddenly slide forward as the bus comes to an immediate stop. What force caused you to slide forward? A) gravity B) the normal force due to your contact with the floor of the bus C) the force due to friction between you and the floor of the bus D) There is not a force causing you to slide forward. Answer: D Var: 1

27) A fireman is sliding down a fire pole. As he speeds up, he tightens his grip on the pole, thus increasing the vertical frictional force that the pole exerts on the fireman. When the force on his hands equals his weight, what happens to the fireman? A) The fireman comes to a stop. B) The fireman descends with slower and slower speed. C) The fireman descends with a smaller but non-zero acceleration. D) The fireman continues to descend, but with constant speed. E) The acceleration of the fireman is now upward. Answer: D Var: 1 28) A person is using a rope to lower a 5.0-N bucket into a well with a constant speed of 2.0 m/s. What is the magnitude of the force exerted by the rope on the bucket? A) 0.00 N B) 2.0 N C) 5.0 N D) 10 N E) 49 N Answer: C Var: 1 29) A person who normally weighs 700 N is riding in a rather swift elevator that is moving at a constant speed of 9.8 m/s. If this person is standing on a bathroom scale inside the elevator, what would the scale read? A) more than 700 N B) less than 700 N C) 700 N D) It could be more or less than 700 N, depending on whether the elevator is going up or down. Answer: C Var: 1 30) A person who normally weighs 700 N is riding in an elevator that is moving upward but slowing down at a steady rate. If this person is standing on a bathroom scale inside the elevator, what would the scale read? A) more than 700 N B) less than 700 N C) 700 N D) It could be more or less than 700 N, depending on whether the magnitude of the acceleration is greater than or less than 9.8 m/s2. Answer: B Var: 1

31) A 75-N box rests on a perfectly smooth horizontal surface. The minimum force need to start the box moving is A) 75 N. B) 7.5 N. C) 750 N. D) any horizontal force greater than zero. Answer: D Var: 1 32) The acceleration due to gravity is lower on the Moon than on Earth. Which one of the following statements is true about the mass and weight of an astronaut on the Moon's surface, compared to Earth? A) Mass is less, weight is the same. B) Mass is the same, weight is less. C) Both mass and weight are less. D) Both mass and weight are the same. Answer: B Var: 1 33) When a 45-kg person steps on a scale in an elevator, the scale reads a steady 480 N. Which of the following statements must be true? (There could be more than one correct choice.) A) The elevator is accelerating upward at a constant rate. B) The elevator is accelerating downward at a constant rate. C) The elevator is moving upward at a constant rate. D) From the given information, we cannot tell if the elevator is moving up or down. Answer: A, D Var: 1 34) When a 45-kg person steps on a scale in an elevator, the scale reads a steady 410 N. Which of the following statements must be true? (There could be more than one correct choice.) A) The elevator is accelerating upward at a constant rate. B) The elevator is accelerating downward at a constant rate. C) The elevator is moving upward at a constant rate. D) From the given information, we cannot tell if the elevator is moving up or down. Answer: B, D Var: 1

35) Inside of a train a ball of weight W is hanging by a light wire at rest from the ceiling. The wire makes an angle θ with the ceiling, as shown in the figure. Which one of the following conditions must be true about the tension T in the wire?

A) T sin θ = W B) T cos θ = W C) T tan θ = W D) T = W E) T = ma Answer: A Var: 1 4.2 Problems 1) What is the mass of an object that experiences a gravitational force of 685 N near Earth's surface where g = 9.80 m/s2? A) 69.9 kg B) 68.5 kg C) 71.3 kg D) 72.7 kg Answer: A Var: 50+ 2) If I weigh 741 N on Earth at a place where g = 9.80 m/s2 and 5320 N on the surface of another planet, what is the acceleration due to gravity on that planet? A) 70.4 m/s2 B) 51.4 m/s2 C) 61.2 m/s2 D) 81.0 m/s2 Answer: A Var: 50+ 3) An astronaut weighs 99 N on the Moon, where the acceleration of gravity is 1.62 m/s2. How much does she weigh on Earth? A) 16 N B) 61 N C) 99 N D) 600 N E) 440 N Answer: D Var: 1

4) An object has a mass of 60 kg on Earth. What are the mass and weight of this object on the surface of the Moon where the acceleration due to gravity is only 1/6 of what it is on Earth? Answer: mass = 60 kg, weight = 98 N Var: 1 5) A net force of 125 N is applied to a certain object. As a result, the object accelerates with an acceleration of 24.0 m/s2. The mass of the object is A) 3000 kg. B) 2880 kg. C) 144 kg. D) 0.200 kg. E) 5.21 kg. Answer: E Var: 1 6) If a net force accelerates a 4.5-kg tool at 40 m/s2, what acceleration would that same net force give to an 18-kg tool? A) 180 m/s2 B) 10 m/s2 C) 160 m/s2 D) 9.8 m/s2 E) 32 m/s2 Answer: B Var: 1 7) A block is on a frictionless table, on earth. The block accelerates at 3.0 m/ when a horizontal force is applied to it. The block and table are set up on the Moon where the acceleration due to gravity is 1.62 m/ . The weight of the block on the Moon is closest to A) 11 N. B) 9.5 N. C) 8.1 N. D) 6.8 N. E) 5.5 N. Answer: A Var: 50+

8) A block is on a frictionless table, on earth. The block accelerates at 5.3 m/ when a horizontal force is applied to it. The block and table are set up on the Moon where the acceleration due to gravity is 1.62 m/ . A horizontal force of 5 N is now applied to the block when it is on the Moon. The acceleration imparted to the block by this force is closest to A) 2.7 m/ . B) 2.4 m/ . C) 2.9 m/ . D) 3.2 m/ . E) 3.4 m/ . Answer: A Var: 50+ 9) A 40-kg crate is being lowered with a downward acceleration is 2.0 m/s2 by means of a rope. (a) What is the magnitude of the force exerted by the rope on the crate? (b) What would be the magnitude of the force exerted by the rope if the crate were being raised with an acceleration of 2.0 m/s2? Answer: (a) 310 N (b) 470 N Var: 1 10) A 450-kg sports car accelerates from rest to 100 km/h in 4.80 s. What magnitude force does a 68.0 kg passenger experience during the acceleration? A) 394 N B) 82.0 N C) 342 N D) 311 N Answer: A Var: 50 11) On its own, a tow truck has a maximum acceleration of 3.0 m/s2. What will be its maximum acceleration when the truck is using a light horizontal chain to tow a bus of twice its own mass? A) 2.5 m/s2 B) 2.0 m/s2 C) 1.5 m/s2 D) 1.0 m/s2 Answer: D Var: 1 12) A car of mass 1100 kg that is traveling at 27 m/s starts to slow down and comes to a complete stop in 578 m. What is the magnitude of the average braking force acting on the car? A) 690 N B) 550 N C) 410 N D) 340 N Answer: A Var: 1 11 Copyright © 2019 Pearson Education, Inc.

13) A certain aircraft has a mass of 300,000 kg. At a certain instant during its landing, its speed is 27.0 m/s. If the braking force is a constant 445,000 N, what is the speed of the airplane 10.0 s later? A) 10.0 m/s B) 12.2 m/s C) 14.0 m/s D) 18.0 m/s E) 20.0 m/s Answer: B Var: 5 14) What magnitude net force is required to accelerate a 1200-kg car uniformly from 0 m/s to 27.0 m/s in 10.0 s? A) 444 N B) 1620 N C) 3240 N D) 4360 N E) 11800 N Answer: C Var: 1 15) A catcher stops a 0.15-kg ball traveling at 40 m/s in a distance of 20 cm. What is the magnitude of the average force that the ball exerts against his glove? Answer: 600 N Var: 1 16) An object that weighs 75 N is pulled on a horizontal surface by a horizontal pull of 50 N to the right. The friction force on this object is 30 N to the left. What is the acceleration of the object? A) 0.27 m/s2 B) 1.1 m/s2 C) 2.6 m/s2 D) 11 m/s2 Answer: C Var: 1 17) A 1200-kg car is pulling a 500-kg trailer along level ground. Friction of the road on the trailer is negligible. The car accelerates with an acceleration of 1.3 m/s2. What is the force exerted by the car on the trailer? A) 550 N B) 600 N C) 650 N D) 700 N E) 750 N Answer: C Var: 1 12 Copyright © 2019 Pearson Education, Inc.

18) In a certain particle accelerator, a proton reaches an acceleration of 9.0 × 1013 m/s2. The mass of a proton is 1.67 × 10-27 kg. What is the force on the proton? Answer: 1.5 × 10-13 N Var: 1 19) During a hard stop, a car and its passengers slow down with an acceleration of 8.0 m/s2. What magnitude force does a 50-kg passenger exert on the seat belt in such a stop? Answer: 400 N Var: 1 20) A flatbed truck is carrying an 800-kg load of timber that is not tied down. The maximum friction force between the truck bed and the load is 2400 N. What is the greatest acceleration that the truck can have without losing its load? Answer: 3.0 m/s2 Var: 1 21) A box of mass 72 kg is at rest on a horizontal frictionless surface. A constant horizontal force of magnitude F then acts on the box, accelerating it to the right. You observe that it takes the box 3.4 seconds to travel 13 meters. What is the magnitude of the force F? Answer: 160 N Var: 50+ 22) A 590-kg rocket is at rest on the launch pad. What upward thrust force is needed to accelerate the rocket uniformly to an upward speed of 28 m/s in 3.3 s? Answer: 1.1 × 104 N Var: 1 23) A 958-N rocket is coming in for a vertical landing. It starts with a downward speed of 25 m/s and must reduce its speed to 0 m/s in 8.0 s for the final landing. (a) During this landing maneuver, what must be the thrust due to the rocket's engines? (b) What must be the direction of the engine thrust force? Answer: (a) 1300 N (b) upward Var: 1 24) Calculate the average force a bumper would have to exert to bring a 1200-kg car to rest in 15 cm when the car had an initial speed of 2.0 m/s (about 4.5 mph). A) 1.8 × 104 N B) 1.6 × 104 N C) 5.4 × 104 N D) 6.5 × 105 N E) 3.2 × 104 N Answer: B Var: 1

25) A 10-kg object is hanging by a very light wire in an elevator that is traveling upward. The tension in the rope is measured to be 75 N. What are the magnitude and direction of the acceleration of the elevator? Answer: 2.3m/s2, downward Var: 1 26) A 45.0-kg person steps on a scale in an elevator. The scale reads 460 N. What is the magnitude of the acceleration of the elevator? A) 4.91 m/s2 B) 9.81 m/s2 C) 46.9 m/s2 D) 0.206 m/s2 E) 0.422 m/s2 Answer: E Var: 1 27) The figure shows an acceleration-versus-force graph for a 125-g object. What should be the value of the first tick-mark on the vertical scale, as indicated by the arrow in the figure?

A) 4 B) 8 C) 0.00400 D) 0.00800 Answer: A Var: 12

28) The figure shows an object's acceleration-versus-force graph. What is the mass of this object?

A) 2.5 g B) 1.6 g C) 630 g D) 400,000 g Answer: A Var: 1 29) The figure shows an acceleration-versus-force graph for three objects pulled by wires. If the mass of object 2 is 36 kg, what are the masses of objects 1 and 3?

A) 12 kg and 90 kg B) 72 kg and 18 kg C) 90 kg and 12 kg D) 12 kg and 72 kg Answer: A Var: 1

College Physics: A Strategic Approach, 4e (Knight) Chapter 5 Applying Newton's Laws 5.1 Conceptual Questions 1) In the figure, a 10-lb weight is suspended from two spring scales, each of which has negligible weight. Which one of the following statements about the readings in the scales is true?

A) Each scale will read 5 lb. B) The top scale will read zero, the lower scale will read 10 lb. C) The lower scale will read zero, the top scale will read 10 lb. D) Each scale will show a reading between one and 10 lb, such that the sum of the two is 10 lb. However, exact readings cannot be determined without more information. E) None of these is true. Answer: E Var: 1

2) Two blocks, A and B, are being pulled to the right along a horizontal surface by a horizontal 100-N pull, as shown in the figure. Both of them are moving together at a constant velocity of 2.0 m/s to the right, and both weigh the same.

Which of the figures below shows a correct free-body diagram of the horizontal forces acting on the upper block, A? A) B) C) D) E) Answer: E Var: 1

3) Two blocks, A and B, are being pulled to the right along a horizontal surface by a horizontal 100-N pull, as shown in the figure. Both of them are moving together at a constant velocity of 2.0 m/s to the right, and both weigh the same.

Which of the figures below shows a correct free-body diagram of the horizontal forces acting on the lower block, B? A)

B) C) D) E) None of these diagrams is correct. Answer: B Var: 1 4) As shown in the figure, a woman is straining to lift a large crate, but without success because it is too heavy. We denote the forces on the crate as follows: P is the magnitude of the upward force being exerted on the crate by the person, C is the magnitude of the vertical contact force on the crate by the floor, and W is the weight of the crate. How are the magnitudes of these forces related while the person is trying unsuccessfully to lift the crate?

A) P + C = W B) P + C < W C) P + C > W D) P = C Answer: A Var: 1

5) A push of magnitude P acts on a box of weight W as shown in the figure. The push is directed at an angle θ below the horizontal, and the box remains a rest. The box rests on a horizontal surface that has some friction with the box. The normal force on the box due to the floor is equal to

A) W. B) W + P. C) W + P cos θ. D) W + P sin θ. E) W - P sin θ. Answer: D Var: 1 6) A push of magnitude P acts on a box of weight W as shown in the figure. The push is directed at an angle θ below the horizontal, and the box remains a rest. The box rests on a horizontal surface that has some friction with the box. The friction force on the box due to the floor is equal to

A) P sin θ B) P cos θ C) 0 D) P cos θ + W E) P + W Answer: B Var: 1

7) In the figure, what does the spring scale read? The pulleys are ideal and the strings and scale are also massless.

A) exactly 2.0 N. B) exactly 1.0 N C) 0.50 N D) 0.00 N E) more than 19.6 N Answer: B Var: 1 8) Two boxes P and Q on a perfectly smooth horizontal surface are connected by a light horizontal cord. The mass of P is greater than that of Q. A horizontal force is applied to box Q as shown in the figure, accelerating the bodies to the right. The magnitude of the force exerted by the connecting cord on body P is

A) zero. B) less than F but not zero. C) equal to F. D) greater than F. Answer: B Var: 1 9) Three boxes are pulled along a horizontal frictionless floor by a constant horizontal pull P. The boxes are connected by very light horizontal strings having tensions T1 and T2 as shown in the figure. Which of the following statements about the tensions is correct? (There could be more than one correct choice.)

A) T1 = P B) T2 = P C) T1 + T2 = P D) T2 > T1 E) T1 > T2 Answer: E Var: 1

10) Two boxes, A and B, are connected by a horizontal string S on a horizontal floor. A very light wire pulls horizontally on box B, as shown in the figure, with a force of 100 N. The reaction force to this pull is

A) the pull that box B exerts on string S. B) the pull that string S exerts on box B. C) the pull that string S exerts on box A. D) the pull of box B on the wire. E) the force that box A exerts on box B. Answer: D Var: 1 11) Two boxes are connected to each other by a string as shown in the figure. The 10-N box slides without friction on the horizontal table surface. The pulley is ideal and the string has negligible mass. What is true about the tension T in the string?

A) T = 10 N B) T = 20 N C) T = 30 N D) T < 30 N E) T > 30 N Answer: D Var: 1

12) Two objects of unequal masses, M and m (M > m), are connected by a very light cord passing over an ideal pulley of negligible mass. When released, the system accelerates, and friction is negligible.

Which one of the following free-body diagrams most realistically represents the forces acting on the two objects in the moving system? A)

Answer: C Var: 1 13) A 200-N sled of slides down a frictionless hillside that rises at 37° above the horizontal. What is the magnitude of the force that the surface of the hill exerts on the sled? A) 200 N B) 120 N C) 160 N D) 150 N E) 0 N Answer: C Var: 1 14) A 200-N sled of slides down a frictionless hillside that rises at 37° above the horizontal. What is the magnitude of the force that the hill exerts on the sled parallel to the surface of the hill? A) 200 N B) 120 N C) 160 N D) 150 N E) 0 N Answer: E Var: 1 8 Copyright © 2019 Pearson Education, Inc.

15) Two objects have masses m and 5m, respectively. They both are placed side by side on a frictionless inclined ramp and allowed to slide down from rest without any air resistance. Which one of the following statements about these objects is correct? A) It takes the lighter object 5 times longer to reach the bottom of the ramp than the heavier. B) It takes the lighter object 10 times longer to reach the bottom of the ramp than the heavier. C) It takes the heavier object 5 times longer to reach the bottom of the ramp than the lighter. D) It takes the heavier object 10 times longer to reach the bottom of the ramp than the lighter. E) The two objects reach the bottom of the ramp at exactly the same time. Answer: E Var: 1 16) A block of mass m sits at rest on a rough inclined ramp that makes an angle θ with the horizontal. What must be true about force of static friction f on the block? A) f > mg B) f > mg cos θ C) f > mg sin θ D) f = mg cos θ E) f = mg sin θ Answer: E Var: 1 17) A block of mass m sits at rest on a rough inclined ramp that makes an angle θ with the horizontal. What must be true about normal force F on the block due to the ramp? A) F > mg B) F > mg cos θ C) F > mg sin θ D) F = mg cos θ E) F = mg sin θ Answer: D Var: 1

5.2 Problems 1) A 50.0-kg crate is being pulled along a horizontal smooth surface. The pulling force is 10.0 N and is directed 20.0° above the horizontal. What is the magnitude of the acceleration of the crate? A) 0.0684 m/s2 B) 0.188 m/s2 C) 0.200 m/s2 D) 0.376 m/s2 E) 0.0728 m/s2 Answer: B Var: 1 2) A 40-kg box is being pushed along a horizontal smooth surface. The pushing force is 15 N directed at an angle of 15° below the horizontal. What is the magnitude of the acceleration of the crate? A) 0.16 m/s2 B) 0.36 m/s2 C) 0.47 m/s2 D) 0.39 m/s2 E) 0.68 m/s2 Answer: B Var: 1 3) A 1000-kg barge is being towed by means of two horizontal cables. One cable is pulling with a force of 80.0 N in a direction 30.0° west of north. In what direction should the second cable pull so that the barge will accelerate northward, if the force exerted by the cable is 120 N? Assume that the water exerts no appreciable frictional drag on the barge. A) 19.5° east of north B) 21.1° east of north C) 39.0° east of north D) 47.5° east of north E) 54.7° east of north Answer: A Var: 1 4) Two forces act on a object. One force has magnitude 65 N directed 59° clockwise from the positive x-axis, and the other has a magnitude 35 N at 32° clockwise from the positive y-axis. What is the magnitude of this object's acceleration? A) 1.1 m/s2 B) 1.3 m/s2 C) 1.5 m/s2 D) 1.7 m/s2 Answer: A Var: 46 10 Copyright © 2019 Pearson Education, Inc.

5) A tightrope walker walks across a 30-m long wire tied between two poles. The center of the wire is displaced vertically downward by 1.0 m when he is halfway across. If the tension in both halves of the wire at this point is what is the mass of the tightrope walker? Neglect the mass of the wire. A) 85 kg B) 43 kg C) 74 kg D) 91 kg Answer: A Var: 50+ 6) A 30.0-kg load is being held in place using massless wires in the ideal pulley arrangement shown in the figure. What is the magnitude of the force F?

Answer: 147 N Var: 1 7) An object is being acted upon by three forces and as a result moves with a constant velocity. One force is 60.0 N along the +x-axis, and the second is 75.0 N along the +y-axis. What is the magnitude of the third force? A) 135 N B) 15.0 N C) 48.0 N D) 67.5 N E) 96.0 N Answer: E Var: 1 8) An object is being acted upon by three forces and moves with a constant velocity. One force is 60 N along the +x-axis, the second is 75 N along a direction making a counterclockwise angle of 150° with the +x-axis. (a) What is the magnitude of the third force? (b) What is the direction of the third force, measured clockwise from the +x-axis? Answer: (a) 38 N (b) 260° Var: 1

9) A piano mover raises a 1000-N piano at a constant speed using a very light rope in a frictionless pulley system, as shown in the figure. With what force is the mover pulling down on the rope?

A) 2000 N B) 1000 N C) 500 N D) 250 N E) Depends on the speed of the piano. Answer: C Var: 1 10) A 6.00-kg ornament is held at rest by two light wires that form 30° angles with the vertical, as shown in the figure. An external force of magnitude F acts vertically downward on the ornament. The tension exerted by each of the two wires is denoted by T. A free-body diagram, showing the four forces that act on the box, is shown in the figure. If the magnitude of force F is 410 N, what is the magnitude of the tension T?

A) 271 N B) 235 N C) 188 N D) 376 N E) 470 N Answer: A Var: 50+

11) The figure shows a block of mass M hanging at rest. The light wire fastened to the wall is horizontal and has a tension of 38 N. The wire fastened to the ceiling is also very light, has a tension of and makes an angle θ with the ceiling. Find the angle θ.

A) 50° B) 40° C) 33° D) 65° E) 45° Answer: A Var: 50+ 12) A very light wire is used to hang a series of 8.0-kg bricks. This wire will break if the tension in it exceeds 450 N. The bricks are hung one below the other from a hook in the ceiling using this wire, as shown in the figure. (a) How many whole bricks can be hung without breaking the wire? (b) If you add one more brick to the number found in part (a), which string will break?

Answer: (a) 5 Var: 1

(b) the top wire

13) A 400-kg box is lifted vertically upward with constant velocity by means of two cables pulling at 40.0° on either side of the vertical direction. What is the tension in each cable? A) 231 N B) 400 N C) 800 N D) 2560 N E) 3920 N Answer: D Var: 1 14) A 10.0-kg picture is held in place by two wires, the first one hanging at 50.0° to the left of the vertical and the second one at 45.0° to the right of the vertical. What is the tension in the first wire? A) 69.6 N B) 50.8 N C) 98.1 N D) 69.4 N E) 23.8 N Answer: A Var: 5 15) Three objects are connected by weightless flexible strings as shown in the figure. The pulley has no appreciable mass or friction, and the string connected to the block on the horizontal bench pulls on it parallel to the bench surface. The coefficients of friction between the bench and the block on it are µ s = 0.66 and µ k = 0.325. You observe that this system remains at rest. (a) Find the mass of the hanging object A. (b) What is the magnitude of the friction force on the block on the bench?

Answer: (a) 22 kg Var: 1

(b) 270 N

16) A load is being lifted vertically upwards by means of two cables attached to it. The first cable exerts a force of 600 N at an angle of 35.0° to the left of the vertical. The second cable exerts a force of 1300 N. At what angle to the right of the vertical is the second cable pulling? A) 15.4° B) 16.2° C) 30.8° D) 67.8° E) 75.8° Answer: A Var: 1 14 Copyright © 2019 Pearson Education, Inc.

17) A 10-kg sign is held by two ropes as shown in the figure. What is the tension on rope A?

A) 44 N B) 69 N C) 72 N D) 88 N E) 98 N Answer: D Var: 1 18) A 3.0-kg and a 5.0-kg box rest side-by-side on a perfectly smooth, level floor. A horizontal force of 32 N is applied to the 3.0-kg box pushing it against the 5.0-kg box, and, as a result, both boxes slide along the floor. How hard do the two boxes push against each other? A) 12 N B) 20 N C) 24 N D) 32 N E) 0 N Answer: B Var: 1 19) A 3.0-kg and a 5.0-kg box rest side-by-side on a smooth, level floor. A horizontal force of 32 N is applied to the 5.0-kg box pushing it against the 3.0-kg box, and, as a result, both boxes slide along the floor. How hard do the two boxes push against each other? A) 12 N B) 20 N C) 24 N D) 32 N E) 0 N Answer: A Var: 1

20) Three boxes rest side-by-side on a smooth, horizontal floor. Their masses are 5.0 kg, 3.0 kg, and 2.0 kg, with the 3.0-kg mass in the center. A force of 50 N pushes on the 5.0-kg box, which pushes against the other two boxes. What magnitude force does the 5.0-kg box exert on the 3.0kg box? A) 0 N B) 10 N C) 25 N D) 40 N E) 50 N Answer: C Var: 1 21) As shown in the figure, two blocks are connected by a very light string, and the upper block is pulled upward by a different string. The masses of the upper and lower blocks are 300 g and 240 g, respectively. The string between the blocks will break if its tension exceeds 3.6 N, and the string that pulls the combination upward will break if its tension exceeds 7.8 N. (a) What is the largest upward acceleration that the blocks can be given without either string breaking? (b) If the upward acceleration is slightly higher than this, which string breaks, the upper one or the lower one?

Answer: (a) 4.6 m/s2 Var: 1

(b) upper string

22) A locomotive is pulling 9 freight cars, each of which is loaded with the same weight. The mass of each loaded car is and we can neglect friction on these 9 cars. If the train is accelerating forward at on a level track, what is the tension in the coupling between the second and third cars? (The car nearest the locomotive is counted as the first car.) Answer: 210,000 N Var: 50+

23) A 5.0-kg block and a 4.0-kg block are connected by a 0.6 kg rod, as shown in the figure. The links between the blocks and the rod are denoted by A and B. A vertical upward force of magnitude F is applied to the upper block. The blocks and rod assembly are moving downward at constant velocity of 85 cm/s. (a) What is the magnitude of the applied force F? (b) What magnitude force does link A exert?

Answer: (a) 94 N Var: 1

(b) 45 N

24) A 5.0-kg block and a 4.0-kg block are connected by a 0.6 kg rod, as shown in the figure. The links between the blocks and the rod are denoted by A and B. A vertical upward force of magnitude F of magnitude 150 N is applied to the upper block. What magnitude force does each of the links A and B exert?

Answer: 72 N (link A), 63 N (link B) Var: 1 25) A 3.0-kg mass and a 5.0-kg mass hang vertically at the opposite ends of a very light rope that goes over an ideal pulley. If the masses are gently released, what is the resulting acceleration of the masses? A) 0.00 m/s2 B) 3.7 m/s2 C) 2.5 m/s2 D) 4.9 m/s2 E) 6.1 m/s2 Answer: C Var: 1

26) A 3.0-kg mass and a 5.0-kg mass hang vertically at the opposite ends of a rope that goes over an ideal pulley. If the masses are gently released from rest, how long does it take for the 3.0-kg mass to rise by 1.0 m? A) 0.41 s B) 0.74 s C) 0.82 s D) 1.8 s E) 0.90 s Answer: E Var: 1 27) As shown in the figure, a 10-kg block on a perfectly smooth horizontal table is connected by a horizontal string to a 63-kg block that is hanging over the edge of the table. What is the magnitude of the acceleration of the 10-kg block when the other block is gently released?

A) 8.5 m/s2 B) 8.1 m/s2 C) 7.5 m/s2 D) 9.0 m/s2 Answer: A Var: 1 28) Three blocks, light connecting ropes, and a light frictionless pulley comprise a system, as shown in the figure. An external force of magnitude P is applied downward on block A, causing block A to accelerate downward at a constant 2.5 m/s2. The tension in the rope connecting block B and block C is equal to 60 N. (a) What is the magnitude of the force P? (b) What is the mass of block C?

Answer: (a) 190 N Var: 1

(b) 4.9 kg

29) The figure shows a 100-kg block being released from rest from a height of 1.0 m. It then takes 0.53 s for it to reach the floor. What is the mass m of the block on the left? There is no friction or mass in the pulley, and the connecting rope is very light.

A) 16 kg B) 14 kg C) 13 kg D) 11 kg Answer: A Var: 50 30) A locomotive is pulling three train cars along a level track with a force of 100,000 N. The car next to the locomotive has a mass of 80,000 kg, the next one, 50,000 kg, and the last one, 70,000 kg. You can neglect the friction on the cars being pulled. (a) What is the magnitude of the force between that the 80,000-kg car exerts on the 50,000-kg car? (b) What is the magnitude of the force that the 50,000-kg car exerts on the 70,000-kg car? Answer: (a) 60,000 N (b) 35,000 N Var: 1 31) In the figure, block A has a mass of 3.00 kg. It rests on a smooth horizontal table and is connected by a very light horizontal string over an ideal pulley to block B, which has a mass of 2.00 kg. When block B is gently released from rest, how long does it take block B to travel 80.0 cm?

A) 0.404 s B) 0.494 s C) 0.639 s D) 0.785 s E) 0.935 s Answer: C Var: 5

32) A 55-kg box rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.30, and the coefficient of kinetic friction is 0.20. What horizontal force must be applied to the box to cause it to start sliding along the surface? Answer: 160 N Var: 1 33) The coefficients of static and kinetic friction between a 3.0-kg box and a horizontal desktop are 0.40 and 0.30, respectively. What is the force of friction on the box when a 15-N horizontal push is applied to the box? A) 12 N B) 8.8 N C) 15 N D) 6.0 N E) 4.5 N Answer: B Var: 1 34) An object slides on a level floor. It slows and comes to a stop with a constant acceleration of magnitude 2.4 m/s2. What is the coefficient of kinetic friction between the object and the floor? A) 0.24 B) 0.48 C) 0.12 D) It is impossible to determine without knowing the mass of the object. Answer: A Var: 1 35) A bulldozer attempts to drag a log weighing 500 N along the rough horizontal ground. The cable attached to the log makes an angle of 30° above the ground. The coefficient of static friction between the log and the ground is 0.50, and the coefficient of kinetic friction is 0.35. What minimum tension is required in the cable in order for the log to begin to slide? Answer: 220 N Var: 1 36) A policeman investigating an accident measures the skid marks left by a car on the horizontal road. He determines that the distance between the point that the driver slammed on the brakes (thereby locking the wheels) and the point where the car came to a stop was 28.0 m. From a reference manual he determines that the coefficient of kinetic friction between the tires and the road under the prevailing conditions was 0.300. How fast was the car going when the driver applied the brakes? A) 10.7 m/s B) 12.8 m/s C) 21.4 m/s D) 32.9 m/s E) 45.7 m/s Answer: B Var: 5 20 Copyright © 2019 Pearson Education, Inc.

37) A 50-kg box is being pushed along a horizontal surface. The coefficient of static friction between the box and the ground is 0.65, and the coefficient of kinetic friction is 0.35. What horizontal force must be exerted on the box for it to accelerate at 1.2 m/s2? A) 60 N B) 120 N C) 170 N D) 230 N E) 490 N Answer: D Var: 1 38) A 50-kg box is resting on a horizontal floor. A force of 250 N directed at an angle of 30.0° below the horizontal is applied to the box. The coefficient of static friction between the box and the surface is 0.40, and the coefficient of kinetic friction is 0.30. What is the force of friction on the box? A) 32 N B) 200 N C) 220 N D) 250 N E) 620 N Answer: C Var: 1 39) A baseball player is running to second base at 5.03 m/s. When he is 4.80 m from the plate he goes into a slide. The coefficient of kinetic friction between the player and the ground is 0.180, and the coefficient of static friction is 3.14. What is his speed when he reaches the plate? A) 4.47 m/s B) 2.89 m/s C) 1.96 m/s D) 2.56 m/s E) He stops before reaching the plate. Answer: B Var: 1 40) A 55-kg box rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.30. A horizontal 140-N force is applied to the box. What is the friction force on the box? A) 140 N B) 160 N C) 16.5 N D) 0.00 N E) 42 N Answer: A Var: 1

41) A horizontal 52-N force is needed to slide a box across a flat surface at a constant velocity of 3.5 m/s. What is the coefficient of kinetic friction between the box and the floor? A) 0.11 B) 0.09 C) 0.10 D) 0.13 Answer: A Var: 50+ 42) In a shuffleboard game, the puck slides a total of 12 m on a horizontal surface before coming to rest. If the coefficient of kinetic friction between the puck and board is 0.10, what was the initial speed of the puck? A) 4.8 m/s B) 48.5 m/s C) 3.8 m/s D) 4.3 m/s Answer: A Var: 31 43) During a hockey game, a puck is given an initial speed of 10 m/s. It slides 50 m on the horizontal ice before it stops due to friction. What is the coefficient of kinetic friction between the puck and the ice? A) 0.090 B) 0.10 C) 0.11 D) 0.12 Answer: B Var: 1 44) A driver in a car traveling at slams on the brakes and skids to a stop. If the coefficient of friction between the tires and the level road is 0.80, how long will the skid marks be? A) 37 m B) 30 m C) 46 m D) 34 m Answer: A Var: 27

45) A flatbed truck is carrying a 20.0-kg crate along a level road. The coefficient of static friction between the crate and the bed is 0.400, and the coefficient of kinetic friction is 0.300. What is the maximum acceleration that the truck can have if the crate is to stay in place relative to the truck? A) 3.92 m/s2 B) 7.84 m/s2 C) 8.00 m/s2 D) 78.5 m/s2 E) 196 m/s2 Answer: A Var: 1 46) You push downward on a trunk at an angle 25° below the horizontal with a force of the trunk is on a flat surface and the coefficient of static friction between the surface and the trunk is 0.61, what is the most massive trunk you will be able to move? A) 81 kg B) 93 kg C) 73 kg D) 112 kg Answer: A Var: 31

47) Jason takes off across level water on his jet-powered skis. The combined mass of Jason and his skis is 75 kg (the mass of the fuel is negligible). The skis produce a forward thrust of 200 N and have a coefficient of kinetic friction with water of 0.10. Unfortunately, the skis run out of fuel after only 90 s. What is Jason's top speed? A) 150 m/s B) 240 m/s C) 24 m/s D) 90 m/s Answer: A Var: 50+ 48) Jason takes off across level water on his jet-powered skis. The combined mass of Jason and his skis is 75 kg (the mass of the fuel is negligible). The skis produce a forward thrust of 200 N and have a coefficient of kinetic friction with water of 0.10. Unfortunately, the skis run out of fuel after only 41 s. How far from his starting point has Jason traveled when he finally coasts to a stop? A) 3900 m B) 2900 m C) 2000 m D) 1400 m Answer: A Var: 50+

49) You push horizontally on a 120-N box that is initially resting on a horizontal table. The coefficient of static friction between the box and the table is 0.75, and the coefficient of kinetic friction is 0.40. Find the friction force on the box if the push is equal to (a) 84 N; (b) 94 N. Answer: (a) 84 N (b) 48 N Var: 1 50) The figure shows a system consisting of three blocks, a light frictionless pulley, and light connecting ropes that act horizontally on the upper two blocks. The 9.0-kg block is on a perfectly smooth horizontal table. The surfaces of the 12-kg block are rough, with µ k = 0.30 between the 12-kg and 9.0-kg blocks. The mass M of the hanging block is set so that it descends at a constant velocity of 3.25 m/s. (a) What is the mass M of the hanging block? (b) The mass M is now changed to 5.0 kg, causing it to accelerate downward after it is released. What is the acceleration of the hanging mass?

Answer: (a) 3.6 kg Var: 1

(b) 0.98 m/s2

51) As shown in the figure, block B on a horizontal tabletop is attached by very light horizontal strings to two hanging blocks, A and C. The pulleys are ideal, and the coefficient of kinetic friction between block B and the tabletop is 0.100. The masses of the three blocks are mA = 12.0 kg, mB = 7.00 kg, and mC = 10.0 kg. Find the magnitude and direction of the acceleration of block B after the system is gently released and has begun to move.

Answer: 0.44 m/s2, to the left Var: 1 52) A flatbed truck is carrying a 20-kg crate up a sloping road. The coefficient of static friction between the crate and the bed is 0.40, and the coefficient of kinetic friction is 0.30. What is the maximum angle of slope that the truck can climb at constant speed if the crate is to stay in place? A) 0.38° B) 13° C) 17° D) 22° E) 68° Answer: D Var: 1 24 Copyright © 2019 Pearson Education, Inc.

53) A 2.8-kg tool can move on a perfectly smooth ramp that slants at 42° above the horizontal. What are the magnitude and direction of the acceleration of this tool if it is sliding (a) up the ram, (b) down the ramp? Answer: (a) 6.6 m/s2 down the ramp (b) 6.6 m/s2 down the ramp Var: 1 54) A slanted roof rises at 35° above the horizontal, and the straight-line distance from the top of the roof to the bottom edge is 4.5 m. The roof is covered with ice, so it offers no friction to objects sliding on it. A piece of ice at the top suddenly breaks loose and begins to slide down from rest. (a) How long will it take for the ice to reach the bottom edge of the roof? (b) How fast will the ice be traveling just as it reaches the bottom edge? Answer: (a) 1.3 s (b) 7.1 m/s Var: 1 55) A 15-kg block is on a frictionless ramp that is inclined at 20° above the horizontal. It is connected by a very light string over an ideal pulley at the top edge of the ramp to a hanging 19kg block, as shown in the figure. The string pulls on the 15-kg block parallel to the surface of the ramp. Find the magnitude of the acceleration of the 19-kg block after the system is gently released?

A) 4.0 m/s2 B) 3.8 m/s2 C) 4.2 m/s2 D) 4.5 m/s2 Answer: A Var: 1 56) A system consisting of blocks, a light frictionless pulley, a frictionless incline, and very light connecting wires is shown in the figure. The wires pull on the left-hand blocks parallel to the surface of the ramp. The 9.0-kg block accelerates downward when the system is released gently from rest. (a) What is the magnitude of the acceleration of the 9.0-kg block? (b) What is the tension in the wire connecting the two blocks on the incline?

Answer: (a) 2.1 m/s2 Var: 1

(b) 42 N

57) A 150-N crate is being pulled up a perfectly smooth ramp that slopes upward at 15° by a pull that is directed at 30° above the surface of the ramp. What is the magnitude of the pull required to make the crate move up the ramp at a constant velocity of 1.75 m/s? Answer: 45 N Var: 1 58) A 7.5-kg stone moves up frictionless hill that slopes upward at 41° above the horizontal. If the stone has an initial velocity of 8.5 m/s at the bottom, how far (as measured along the surface of the hill) will it go before stopping? Answer: 5.6 m Var: 1 59) A 5.0-kg box slides on the surface on a ramp that rises at 37° above the horizontal. The coefficient of kinetic friction between the box and the surface of the ramp is 0.60. What are the magnitude and direction of the acceleration of the box if it is sliding (a) up the ramp, (b) down the ramp? Answer: (a) 11 m/s2 down the ramp (b) 1.2 m/s2 down the ramp Var: 1 60) A 6.0-kg box slides down an inclined plane that makes an angle of 39° with the horizontal. If the coefficient of kinetic friction is 0.40, at what rate does the box accelerate down the slope? A) 3.1 m/s2 B) 3.4 m/s2 C) 3.7 m/s2 D) 4.1 m/s2 Answer: A Var: 50+ 61) A 200-g hockey puck is launched at an initial speed of 16 m/s up a metal ramp that is inclined at a 30° angle. The coefficients of static and kinetic friction between the hockey puck and the metal ramp are µ s = 0.40 and µ k = 0.30, respectively. What vertical height does the puck reach above its starting point? A) 8.6 cm B) 17 cm C) 13 cm D) 4.2 cm Answer: A Var: 50+

62) The figure shows a block of mass m resting on a 20° slope. The block has coefficients of friction and with the surface of the slope. It is connected using a very light string over an ideal pulley to a hanging block of mass 2.0 kg. The string above the slope pulls parallel to the surface. What is the minimum mass m so the system will remain at rest when it is released from rest?

A) 2.1 kg B) 3.3 kg C) 1.3 kg D) 3.6 kg Answer: A Var: 50+ 63) A 200-g hockey puck is launched up a ramp that is inclined at a 30° angle above the horizontal. The coefficients of static and kinetic friction between the puck and the ramp are µ s = 0.40 and µ k = 0.30, respectively, and the puck's initial velocity at the base is 3.8 m/s parallel to the sloping surface of the ramp. What speed does the puck have when it slides back down to its starting point? Answer: 2.1 m/s Var: 1 64) Two packages are connected by a very light string that goes over an ideal pulley as shown in the figure. Package A has a mass of 3.0 kg and can slide along a rough plane inclined at 30° above the horizontal. The string acts on package A parallel to the surface of the plane. The coefficient of static friction between package A and the plane is 0.40. What minimum mass should package B have in order to start package A sliding up the ramp?

Answer: 2.5 kg Var: 1

65) A 50.0-kg block is being pulled up a 16.0° slope by a force of 250 N that is parallel to the slope. The coefficient of kinetic friction between the block and the slope is 0.200. What is the acceleration of the block? A) 0.528 m/ B) 0.158 m/ C) 0.412 m/ D) 0.983 m/ E) 0.260 m/ Answer: C Var: 5

College Physics: A Strategic Approach, 4e (Knight) Chapter 6 Gravity 6.1 Conceptual Questions 1) You are making a circular turn in your car on a horizontal road when you hit a big patch of ice, causing the force of friction between the tires and the road to become zero. While the car is on the ice, it A) moves along a straight-line path away from the center of the circle. B) moves along a straight-line path toward the center of the circle. C) moves along a straight-line path in its original direction. D) continues to follow a circular path, but with a radius larger than the original radius. E) moves along a path that is neither straight nor circular. Answer: C Var: 1 2) When a car goes around a circular curve on a horizontal road at constant speed, what force causes it to follow the circular path? A) the normal force from the road B) the friction force from the road C) gravity D) No force causes the car to do this because the car is traveling at constant speed and therefore has no acceleration. Answer: B Var: 1 3) A car goes around a circular curve on a horizontal road at constant speed. What is the direction of the friction force on the car due to the road? A) tangent to the curve in the forward direction B) tangent to the curve opposite to the direction of the car's motion C) perpendicular to the curve outward D) perpendicular to the curve inward E) There is no friction on the car because its speed is constant. Answer: D Var: 1 4) When an object moves in uniform circular motion, the direction of its acceleration is A) in the same direction as its velocity vector. B) in the opposite direction of its velocity vector. C) is directed toward the center of its circular path. D) is directed away from the center of its circular path. E) depends on the speed of the object. Answer: C Var: 1

5) If you swing a bucket of water fast enough in a vertical circle, at the highest point the water does not spill out. This happens because an outward force balances the pull of gravity on the water. A) True B) False Answer: B Var: 1 6) When a car goes around a banked circular curve at the proper speed speed for the banking angle, what force cause it to follow the circular path? A) the normal force from the road B) the friction force from the road C) gravity D) No force causes the car to do this because the car is traveling at constant speed and therefore has no acceleration. Answer: A Var: 1 7) Two cars go around a banked curve at the proper speed for the banking angle. One car has tires with excellent traction, while the other car has bald slippery tires. Which of these cars is more likely to slide on the pavement as it goes around the curve? A) the car with the new tires B) the car with the bald tires C) Neither car will slide. D) It depends on if the pavement is wet or dry. Answer: C Var: 1 8) Two small balls, A and B, attract each other gravitationally with a force of magnitude F. If we now double both masses and the separation of the balls, what will now be the magnitude of the attractive force on each one? A) 16F B) 8F C) 4F D) F E) F/4 Answer: D Var: 1

9) Two small objects, with masses m and M, are originally a distance r apart, and the magnitude of the gravitational force on each one is F. The masses are changed to 2m and 2M, and the distance is changed to 4r. What is the magnitude of the new gravitational force? A) F/16 B) F/4 C) 16F D) 4F E) F/2 Answer: B Var: 1 10) Two small objects, with masses m and M, are originally a distance r apart, and the gravitational force on each one has magnitude F. The second object has its mass changed to 2M, and the distance is changed to r/4. What is the magnitude of the new gravitational force? A) F/32 B) F/16 C) 16F D) 32F E) 2F Answer: D Var: 1 11) A spaceship is traveling to the Moon. At what point is it beyond the pull of Earth's gravity? A) when it gets above the atmosphere B) when it is half-way there C) when it is closer to the Moon than it is to Earth D) It is never beyond the pull of Earth's gravity. Answer: D Var: 1 12) If you stood on a planet having a mass four times that of Earth's mass, and a radius two times that of Earth's radius, you would weigh A) the same as you do on Earth. B) two times more than you do on Earth. C) two times less than you do on Earth. D) four times more than you do on Earth. Answer: A Var: 1

13) An piece of space debris is released from rest at an altitude that is two earth radii from the center of the earth. Compared to its weight on Earth, the weight of this debris is A) zero. B) the same as on the surface of the earth. C) one-half of its weight on the surface of the earth. D) one-third of its weight on the surface of the earth. E) one-quarter of its weight on the surface of the earth. Answer: E Var: 1 14) A satellite encircles Mars at a distance above its surface equal to 3 times the radius of Mars. If gm is the acceleration due to gravity at the surface of Mars, what is the acceleration due to gravity at the location of the satellite? A) gm/9 B) 0 C) gm D) gm/3 E) gm/16 Answer: E Var: 1 15) A hypothetical planet has a mass of one-half that of the earth and a radius of twice that of the earth. What is the acceleration due to gravity on the planet in terms of g, the acceleration due to gravity at the surface of the earth? A) g B) g/2 C) g/4 D) g/8 E) g/16 Answer: D Var: 1 16) The acceleration due to gravity on Planet A is one-sixth what it is on Planet B, and the radius of the Planet A is one-fourth that of Planet B. The mass of Planet A is what fraction of the mass of Planet B? A) 1/6 B) 1/16 C) 1/24 D) 1/96 E) 1/12 Answer: D Var: 1

17) Two planets have the same surface gravity, but planet B has twice the radius of planet A. If planet A has mass m, what is the mass of planet B? A) m/ B) m C) m D) 4m E) m/4 Answer: D Var: 1 18) Two planets have the same surface gravity, but planet B has twice the mass of planet A. If planet A has radius r, what is the radius of planet B? A) r/ B) r C) r D) 4r E) 2r Answer: C Var: 1 19) Planet A has twice the mass of Planet B. From this information, what can we conclude about the acceleration due to gravity at the surface of Planet A compared to that at the surface of Planet B? A) The acceleration due to gravity on Planet A must be twice as great as the acceleration due to gravity on Planet B. B) The acceleration due to gravity on Planet A must be four times as great as the acceleration due to gravity on Planet B. C) The acceleration due to gravity on Planet A is the same as the acceleration due to gravity on Planet B. D) The acceleration due to gravity on Planet A is greater than the acceleration due to gravity on Planet B, but we cannot say how much greater. E) We cannot conclude anything about the acceleration due to gravity on Planet A without knowing the radii of the two planets. Answer: E Var: 1 20) The reason an astronaut in an earth satellite feels weightless is that A) the astronaut is beyond the range of the earth's gravity. B) the astronaut is falling. C) the astronaut is at a point in space where the effects of the moon's gravity and the earth's gravity cancel. D) this is a psychological effect associated with rapid motion. E) the astronaut's acceleration is zero. Answer: B Var: 1

21) If Earth had twice its present mass but it orbited at the same distance from the sun as it does now, its orbital period would be A) 4 years. B) 3 years. C) 2 years. D) 1 year. E) 6 months. Answer: D Var: 1 22) Satellite A has twice the mass of satellite B, and moves at the same orbital distance from Earth as satellite B. Compare the speeds of the two satellites. A) The speed of B is twice the speed of A. B) The speed of B is one-half the speed of A. C) The speed of B is one-fourth the speed of A. D) The speed of B is equal to the speed of A. E) The speed of B is four times the speed of A. Answer: D Var: 1 23) Suppose our sun had 4 times its present mass but the earth orbited it at the same distance as it presently does. What would be the length of the year on the earth under those conditions? A) 1/4 as long as the present year B) 1/2 as long as the present year C) the same as the present year D) twice as long as the present year E) four times as long as the present year Answer: B Var: 1

6.2 Problems 1) A particularly scary roller coaster contains a loop-the-loop in which the car and rider are completely upside down. If the radius of the loop is with what minimum speed must the car traverse the loop so that the rider does not fall out while upside down at the top? Assume the rider is not strapped to the car. A) 11.4 m/s B) 12.5 m/s C) 10.1 m/s D) 14.9 m/s Answer: A Var: 50+ 2) A 1000-kg car is moving at 30 m/s around a horizontal unbanked curve whose diameter is 0.20 km. What is the magnitude of the friction force required to keep the car from sliding? A) 9000 N B) 9800 N C) 300 N D) 900 N E) 3000 N Answer: A Var: 1 3) The curved section of a horizontal highway is a circular unbanked arc of radius 740 m. If the coefficient of static friction between this roadway and typical tires is 0.40, what would be the maximum safe driving speed for this horizontal curved section of highway? A) 54 m/s B) 52 m/s C) 50 m/s D) 48 m/s E) 46 m/s Answer: A Var: 50+ 4) A 250-kg motorcycle goes around an unbanked turn of radius 13.7 m at a steady 96.5 km/h. What is the magnitude of the net force on the motorcycle? A) 719 N B) 2.95 × 103 N C) 1.31 × 104 N D) 4.31 × 104 N Answer: C Var: 1

5) A 0.50-kg toy is attached to the end of a 1.0-m very light string. The toy is whirled in a horizontal circular path on a frictionless tabletop. If the maximum tension that the string can withstand without breaking is 350 N. What is the maximum speed the mass can have without breaking the string? A) 700 m/s B) 26 m/s C) 19 m/s D) 13 m/s Answer: B Var: 1 6) A jet plane flying 600 m/s experiences an acceleration of 4.0 g when pulling out of a circular dive. What is the radius of curvature of the circular part of the path in which the plane is flying? A) 640 m B) 1200 m C) 7100 m D) 9200 m Answer: D Var: 1 7) One way that future space stations may create artificial gravity is by rotating the station. Consider a cylindrical space station 380 m in diameter that is rotating about its longitudinal axis. Astronauts walk on the inside surface of the space station. How long will it take for each rotation of the cylinder if it is to provide "normal" gravity for the astronauts? A) 28 s B) 39 s C) 6.2 s D) 4.4 s Answer: A Var: 50+ 8) A Ferris wheel has radius 5.0 m and makes one revolution every 8.0 s with uniform rotation. A person who normally weighs 670 N is sitting on one of the benches attached at the rim of the wheel. What is the apparent weight (the normal force exerted on her by the bench) of the person as she passes through the highest point of her motion? Answer: 460 N Var: 1 9) A 2.0-kg ball is moving with a constant speed of 5.0 m/s in a horizontal circle whose diameter is 1.0 m. What is the magnitude of the net force on the ball? A) 0 N B) 20 N C) 40 N D) 50 N E) 100 N Answer: E Var: 1 8 Copyright © 2019 Pearson Education, Inc.

10) A 1000-kg car is slowly picking up speed as it goes around a horizontal unbanked curve whose radius is 100 m. The coefficient of static friction between the tires and the road is 0.35. At what speed will the car begin to skid sideways? A) 9.3 m/s B) 24 m/s C) 34 m/s D) 35 m/s E) 19 m/s Answer: E Var: 1 11) A car moving at a steady 10 m/s on a level highway encounters a bump that has a circular cross-section with a radius of 30 m. The car maintains its speed over the bump. What is the normal force exerted by the seat of the car on a 60.0-kg passenger when the car is at the top of the bump? A) 200 N B) 390 N C) 790 N D) 490 N E) 590 N Answer: B Var: 1 12) A car moving at a steady 10 m/s on a level highway encounters a depression that has a circular cross-section with a radius of 30 m. The car maintains its speed as it drives through the depression. What is the normal force exerted by the seat of the car on a 60.0-kg passenger when the car is at the bottom of the depression? A) 200 N B) 390 N C) 790 N D) 490 N E) 590 N Answer: C Var: 1 13) Pulling out of a dive, the pilot of an airplane guides his plane into a vertical circle with a radius of 600 m. At the bottom of the dive, the speed of the airplane is 150 m/s. What is the apparent weight of the 70-kg pilot at that point? A) 3300 N B) 690 N C) 2600 N D) 490 N E) 1400 N Answer: A Var: 1 9 Copyright © 2019 Pearson Education, Inc.

14) Pulling out of a dive, the pilot of an airplane guides his plane into a vertical circle. At the bottom of the dive, the speed of the airplane is 320 m/s. What is the smallest radius allowable for the vertical circle if the pilot's apparent weight is not to exceed 7.0 times his true weight? A) 1700 m B) 1500 m C) 2200 m D) 230 m E) 42 m Answer: A Var: 1 15) In order to simulate weightlessness for astronauts in training, they are flown in a vertical circle. If the passengers are to experience weightlessness, how fast should an airplane be moving at the top of a vertical circle with a radius of 2.5 km? A) 79 m/s B) 310 m/s C) 260 m/s D) 160 m/s E) 510 m/s Answer: D Var: 1 16) In a carnival ride, passengers stand with their backs against the wall of a cylinder. The cylinder is set into rotation and the floor is lowered away from the passengers, but they remain stuck against the wall of the cylinder. For a cylinder with a 2.0-m radius, what is the minimum speed that the passengers can have so they do not fall if the coefficient of static friction between the passengers and the wall is 0.25? A) 8.9 m/s B) 2.3 m/s C) 3.0 m/s D) 4.9 m/s E) It depends on the mass of the passengers. Answer: A Var: 1

17) A 20-g bead is attached to a light 120-cm-long string as shown in the figure. This bead moves in a horizontal circle with a constant speed of 1.5 m/s. What is the tension in the string if the angle α is measured to be 25°?

A) 0.089 N B) 0.041 N C) 0.20 N D) 0.22 N E) 0.46 N Answer: D Var: 1 18) A 20-g bead is attached to a light 120 cm-long string as shown in the figure. If the angle α is measured to be 18°, what is the speed of the mass?

A) 0.55 m/s B) 2.0 m/s C) 3.8 m/s D) 1.3 m/s E) 1.1 m/s Answer: E Var: 1 19) A small 175-g ball on the end of a light string is revolving uniformly on a frictionless surface in a horizontal circle of diameter 1.0 m. The ball makes 2.0 revolutions every 1.0 s. (a) What are the magnitude and direction of the acceleration of the ball? (b) Find the tension in the string. Answer: (a) 79.0 m/s2 toward the center of the circle (b) 13.8 N Var: 1

20) A car traveling at a steady 20 m/s rounds an 80-m radius horizontal unbanked curve with the tires on the verge of slipping. What is the maximum speed with which this car can round a second unbanked curve of radius 320 m if the coefficient of static friction between the car's tires and the road surface is the same in both cases? A) 160 m/s B) 80 m/s C) 70 m/s D) 40 m/s E) 30 m/s Answer: D Var: 1 21) A future use of space stations may be to provide hospitals for severely burned persons. It is very painful for a badly burned person on Earth to lie in bed. In a space station, the effect of gravity can be reduced or even eliminated. How long should each rotation take for a doughnutshaped hospital of 200-m radius so that persons on the outer perimeter would experience 1/10 the normal gravity of Earth? A) 91 min B) 8.7 min C) 4.6 min D) 1.5 min E) 0.011 min Answer: D Var: 1 22) A 600-kg car is going around a banked curve with a radius of 110 m at a steady speed of 24.5 m/s. What is the appropriate banking angle so that the car stays on its path without the assistance of friction? A) 29.1° B) 13.5° C) 33.8° D) 56.2° E) 60.9° Answer: A Var: 5 23) The curved section of a speedway is a circular arc having a radius of 190 m. This curve is properly banked for racecars moving at 34 m/s. At what angle with the horizontal is the curved part of the speedway banked? A) 32° B) 34° C) 30° D) 28° E) 26° Answer: A Var: 50+ 12 Copyright © 2019 Pearson Education, Inc.

24) A curved portion of highway has a radius of curvature of 65 m. As a highway engineer, you want to bank this curve at the proper angle for a steady speed of 22 m/s. (a) What banking angle should you specify for this curve? (b) At the proper banking angle, what normal force and what friction force does the highway exert on a 750-kg car going around the curve at the proper speed? Answer: (a) 37° (b) 9200 N (normal force), 0 N (friction) Var: 1 25) Two horizontal curves on a bobsled run are banked at the same angle, but one has twice the radius of the other. The safe speed (for which no friction is needed to stay on the run) for the smaller radius curve is v. What is the safe speed on the larger-radius curve? A) v / B) 2v C) v D) v/2 Answer: C Var: 1 26) What is the proper banking angle for an Olympic bobsled to negotiate a 100-m radius turn at 35 m/s without skidding? A) 31° B) 41° C) 51° D) 61° Answer: C Var: 1 27) A highway curve of radius 100 m, banked at an angle of 45°, may be negotiated without friction at a speed of A) 22 m/s. B) 31 m/s. C) 44 m/s. D) 67 m/s. Answer: B Var: 1 28) A highway curve of radius 80 m is banked at 45°. Suppose that an ice storm hits, and the curve is effectively frictionless. What is the speed with which to take the curve without tending to slide either up or down the surface of the road? A) 9.4 m/s B) 28 m/s C) 780 m/s D) The curve cannot be taken safely at any speed. Answer: B Var: 1

29) What is the gravitational force acting on a 59-kg person due to another 59-kg person standing 2.0 m away? We can model each person as a small sphere. (G = 6.67 × 10-11 N ∙ m2/kg2) A) 5.8 × 10-8 N B) 8.5 × 103 N C) 1.2 × 10-7 N D) 9.8 × 10-10 N E) 2.0 × 10-9 N Answer: A Var: 50+ 30) What is the magnitude of the gravitational force that two small 7.00-kg balls exert on each other when they are 35.0 cm apart? (G = 6.67 × 10-11 N ∙ m2/kg2) Answer: 2.67 × 10-8 N Var: 1 31) Two identical tiny balls of highly compressed matter are 1.50 m apart. When released in an orbiting space station, they accelerate toward each other at 2.00 cm/s2. What is the mass of each of them? (G = 6.67 × 10-11 N ∙ m2/kg2) Answer: 6.75 × 108 kg Var: 1 32) As a 70-kg person stands at the seashore gazing at the tides (which are caused by the Moon), how large is the gravitational force on that person due to the Moon? The mass of the Moon is 7.35 × 1022 kg, the distance to the Moon is 3.82 × 108 m, and G = 6.67 × 10-11 N ∙ m2/kg2. A) 0.24 N B) 0.024 N C) 0.0024 N D) 0.00024 N Answer: C Var: 1 33) A very dense 1500-kg point mass (A) and a dense 1200-kg point mass (B) are held in place 1.00 m apart on a frictionless table. A third point mass is placed between the other two at a point that is 20.0 cm from B along the line connecting A and B. When the third mass is suddenly released, find the magnitude and direction (toward A or toward B) of its initial acceleration. (G = 6.67 × 10-11 N ∙ m2/kg2) Answer: 1.8 × 10-6 m/s2, toward B Var: 1

34) When a spacecraft is launched from the earth toward the sun, at what distance from the earth will the gravitational forces due to the sun and the earth cancel? Earth's mass is 5.97 × 1024 kg, the sun's mass is 1.99 × 1030 kg, and the Earth-sun distance is 1.5 × 1011 m. A) 1.3 × 108 m B) 2.6 × 108 m C) 1.3 × 1010 m D) 2.6 × 1010 m Answer: B Var: 1 35) Moon A Moon B

Mass 4.0 × 1020 kg 1.5 × 1020 kg

Radius unknown 2.0 × 105 m

Orbital radius Orbital period 2.0 × 108 m 4.0 × 106 s unknown 3.0 × 108 m

Mithra is an unknown planet that has two moons, A and B, in circular orbits around it. The table summarizes the hypothetical data about these moons. What is the magnitude of the maximum gravitational force that Moon A exerts on Moon B? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 1.6 × 1013 N B) 4.4 × 1013 N C) 1.0 × 1014 N D) 2.0 × 1014 N E) 4.0 × 1014 N Answer: E Var: 1 36) At their closest approach, Venus and Earth are 4.20 × 1010 m apart. The mass of Venus is 4.87 × 1024 kg, the mass of Earth is 5.97 × 1024 kg, and G = 6.67 × 10-11 N ∙ m2/kg2. What is the magnitude of the gravitational force exerted by Venus on Earth at that point? A) 1.10 × 1018 N B) 4.62 × 1028 N C) 5.43 × 1026 N D) 6.30 × 1020 N E) 1.72 × 1019 N Answer: A Var: 1

37) A spaceship with a mass of 2.8 × 106 kg is traveling toward two spherical asteroids, each with a mass of 5.0 × 1016 kg, that are 40 km apart center-to-center. Its path is perpendicular to the line joining the asteroids and is aimed at the midpoint of that line. What is the net gravitational force exerted by the asteroids on the spaceship when the spaceship is 30 km away from that midpoint? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 12,000 N B) 8,000 N C) 16,000 N D) 6,200 N E) 18,000 N Answer: A Var: 1 38) Three identical 50-kg balls are held at the corners of an equilateral triangle, 30 cm on each side. If one of the balls is released, what is the magnitude of its initial acceleration if the only forces acting on it are the gravitational forces due to the other two masses? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 3.7 × 10-8 m/s2 B) 2.5 × 10-8 m/s2 C) 1.9 × 10-8 m/s2 D) 4.2 × 10-8 m/s2 E) 6.4 × 10-8 m/s2 Answer: E Var: 1 39) What is the distance from the center of the Moon to the point between Earth and the Moon where the gravitational pulls of Earth and Moon are equal? The mass of Earth is 5.97 × 1024 kg, the mass of the Moon is 7.35 × 1022 kg, the center-to-center distance between Earth and the Moon is 3.84 × 108 m, and G = 6.67 × 10-11 N ∙ m2/kg2. A) 3.45 × 108 m B) 3.84 × 107 m C) 4.69 × 106 m D) 3.83 × 106 m E) 4.69 × 107 m Answer: B Var: 1

40) From what height above the surface of the earth should an object be dropped to initially experience an acceleration of 0.54g? (G = 6.67 × 10-11 N ∙ m2/kg2, Mearth = 5.97 × 1024 kg, Rearth = 6.38 × 106 m) A) 2300 km B) 1700 km C) 5400 km D) 2900 km Answer: A Var: 1 41) At a given point above Earth's surface, the acceleration due to gravity is equal to What is the altitude of this point above Earth's surface? (G = 6.67 × 10-11 N ∙ m2/kg2, Mearth = 5.97 × 1024 kg, Rearth = 6.38 × 106 m) A) 770 km B) 970 km C) 1500 km D) 2000 km E) 2400 km Answer: A Var: 39 42) In another solar system, a planet has an airless moon Zygo that is 4.0 × 105 m in diameter. Experiments reveal that a freely falling object at the surface of Zygo accelerates at 0.20 m/s2. What is the mass of Zygo? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 2.4 × 1019 kg B) 4.8 × 1019 kg C) 1.2 × 1020 kg D) 2.4 × 1020 kg E) 4.8 × 1020 kg Answer: C Var: 1

43) Moon A Moon B

Mass 4.0 × 1020 kg 1.5 × 1020 kg

Radius unknown 2.0 × 105 m

Orbital radius Orbital period 2.0 × 108 m 4.0 × 106 s unknown 3.0 × 108 m

Mithra is an unknown planet that has two airless moons, A and B, in circular orbits around it. The table summarizes the hypothetical data about these moons. If you dropped a laser at the surface of Moon B, at what rate would it accelerate toward the ground? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 0.10 m/s2 B) 0.15 m/s2 C) 0.20 m/s2 D) 0.25 m/s2 E) 0.30 m/s2 Answer: D Var: 1 44) Planet Z-34 has a mass equal to one-third that of Earth and a radius equal to one-third that of Earth. With g representing, as usual, the acceleration due to gravity at the surface of Earth, the acceleration due to gravity at the surface of Z-34 is A) g/3. B) 3g. C) 6g. D) g/9. E) 9g. Answer: B Var: 1 45) What would be the weight of a 59.1-kg astronaut on a planet twice as massive as Earth and having twice Earth's radius? A) 580 N B) 290 N C) 1160 N D) 118 N E) 1200 N Answer: B Var: 1

46) What would be the weight of a 59.1-kg astronaut on a planet with the same density as Earth and having twice Earth's radius? A) 580 N B) 290 N C) 1160 N D) 2320 N E) 1200 N Answer: C Var: 1 47) The mass of the Moon is 7.4 × 1022 kg, its radius is 1.74 × 103 km, and it has no atmosphere. What is the acceleration due to gravity at the surface of the Moon? (G = 6.67 × 1011 N ∙ m2/kg2) A) 2.8 × 106 m/s2 B) 9.8 m/s2 C) 4.9 m/s2 D) 1.6 m/s2 E) 0.80 m/s2 Answer: D Var: 1 48) An astronaut goes out for a "space-walk" at a distance above the earth equal to the radius of the earth. What is her acceleration due to gravity at that point? A) zero B) g C) g/2 D) g/4 E) g/ Answer: D Var: 1 49) The radius of the earth is R. At what distance above the earth's surface will the acceleration of gravity be 4.9 m/s2? A) 0.41 R B) 0.50 R C) 1.00 R D) 1.41 R E) 0.25 R Answer: A Var: 1

50) The mass of Pluto is 1.31 × 1022 kg and its radius is 1.15 × 106 m. What is the acceleration of a freely-falling object at the surface of Pluto if it has no atmosphere? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 0.661 m/s2 B) 9.81 m/s2 C) 1.62 m/s2 D) 3.72 m/s2 E) 0.140 m/s2 Answer: A Var: 1 51) An astronaut drops a marble on the surface of the airless Planet Z-49 and observes that it takes 1.02 s for the marble to fall 2.00 m starting from rest. She also knows that the radius of Z49 is 3.39 × 106 m. From this information, what will she determine for the mass of Z-49? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 3.30 × kg. B) 6.62 × kg. C) 4.62 × kg. D) 8.09 × kg. E) 9.95 × kg. Answer: B Var: 5 52) At a distance of 14,000 km from the center of Planet Z-99, the acceleration due to gravity is 32 m/s2. What is the acceleration due to gravity at a point 28,000 km from the center of this planet? A) 8.0 m/s2 B) 16 m/s2 C) 128 m/s2 D) 4.0 m/s2 E) 2.0 m/s2 Answer: A Var: 1 53) An object weighs 432 N on the surface of the earth. The earth has radius R. If the object is raised to a height of 3R above the earth's surface, what is its weight? A) 108 N B) 48.0 N C) 27.0 N D) 305 N E) 144 N Answer: C Var: 1 20 Copyright © 2019 Pearson Education, Inc.

54) By how many newtons does the weight of a 100-kg person decrease when he goes from sea level to mountain top at an altitude of 5000 m? The mean radius of the earth is 6.38 × 106 m. A) 0.60 N B) 1.5 N C) 2.6 N D) 3.6 N E) 9.8 N Answer: B Var: 1 55) The earth has radius R. A satellite of mass 100 kg is in orbit at an altitude of 3R above the earth's surface. What is the satellite's weight at the altitude of its orbit? A) 61 N B) 110 N C) 9000 N D) 16,000 N Answer: A Var: 1 56) A spherically symmetric planet has four times the earth's mass and twice its radius. If a jar of peanut butter weighs 12 N on the surface of the Earth, how much would it weigh on the surface of this planet? A) 3.0 N B) 6.0 N C) 12 N D) 24 N E) 36 N Answer: C Var: 1 57) A 2.10-kg hammer is transported to the Moon. The radius of the Moon is 1.74 × 106 m, its mass is 7.35 × 1022 kg, and G = 6.67 × 10-11 N ∙ m2/kg2. How much does the hammer weigh on Earth and on the Moon? Answer: 20.6 N (on Earth), 3.40 N (on the Moon) Var: 1 58) A satellite orbits the Earth once every 6.0 hours in a circle. What are the magnitude and direction of the acceleration of the satellite? (G = 6.67 × 10-11 N ∙ m2/kg2, Mearth = 5.97 × 1024 kg) Answer: 1.4 m/s2 toward the center of the earth Var: 1

59) Suppose NASA wants a satellite to revolve around Earth 5 times a day. What should be the radius of its orbit if we neglect the presence of the Moon? (G = 6.67 × 10-11 N ∙ m2/kg2, Mearth = 5.97 × 1024 kg) A) 1.44 × 107 m B) 0.69 × 107 m C) 7.22 × 107 m D) 2.11 × 107 m Answer: A Var: 9 60) The captain of a spaceship orbiting planet X discovers that to remain in orbit at from the planet's center, she needs to maintain a speed of What is the mass of planet X? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 2.8 × 1019 kg B) 4.2 × 1017 kg C) 2.8 × 1016 kg D) 4.2 × 1014 kg Answer: A Var: 50+ 61) Find the orbital speed of an ice cube in the rings of Saturn. The mass of Saturn is 5.68 x 1026 kg, and use an orbital radius of 1.00 x 105 km. (G = 6.67 × 10-11 N ∙ m2/kg2) A) 19.5 km/s B) 27.5 km/s C) 13.8 km/s Answer: A Var: 1 62) You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be 1.8 × 107 m. You have previously determined that the planet orbits 2.9 × 1011 m from its star with a period of 402 earth days. Once on the surface you find that the acceleration due to gravity is 19.5 m/s2. What are the masses of (a) the planet and (b) the star? (G = 6.67 × 10-11 N ∙ m2/kg2) A) (a) 2.4 kg × kg, (b) 1.2 kg × kg B) (a) 4.3 kg × kg, (b) 1.2 kg × kg C) (a) 2.4 kg × kg, (b) 7.1 kg × kg D) (a) 4.3 kg × kg, (b) 7.1 kg × kg Answer: A Var: 50+

63) A satellite that is in a circular orbit 230 km above the surface of the planet Zeeman-474 has an orbital period of 89 min. The radius of Zeeman-474 is 6.38 × 106 m. What is the mass of this planet? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 5.0 × 1024 kg B) 5.5 × 1024 kg C) 6.0 × 1024 kg D) 6.5 × 1024 kg Answer: C Var: 1 64) Asteroid Ida was photographed by the Galileo spacecraft in 1993, and the photograph revealed that the asteroid has a small moon, which has been named Dactyl. From the dimensions of Ida and its general features, one can estimate the mass of Ida to be 4.5 × 1016 kg, and the distance between Dactyl and Ida is approximately 90 km. Assuming a circular orbit, what would be the orbital speed of Dactyl? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 5.8 m/s B) 11 m/s C) 2.3 m/s D) 2.9 m/s E) 30 m/s Answer: A Var: 1 65) In another solar system, a planet has a moon that is 4.0 × 105 m in diameter. Measurements reveal that this moon takes 3.0 x 105 s to make each orbit of diameter 1.8 × 108 m. What is the mass of the planet? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 1.2 × 1024 kg B) 1.7 × 1024 kg C) 2.4 × 1024 kg D) 3.4 × 1024 kg E) 4.8 × 1024 kg Answer: E Var: 1

66) Moon A Moon B

Mass 4.0 × 1020 kg 1.5 × 1020 kg

Radius unknown 2.0 × 105 m

Orbital radius Orbital period 2.0 × 108 m 4.0 × 106 s unknown 3.0 × 108 m

Mithra is an unknown planet that has two moons, A and B, in circular orbits around it. The table summarizes the hypothetical data about these moons. What is the mass of Mithra? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 1 × 1022 kg B) 3 × 1022 kg C) 1 × 1023 kg D) 3 × 1023 kg E) 1 × 1024 kg Answer: D Var: 1 67) The International Space Station is orbiting at an altitude of about 370 km above the earth's surface. The mass of the earth is 5.97 × 1024 kg, the radius of the earth is 6.38 × 106 m, and G = 6.67 × 10-11 N ∙ m2/kg2. Assume a circular orbit. (a) What is the period of the International Space Station's orbit? (b) What is the speed of the International Space Station in its orbit? Answer: (a) 5.5 ×103 s (b) 7.7 ×103 m/s Var: 1 68) A satellite of mass 500 kg orbits the earth with a period of 6,000 s. The earth has a mass of 5.97 × 1024 kg, a radius of 6.38 × 106 m, and G = 6.67 × 10-11 N ∙ m2/kg2. (a) Calculate the magnitude of the earth's gravitational force on the satellite. (b) Determine the altitude of the satellite above the earth's surface. Answer: (a) 3900 N (b) 7.5 × 105 m Var: 1 69) A satellite having orbital speed V orbits a planet of mass M. If the planet had half as much mass, the orbital speed of the satellite at the same distance from the center would be A) V . B) 2V. C) V. D) V/ . E) V/2. Answer: D Var: 1

70) A satellite of mass M takes time T to orbit a planet. If the satellite had twice as much mass, the time for it to orbit the planet at the same altitude would be A) 4T. B) 2T. C) T. D) T/2. E) T/4. Answer: C Var: 1 71) A large telescope of mass 8410 kg is in a circular orbit around the earth, making one revolution every 927 minutes. What is the magnitude of the gravitational force exerted on the satellite by the earth? (G = 6.67 × 10-11 N ∙ m2/kg2, Mearth = 6.0 × 1024 kg) Answer: 3.4 × 103 N Var: 50+ 72) Europa, a satellite of Jupiter, has an orbital diameter of 1.34 × 109 m and a period of 3.55 days. What is the mass of Jupiter? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 1.53 × 1027 kg B) 1.65 × 1027 kg C) 1.07 × 1027 kg D) 1.89 × 1027 kg E) 3.08 × 1027 kg Answer: D Var: 1 73) The innermost satellite of Jupiter orbits the planet with a radius of 422 × 103 km and a period of 1.77 days. What is the mass of Jupiter? (G = 6.67 × 10-11 N ∙ m2/kg2) A) 1.33 × 1027 kg B) 1.50 × 1027 kg C) 1.72 × 1027 kg D) 1.89 × 1027 kg E) 3.08 × 1027 kg Answer: D Var: 1

College Physics: A Strategic Approach, 4e (Knight) Chapter 7 Rotational Motion 7.1 Conceptual Questions 1) There must be equal amounts of mass on both sides of the center of mass (or center of gravity) of a system. A) True B) False Answer: B Var: 1 2) When a rigid object rotates about a fixed axis, what is true about all the points in the object? (There could be more than one correct choice.) A) They all have the same angular speed. B) They all have the same tangential speed. C) They all have the same angular acceleration. D) They all have the same tangential acceleration. E) They all have the same radial acceleration. Answer: A, C Var: 1 3) Two children, Ahmed and Jacques, ride on a merry-go-round. Ahmed is at a greater distance from the axis of rotation than Jacques. Which of the following are true statements? (There could be more than one correct choice.) A) Jacques has a greater angular speed than Ahmed. B) Jacques and Ahmed have the same angular speed. C) Jacques has a smaller angular speed than Ahmed. D) Ahmed has a greater tangential speed than Jacques. E) Jacques and Ahmed have the same tangential speed. Answer: B, D Var: 1 4) A car is traveling along a freeway at 65 mph. What is the linear speed, relative to the highway, of each of the following points on one of its tires? (a) the highest point on the tire (b) the lowest point on a tire (c) the center of the tire Answer: (a) 130 mph (b) 0 mps (c) 65 mph Var: 1

5) The figure shows scale drawings of four objects, each of the same mass and uniform thickness, with the mass distributed uniformly. Which one has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing at point P?

A) A B) B C) C D) D E) The moment of inertia is the same for all of these objects. Answer: B Var: 1 6) Two forces produce equal torques on a door about the door hinge. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force has a greater magnitude? A) the first force (at the midpoint) B) the second force (at the doorknob) C) The two forces are equal. Answer: A Var: 1 7) Two equal-magnitude forces are applied to a door at the doorknob. The first force is applied perpendicular to the door, and the second force is applied at 30° to the plane of the door. Which force exerts the greater torque about the door hinge? A) the first force (applied perpendicular to the door) B) the second force (applied at an angle) C) Both forces exert equal non-zero torques. D) Both forces exert zero torque. Answer: A Var: 1

8) As shown in the figure, a given force is applied to a rod in several different ways. In which case is the torque about the pivot P due to this force the greatest?

A) 1 B) 2 C) 3 D) 4 E) 5 Answer: A Var: 1 9) Five forces act on a rod that is free to pivot at point P, as shown in the figure. Which of these forces is producing a counter-clockwise torque about point P? (There could be more than one correct choice.)

A) force A B) force B C) force C D) force D E) force E Answer: C Var: 1 10) The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left), or a distance r/2 from the axis of rotation (right). If you release the hanging blocks simultaneously from rest,

7.2 Problems 1) In the figure, four point masses are placed as shown. Assume that all the numbers in the figure are accurate to two significant figures. What are the x and y coordinates of the center of mass (or center of gravity) of this arrangement?

A) (2.2 m, 2.6 m) B) (2.2 m, 2.7 m) C) (2.3 m, 2.6 m) D) (2.3 m, 2.7 m) E) (2.3 m, 2.8 m) Answer: E Var: 1 2) As shown in the figure, a 60-cm length of uniform wire, of mass 60 g, is bent into a right triangle. What are the x and y coordinates of the center of mass (or center of gravity) of this triangle?

A) (8.0 cm, 3.0 cm) B) (8.0 cm, 5.0 cm) C) (9.0 cm, 4.0 cm) D) (10 cm, 3.0 cm) E) (10 cm, 5.0 cm) Answer: D Var: 1 3) A 60.0-kg man stands at one end of a 20.0-kg uniform 10.0-m long board. How far from the man is the center of mass (or center of gravity) of the man-board system? A) 1.25 m B) 2.50 m C) 5.00 m D) 7.50 m E) 9.00 m Answer: A Var: 1 4 Copyright © 2019 Pearson Education, Inc.

4) A 2.0-m rope is lying on a table. You pick up one end and start raising it vertically. How high above the table is the center of mass (or center of gravity) of the rope when half of the rope has lifted off the table? A) 0.25 m B) 0.50 m C) 0.75 m D) 1.0 m E) 1.5 m Answer: A Var: 1 5) Three masses are located in the x-y plane as follows: a mass of 6 kg is at (0 m, 0 m), a mass of 4 kg is at (3 m, 0 m), and a mass of 2 kg is at (0 m, 3 m). Where is the center of mass (or center of gravity) of the system? A) (1 m, 2 m) B) (2 m, 1 m) C) (1 m, 1 m) D) (1 m, 0.5 m) E) (0.5 m, 1 m) Answer: D Var: 1 6) Three balls are moving along a straight line having the instantaneous positions shown in the figure. At that instant, find the location and velocity of the center of mass (or center of gravity) of this system.

Answer: 7.00 m to the right of the 2.00 kg ball, 1.11 m/s to the right Var: 1 7) A 30-kg child stands at one end of a floating 20-kg canoe that is 5.0-m long and initially at rest in the water. The child then slowly walks to the other end of the canoe. How far does the canoe move in the water, assuming water friction is negligible? A) 1.0 m B) 2.0 m C) 3.0 m D) 4.0 m E) 5.0 m Answer: C Var: 1

8) The center of mass (or center of gravity) of a two-particle system is at the origin. One particle is located at (3.0 m, 0.0 m) and has a mass of 2.0 kg. The other particle has a mass of 3.0 kg. What is the location of the 3.0-kg particle? A) (-3.0 m, 0.0 m) B) (-2.0 m, 0.0 m) C) (2.0 m, 0.0 m) D) (3.0 m, 0.0 m) Answer: B Var: 1 9) Three small masses are positioned at the following coordinates: 3.0 kg at (3.0 m, 2.0 m); 4.0 kg at (0.0 m, -1.0 m); and 5.0 kg at (5.0 m, -7.0 m). What are the coordinates of the center of mass (or center of gravity) of this system? Answer: (2.8 m, -2.8 m) Var: 1 10) Three small masses are positioned as follows: 2.0 kg at (0.0 m, 0.0 m), 2.0 kg at (2.0 m, 0.0 m), and 4.0 kg at (2.0 m, 1.0 m). Determine the coordinates of the center of mass (or center of gravity) of this system. A) (0.50 m, 1.5 m) B) (1.5 m, 0.50 m) C) (2.5 m, 1.5 m) D) (2.5 m, 0.50 m) Answer: B Var: 1 11) Three masses, 1.0 kg, 2.0 kg, and 3.0 kg, are located at (0.0 m, 0.0 m), (1.0 m, 1.0 m), and (2.0 m, -2.0 m), respectively. What is the location of the center of mass (or center of gravity) of this system? A) (1.3 m, 0.67 m) B) (1.3 m, -0.67 m) C) (-1.3 m, 0.67 m) D) (-1.3 m, -0.67 m) Answer: B Var: 1 12) A 3.0-kg mass is located at (0.0 m, 8.0 m), and a 1.0-kg mass is located at (12 m, 0.0 m). You want to add a 4.0-kg mass so that the center of mass (or center of gravity) of the three-mass system will be at the origin. What should be the coordinates of the 4.0-kg mass? A) (-3.0 m, -6.0 m) B) (-12 m, -8.0 m) C) (3.0 m, 6.0 m) D) (-6.0 m, -3.0 m) Answer: A Var: 1

13) A 1.0-g bead is at (-2.0 cm, 2.0 cm), a 2.0-g bead is at (2.0 cm, -4.0 cm), and a 3.0-g bead is at (2.0 cm, 0.0 cm). What are the coordinates of the center of mass (or center of gravity) of this system of beads? Answer: 1.3 cm, -1.0 cm Var: 1 14) Consider the sun and its largest planet Jupiter. On the line joining them, how far from the center of the sun is their center mass? Is it within or outside the sun? (Jupiter-sun distance is 778 × 106 km, diameter of the sun is 1.4 × 106 km, the sun is 1000 times as massive as Jupiter) Answer: 0.78 × 106 km from the center of the sun, just outside the solar surface Var: 1 15) The diameter of the Moon is 3.47 × 106 m, and it subtends an angle of 0.00904 rad when viewed from the surface of Earth. How far is the Moon from Earth? Answer: 3.84 × 108 m Var: 1 16) The sun subtends an angle of 0.00928 rad when viewed from the surface of the earth, and its distance from Earth is 1.5 × 1011 m. What is the diameter of the sun? Answer: 1.4 × 109 m Var: 1 17) What is the angular speed, in rad/s, of a flywheel turning at 813.0 rpm? A) 85.14 rad/s B) 13.53 rad/s C) 63.84 rad/s D) 95.33 rad/s Answer: A Var: 1 18) Through how many degrees does a 33 rpm turntable rotate in A) 63° B) 35° C) 46° D) 74° Answer: A Var: 26 19) Express the angular speed of an old 33 1/3 rpm LP in rad/s. Answer: 3.49 rad/s Var: 1 20) An artificial satellite in a low orbit circles the earth every 98 minutes. What is its angular speed in rad/s? Answer: 0.0011 rad/s Var: 1 7 Copyright © 2019 Pearson Education, Inc.

21) A chicken is running in a circular path with an angular speed of 1.52 rad/s. How long does it take the chicken to complete one revolution? A) 4.13 s B) 2.07 s C) 118 s D) 4.77 s E) 8.26 s Answer: A Var: 1 22) At a certain instant, a compact disc is rotating at 210 rpm. What is its angular speed in rad/s? A) 11 rad/s B) 22 rad/s C) 45 rad/s D) 69 rad/s E) 660 rad/s Answer: B Var: 1 23) When a fan is turned off, its angular speed decreases from 10 rad/s to 6.3 rad/s in 5.0 s. What is the magnitude of the average angular acceleration of the fan? A) 0.86 rad/s2 B) 0.74 rad/s2 C) 0.37 rad/s2 D) 11 rad/s2 E) 1.2 rad/s2 Answer: B Var: 1 24) A bicycle wheel has an outside diameter of 66 cm. Through what distance does a point on the rim move as the wheel rotates through an angle of 70°? Answer: 40 cm Var: 1 25) When Mary is 3.00 m from the center of a merry-go-round, her tangential speed is a constant 1.88 m/s. (a) What is her angular speed in rad/s? (b) What is the magnitude of her linear acceleration? Answer: (a) 0.627 rad/s (b) 1.18 m/s2 Var: 1 26) A cylinder of radius 8.0 cm rolls 20 cm in 5.0 s without slipping. Through how many degrees does the cylinder turn during this time? Answer: 140° Var: 1 8 Copyright © 2019 Pearson Education, Inc.

27) A wheel of diameter 0.70 m rolls on the floor without slipping. A point at the top of the wheel moves with a speed 2.0 m/s relative to the floor. (a) At what speed is the central axis of the wheel moving relative to the floor? (b) What is the angular speed of the wheel? Answer: (a) 1.0 m/s (b) 2.9 rad/s Var: 1 28) A child is riding a merry-go-round that is turning at 7.18 rpm. If the child is standing 4.65 m from the center of the merry-go-round, how fast is the child moving? A) 5.64 m/s B) 3.50 m/s C) 0.556 m/s D) 1.75 m/s E) 1.80 m/s Answer: B Var: 1 29) An electrical motor spins at a constant linear acceleration of the edge of the rotor? A) 5707 m/s2 B) 281.6 m/s2 C) 572,400 m/s2 D) 28.20 m/s2 Answer: A Var: 50+

If the rotor radius is

what is the

30) A string is wound tightly around a fixed pulley having a radius of 5.0 cm. As the string is pulled, the pulley rotates without any slipping of the string. What is the angular speed of the pulley when the string is moving at 5.0 m/s? A) 100 rad/s B) 50 rad/s C) 25 rad/s D) 20 rad/s E) 10 rad/s Answer: A Var: 1

31) A scooter has wheels with a diameter of 120 mm. What is the angular speed of the wheels when the scooter is moving forward at 6.00 m/s? A) 47.7 rpm B) 955 rpm C) 72.0 rpm D) 50.0 rpm E) 100 rpm Answer: B Var: 1 32) A bicycle has wheels that are 60 cm in diameter. What is the angular speed of these wheels when it is moving at 4.0 m/s? A) 1.2 rad/s B) 4.8 rad/s C) 0.36 rad/s D) 13 rad/s E) 7.6 rad/s Answer: D Var: 1 33) A bowling ball of mass 7.5 kg and diameter 18 cm rolls without slipping down a 10-m bowling lane with a constant speed 4.3 m/s. (a) Through what angle does the bowling ball turn as it travels the length of the lane? (b) What is the angular speed of the bowling ball? (c) Calculate the maximum radial acceleration that a point on the surface of the bowling ball could have. (d) Calculate the tangential acceleration of a point on the surface of the bowling ball. Answer: (a) 110 rad (b) 48 rad/s (c) 210 m/s2 (d) 0 m/s2 Var: 1 34) A rolling wheel of diameter of 68 cm slows down uniformly from 8.4 m/s to rest over a distance of 115 m. What is the magnitude of its angular acceleration if there was no slipping? A) 1.8 rad/s2 B) 0.90 rad/s2 C) 5.7 rad/s2 D) 11 rad/s2 Answer: B Var: 1

35) A child is riding a merry-go-round that has an instantaneous angular speed of 1.25 rad/s and an angular acceleration of 0.745 rad/s2. The child is standing 4.65 m from the center of the merry-go-round. What is the magnitude of the linear acceleration of the child? A) 8.05 m/s2 B) 7.27 m/s2 C) 2.58 m/s2 D) 3.46 m/s2 E) 4.10 m/s2 Answer: A Var: 1 36) When an old LP turntable was revolving at 33 rpm, it was shut off and uniformly slowed down and stopped in 5.5 seconds. (a) What was the magnitude of its angular acceleration (in rad/s2) as it slowed down? (b) Through how many revolutions did it turn while stopping? Answer: (a) 0.63 rad/s2 (b) 1.5 rev Var: 1 37) A wheel accelerates with a constant angular acceleration of 4.5 rad/s2 from an initial angular speed of 1.0 rad/s. (a) Through what angle does the wheel turn in the first 2.0 s, and (b) what is its angular speed at that time? Answer: (a) 11 rad (b) 10 rad/s Var: 1 38) A wheel starts from rest and has a uniform angular acceleration of 4.0 rad/s2. After the wheel completes its first revolution, how long does it take for it to make its second complete revolution? Answer: 0.73 s Var: 1 39) A bicycle wheel has an initial angular speed of 7.2 rad/s. After turning through of a revolution, the angular speed is reduced to 2.2 rad/s. If the angular acceleration of the wheel was constant during the motion, how long will it take the wheel to make the revolution? Answer: 0.67 s Var: 50+

40) How long does it take for a rotating object to speed up from 15.0 rad/s to 33.3 rad/s if it has a uniform angular acceleration of 3.45 rad/s2? A) 4.35 s B) 5.30 s C) 9.57 s D) 10.6 s E) 63.1 s Answer: B Var: 1 41) A wheel accelerates from rest to at a uniform rate of radians) did the wheel turn while accelerating? A) 30 rad B) 24 rad C) 60 rad D) 38 rad Answer: A Var: 50+

Through what angle (in

42) A machinist turns on the power to a grinding wheel at time t = 0 s. The wheel accelerates uniformly from rest for 10 s and reaches the operating angular speed of The wheel is run at that angular speed for 30 s and then power is shut off. The wheel slows down uniformly at until the wheel stops. In this situation, what is the angular acceleration of the wheel between and A) 3.8 rad/ B) 4.6 rad/ C) 5.3 rad/ D) 6.1 rad/ E) 6.8 rad/ Answer: A Var: 50+ 43) A machinist turns on the power on to a grinding wheel at time t = 0 s. The wheel accelerates uniformly from rest for 10 s and reaches the operating angular speed of The wheel is run at that angular velocity for 30 s, and then power is shut off. The wheel slows down uniformly at until the wheel stops. What is the total number of revolutions made by the wheel in this situation? A) 510 B) 280 C) 320 D) 470 E) 750 Answer: A Var: 50+

44) A machinist turns on the power on to a grinding wheel at time t = 0 s. The wheel accelerates uniformly from rest for 10 s and reaches the operating angular speed of The wheel is run at that angular velocity for 40 s and then power is shut off. The wheel slows down uniformly at until the wheel stops. For how long a time after the power is shut off does it take the wheel to stop? A) 64 s B) 62 s C) 66 s D) 68 s E) 70 s Answer: A Var: 50+ 45) In the figure, point P is on the rim of a wheel of radius 2.0 m. At time t = 0, the wheel is at rest, and P is on the x-axis. The wheel undergoes a uniform counterclockwise angular acceleration of 0.010 rad/s2 about the center O. (a) At time t = 0, what is the tangential acceleration of P? (b) What is the linear speed of P when it reaches the y-axis? (c) What is the magnitude of the net linear acceleration of P when it reaches the y-axis? (d) How long after starting does it take for P to return to its original position on the x-axis?

Answer: (a) 0.020 m/s2 Var: 1

(b) 0.35 m/s

(d) 35 s

46) An old LP record that is originally rotating at 33.3 rad/s is given a uniform angular acceleration of 2.15 rad/s2. Through what angle has the record turned when its angular speed reaches 72.0 rad/s? A) 83.2 rad B) 316 rad C) 697 rad D) 66.8 rad E) 948 rad Answer: E Var: 1

47) A wheel rotates through an angle of 13.8 rad as it slows down uniformly from 22.0 rad/s to 13.5 rad/s. What is the magnitude of the angular acceleration of the wheel? A) 0.616 rad/s2 B) 5.45 rad/s2 C) 111 rad/s2 D) 22.5 rad/s2 E) 10.9 rad/s2 Answer: E Var: 1 48) A pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41 rad/s2. Through what angle does the pulley turn in 5.26 s? A) 113 rad B) 22.6 rad C) 42.6 rad D) 19.3 rad E) 160 rad Answer: A Var: 1 49) An old 78 rpm record rotates through an angle of 320° as it slows down uniformly from 78.0 rpm to 22.8 rpm. What is the magnitude of the angular acceleration of the record? A) 2.34 rad/s2 B) 5.46 rad/s2 C) 6.50 rad/s2 D) 8.35 rad/s2 E) 10.9 rad/s2 Answer: B Var: 1 50) A turntable 45 cm in diameter starts from rest and makes its first complete revolution in 3.4 s with constant angular acceleration. If it maintains the same acceleration, how long will it take the turntable to make its second complete revolution? Answer: 1.4 s Var: 1 51) A Ferris wheel rotating at 20 rad/s slows down with a constant angular acceleration of magnitude 5.0 rad/s2. How many revolutions does it make while slowing down before coming to rest? A) 40 B) 20 C) 6.4 D) 3.2 Answer: C Var: 1 14 Copyright © 2019 Pearson Education, Inc.

52) A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it makes 50 complete turns at a constant angular acceleration before coming to rest. (a) What was the magnitude of the angular acceleration of the centrifuge as it slowed down? (d) How long did it take for the centrifuge to come to rest after being turned off? Answer: (a) 230 rad/s2 (b) 1.7 s Var: 1 53) A majorette fastens two batons together at their centers to form an X shape. Each baton consists of an extremely light 1.2-m bar with small 0.25-kg balls at each end. What is the moment of inertia of this baton about an axis through the center of the X? Answer: 0.36 kg ∙ m2 Var: 1 54) A triatomic molecule is oriented as follows along the x-axis: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia of this molecule about the y-axis? A) 2ma2 B) 3ma2 C) 12ma2 D) 14ma2 Answer: D Var: 1 55) Two uniform solid spheres have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia about a central axis to that of the smaller sphere is A) 4/5. B) 8/5. C) 1/2. D) 2. E) 4. Answer: E Var: 1

56) The L-shaped object shown in the figure consists of three small masses connected by extremely light rods. Assume that the masses shown are accurate to three significant figures. What is the moment of inertia of this object (a) about the x-axis, and (b) about the y-axis?

Answer: (a) 6.48 kg ∙ m2 Var: 1

(b) 32.7 kg ∙ m2

57) The L-shaped object shown in the figure consists of three small masses connected by thin uniform rods, each rod of mass 3.00 kg. Assume that the masses shown are accurate to three significant figures. What is the moment of inertia of this object (a) about the x-axis, and (b) about the y-axis?

Answer: (a) 19.4 kg ∙ m2 Var: 1

(b) 76.2 kg ∙ m2

58) In the figure, a weightlifter's barbell consists of two identical small but dense spherical weights, each of mass 50 kg. These weights are connected by a thin 0.96-m rod with a mass of 24 kg. Find the moment of inertia of the barbell through the axis perpendicular to the rod at its center, assuming the two weights are small enough to be treated as point masses.

Answer: 24.9 kg ∙ m2 Var: 1 59) A potter's wheel has the shape of a solid uniform disk of mass and radius 0.65 m. It spins about an axis perpendicular to the disk at its center. A small 2.1 kg lump of very dense clay is dropped onto the wheel at a distance 0.41 m from the axis. What is the moment of inertia of the system about the axis of spin? A) 1.8 kg ∙ m2 B) 1.5 kg ∙ m2 C) 0.40 kg ∙ m2 D) 2.5 kg ∙ m2 Answer: A Var: 31 16 Copyright © 2019 Pearson Education, Inc.

60) The lug nuts on a car wheel require tightening to a torque of 90 N ∙ m. If a 30-cm long wrench is used, what is the magnitude of the minimum force required using the wrench? A) 300 N B) 150 N C) 30 N D) 15 N Answer: A Var: 3 61) A man in a gym is holding an 8.0-kg weight at arm's length, a distance of 0.55 m from his shoulder joint. What is the torque about his shoulder joint due to the weight if his arm is horizontal? A) 0.24 N ∙ m B) 4.4 N ∙ m C) 43 N ∙ m D) 15 N ∙ m E) 0 N ∙ m Answer: C Var: 1 62) A man in a gym is holding an 8.0-kg weight at arm's length, a distance of 0.55 m from his shoulder joint. What is the torque about his shoulder joint due to the weight if his arm is held at 30° below the horizontal? A) 22 N ∙ m B) 2.2 N ∙ m C) 4.4 N ∙ m D) 13 N ∙ m E) 37 N ∙ m Answer: E Var: 1 63) A force of 17 N is applied to the end of a 0.63-m long torque wrench at an angle 45° from a line joining the pivot point to the handle. What is the magnitude of the torque about the pivot point produced by this force? A) 7.6 N ∙ m B) 10.7 N ∙ m C) 12.0 N ∙ m D) 9.7 N ∙ m Answer: A Var: 12

64) A 95-N force exerted at the end of a 0.32-m long torque wrench produces a torque of 15 N ∙ m. What is the angle (less than 90°) between the wrench handle and the direction of the applied force? A) 30° B) 24° C) 36° D) 42° Answer: A Var: 50+ 65) The figure shows a person's foot. In that figure, the Achilles tendon exerts a force of magnitude F = 720 N. What is the magnitude of the torque that this force produces about the ankle joint?

A) 12 N ∙ m B) 16 N ∙ m C) 21 N ∙ m D) 26 N ∙ m E) 36 N ∙ m Answer: B Var: 1 66) The drive chain in a bicycle is applying a torque of 0.850 N ∙ m to the wheel of the bicycle. The wheel has a moment of inertia of 0.100 kg ∙ m2. What is the angular acceleration of the wheel? Answer: 8.50 rad/s2 Var: 1

67) The drive chain in a bicycle is applying a torque of 0.850 N ∙ m to the wheel of the bicycle. You can treat the wheel as a thin uniform hoop (or ring) with a mass of 0.750 kg and a radius of 33.0 cm. What is the angular acceleration of the wheel? A) 10.4 rad/s2 B) 20.8 rad/s2 C) 5.20 rad/s2 D) 3.43 rad/s2 E) 1.06 rad/s2 Answer: A Var: 1 68) A mechanic is examining the wheel of a bicycle to adjust the brake. With the bicycle off the ground, he manually rotates the wheel until it reaches an angular speed of 12.0 rad/s and then allows it to coast to a stop. If the wheel has a moment of inertia of 0.100 kg ∙ m2, and the wheel slows uniformly to a stop in 160 s, what is the magnitude of the retarding torque? A) 1.00 N ∙ m B) 0.00750 N ∙ m C) 0.0787 N ∙ m D) 1.33 N ∙ m E) 1.67 N ∙ m Answer: B Var: 1 69) A force of is applied tangentially to a wheel of radius 0.340 m and causes an angular acceleration of 1.20 rad/s2. What is the moment of inertia of the wheel? A) 4.78 kg ∙ m2 B) 3.59 kg ∙ m2 C) 5.98 kg ∙ m2 D) 7.17 kg ∙ m2 Answer: A Var: 50+ 70) A torque of 12 N ∙ m is applied to a solid, uniform disk of radius 0.50 m. If the disk accelerates at what is the mass of the disk? A) 60 kg B) 45 kg C) 30 kg D) 15 kg Answer: A Var: 50+

71) A particular motor can provide a maximum torque of 110 N ∙ m. Assuming that all of this torque is used to accelerate a solid, uniform, cylindrical flywheel of mass 10.0 kg and radius 3.00 m, how long will it take for the flywheel to accelerate from rest to A) 3.33 s B) 2.83 s C) 4.03 s D) 4.36 s Answer: A Var: 50+ 72) The drum shown in the figure has a radius of 0.40 m and a moment of inertia of 2.3 about an axis perpendicular to it through its center. The frictional torque at the drum axle is 3.0 N ∙ m. A 14-m length of rope is wound around the rim. The drum is initially at rest. A constant force is applied to the free end of the rope until the rope is completely unwound and slips off. At that instant, the angular speed of the drum is The drum then slows down at a constant rate and comes to a halt. In this situation, what was the magnitude of the constant force applied to the rope?

A) 51 N B) 40 N C) 29 N D) 18 N E) 7.5 N Answer: A Var: 50+ 73) In a laboratory experiment, a student brings up the rotational speed of a flywheel to 30.0 rpm. She then allows it to slow down on its own, and counts 240 revolutions before the apparatus uniformly comes to a stop. The moment of inertia of the flywheel is 0.0850 kg ∙ m2. What is the magnitude of the retarding torque on the flywheel? A) 0.0425 N ∙ m B) 0.159 N ∙ m C) 0.0787 N ∙ m D) 0.000278 N ∙ m E) 0.0000136 N ∙ m Answer: D Var: 1

74) A uniform, solid, 100-kg cylinder with a diameter of 1.0 m is mounted so it is free to rotate about fixed, horizontal, frictionless axis that passes through the centers of its circular ends. A 10kg block is hung from a very light thin cord wrapped around the cylinder's circumference. When the block is released, the cord unwinds and the block accelerates downward, as shown in the figure. What is the acceleration of the block?

Answer: 1.6 m/s2 Var: 1 75) A cinder block of mass m = 4.0 kg is hung from a nylon string that is wrapped around a frictionless pulley having the shape of a cylindrical shell, as shown in the figure. If the cinder block accelerates downward at 4.90 m/s2 when it is released, what is the mass M of the pulley?

A) 2.0 kg B) 4.0 kg C) 6.0 kg D) 8.0 kg E) 10 kg Answer: D Var: 1

76) A uniform rod is 2.0 m long. It is hinged to a wall at its left end, and held in a horizontal position at its right end by a vertical very light string, as shown in the figure. What is the angular acceleration of the rod at the moment after the string is released if there is no friction in the hinge?

A) 15 rad/s2 B) 3.3 rad/s2 C) 7.4 rad/s2 D) 11 rad/s2 E) It cannot be calculated without knowing the mass of the rod. Answer: C Var: 1 77) A uniform solid cylinder of mass 10 kg can rotate about a frictionless axle through its center O, as shown in the cross-sectional view in the figure. A rope wrapped around the outer radius R1 = 1.0 m exerts a force of magnitude F1 = 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force of magnitude F2 = 6.0 N downward. What is the angular acceleration of the cylinder?

A) 1.0 rad/s2 B) 0.60 rad/s2 C) 0.40 rad/s2 D) 0.80 rad/s2 Answer: C Var: 1

78) A uniform solid cylinder of mass 10 kg can rotate about a frictionless axle through its center O, as shown in the cross-sectional view in the figure. A rope wrapped around the outer radius R1 = 1.0 m exerts a force of magnitude F1 = 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force of magnitude F2 = 6.0 N downward. How many radians does the cylinder rotate through in the first 5.0 seconds, if it starts from rest?

A) 13 rad B) 7.5 rad C) 5.0 rad D) 10 rad Answer: C Var: 1 79) The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left), or a distance r/2 from the axis of rotation (right). If you release the hanging blocks simultaneously from rest, and call tL the time taken by the block on the left and tR the time taken by the block on the right to reach the bottom, respectively, then

A) tL > tR. B) tL = tR. C) tL < tR. Answer: A Var: 1 80) A 1.53-kg bucket hangs on a rope wrapped around a pulley of mass 7.07 kg and radius 66 cm. This pulley is frictionless in its axle, and has the shape of a solid uniform disk. After the bucket has been released, (a) what is the angular acceleration of the pulley, and (b) what is the acceleration of the bucket? Answer: (a) 4.5 rad/s2 (b) 3.0 m/s2 Var: 1

81) A 350-g air track cart on a horizontal air track is attached to a string that goes over a frictionless pulley with a moment of inertia of 6.00 × 10-6 kg ∙ m2 and a radius of 1.35 cm. If the string is pulled vertically downward by a force of 2.50 N, (a) what is the magnitude of the acceleration of the cart, and (b) what is the tension in the horizontal string between the pulley and the cart? Answer: (a) 6.53 m/s2 (b) 2.29 N Var: 1 82) A 375-g stone hangs from a thin light string that is wrapped around the circumference of a frictionless pulley with a moment of inertia of 0.0125 kg ∙ m2 and a radius of 26 cm. When the stone is released, the stone accelerates downward and the pulley rotates about its axis as the string unwinds. (a) What is the magnitude of the acceleration of the stone? (b) What is the tension in the string? Answer: (a) 6.6 m/s2 (b) 1.2 N Var: 1 83) As shown in the figure, a 35.30-kg box is attached to a light string that is wrapped around a cylindrical frictionless spool of radius 10.0 cm and moment of inertia 4.00 kg ∙ m2. The spool is suspended from the ceiling, and the box is then released from rest a distance 3.50 m above the floor. How long does it take for the box to reach the floor?

A) 2.97 s B) 2.85 s C) 0.892 s D) 4.18 s E) 5.89 s Answer: A Var: 50+

84) A 385-g tile hangs from one end of a string that goes over a pulley with a moment of inertia of and a radius of 15.0 cm. A mass of 710 g hangs from the other end of the string. When the tiles are released, the larger one accelerates downward while the lighter one accelerates upward. The pulley has no friction in its axle and turns without the string slipping. What is the tension in the string on the side of the 710-g tile? A) 9.77 N B) 6.87 N C) 5.59 N D) 4.41 N E) 3.68 N Answer: C Var: 5 85) A small 355-g box hangs from one end of a thin light string that goes over a frictionless pulley having a moment of inertia of 0.0125 kg ∙ m2 and a radius of 15 cm. A second small package, this one of mass 680 g, hangs from the other end of the string. When the packages are released, the larger one accelerates downward, the lighter one accelerates upward, and the pulley turns without the string slipping. (a) What is the tension in the string on the side of the 355-g package? (b) At what rate do the packages change their speeds? Answer: (a) 4.2 N (b) 2.0 m/s2 Var: 1

College Physics: A Strategic Approach, 4e (Knight) Chapter 8 Equilibrium ad Elasticity 8.1 Conceptual Questions 1) If the sum of the external forces on an object is zero, then the sum of the external torques on it must also be zero. A) True B) False Answer: B Var: 1 2) If the sum of the external torques on an object is zero, then the sum of the external forces on it must also be zero. A) True B) False Answer: B Var: 1 3) If the sum of both the external torques and the external forces on an object is zero, then the object must be at rest. A) True B) False Answer: B Var: 1 4) If an object remains at rest, then the sum of both the external torques and the external forces on the object must be zero. A) True B) False Answer: A Var: 1 5) When a car is weighed, it is driven slowly on a horizontal floor over a scale that records a reading as the front wheels go over the scale, and then records a second reading as the rear wheels go over the scale. The weight of the car is equal to A) the weight under the front wheels. B) the weight under the rear wheels. C) the average of the two weights. D) the sum of the two weights. E) the difference of the two weights. Answer: D Var: 1

6) A croquet mallet balances when suspended from its center of mass, as shown in the left part of the figure. If you cut the mallet into two pieces at its center of mass, as shown in the right part of the figure, how do the masses of the two pieces compare? (There could be more than one correct choice.)

A) The masses are equal. B) The piece with the head of the mallet has the greater mass. C) The piece with the head of the mallet has the smaller mass. D) It is impossible to tell. Answer: B, D Var: 1 7) Tensile stress is A) the strain per unit length. B) the same as force. C) the ratio of the change in length. D) applied force per cross-sectional area. Answer: D Var: 1 8) Tensile strain is A) the ratio of the change in length to the original length. B) the stress per unit area. C) the applied force per unit area. D) the ratio of stress to elastic modulus. Answer: A Var: 1 9) Which one of the following is an accurate statement? A) The ratio of tensile stress to tensile strain is called Young's modulus. B) "Strain" has a meaning very close to "force." C) "Stress" has a meaning very close to "stretch." D) Tensile stress is measured in newtons. E) Tensile strain is measured in meters. Answer: A Var: 1

10) The graph in the figure shows the tensile stress as a function of the tensile strain in a certain wire. What does the slope of this graph give us for this wire?

A) the pressure in the wire B) Young's modulus for the material of the wire C) the tensile stress in the wire D) the tension in the wire E) the percent change in the length of the wire Answer: B Var: 1 11) A large 75-kg lighting fixture can be hung from wires of identical size and shape made of aluminum, brass, or copper. The values of Young's modulus for these metals are 0.70 × 1011 Pa (aluminum), 0.91 × 1011 (brass), and 1.1 × 1011 (copper). Which wire would stretch the least distance? A) aluminum B) brass C) copper D) They will all stretch the same distance. Answer: C Var: 1 12) A 25-kg piece of equipment can be hung by steel wires of length 1.00 m, 2.00 m, or 3.00 m. If all the wires have the same diameter, which one will stretch the greatest distance? A) the 1.00-m wire B) the 2.00-m wire C) the 3.00-m wire D) They will all stretch by the same distance. Answer: C Var: 1 13) A 25-kg piece of equipment can be hung by steel wires of length 1.00 m, 2.00 m, or 3.00 m. If all the wires have the same diameter, which one will stretch the greatest percent? A) the 1.00-m wire B) the 2.00-m wire C) the 3.00-m wire D) They will all stretch by the same percent. Answer: D Var: 1

14) Two wires are made out of the same metal, but one wire is twice as long as the other wire. Which wire will have the greatest elastic modulus? A) the shorter wire B) the longer wire C) It will be the same for both wires. Answer: C Var: 1 15) Which of the following are SI units of Young's modulus? (There could be more than one correct choice.) A) N/m ∙ s2 B) kg/m2 C) kg ∙ m/s2 D) kg/m ∙ s2 E) kg ∙ m2/s2 Answer: D Var: 1 16) As one stretches a metal wire, which condition is reached first? A) the elastic limit B) the breaking point C) the proportional limit Answer: C Var: 1 8.2 Problems 1) An ornament of mass 40.0 g is attached to a vertical ideal spring with a force constant (spring constant) of 20.0 N/m. The ornament is then lowered very slowly until the spring stops stretching. How much does the spring stretch? A) 0.00200 m B) 0.0196 m C) 0.0816 m D) 0.800 m E) 0.200 m Answer: B Var: 1 2) A force of stretches a very light ideal spring constant (spring constant) of the spring? A) 41 N/m B) 22 N/m C) 34 N/m D) 46 N/m Answer: A Var: 50+

from equilibrium. What is the force

3) A very light ideal spring stretches by when it is used to hang a 135-N object. What is the weight of a piece of electronic equipment that would stretch the spring by if you hung the equipment using the spring? A) 289 N B) 63 N C) 176 N D) 405 N Answer: A Var: 50+ 4) An object attached to a spring is pulled across a horizontal frictionless surface. If the force constant (spring constant) of the spring is 45 N/m and the spring is stretched by 0.88 m when the object is accelerating at what is the mass of the object? A) 28 kg B) 24 kg C) 31 kg D) 36 kg Answer: A Var: 18 5) A 3.0-kg brick rests on a perfectly smooth ramp inclined at 34° above the horizontal. The brick is kept from sliding down the plane by an ideal spring that is aligned with the surface and attached to a wall above the brick. The spring has a spring constant (force constant) of 120 N/m. By how much does the spring stretch with the brick attached? A) 360 cm B) 240 cm C) 14 cm D) 24 cm E) 36 cm Answer: C Var: 5 6) A very light ideal spring having a spring constant (force constant) of 8.2 N/cm is used to lift a 2.2-kg tool with an upward acceleration of 3.25 m/s2. If the spring has negligible length when it us not stretched, how long is it while it is pulling the tool upward? Answer: 3.5 cm Var: 1 7) A very light ideal spring with a spring constant (force constant) of 2.5 N/cm pulls horizontally on an 18-kg box that is resting on a horizontal floor. The coefficient of static friction between the box and the floor is 0.65, and the coefficient of kinetic friction is 0.45. (a) How long is the spring just as the box is ready to move? (b) If the spring pulls the box along with a constant forward velocity of 1.75 m/s, how long is the spring? (c) How long is the spring if it pulls the box forward at a constant 2.75 m/s? Answer: (a) 46 cm (b) 32 cm (c) 32 cm Var: 1 5 Copyright © 2019 Pearson Education, Inc.

8) A very light ideal spring of spring constant (force constant) 2.5 N/cm is 15 cm long when nothing is attached to it. It is now used to pull horizontally on a 12.5-kg box on a perfectly smooth horizontal floor. You observe that the box starts from rest and moves 96 cm during the first 1.6 s of its motion with constant acceleration. How long is the spring during this motion? Answer: 19 cm Var: 1 9) A 15-kg child is sitting on a playground teeter-totter, 1.5 m from the pivot. What is the magnitude of the minimum force, applied 0.30 m on the other side of the pivot, that is needed to make the child lift off the ground? A) 75 N B) 740 N C) 23 N D) 44 N E) 66 N Answer: B Var: 1 10) A 15-kg child is sitting on a playground teeter-totter, 1.5 m from the pivot. What is the minimum distance, on the other side of the pivot, such that a 220-N force will make the child lift off the ground? A) 1.0 m B) 1.5 m C) 0.10 m D) 9.8 m E) 2.4 m Answer: A Var: 1 11) An 82-kg painter stands on a long horizontal board 1.55 m from one end. This 27-kg board is uniform, 5.5 m long, and supported at each end by vertical posts. (a) What is the magnitude of the total force provided by both posts? (b) With what force does the post that is closest to the painter push upward on the board? Answer: (a) 1100 N (b) 710 N Var: 1

12) An 82-kg diver stands at the edge of a light 5.0-m diving board, which is supported by two vertical pillars that are 1.6 m apart, as shown in the figure. Find the magnitude and direction of the force exerted by each pillar.

Answer: A: 1.7 kN downward, B: 2.5 kN upward Var: 1 13) An irregularly shaped object that is 10 m long is placed with each end on a scale. If the scale on the right reads while the scale on the left reads how far from the left end is the center of gravity of this object? A) 5.7 m B) 7.4 m C) 4.3 m D) 14 m Answer: A Var: 50+ 14) A uniform 1200-N piece of medical apparatus that is 3.5 m long is suspended horizontally by two vertical wires at its ends. A small but dense 550-N weight is placed on the apparatus 2.0 m from one end, as shown in the figure. What are the tensions, A and B, in the two wires?

A) A = 880 N, B = 880 N B) A = 840 N, B = 910 N C) A = 9000 N, B = 8200 N D) A = 910 N, B = 840 N E) A = 8200 N, B = 9000 N Answer: D Var: 1

15) A meter stick balances at the 50.0-cm mark. If a mass of 50.0 g is placed at the 90.0-cm mark, the stick balances at the 61.3-cm mark. What is the mass of the meter stick? A) 127 g B) 178 g C) 89.7 g D) 32.6 g E) 73.4 g Answer: A Var: 1 16) As shown in the figure, a uniform rectangular crate 0.40 m wide and 1.0 m tall sits on a horizontal surface. The crate weighs 460 N, and its center of gravity is at its geometric center. A horizontal force of magnitude F is applied at a distance h above the floor. Friction at the floor is great enough to prevent the crate from sliding. If what minimum value of F is required to make the crate start to tip over?

Answer: 133 N Var: 50+ 17) As shown in the figure, a 10.0 m long bar is attached by a frictionless hinge to a wall and held horizontal by a light rope that makes an angle θ = 49° with the bar. The bar is uniform and weighs What distance x from the hinge should a 10.0 kg mass be suspended for the tension in the rope to be 177 N?

Answer: 10 m Var: 50+

18) A uniform ladder 12 meters long rests against a vertical frictionless wall, as shown in the figure. The ladder weighs 400 N and makes an angle θ = 51° with the floor. A man weighing 874 N climbs slowly up the ladder. When he is 78 m from the bottom of the ladder, it just starts to slip. What is the coefficient of static friction between the floor and the ladder?

Answer: 0.49 Var: 50+ 19) A child is trying to stack two uniform bricks, each 24 cm long, so they will protrude as far as possible over the edge of a table without tipping over, as shown in the figure. What is the maximum possible overhang distance d?

A) 10 cm B) 12 cm C) 14 cm D) 16 cm E) 18 cm Answer: E Var: 1 20) A uniform 40-N board supports two children weighing 500 N and 350 N. If the support is at the center of the board and the 500-N child is 1.5 m from its center, how far is the 350-N child from the center? A) 1.1 m B) 1.5 m C) 2.1 m D) 2.7 m Answer: C Var: 1

21) To determine the location of the center of mass (or center of gravity) of a car, the car is driven over a scale on a horizontal floor. When the front wheels are over the scale, the weight recorded by the scale is 5800 N, and when the rear wheels are over the scale, the scale reads 6500 N. The distance between the front and rear wheels is measured to be 3.20 m. How far behind the front wheels is the center of mass located? A) 0.845 m B) 1.50 m C) 1.59 m D) 1.69 m E) 1.72 m Answer: D Var: 1 22) A 120-kg refrigerator that is 2.0 m tall and 85 cm wide has its center of mass at its geometrical center. You are attempting to slide it along the floor by pushing horizontally on the side of the refrigerator. The coefficient of static friction between the floor and the refrigerator is 0.30. Depending on where you push, the refrigerator may start to tip over before it starts to slide along the floor. What is the highest distance above the floor that you can push the refrigerator so that it will not tip before it begins to slide? A) 0.71 m B) 1.0 m C) 1.2 m D) 1.4 m E) 1.6 m Answer: D Var: 1 23) A uniform rod weighs 40 N and is 1.0 m long. It is hinged to a wall at the left end, and held in a horizontal position at the right end by a vertical string of negligible weight, as shown in the figure. What is the magnitude of the torque due to the string about a horizontal axis that passes through the hinge and is perpendicular to the rod? The hinge is very small with negligible friction.

A) 40 N ∙ m B) 10 N ∙ m C) 5.0 N ∙ m D) 20 N ∙ m E) 30 N ∙ m Answer: D Var: 1

24) A 10-m uniform beam weighing 100 N is supported by two vertical ropes at its ends. If a 400-N person sits at a point 2.0 m from the left end of the beam, what is the tension in each rope? Answer: 370 N (left rope), 130 N (right rope) Var: 1 25) A light board that is 10 m long is supported by two sawhorses, one at one end of the board and a second at the midpoint. A 40-N weight is placed between the two sawhorses, 3.0 m from the end and 2.0 m from the center. What magnitude forces do the sawhorses exert on the board? Answer: 16 N at the end, 24 N at the midpoint Var: 1 26) A light board that is 10 m long is supported by two sawhorses, one at one end of the board and a second at the midpoint. A 40-N object is placed between the two sawhorses, 3.0 m from the end and 2.0 m from the center. A second object, with a weight of 15 N, is placed on the supported end. What magnitude forces do the sawhorses exert on the board? Answer: 1.0 N at the end, 54 N at the midpoint Var: 1 27) The mobile shown in the figure is perfectly balanced, and the horizontal supports have insignificant masses. What must be the masses of the suspended objects m1, m2, and m3 to maintain balance?

Answer: m1 = 1 g, m2 = 2 g, and m3 = 4 g Var: 1

28) A mobile is shown in the figure. The horizontal supports have negligible mass. Assume that all the numbers given in the figure are accurate to two significant figures. What mass M is required to balance the mobile?

A) 18 g B) 30 g C) 36 g D) 60 g E) 90 g Answer: C Var: 1 29) An athlete holds a 7.5-kg shot put in his hand with his lower arm horizontal, as shown in the figure. His lower arm has a mass of 2.8 kg and its center of gravity (or center of mass) is 12 cm from the elbow-joint pivot. How much force must the extensor muscle (which is M in the figure) in the upper arm exert on the lower arm?

A) 100 N B) 500 N C) 1000 N D) 1500 N Answer: C Var: 1

30) A store's sign has a mass of 20 kg and is 3.0 m long. It is uniform, so its center of gravity is at the center of the sign. It is supported horizontally by a small loose bolt attached to the wall at one end and by a wire at the other end, as shown in the figure. What is the tension in the wire?

A) 460 N B) 230 N C) 120 N D) 200 N E) 300 N Answer: B Var: 1 31) A store's sign has a mass of 20 kg and is 3.0 m long. It is uniform, so its center of gravity is at the center of the sign. It is supported horizontally by a small loose bolt attached to the wall at one end and by a wire at the other end, as shown in the figure. What is the magnitude of the net force that the bolt exerts on the sign?

A) 460 N B) 230 N C) 200 N D) 120 N E) 300 N Answer: B Var: 1

32) A 40-kg uniform ladder that is 5.0 m long is placed against a smooth wall at a height of h = 4.0 m, as shown in the figure. The base of the ladder rests on a rough horizontal surface whose coefficient of static friction with the ladder is 0.40. An 80-kg bucket is suspended from the top rung of the ladder, just at the wall. What is the magnitude of the force that the ladder exerts on the wall?

A) 740 N B) 1300 N C) 980 N D) 900 N E) 1100 N Answer: A Var: 50+ 33) A 100-kg nonuniform boom that is 6.0 m long is loosely pinned at the pivot at P. A 600-kg concrete block is suspended from the end of the boom at A, as shown in the figure. The boom forms a 30° angle above the horizontal, and is supported by a 4.0-m cable between points D and B. Point B is 4.0 m from P, and point D is 4.0 m above P. The center of mass of the boom is at point C, which is 2.0 m from P. Assume that all the quantities shown in the figure are accurate to two significant figures. What is the tension in the cable connected between points B and D?

A) 9300 N B) 8400 N C) 8100 N D) 7500 N E) 6900 N Answer: A Var: 7

34) In the figure, a uniform ladder of weight 200 N and length 10 m leans against a perfectly smooth wall. A firefighter of weight 600 N climbs a distance x up the ladder. The coefficient of static friction between the ladder and the floor is 0.50. What is the maximum value of x for which the ladder will not slip?

A) 3.9 m B) 5.0 m C) 6.0 m D) 6.3 m E) 8.4 m Answer: D Var: 1 35) A 3.00-m-long ladder, weighing 200 N, leans against a smooth vertical wall with its base on a horizontal rough floor, a distance of 1.00 m away from the wall. The ladder is not completely uniform, so its center of gravity is 1.20 m from its base. What force of friction must the floor exert on the base of the ladder to prevent the ladder from sliding down? A) 93.3 N B) 130 N C) 28.3 N D) 102 N E) 150 N Answer: C Var: 5 36) A 5.00-m-long uniform ladder, weighing 200 N, rests against a smooth vertical wall with its base on a horizontal rough floor, a distance of 1.20 m away from the wall. The coefficient of static friction between the ladder and the floor is 0.200. How far up the ladder, measured along the ladder, can a 600-N person climb before the ladder begins to slip? A) 1.50 m B) 1.26 m C) 1.05 m D) 3.95 m E) 4.56 m Answer: E Var: 5

37) A stepladder consists of two halves that are hinged at the top and connected by a tie rod which keeps the two halves from spreading apart. In this particular instance, the two halves are 2.5 m long, the tie rod is connected to the center of each half and is 70 cm long. An 800-N person stands 3/5 of the way up the stepladder, as shown in the figure. The ladder is light enough that we can neglect its weight, and it rests on an extremely smooth floor. What is the tension in the tie rod? (Note: To solve this problem, it is helpful to imagine cutting the ladder in half vertically and consider the forces and torques acting on each half of the ladder.)

A) 140 N B) 240 N C) 280 N D) 360 N E) 560 N Answer: A Var: 1 38) A 320-g ball and a 400-g ball are attached to the two ends of a string that goes over a pulley with a radius of 8.7 cm. Because of friction in its axle, the pulley does not begin to rotate. What is the magnitude of the frictional torque at the axle of the pulley if the system remains at rest when the balls are released? A) 0.068 N ∙ m B) 0.61 N ∙ m C) 0.079 N ∙ m D) 0.063 N ∙ m E) 0.00070 N ∙ m Answer: A Var: 1 39) A 50-kg bucket of concrete is suspended from a steel wire that is 1.0 mm in diameter 1.0 mm and 11.2 m long. What distance will the wire stretch? Young's modulus for steel is 2.0 x 1011 Pa. Answer: 35 mm Var: 1

40) A 7.0-kg pipe is hung from a steel wire that is 2.5 m long and has a diameter of 0.75 mm. Young's modulus for steel is 2.0 × 1011 N/m2. (a) By what distance does the wire stretch? (b) If the wire diameter were doubled, what would be the stretch? Answer: (a) 1.9 mm (b) 0.49 mm Var: 1 41) A steel wire, 3.2 m long, has a diameter of 1.2 mm. The wire stretches 1.6 mm when it bears a load. Young's modulus for steel is 2.0 × 1011 Pa. The mass of the load is closest to A) 12 kg. B) 16 kg. C) 20 kg. D) 24 kg. E) 28 kg. Answer: A Var: 1 42) An aluminum wire and a steel wire, each of length 2.0 m, are hung from the ceiling. A 5.0-kg mass is suspended from the lower end of each wire. The aluminum wire has a diameter of 2.2 mm. What must be the diameter of the steel wire if it is to stretch the same distance as the aluminum wire, so that the two wires maintain equal lengths after the masses are attached? Young's modulus for aluminum is 0.70 × 1011 Pa and for steel it is 2.0 × 1011 Pa. Answer: 1.3 mm Var: 1 43) When a 125-kg piece of equipment is hung from a steel wire of diameter 6.00 mm, it stretches the wire by 4.00 mm. If instead the wire had a diameter of 3.00 mm, but all else were the same, by what distance would the same equipment stretch the wire? A) 16.0 mm B) 8.00 mm C) 4.00 mm D) 2.00 mm E) 1.00 mm Answer: A Var: 1 44) When a 125-kg piece of equipment is hung from a steel wire of length 75 cm, it stretches the wire by 4.00 mm. If instead the wire had a length of 150 cm, but all else were the same, by what distance would the same equipment stretch the wire? A) 16.0 mm B) 8.00 mm C) 4.00 mm D) 2.00 mm E) 1.00 mm Answer: B Var: 1 17 Copyright © 2019 Pearson Education, Inc.

45) A cable is 100-m long and has a cross-sectional area of 1.0 mm2. A 1000-N force is applied to stretch the cable. Young's modulus for the cable is 1.0 × 1011 N/m2. How far does the cable stretch? A) 0.010 m B) 0.10 m C) 1.0 m D) 10 m Answer: C Var: 1 46) A solid steel column is 4.0 m long and 0.20 m in diameter. Young's modulus for this steel is 2.0 × 1011 N/m2. By what distance does the column shrink when a 5000-kg truck is supported by it? A) 8.0 × 10-7 m B) 3.2 × 10-6 m C) 7.8 × 10-6 m D) 3.1 × 10-5 m Answer: D Var: 1 47) A wire of diameter 0.20 mm stretches by 0.20% when a 6.28-N force is applied to it. What is Young's modulus for this wire? A) 2.5 × 1010 Pa B) 1.0 × 1011 Pa C) 2.5 × 1012 Pa D) 1.0 ×1012 Pa Answer: B Var: 1 48) A 50-kg load is suspended from a steel wire of diameter 1.0 mm and length 11.2 m. By what distance will the wire stretch? Young's modulus for steel is 2.0 × 1011 Pa. A) 1.5 cm B) 2.5 cm C) 3.5 cm D) 4.5 cm Answer: C Var: 1

49) A bridge piling has a cross-sectional area of 1.250 m2 and supports a load of 1875 N. What is the stress on the column? A) 1875 N B) 1875 N/m2 C) 1500 N/m2 D) 2344 N/m2 Answer: C Var: 1 50) An aluminum wire 2.0 m long and 2.0 mm in diameter supports a 10.0-kg fixture. What is the stress in the wire? Young's modulus for aluminum is 7.0 × 1010 N/m2. A) 3.1 × 107 N/m2 B) 6.2 × 107 N/m2 C) 9.3 × 107 N/m2 D) 1.2 × 108 N/m2 Answer: A Var: 3 51) A brass wire 2.0 m long and 2.0 mm in diameter supports a 10.0-kg fixture. By what distance did this fixture stretch the wire? Young's modulus for brass is 10 × 1010 N/m2. A) 0.11 mm B) 0.22 mm C) 0.33 mm D) 0.62 mm Answer: D Var: 6 52) A vertical 30-cm steel rod, 1.0 cm in diameter, supports a 300-kg mass. What is the change in length of the rod caused by this mass? Young's modulus for steel is 2.0 × 1011 N/m2. A) 5.6 × 10-5 m B) 6.5 × 10-5 m C) 5.6 × 10-6 m D) 6.5 × 10-6 m E) 6.5 × 10-4 m Answer: A Var: 1

53) A 50-kg air conditioner is placed on top of a concrete pad that is 20 cm thick and has a crosssectional area of 3.0 m2. What is the change in thickness of the pad caused by the air conditioner? Young's modulus for concrete is 2.3 × 1010 N/m2. A) 1.4 × 10-9 m B) 2.8 × 10-9 m C) 1.4 × 10-8 m D) 1.4 × 10-7 m E) 2.8 × 10-8 m Answer: A Var: 1 54) A 1200-kg car is being raised at a constant speed if 25 cm/s by a crane, using a 20-m long steel cable that is 1.5 cm in diameter. Young's modulus for steel is 2.0 × 1011 Pa. What is the change in length of the cable caused by the car? A) 6.7 mm B) 6.7 cm C) 3.3 mm D) 3.3 cm E) 3.3 m Answer: A Var: 1 55) A 1200-kg car is being raised with a constant acceleration of 2.53 m/s2 by a crane, using a 20-m long steel cable that is 1.5 cm in diameter. Young's modulus for steel is 2.0 × 1011 N/m2. What is the change in length of the cable caused by lifting the car? A) 8.4 mm B) 8.4 cm C) 4.9 mm D) 4.9 cm E) 4.9 m Answer: A Var: 1 56) A piano wire has a radius of 0.50 mm. One end is fixed and the other is wrapped around a tuning peg, which has a diameter of 3.5 mm and is 80 cm away. After the wire just becomes taut, the peg is given three full turns. What is the tension in the wire? Young's modulus for steel is 2.0 × 1011 N/m2. A) 3.8 kN B) 4.3 kN C) 6.5 kN D) 8.7 kN E) 9.8 kN Answer: C Var: 1

57) A wire that is 1.0 mm in diameter and 3.5 m long stretches 3.5 mm when an 8.0-kg tool is hung from it. (a) What is Young's modulus for the material from this wire is made? (b) What is the effective spring constant for the stretching wire? Answer: (a) 1.0 × 1011 Pa (b) 2.2 × 104 N/m Var: 1

College Physics: A Strategic Approach, 4e (Knight) Chapter 9 Momentum 9.1 Conceptual Questions 1) A rubber ball and a lump of clay have equal mass. They are thrown with equal speed against a wall. The ball bounces back with nearly the same speed with which it hit. The clay sticks to the wall. Which one of these objects experiences the greater momentum change? A) the ball B) the clay C) Both of them experience the same non-zero momentum change. D) Both of them experience zero momentum change. Answer: A Var: 1 2) Which of the following quantities are units of momentum? (There could be more than one correct choice.) A) N ∙ m B) kg ∙ s/m C) kg ∙ m/s D) N ∙ s E) kg ∙ m2/s2 Answer: C, D Var: 1 3) A tiger is running in a straight line. If we double both the mass and speed of the tiger, the magnitude of its momentum will increase by what factor? A) B) 2 C) 4 D) 8 E) 16 Answer: C Var: 1 4) A very elastic rubber ball is dropped from a certain height and hits the floor with a downward speed v. Since it is so elastic, the ball bounces back with the same speed v going upward. Which of the following statements about the bounce are correct? (There could be more than one correct choice.) A) The ball had the same momentum just before and just after the bounce. B) The magnitude of the ball's momentum was the same just before and just after the bounce. C) The ball's momentum was conserved during the bounce. D) None of the above statements are correct. Answer: B Var: 1 1 Copyright © 2019 Pearson Education, Inc.

5) The momentum of an isolated system is conserved A) only in inelastic collisions. B) only in elastic collisions. C) in both elastic and inelastic collisions. Answer: C Var: 1 6) Two friends are standing on opposite ends of a canoe that is initially at rest with respect to a frictionless lake. The person in the front throws a very massive ball toward the back, and the person in the back catches it. After the ball is caught, the canoe is A) moving backward. B) stationary. C) moving forward. Answer: B Var: 1 7) You are standing on a skateboard, initially at rest. A friend throws a very heavy ball towards you. You have two choices about what to do with the ball: either catch the ball or deflect it back toward your friend with the same speed as it was originally thrown. Which choice should you make in order to maximize your speed on the skateboard? A) Catch the ball. B) Deflect the ball back. C) Your final speed on the skateboard will be the same regardless whether you catch the ball or deflect the ball. Answer: B Var: 1 8) A small car meshes with a large truck in a head-on collision. Which of the following statements concerning the magnitude of the momentum change during the collision is correct? (There could be more than one correct choice.) A) The truck experiences the greater magnitude momentum change. B) The small car experiences the greater magnitude momentum change. C) The small car and the truck experience the same magnitude momentum change. D) The magnitude of the momentum change experienced by each one is inversely proportional to its mass. E) The magnitude of the momentum change experienced by each one is directly proportional to its mass. Answer: C Var: 1

9) A small car meshes with a large truck in a head-on collision. Which of the following statements concerning the momentum during the collision are correct? (There could be more than one correct choice.) A) The momentum of the truck is conserved. B) The momentum of the car is conserved. C) The car and the truck must undergo the same change in speed. D) The momentum of the car and the momentum of the truck are each conserved. E) The momentum of the car-truck system is conserved, but the momentum of each one separately is not conserved. Answer: E Var: 1 10) Consider two less-than-desirable options. In the first you are driving 30 mph and crash headon into an identical car also going 30 mph. In the second option you are driving 30 mph and crash head-on into a stationary brick wall. In neither case does your car bounce back from the thing it hits, and the collision time is the same in both cases. Which of these two situations would result in the greater impact force on your car? A) hitting the other car B) hitting the brick wall C) The force would be the same in both cases. D) None of the above choices are correct. Answer: C Var: 1 11) A rocket explodes into two fragments, one 25 times heavier than the other. The magnitude of the momentum change of the lighter fragment is A) 25 times as great as the momentum change of the heavier fragment. B) The same as the momentum change of the heavier fragment. C) 1/25 as great as the momentum change of the heavier fragment. D) 5 times as great as the momentum change of the heavier fragment. E) 1/4 as great as the momentum change of the heavier fragment. Answer: B Var: 1 12) Which of the following quantities are units of impulse? (There could be more than one correct choice.) A) N ∙ m B) kg ∙ s/m C) kg ∙ m/s D) N ∙ s E) kg ∙ m2/s2 Answer: C, D Var: 1

13) Three cars, car X, car Y, and car Z, begin accelerating from rest at the same time. Car X is more massive than car Y, which is more massive than car Z. The net accelerating force exerted on each car is identical. After 10 seconds, which car has the most amount of momentum? A) They all have the same amount of momentum. B) Car X C) Car Y D) Car Z Answer: A Var: 1 14) During World War I, Germany used a "Big Bertha" cannon to hurl shells into Paris 30 miles away. This gun also had a very long barrel. What was the reason for using a long barrel in these guns? A) to exert a larger force on the shells B) to reduce frictional losses C) to allow the force of the expanding gases from the gunpowder to act for a longer time D) to increase the force exerted on the bullet due to the expanding gases from the gunpowder E) to reduce the force exerted on the bullet due to the expanding gases from the gunpowder Answer: C Var: 1 15) In a collision between two unequal masses, which mass receives a greater magnitude impulse? A) the larger mass B) the smaller mass C) They receive equal impulses. Answer: C Var: 1 16) Identical forces act for the same length of time on two different objects. The magnitude of the change in momentum of the lighter object is A) smaller than the magnitude of the change in momentum of the larger mass, but not zero. B) larger than the magnitude of the change in momentum of the larger mass. C) exactly equal to the magnitude of the change in momentum of the larger mass. D) zero. E) There is not enough information to answer the question. Answer: C Var: 1

17) A very light ping-pong ball moving east at a speed of 4 m/s collides with a very heavy stationary bowling ball. The Ping-Pong ball bounces back to the west, and the bowling ball moves very slowly to the east. Which object experiences the greater magnitude impulse during the collision? A) Neither; both experienced the same magnitude impulse. B) the Ping-Pong ball C) the bowling ball D) It is impossible to tell since the actual mass values are not given. E) It is impossible to tell since the velocities after the collision are unknown. Answer: A Var: 1 18) A small car meshes with a large truck in a head-on collision. Which of the following statements concerning the magnitude of the average force during the collision is correct? A) The truck experiences the greater average force. B) The small car experiences the greater average force. C) The small car and the truck experience the same average force. D) The force experienced by each one is inversely proportional to its mass. E) The force experienced by each one is directly proportional to its mass. Answer: C Var: 1 19) In an inelastic collision involving an isolated system, the final total momentum is A) exactly the same as the initial momentum. B) more than the initial momentum. C) less than the initial momentum. Answer: A Var: 1 20) A 5-kg ball collides inelastically head-on with a 10-kg ball, which is initially stationary. Which of the following statements is true? (There could be more than one correct choice.) A) The magnitude of the change of velocity the 5-kg ball experiences is greater than that of the 10-kg ball. B) The magnitude of the change of velocity the 5-kg ball experiences is less than that of the 10kg ball. C) The magnitude of the change of velocity the 5-kg ball experiences is equal to that of the 10-kg ball. D) The magnitude of the change of the momentum of the 5-kg ball is equal to the magnitude of the change of momentum of the 10-kg ball. E) Both balls lose all their momentum since the collision is inelastic. Answer: A, D Var: 1

21) A 2.0-kg ball moving eastward at 3.0 m/s suddenly collides with and sticks to a 4.0-kg ball moving northward at 2.0 m/s. What is the magnitude of the momentum of this system just after the collision? A) 14 kg ∙ m/s B) 2.0 kg ∙ m/s C) 10 kg ∙ m/s D) 6.0 kg ∙ m/s E) 8.0 kg ∙ m/s Answer: C Var: 1 22) A person sits on a freely spinning lab stool that has no friction in its axle. When this person extends her arms, A) her moment of inertia decreases and her angular speed increases. B) her moment of inertia decreases and her angular speed decreases. C) her moment of inertia increases and her angular speed increases. D) her moment of inertia increases and her angular speed decreases. E) her moment of inertia increases and her angular speed remains the same. Answer: D Var: 1 23) A merry-go-round spins freely when Diego moves quickly to the center along a radius of the merry-go-round. As he does this, it is true to say that A) the moment of inertia of the system decreases and the angular speed increases. B) the moment of inertia of the system decreases and the angular speed decreases. C) the moment of inertia of the system decreases and the angular speed remains the same. D) the moment of inertia of the system increases and the angular speed increases. E) the moment of inertia of the system increases and the angular speed decreases. Answer: A Var: 1 9.2 Problems 1) What is the magnitude of the momentum of a 0.140 kg baseball traveling at 45.0 m/s? Answer: 6.30 kg ∙ m/s Var: 1 2) A 0.14-kg baseball is dropped from rest from a height of 2.0 m above the ground. What is the magnitude of its momentum just before it hits the ground if we neglect air resistance? A) 0.28 kg ∙ m/s B) 0.88 kg ∙ m/s C) 0.44 kg ∙ m/s D) 0.62 kg ∙ m/s E) 1.4 kg ∙ m/s Answer: B Var: 1 6 Copyright © 2019 Pearson Education, Inc.

3) Three objects are moving along a straight line as shown in the figure. Taking the positive direction to be to the right, what is the total momentum of this system?

A) +106 kg ∙ m/s B) -106 kg ∙ m/s C) +14.0 kg ∙ m/s D) -14.0 kg ∙ m/s E) 0.00 kg ∙ m/s Answer: D Var: 1 4) A 0.330-kg volleyball is thrown vertically downward with a speed of 0.150 m/s in a place where g = 9.81 m/s2. It takes it 0.0655 s to reach the ground. What is the magnitude of its momentum just before it hits the ground? A) 0.212 kg ∙ m/s B) 0.262 kg ∙ m/s C) 0.163 kg ∙ m/s D) 0.0216 kg ∙ m/s E) 0.0418 kg ∙ m/s Answer: B Var: 1 5) Two air track carts move along an air track towards each other. Cart A has a mass of 450 g and moves toward the right with a speed of 0.850 m/s. Cart B has a mass of 300 g and moves toward the left with a speed of 1.12 m/s. What is the total momentum of the two-cart system? A) 0.047 kg ∙ m/s toward the right B) 0.719 kg ∙ m/s toward the right C) 0.719 kg ∙ m/s toward the left D) 0.750 kg ∙ m/s toward the right E) 0.750 kg ∙ m/s toward the left Answer: A Var: 1 6) A 100-g ball falls from a window that is 12 m above ground level and experiences no significant air resistance as it falls. What is its momentum when it strikes the ground? A) 3.3 kg ∙ m/s B) 4.8 kg ∙ m/s C) 1.8 kg ∙ m/s D) 1.5 kg ∙ m/s E) 2.4 kg ∙ m/s Answer: D Var: 1

7) A 0.140-kg baseball is dropped and reaches a speed of 1.20 m/s just before it hits the ground and bounces. It rebounds with an upward velocity of 1.00 m/s. What is the change of the ball's momentum during the bounce? A) 0.0280 kg ∙ m/s upwards B) 0.0280 kg ∙ m/s downwards C) 0.308 kg ∙ m/s upwards D) 0.308 kg ∙ m/s downwards E) 0.000 kg ∙ m/s Answer: C Var: 1 8) A firecracker breaks up into two pieces, one of which has a mass of 200 g and flies off along the +x-axis with a speed of 82.0 m/s. The second piece has a mass of 300 g and flies off along the +y-axis with a speed of 45.0 m/s. What is the total momentum of the two pieces? A) 361 kg ∙ m/s at 56.3° from the +x-axis B) 93.5 kg ∙ m/s at 28.8° from the +x-axis C) 21.2 kg ∙ m/s at 39.5° from the +x-axis D) 361 kg ∙ m/s at 0.983° from the +x-axis E) 21.2 kg ∙ m/s at 56.3° from the +x-axis Answer: C Var: 1 9) Find the magnitude and direction of the net momentum of the system shown in the figure. Express the direction by giving the angle the net momentum makes with the +x-axis.

Answer: 123 kg . m/s , 212° Var: 1 10) A 600-kg car makes a 90° turn. Its speed before the turn is 21.0 m/s and after the turn it is 24.0 m/s. What is the magnitude of the change in the car's momentum during the turn? A) 19.1 × 103 kg∙m/s B) 10.2 × 103 kg∙m/s C) 9.55 × 103 kg∙m/s D) 12.0 × 103 kg∙m/s E) 22.2 × 103 kg∙m/s Answer: A Var: 5

11) A 0.10-kg ball, traveling horizontally at 25 m/s, strikes a wall and rebounds at 19 m/s. What is the magnitude of the change in the momentum of the ball during the rebound? A) 1.2 kg ∙ m/s B) 1.8 kg ∙ m/s C) 4.4 kg ∙ m/s D) 5.4 kg ∙ m/s E) 72 kg ∙ m/s Answer: C Var: 1 12) A 60-kg swimmer suddenly dives horizontally from a 150-kg raft with a speed of 1.5 m/s. The raft is initially at rest. What is the speed of the raft immediately after the diver jumps if the water has negligible effect on the raft? Answer: 0.60 m/s Var: 1 13) A 14,000-kg boxcar is coasting at 1.50 m/s along a horizontal track when it suddenly hits and couples with a stationary 10,000-kg boxcar. What is the speed of the cars just after the collision? Answer: 0.875 m/s Var: 1 14) In a police ballistics test, 2.00-g bullet traveling at 700 m/s suddenly hits and becomes embedded in a stationary 5.00-kg wood block. What is the speed of the block immediately after the bullet has stopped moving relative to the block? Answer: 0.280 m/s Var: 1 15) A 328-kg car moving at 19.1 m/s in the +x direction hits from behind a second car moving at in the same direction. If the second car has a mass of and a speed of right after the collision, what is the velocity of the first car after this sudden collision? A) 14.0 m/s B) 18.2 m/s C) 24.2 m/s D) -14.0 m/s Answer: A Var: 50+ 16) A 1200-kg ore cart is rolling at 10.8 m/s across a flat friction-free surface. A crane suddenly drops of ore vertically into the cart. How fast does the cart move just after being loaded with the ore? A) 6.30 m/s B) 3.80 m/s C) 4.20 m/s D) 5.70 m/s Answer: A Var: 50+ 9 Copyright © 2019 Pearson Education, Inc.

17) An empty train car of mass 2.0 x 104 kg coasts along at 10 m/s. A 3000-kg boulder is suddenly dropped vertically into the car. Find the speed of the car immediately after the boulder is dropped in. Answer: 8.7 m/s Var: 1 18) Two ice skaters suddenly push off against one another starting from a stationary position. The 45-kg skater acquires a speed of 0.375 m/s relative to the ice. What speed does the 60-kg skater acquire relative to the ice? A) 0.50 m/s B) 0.28 m/s C) 0.38 m/s D) 0.75 m/s E) 0.00 m/s Answer: B Var: 1 19) A 1200-kg cannon suddenly fires a cannonball at What is the recoil speed of the cannon? Assume that frictional forces are negligible and the cannon is fired horizontally. A) 2.9 m/s B) 35 m/s C) 3.5 m/s D) 3.2 m/s Answer: A Var: 50+ 20) A dinner plate falls vertically to the floor and breaks up into three pieces, which slide horizontally along the floor. Immediately after the impact, a 200-g piece moves along the +x-axis with a speed of 2.00 m/s, a 235-g piece moves along the +y-axis with a speed of 1.50 m/s. The third piece has a mass of 100 g. What is the speed of the third piece? A) 2.51 m/s B) 2.57 m/s C) 3.50 m/s D) 5.33 m/s E) 6.83 m/s Answer: D Var: 5

21) A dinner plate falls vertically to the floor and breaks up into three pieces, which slide horizontally along the floor. Immediately after the impact, a 320-g piece moves along the +x-axis with a speed of 2.00 m/s and a 355-g piece moves along the +y-axis with a speed of 1.50 m/s. The third piece has a mass of 100 g. In what direction relative to the +x-axis does the third piece move? A) 216.9° from the +x-axis B) 219.8° from the +x-axis C) 36.9° from the +x-axis D) 39.9° from the +x-axis E) 39.8° from the +x-axis Answer: B Var: 5 22) In a police ballistics test, a 10.0-g bullet moving at 300 m/s is fired into a 1.00-kg block at rest. The bullet goes through the block almost instantaneously and emerges with 50.0% of its original speed. What is the speed of the block just after the bullet emerges? A) 1.50 m/s B) 2.97 m/s C) 3.00 m/s D) 273 m/s Answer: A Var: 1 23) Two astronauts, of masses 60 kg and 80 kg, are initially right next to each other and at rest in outer space. They suddenly push each other apart. What is their separation after the heavier astronaut has moved 12 m? A) 9.0 m B) 16 m C) 21 m D) 24 m E) 28 m Answer: E Var: 1 24) Two astronauts, of masses 60 kg and 80 kg, are initially right next to each other and at rest in outer space. They suddenly push each other apart. How far has the heavier astronaut moved when the lighter astronaut has moved 12 m? A) 16 m B) 9.0 m C) 21 m D) 7.0 m E) 12 m Answer: B Var: 1

25) Astronaut Jennifer's lifeline to her spaceship comes loose and she finds herself stranded, "floating" 100 m from the mothership. She suddenly throws her 2.00-kg wrench at 20 m/s in a direction away from the ship. If she and her spacesuit have a combined mass of 200 kg, how long does it take her to coast back to her spaceship? A) 1000 s B) 750 s C) 500 s D) 250 s E) 2.50 min Answer: C Var: 1 26) A 14-cm diameter champagne bottle rests on its side on top of a frictionless horizontal table. Suddenly, the cork pops and the bottle slides backward, covering a distance of in If the mass of the bottle is 500 times the mass of the cork, find the distance from the original position that the cork will land on the table. Neglect air resistance and assume that the cork is very small compared to the bottle. A) 3000 cm B) 60 m C) 85 m D) 8.5 cm Answer: A Var: 50+ 27) The graph in the figure shows the x component F of the net force that acts for 10 s on a 100kg crate. What is the change in the momentum of the crate during the 10 s that this force acts?

A) -100 kg ∙ m/s B) -25 kg ∙ m/s C) 75 kg ∙ m/s D) -75 kg ∙ m/s E) 25 kg ∙ m/s Answer: D Var: 1

28) A forklift pushes a 100-kg crate, starting from rest, with a horizontal force of magnitude F. The graph in the figure shows the x component of this force as a function of time. What is the instantaneous velocity of the crate at time t = 10 s?

A) 25 cm/s B) 0.00 cm/s C) 75 cm/s D) -25 cm/s E) -75 cm/s Answer: E Var: 1 29) A batter applies an average force of 8000 N to a baseball for 1.1 ms. What is the magnitude of the impulse delivered to the baseball by the bat? Answer: 8.8 N ∙ s Var: 1 30) A batter hits a 0.140-kg baseball that was approaching him at 30 m/s and, as a result, the ball leaves the bat at 40 m/s in the reverse of its original direction. The ball remains in contact with the bat for 2.0 ms. What is the magnitude of the average force exerted by the bat on the ball? Answer: 4900 N Var: 1 31) Jennifer hits a stationary 0.20-kg ball, and it leaves her racket at 40 m/s. Time-lapse photography shows that the ball was in contact with the racket for 40 ms. (a) What average force did the ball exert on the racket? (b) What is the ratio of this force to the weight of the ball? Answer: (a) 0.20 kN (b) 100 Var: 1 32) A 0.17-kg baseball is thrown with a speed of 38 m/s and it is hit straight back toward the pitcher with a speed of 62 m/s. What is the magnitude of the impulse exerted upon the ball by the bat? Answer: 17 N ∙ s Var: 1

33) A super dart of mass 20 g, traveling at 350 m/s, strikes a steel plate at an angle of 30° with the plane of the plate, as shown in the figure. It bounces off the plate at the same angle but at a speed of 320 m/s. What is the magnitude of the impulse that the plate gives to the bullet?

A) 0.52 N ∙ s B) 4.3 N ∙ s C) 300 N ∙ s D) 6.7 N ∙ s E) 0.30 N ∙ s Answer: D Var: 1 34) A golf club exerts an average horizontal force of 1000 N on a 0.045-kg golf ball that is initially at rest on the tee. The club is in contact with the ball for 1.8 ms. What is the speed of the golf ball just as it leaves the tee? A) 30 m/s B) 35 m/s C) 40 m/s D) 45 m/s E) 50 m/s Answer: C Var: 1 35) A 0.140-kg baseball is thrown with a velocity of It is struck by the bat with an average force of 5000 N, which results in a velocity of 37.0 m/s in the opposite direction from the original velocity. How long were the bat and ball in contact? A) 1.79 × 10-3 s B) 1.28 × 10-2 s C) 3.07 × 10-2 s D) 4.30 × 10-3 s Answer: A Var: 50+

36) Calculate the impulse due to a force of A) 6.3 kg∙ m/s B) 5.0 kg∙ m/s C) 5.7 kg∙ m/s D) 6.9 kg∙ m/s Answer: A Var: 50+

that lasts for

37) A girl of mass 55 kg throws a ball of mass 0.80 kg against a wall. The ball strikes the wall horizontally with a speed of and it bounces back with this same speed. The ball is in contact with the wall What is the magnitude of the average force exerted on the wall by the ball? A) 800 N B) 400 N C) 55,000 N D) 27,500 N E) 13,750 N Answer: A Var: 50+ 38) A 475-gram ball is traveling horizontally at 12.0 m/s to the left when it is suddenly struck horizontally by a bat, causing it to reverse direction and initially travel at 8.50 m/s to the right. If the bat produced an average force of 1275 N on the ball, for how long (in milliseconds) was it in contact with the ball? Answer: 7.64 ms Var: 1 39) A 0.140 kg baseball is thrown horizontally with a velocity of 28.9 m/s. It is struck with a constant horizontal force that lasts for 1.85 ms, which results in a velocity of 37.0 m/s in the opposite direction. What was the magnitude of the horizontal force? A) 0.613 kN B) 2.19 kN C) 2.80 kN D) 4.99 kN Answer: D Var: 1 40) A golf ball of mass 0.050 kg is at rest on the tee. Just after being struck, it has a velocity of 102 m/s. If the club and ball were in contact for what is the average force exerted on the ball by the club? A) 6.3 kN B) 7.1 kN C) 5.5 kN D) 4.9 kN Answer: A Var: 44 15 Copyright © 2019 Pearson Education, Inc.

41) A 0.24 kg blob of clay is thrown at a wall with an initial horizontal velocity of If the clay comes to a stop in what is the average horizontal force on the clay due to the wall? A) 42 N B) 26 N C) 35 N D) 51 N Answer: A Var: 14 42) A steady horizontal force lasting for 2.1 s gives a 1.25 kg object an acceleration of 3.2 m/s2 on a frictionless table. What impulse does this force give to the object? A) 26 kg ∙ m/s B) 11 kg ∙ m/s C) 8.4 kg ∙ m/s D) 2.6 kg ∙ m/s Answer: C Var: 1 43) A block of mass m = 34 kg and speed V is behind a block of mass M = 81 kg and speed of as shown in the figure. The surface is frictionless and the blocks collide and couple. After the collision, the blocks have a common speed of What is the magnitude of the impulse on the 34-kg block due to the collision?

A) 32 N ∙ s B) 14 N ∙ s C) 41 N ∙ s D) 57 N ∙ s E) 73 N ∙ s Answer: A Var: 50+ 44) A very small 51-g steel ball is released from rest and falls vertically onto a steel plate. The ball strikes the plate and is in contact with it for 0.50 ms. The ball rebounds elastically and returns to its original height. The total time interval for a round trip is 3.00 s. What is the magnitude of the average force exerted on the ball by the plate during contact with the plate? A) 3000 N B) 1500 N C) 2490 N D) 2000 N E) 3500 N Answer: A Var: 50+

45) A 0.140-kg baseball is dropped from rest. It has a speed of 1.20 m/s just before it hits the ground, and it rebounds with an upward speed of 1.00 m/s. The ball is in contact with the ground for 0.0140 s. What is the average force exerted by the ground on the ball during the time of contact? A) 2.00 N upwards B) 2.00 N downwards C) 22.0 N upwards D) 22.0 N downwards E) 0.00 N Answer: C Var: 1 46) A batter hits a foul ball. The 0.14-kg baseball that was approaching him at 40 m/s leaves the bat at 30 m/s in a direction perpendicular to the line between the batter and the pitcher. What is the magnitude of the impulse delivered to the baseball? A) 9.8 N ∙ s B) 1.4 N ∙ s C) 3.5 N ∙ s D) 5.6 N ∙ s E) 7.0 N ∙ s Answer: E Var: 1 47) A block of mass m = 5.6 kg, moving on a frictionless surface with a velocity of to the right, collides with a block of mass M at rest, as shown in the figure. After the collision, the 5.6-kg block recoils with a velocity of to the left. If the blocks are in contact for 0.20 s, what is the magnitude of the average force on the 5.6-kg block, while the two blocks are in contact?

A) 202 N B) 192 N C) 182 N D) 0 N E) 0 N Answer: A Var: 50+ 48) A force of 5.3 N is needed to hold on to an umbrella in a strong wind. If the air molecules each have a mass of 4.7 ×10-26 kg, and each one strikes the umbrella (without rebounding) with a speed of 2.0 m/s in the same direction, how many atoms strike the umbrella each second? Assume that the wind blows horizontally so that the gravity can be neglected. Answer: 5.6 ×1025 per second Var: 1 17 Copyright © 2019 Pearson Education, Inc.

49) A fire hose is turned on the door of a burning building in order to knock the door down. This requires a force of 1000 N. If the hose delivers 40 kg of water per second, what is the minimum velocity of the stream needed to knock down the door, assuming the water doesn't bounce back? A) 15 m/s B) 20 m/s C) 25 m/s D) 30 m/s Answer: C Var: 1 50) A 2200-kg auto moving northward at 12.0 m/s runs into a 3800-kg truck which is also moving northward, but at 5.00 m/s. If the vehicles lock bumpers, how fast are they moving just after the collision? Answer: 7.57 m/s Var: 1 51) A 1200-kg car moving at suddenly collides with a stationary car of mass If the two vehicles lock together, what is their combined velocity immediately after the collision? A) 6.9 m/s B) 8.6 m/s C) 12.1 m/s D) 5.5 m/s Answer: A Var: 50+ 52) A 1000-kg whale swims horizontally to the right at a speed of 6.0 m/s. It suddenly collides directly with a stationary seal of mass 200 kg. The seal grabs onto the whale and holds fast. What is the momentum of these two sea creatures just after their collision? You can neglect any drag effects of the water during the collision. A) 0.00 kg ∙ m/s B) 1200 kg ∙ m/s C) 2000 kg ∙ m/s D) 7200 kg ∙ m/s E) 6000 kg ∙ m/s Answer: E Var: 1

53) A 1000-kg whale swims horizontally to the right at a speed of 6.0 m/s. It suddenly collides directly with a stationary seal of mass 200 kg. The seal grabs onto the whale and holds fast. What is the speed of these two sea creatures just after their collision? You can neglect any drag effects of the water during the collision. A) 0.00 m/s B) 3.0 m/s C) 4.0 m/s D) 5.0 m/s E) 6.0 m/s Answer: D Var: 1 54) A 2.0-kg mass moving at 5.0 m/s suddenly collides head-on with a 3.0-kg mass at rest. If the collision is perfectly inelastic, what is the speed of the masses just after the collision? A) 10 m/s B) 2.5 m/s C) 2.0 m/s D) 0 m/s, since the collision is inelastic Answer: C Var: 3 55) An 80-kg man is skating northward and happens to suddenly collide with a 20-kg boy who is ice skating toward the east. Immediately after the collision, the man and boy are seen to be moving together at 2.5 m/s in a direction 60° north of east. How fast was the boy moving just before the collision? Answer: 6.3 m/s Var: 1 56) A car (of mass 1500 kg) and a small truck (of mass 2000 kg) collide suddenly at right angles at an icy intersection. The car was originally traveling eastward at 20.0 m/s and the truck was traveling northward at 20.0 m/s just before the collision took place. What is the speed of the combined wreck just after the collision if the vehicles become enmeshed? Answer: 14.3 m/s Var: 1 57) Two vehicles approach a right angle intersection and then suddenly collide. After the collision, they become entangled. If their mass ratios were 1:4 and their respective speeds as they approached the intersection were both 13 m/s, find the magnitude and direction of the final velocity of the wreck. A) 11 m/s at 14° with respect to the original direction of the lighter car B) 16 m/s at 76° with respect to the original direction of the lighter car C) 11 m/s at 76° with respect to the original direction of the lighter car D) 16 m/s at 14° with respect to the original direction of the lighter car Answer: C Var: 1

58) A car heading north suddenly collides at an intersection with a truck of the same mass heading east. If they lock together and travel at at 15° north of east just after the collision, how fast was the car initially traveling? A) 14 m/s B) 7 m/s C) 28 m/s D) 11 m/s Answer: A Var: 41 59) A puck with a mass m1 = 50 g moving at 1.0 m/s approaches a stationary puck with a mass m2 = 100 g on a frictionless air table, and they undergo a sudden two-dimensional elastic collision. After the collision, both pucks have identical speeds, but travel in different directions. What is the angle between the original and final paths of puck with mass m1? A) 30° B) 60° C) 90° D) 120° E) 150° Answer: C Var: 1 60) A 900-kg car traveling east at 15.0 m/s suddenly collides with a 750-kg car traveling north at 20.0 m/s. The cars stick together after the collision. What is the speed of the wreckage just after the collision? A) 6.10 m/s B) 12.2 m/s C) 25.0 m/s D) 35.0 m/s E) 17.3 m/s Answer: B Var: 1 61) A 900-kg car traveling east at 15.0 m/s suddenly collides with a 750-kg car traveling north at 20.0 m/s. The cars stick together after the collision. In what direction does the wreckage move just after the collision? A) 36.9° N of E B) 42.0° N of E C) 45.0° N of E D) 53.1° N of E E) 48.0° N of E Answer: E Var: 1

62) A 900-kg car traveling 30.0° south of east at 12.0 m/s suddenly collides with a 750-kg car traveling north at 17.0 m/s. The cars stick together after colliding. What is the speed of the wreckage just after the collision? A) 7.21 m/s B) 12.2 m/s C) 20.4 m/s D) 25.0 m/s E) 17.3 m/s Answer: A Var: 5 63) A 1500-kg car traveling at 90 km/h toward the east suddenly collides with a 3000-kg car traveling at 60 km/h toward the south. The two cars stick together after the collision. What is the speed of the cars after collision? A) 8.3 m/s B) 14 m/s C) 17 m/s D) 22 m/s Answer: B Var: 1 64) A 1500-kg car traveling at 90 km/h toward the east suddenly collides with a 3000-kg car traveling at 60 km/h toward the south. The two cars stick together after the collision. What is the direction of motion of the cars after collision? A) 36.9° S of E B) 36.9° E of S C) 53.1° S of E D) 53.1° E of S Answer: C Var: 1 65) Two dogs, Rover and Fido, run on a level frictionless surface. Rover runs eastward with a momentum of 24 kg . m/s, and Fido runs northward with momentum 10 kg . m/s. They make a sudden perfectly inelastic collision. What is the magnitude of their combined momentum after the collision? A) 14 kg . m/s B) 26 kg . m/s C) 34 kg . m/s D) It cannot be determined without knowing the masses and velocities of the dogs. Answer: B Var: 1 66) A ballerina spins initially at 1.5 rev/s when her arms are extended. She then draws in her arms to her body and her moment of inertia becomes 0.88 kg ∙ m2, and her angular speed increases to 4.0 rev/s. What was her initial moment of inertia? Answer: 2.3 kg ∙ m2 Var: 1 21 Copyright © 2019 Pearson Education, Inc.

67) In a certain cyclotron, a proton of mass 1.67 × 10-27 kg moves in a circle of diameter 1.6 m with an angular speed of 2.0 × 106 rad/s. What is the angular momentum of the proton? A) 1.3 × 10-21 kg ∙ m2/s B) 1.8 × 10-21 kg ∙ m2/s C) 2.1 × 10-21 kg ∙ m2/s D) 3.2 × 10-21 kg ∙ m2/s Answer: C Var: 1 68) Three solid, uniform, cylindrical flywheels, each of mass 65.0 kg and radius 1.47 m, rotate independently around a common axis through their centers. Two of the flywheels rotate in one direction at 8.94 rad/s, but the other one rotates in the opposite direction at 3.42 rad/s. Calculate the magnitude of the net angular momentum of the system. A) 1020 kg ∙ m2/s B) 1500 kg ∙ m2/s C) 975 kg ∙ m2/s D) 940 kg ∙ m2/s Answer: A Var: 1 69) A uniform, solid, cylindrical flywheel of radius 1.4 m and mass 15 kg rotates at What is the magnitude of the flywheel's angular momentum? A) 40 kg ∙ m2/s B) 20 kg ∙ m2/s C) 80 kg ∙ m2/s D) 60 kg ∙ m2/s Answer: A Var: 48 70) A uniform 135-g meter stick rotates about an axis perpendicular to the stick passing through its center with an angular speed of 3.50 rad/s. What is the magnitude of the angular momentum of the stick? A) 0.0394 kg ∙ m2/s B) 0.473 kg ∙ m2/s C) 0.0739 kg ∙ m2/s D) 0.158 kg ∙ m2/s E) 0.0236 kg ∙ m2/s Answer: A Var: 1

71) An ice skater has a moment of inertia of 5.0 kg ∙ m2 when her arms are outstretched, and at this time she is spinning at 3.0 rev/s. If she pulls in her arms and decreases her moment of inertia to 2.0 kg ∙ m2, how fast will she be spinning? A) 2.0 rev/s B) 3.3 rev/s C) 7.5 rev/s D) 10 rev/s Answer: C Var: 1 72) A figure skater rotating at 5.00 rad/s with arms extended has a moment of inertia of 2.25 kg ∙ m2. If he pulls in his arms so his moment of inertia decreases to 1.80 kg ∙ m2, what will be his new angular speed? A) 2.25 rad/s B) 4.60 rad/s C) 6.25 rad/s D) 0.81 rad/s Answer: C Var: 1 73) A solid wood door, 90.0 cm wide by 2.00 m tall has a mass of 35.0 kg. It is open and at rest. A small 500-g ball is thrown perpendicular to the door with a speed of 20.0 m/s and hits the door 60.0 cm from the hinged side. The ball rebounds with a speed of 16.0 m/s along the same line. What is the angular speed of the door just after the collision with the ball? A) 0.127 rad/s B) 0.925 rad/s C) 1.14 rad/s D) 2.28 rad/s E) 4.57 rad/s Answer: C Var: 1 74) A light-weight potter's wheel, having a moment of inertia of is spinning freely at 40.0 rpm. The potter drops a small but dense lump of clay onto the wheel, where it sticks a distance 1.2 m from the rotational axis. If the subsequent angular speed of the wheel and clay is 32 rpm, what is the mass of the clay? A) 4.2 kg B) 2.8 kg C) 3.7 kg D) 4.6 kg Answer: A Var: 38

75) A 40.0-kg child running at 3.00 m/s suddenly jumps onto a stationary playground merry-goround at a distance 1.50 m from the axis of rotation of the merry-go-round. The child is traveling tangential to the edge of the merry-go-round just before jumping on. The moment of inertia about its axis of rotation is 600 kg ∙ m2 and very little friction at its rotation axis. What is the angular speed of the merry-go-round just after the child has jumped onto it? A) 0.788 rad/s B) 0.261 rad/s C) 6.28 rev/s D) 2.00 rad/s E) 3.14 rev/s Answer: B Var: 1 76) A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg ∙ m2 is rotating freely with an angular speed of 1.0 rad/s. Two people, each of mass 60 kg, are standing right outside the edge of the merry-go-round and suddenly step onto the edge with negligible speed relative to the ground. What is the angular speed of the merry-go-round right after the two people have stepped on? A) 0.20 rad/s B) 0.40 rad/s C) 0.60 rad/s D) 0.80 rad/s E) 0.67 rad/s Answer: B Var: 1 77) A 24.5-kg child is standing on the outer edge of a horizontal merry-go-round that has a moment of inertia of about a vertical axis through its center and a radius of 2.40 m. The entire system (including the child) is initially rotating at 0.180 rev/s. Find the angular velocity if the child moves to a new position 1.10 m from the center of the merry-go-round. Answer: 0.200 rev/s Var: 50+

78) Initially, a small 2.0-kg rock is whirling at the end of a very thin string in a circular path of radius 0.75 m on a horizontal frictionless surface, as shown in the figure. The initial tangential speed of the rock was 5.0 m/s. The string has been slowly winding around a vertical rod, and a few seconds later the length of the string has shortened to 0.25 m. What is the instantaneous speed of the mass at the moment the string reaches a length of 0.25 m?

A) 3.9 m/s B) 9.3 m/s C) 15 m/s D) 225 m/s E) 75 m/s Answer: C Var: 1 79) A solid, uniform, horizontal disk with a diameter of 2.0 m and a mass of 4.0 kg freely rotates at 36 rpm about a vertical axis through its center. A small 0.50-kg stone is suddenly dropped onto the disk and sticks to the disk at a distance of 80 cm from the axis of rotation. The figure shows before and after views. (a) Before the stone fell, what was the moment of inertia of the disk about its central axis? (b) After the stone stuck, what was the moment of inertia of the system about the same axis? (c) What is the angular velocity of the disk (in rpm) after the stone fell onto the disk?

Answer: (a) 2.0 kg ∙ m2 Var: 1

(b) 2.3 kg ∙ m2

80) A puck moves on a horizontal air table. It is attached to a string that passes through a hole in the center of the table. As the puck rotates about the hole, the string is pulled downward very slowly and shortens the radius of rotation, so the puck gradually spirals in towards the center. By what factor will the puck's angular speed have changed when the string's length has decreased to one-half of its original length? A) 2 B) 4 C) D) 1 E) 1/2 Answer: B Var: 1

College Physics: A Strategic Approach, 4e (Knight) Chapter 10 Energy and Work 10.1 Conceptual Questions 1) Person X pushes twice as hard against a stationary brick wall as person Y. Which one of the following statements is correct? A) Both do positive work, but person X does four times the work of person Y. B) Both do positive work, but person X does twice the work of person Y. C) Both do the same amount of positive work. D) Both do zero work. E) Both do positive work, but person X does one-half the work of person Y. Answer: D Var: 1 2) Two men, Joel and Jerry, push against a car that has stalled, trying unsuccessfully to get it moving. Jerry stops after 10 min, while Joel is able to push for 5.0 min longer. Compare the work they do on the car. A) Joel does 75% more work than Jerry. B) Joel does 50% more work than Jerry. C) Jerry does 50% more work than Joel. D) Joel does 25% more work than Jerry. E) Neither of them does any work. Answer: E Var: 1 3) If the force on an object is in the negative direction, the work it does on the object must be A) negative. B) positive. C) The work could be either positive or negative, depending on the direction the object moves. Answer: C Var: 1 4) A 35-N bucket of water is lifted vertically 3.0 m and then returned to its original position. How much work did gravity do on the bucket during this process? A) 180 J B) 90 J C) 45 J D) 0 J E) 900 J Answer: D Var: 1

5) You throw a baseball straight up. Compare the sign of the work done by gravity while the ball goes up with the sign of the work done by gravity while it goes down. A) The work is positive on the way up and positive on the way down. B) The work is positive on the way up and negative on the way down. C) The work is negative on the way up and positive on the way down. D) The work is negative on the way up and on the way down because gravity is always downward. Answer: C Var: 1 6) Which one has larger kinetic energy: a 500-kg object moving at 40 m/s or a 1000-kg object moving at 20 m/s? A) The 500-kg object B) The 1000-kg object C) Both have the same kinetic energy. Answer: A Var: 1 7) A truck has four times the mass of a car and is moving with twice the speed of the car. If Kt and Kc refer to the kinetic energies of truck and car respectively, it is correct to say that A) Kt = 16Kc. B) Kt = 4Kc. C) Kt = 2Kc. D) Kt = Kc. E) Kt = Kc. Answer: A Var: 1 8) Three cars (car F, car G, and car H) are moving with the same speed and slam on their brakes. The most massive car is car F, and the least massive is car H. If the tires of all three cars have identical coefficients of kinetic friction with the road surface, which car travels the longest distance to skid to a stop? A) They all travel the same distance in stopping. B) Car F C) Car G D) Car H Answer: A Var: 1

9) Three cars (car L, car M, and car N) are moving with the same speed and slam on their brakes. The most massive car is car L, and the least massive is car N. If the tires of all three cars have identical coefficients of kinetic friction with the road surface, for which car is the amount of work done by friction in stopping it the greatest? A) The amount of work done by friction is the same for all cars. B) Car L C) Car M D) Car N Answer: B Var: 1 10) A 4.0 kg object is moving with speed 2.0 m/s. A 1.0 kg object is moving with speed 4.0 m/s. Both objects encounter the same constant braking force, and are brought to rest. Which object travels the greater distance before stopping? A) the 4.0 kg object B) the 1.0 kg object C) Both objects travel the same distance. D) It cannot be determined from the information given. Answer: C Var: 1 11) You slam on the brakes of your car in a panic, and skid a certain distance on a straight level road. If you had been traveling twice as fast, what distance would the car have skidded, under the same conditions? A) It would have skidded 4 times farther. B) It would have skidded twice as far. C) It would have skidded 1.4 times farther. D) It would have skidded one half as far. E) It is impossible to tell from the information given. Answer: A Var: 1 12) Which requires more work, increasing a car's speed from 0 mph to 30 mph or from 50 mph to 60 mph? A) 0 mph to 30 mph B) 50 mph to 60 mph C) It is the same in both cases. Answer: B Var: 1

13) A stone is held at a height h above the ground. A second stone with four times the mass of the first one is held at the same height. The gravitational potential energy of the second stone compared to that of the first stone is A) one-fourth as much. B) one-half as much. C) twice as much. D) four times as much. E) the same. Answer: D Var: 1 14) You and your friend, who weighs the same as you, want to go to the top of the Eiffel Tower. Your friend takes the elevator straight up. You decide to walk up the spiral stairway, taking longer to do so. Compare the gravitational potential energy of you and your friend, after you both reach the top. A) It is impossible to tell, since the times you both took are unknown. B) It is impossible to tell, since the distances you both traveled are unknown. C) Your friend's gravitational potential energy is greater than yours, because he got to the top faster. D) Both of you have the same amount of gravitational potential energy at the top. E) Your gravitational potential energy is greater than that of your friend, because you traveled a greater distance in getting to the top. Answer: D Var: 1

15) The graphs shown show the magnitude F of the force exerted by a spring as a function of the distance x the spring has been stretched. For which one of the graphs does the spring obey Hooke's law?

A) Graph a B) Graph b C) Graph c D) Graph d E) Graph e Answer: B Var: 1 16) A heavy dart and a light dart are launched horizontally on a frictionless table by identical ideal springs. Both springs were initially compressed by the same amount. Which of the following statements about these darts are correct? (There could be more than one correct choice.) A) The darts both have the same kinetic energy just as they move free of the spring. B) The lighter dart leaves the spring moving faster than the heavy dart. C) The heavy dart had more initial elastic potential energy than the light dart. D) Both darts move free of the spring with the same speed. E) Both darts had the same initial elastic potential energy. Answer: A, B, E Var: 1

17) When you throw a pebble straight up with initial speed V, it reaches a maximum height H with no air resistance. At what speed should you throw it up vertically so it will go twice as high? A) 16V B) 8V C) 4V D) 2V E) V Answer: E Var: 1 18) When you drop a pebble from height H, it reaches the ground with speed V if there is no air resistance. From what height should you drop it so it will reach the ground with twice speed? A) H B) 2H C) 4H D) 8H E) 16H Answer: C Var: 1 19) When you drop a pebble from height H, it reaches the ground with kinetic energy K if there is no air resistance. From what height should you drop it so it will reach the ground with twice as much kinetic energy? A) H B) 2H C) 4H D) 8H E) 16H Answer: B Var: 1 20) Two objects, one of mass m and the other of mass 2m, are dropped from the top of a building. If there is no air resistance, when they hit the ground A) both will have the same kinetic energy. B) the heavier one will have twice the kinetic energy of the lighter one. C) the heavier one will have four times the kinetic energy of the lighter one. D) the heavier one will have half the kinetic energy of the lighter one. E) the heavier one will have one-fourth the kinetic energy of the lighter one. Answer: B Var: 1

21) Swimmers at a water park have a choice of two frictionless water slides, as shown in the figure. Although both slides drop over the same height h, slide 1 is straight while slide 2 is curved, dropping quickly at first and then leveling out. How does the speed v1 of a swimmer reaching the bottom of slide 1 compare with v2, the speed of a swimmer reaching the end of slide 2?

A) v1 > v2 B) v1 < v2 C) v1 = v2 D) The heavier swimmer will have a greater speed than the lighter swimmer, no matter which slide he uses. E) No simple relationship exists between v1 and v2. Answer: C Var: 1 22) Two frisky otters slide down frictionless hillsides of the same height but different slopes. The slope of the hill of otter 1 is 30°, while the slope of the hill of otter 2 is 60°. If both start from rest, which otter is moving faster when she reaches the bottom of her hill? A) Otter 1 is moving faster. B) Otter 2 is moving faster. C) The heavier otter is moving faster, no matter which hill she used. D) Both otters have the same speed at the bottom. E) The otter that took the shorter time is moving faster. Answer: D Var: 1 23) A lightweight object and a very heavy object are sliding with equal speeds along a level frictionless surface. They both slide up the same frictionless hill with no air resistance. Which object rises to a greater height? A) The heavy object, because it has greater initial kinetic energy. B) The light object, because gravity slows it down less. C) The lightweight object, because the force of gravity on it is less. D) The heavy object, because it has more mass to carry it up the hill. E) They both slide to exactly the same height. Answer: E Var: 1

24) A person stands on the edge of a cliff. She throws three identical rocks with the same speed. Rock X is thrown vertically upward, rock Y is thrown horizontally, and rock Z is thrown vertically downward. If the ground at the base of the cliff is level, which rock hits the ground with the greatest speed if there is no air resistance? A) Rock X B) Rock Y C) Rock Z D) They all hit the ground with the same speed. Answer: D Var: 1 25) Joe and Bill throw identical balls vertically upward. Joe throws his ball with an initial speed twice as high as Bill. If there is no air resistance, the maximum height of Joe's ball will be A) four times that of Bill's ball. B) two times that of Bill's ball. C) equal to that of Bill's ball. D) eight times that of Bill's ball. E) roughly 1.4 times that of Bill's ball. Answer: A Var: 1 26) A stone can slide down one of four different frictionless ramps, as shown in the figure. For which ramp will the speed of the ball be the greatest at the bottom?

A) Ramp X B) Ramp Y C) Ramp Z D) The speed of the ball will be the same for all ramps. Answer: D Var: 1

27) A girl throws a stone from a bridge. Consider the following ways she might throw the stone. The speed of the stone as it leaves her hand is the same in each case. Case A: Thrown straight up. Case B: Thrown straight down. Case C: Thrown out at an angle of 45° above horizontal. Case D: Thrown straight out horizontally. In which case will the speed of the stone be greatest when it hits the water below if there is no significant air resistance? A) Case A B) Case B C) Case C D) Case D E) The speed will be the same in all cases. Answer: E Var: 1 28) A heavy frog and a light frog jump straight up into the air. They push off in such away that they both have the same kinetic energy just as they leave the ground. Air resistance is negligible. Which of the following statements about these frogs are correct? (There could be more than one correct choice.) A) Just as they leave the ground, the heavier frog is moving faster than the lighter frog. B) Just as they leave the ground, the lighter frog is moving faster than the heavier frog. C) They both leave the ground with the same speed. D) The lighter frog goes higher than the heavier frog. E) The heavier frog goes higher than the lighter frog. F) Both frogs reach the same maximum height. Answer: B, F Var: 1 29) Two identical grasshoppers jump into the air with the same initial speed and experience no air resistance. Grasshopper A goes straight up, but grasshopper B goes up at a 66° angle above the horizontal. Which of the following statements about these grasshoppers are correct? (There could be more than one correct choice.) A) At their highest point, both of them have the same amount of gravitational potential energy. B) At their highest point, both of them have the same amount of kinetic energy. C) At their highest point, both of them have the same amount of mechanical energy. D) At their highest point, grasshopper B is moving faster than grasshopper A. E) At their highest point, grasshopper A has more gravitational potential energy than grasshopper B. Answer: C, D, E Var: 1

30) A heavy rock and a light rock are dropped from the same height and experience no significant air resistance as they fall. Which of the following statements about these rocks are correct? (There could be more than one correct choice.) A) Both rocks have the same kinetic energy when they reach the ground. B) Both rocks have the same speed when they reach the ground. C) The heavier rock reaches the ground before the lighter rock. D) Just as they were released, both rocks had the same amount of gravitational potential energy. E) When they reach the ground, the heavier rock has more kinetic energy than the lighter rock. Answer: B, E Var: 1 31) A heavy stone and a light stone are released from rest in such away that they both have the same amount of gravitational potential energy just as they are released. Air resistance is negligibly small. Which of the following statements about these stones are correct? (There could be more than one correct choice.) A) The initial height of the light stone is greater than the initial height of the heavy stone. B) The stones must have been released from the same height. C) The stones both have the same speed just as they reach the ground. D) Just as it reaches the ground, the light stone is traveling faster than the heavy stone. E) The stones both have the same kinetic energy just as they reach the ground. Answer: A, D, E Var: 1 32) A 1-kg ball is released from a height of 6 m, and a 2-kg ball is released from a height of 3 m. Air resistance is negligible as they fall. Which of the following statements about these balls are correct? (There could be more than one correct choice.) A) As they reach the ground, the 1-kg ball will have more kinetic energy than the 2-kg ball because it was dropped from a greater height. B) As they reach the ground, the 1-kg ball will be moving faster than the 2-kg ball. C) Both balls will reach the ground with the same speed. D) Both balls will reach the ground with the same kinetic energy. E) Both balls will take the same time to reach the ground. Answer: B, D Var: 1 33) A heavy dart and a light dart are launched vertically by identical ideal springs. Both springs were initially compressed by the same amount. There is no significant air resistance. Which of the following statements about these darts are correct? (There could be more than one correct choice.) A) The heavy dart goes higher than the light dart. B) The light dart goes higher than the heavy dart. C) Both darts reach the same maximum height. D) At the maximum height, both darts have the same gravitational potential energy. E) Both darts began moving upward with the same initial speed. Answer: B, D Var: 1 10 Copyright © 2019 Pearson Education, Inc.

34) A heavy sled and a light sled, both moving horizontally with the same speed, suddenly slide onto a rough patch of snow and eventually come to a stop. The coefficient of kinetic friction between the sleds and the rough snow is the same for both of them. Which of the following statements about these sleds are correct? (There could be more than one correct choice.) A) Both sleds will slide the same distance on the rough snow before stopping. B) The heavy sled will slide farther on the rough snow than the light sled. C) The light sled will slide farther on the rough snow than the heavy sled. D) The friction from the snow will do more negative work on the heavy sled than on the light sled. E) The friction from the snow will do the same amount of work on both sleds. Answer: A, D Var: 1 35) A heavy sled and a light sled, both moving horizontally with the same kinetic energy, suddenly slide onto a rough patch of snow and eventually come to a stop. The coefficient of kinetic friction between the sleds and the rough snow is the same for both of them. Which of the following statements about these sleds are correct? (There could be more than one correct choice.) A) Both sleds will slide the same distance on the rough snow before stopping. B) The heavy sled will slide farther on the rough snow than the light sled. C) The light sled will slide farther on the rough snow than the heavy sled. D) On the rough snow, the change in kinetic energy will be the same for both sleds. E) The friction from the snow will do the same amount of work on both sleds. Answer: C, D, E Var: 1 36) If a stone is dropped with an initial gravitational potential energy of 100 J but reaches the ground with a kinetic energy of only 75 J, this is a violation of the principle of conservation of energy. A) True B) False Answer: B Var: 1 37) If the units of your answer are kg ∙ m2/s3, which of the following types of quantities could your answer be? (There could be more than one correct choice.) A) kinetic energy B) potential energy C) force D) power E) work Answer: D Var: 1

38) Two cyclists who weigh the same and have identical bicycles ride up the same mountain, both starting at the same time. Joe rides straight up the mountain, and Bob rides up the longer road that has a lower grade. Joe gets to the top before Bob. Ignoring friction and wind resistance, which one of the following statements is true? A) The amount of work done by Joe is equal to the amount of work done by Bob, but the average power exerted by Joe is greater than that of Bob. B) The amount of work done by Joe is greater than the amount of work done by Bob, and the average power exerted by Joe is greater than that of Bob. C) Bob and Joe exerted the same amount of work, and the average power of each cyclist was also the same. D) The average power exerted by Bob and Joe was the same, but Joe exerted more work in getting there. Answer: A Var: 1 39) Jill does twice as much work as Jack does and in half the time. Jill's power output is A) the same as Jack's power output. B) one-fourth as much as Jack's power output. C) one-half as much as Jack's power output. D) twice Jack's power output. E) four times Jack's power output. Answer: E Var: 1 40) A force produces power P by doing work W in a time T. What power will be produced by a force that does six times as much work in half as much time? A) 12P B) 6P C) P D) P E)

Answer: A Var: 1 41) In a game of pool, the white cue ball hits the #5 ball and stops, while the #5 ball moves away with the same velocity as the cue ball had originally. Both balls have the same mass. This type of collision is A) somewhat inelastic. B) elastic. C) completely inelastic. Answer: B Var: 1

42) In the figure, determine the character of the collision. The masses of the blocks, and the velocities before and after, are shown. The collision is

A) perfectly elastic. B) partially inelastic. C) completely inelastic. D) characterized by an increase in kinetic energy. E) not possible because momentum is not conserved. Answer: A Var: 1 43) In the figure showing an isolated system, determine the character of the collision. The masses of the blocks, and the velocities before and after, are shown. The collision is

A) perfectly elastic. B) partially inelastic. C) completely inelastic. D) characterized by an increase in kinetic energy. E) not possible because momentum is not conserved. Answer: E Var: 1 44) In the figure, determine the character of the collision. The masses of the blocks, and the velocities before and after, are shown. The collision is

A) perfectly elastic. B) partially inelastic. C) completely inelastic. D) characterized by an increase in kinetic energy. E) not possible because momentum is not conserved. Answer: C Var: 1

45) An egg falls from a bird's nest in a tree and feels no effects due to the air. As it falls, A) only its kinetic energy is conserved. B) only its momentum is conserved. C) both its kinetic energy and its momentum are conserved. D) only its mechanical energy is conserved. E) both its mechanical energy and its momentum are conserved. Answer: D Var: 1 46) If a quantity you calculated had units of kg ∙ m/s, what type of quantity could it be? (There could be more than one correct choice.) A) momentum B) kinetic energy C) work D) impulse E) force Answer: A, D Var: 1 47) A railroad car collides with and sticks to an identical railroad car that is initially at rest. After the collision, the kinetic energy of the system A) is the same as before. B) is half as much as before. C) is one third as much as before. D) is one fourth as much as before. E) is one quarter as much as before. Answer: B Var: 1 48) A rubber ball bounces off of a wall with an initial speed v and reverses its direction so its speed is v right after the bounce. As a result of this bounce, which of the following quantities of the ball are conserved? (There could be more than one correct choice.) A) the kinetic energy of the ball B) the momentum of the ball C) both the momentum and the kinetic energy of the ball D) None of the above quantities are conserved. Answer: A Var: 1

49) On a horizontal frictionless air table, a puck runs into an ideal horizontal spring that is fastened to the table. The puck compresses the spring by 15 cm before coming to rest. During the compression process, which quantities are conserved? A) only the momentum of the puck B) only the kinetic energy of the puck C) only the mechanical energy (kinetic plus potential) of the puck D) the momentum and the mechanical energy of the puck E) the momentum and the kinetic energy of the puck Answer: C Var: 1 50) Two objects of different mass have equal, non-zero kinetic energies. Which object has the greater magnitude momentum? A) the heavier object B) the lighter object C) They both have the same magnitude momentum. Answer: A Var: 1 51) Two objects of different masses have momentum of equal, non-zero magnitude. Which object has more kinetic energy? A) the heavier object B) the lighter object C) They both have the same kinetic energy. Answer: B Var: 1 52) If you want to double the kinetic energy of a gas molecule, by what factor must you increase its momentum? A) B) 2 C) 2 D) 4 E) 16 Answer: A Var: 1 53) If you want to double the momentum of a gas molecule, by what factor must you increase its kinetic energy? A) B) 2 C) 2 D) 4 E) 16 Answer: D Var: 1 15 Copyright © 2019 Pearson Education, Inc.

54) A firecracker explodes in midair and breaks up into many fragments. Which of the following statements are true regarding conditions immediately before and immediately after the explosion: I. The total momentum of the fragments is equal to the original momentum of the firecracker. II. The total kinetic energy of the fragments is equal to the original kinetic energy of the firecracker. A) Statement I only B) Statement II only C) Both Statement I and Statement II D) Neither statement is true. Answer: A Var: 1 55) Consider a uniform hoop of radius R and mass M rolling without slipping. Which is larger, its translational kinetic energy or its rotational kinetic energy? A) Translational kinetic energy is larger. B) Rotational kinetic energy is larger. C) Both are equal. D) You need to know the speed of the hoop to tell. Answer: C Var: 1 56) Consider a solid uniform sphere of radius R and mass M rolling without slipping. Which form of its kinetic energy is larger, translational or rotational? A) Translational kinetic energy is larger. B) Rotational kinetic energy is larger. C) Both are equal. D) You need to know the speed of the sphere to tell. Answer: A Var: 1 57) A solid sphere and a solid cylinder, both uniform and of the same mass and radius, roll without slipping at the same forward speed. It is correct to say that the total kinetic energy of the solid sphere is A) more than the total kinetic energy of the cylinder. B) less than the total kinetic energy of the cylinder. C) equal to the total kinetic energy of the cylinder. Answer: B Var: 1

58) A disk and a hoop of the same mass and radius are released at the same time at the top of an inclined plane. If both are uniform, which one reaches the bottom of the incline first if there is no slipping? A) The hoop B) The disk C) Both reach the bottom at the same time. Answer: B Var: 1 59) A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii. If the three of them are released simultaneously at the top of an inclined plane and do not slip, which one will reach the bottom first? A) sphere B) pipe C) cylinder D) The pipe and cylinder arrive together before the sphere. E) They all reach the bottom at the same time. Answer: A Var: 1 60) A disk, a hoop, and a solid sphere are released at the same time at the top of an inclined plane. They are all uniform and roll without slipping. In what order do they reach the bottom? A) disk, hoop, sphere B) hoop, sphere, disk C) sphere, disk, hoop D) hoop, disk, sphere Answer: C Var: 1 61) A small uniform disk and a small uniform sphere are released simultaneously at the top of a high inclined plane, and they roll down without slipping. Which one will reach the bottom first? A) the one of smallest diameter B) the one of greatest mass C) the disk D) the sphere E) They will reach the bottom at the same time. Answer: D Var: 1

62) Suppose a uniform solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on A) the mass of the sphere. B) the radius of the sphere. C) both the mass and the radius of the sphere. D) neither the mass nor the radius of the sphere. Answer: D Var: 1 63) Suppose a solid uniform sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on A) the mass of the sphere. B) the radius of the sphere. C) both the mass and the radius of the sphere. D) neither the mass nor the radius of the sphere. Answer: B Var: 1 64) A uniform ball is released from rest on a no-slip surface, as shown in the figure. After reaching its lowest point, the ball begins to rise again, this time on a frictionless surface. When the ball reaches its maximum height on the frictionless surface, it is

A) higher than when it was released. B) lower than when it was released. C) at the same height from which it was released. D) It is impossible to tell without knowing the mass of the ball. E) It is impossible to tell without knowing the radius of the ball. Answer: B Var: 1 65) Two uniform solid balls, one of radius R and mass M, the other of radius 2R and mass 8M, roll down a high incline. They start together from rest at the top of the incline. Which one will reach the bottom of the incline first? A) The small sphere arrives first. B) Both reach the bottom at the same time. C) The large sphere arrives first. Answer: B Var: 1 18 Copyright © 2019 Pearson Education, Inc.

66) If the answer to your calculation has units of kg ∙ m2/s, what type of quantity could it be? (There could be more than one correct choice). A) force B) work C) angular momentum D) linear momentum E) power F) rotational kinetic energy G) moment of inertia H) torque Answer: C Var: 1 67) If the answer to your calculation has units of kg ∙ m2/s2 , what type of quantity could it be? (There could be more than one correct choice.) A) force B) work C) angular momentum D) linear momentum E) power F) rotational kinetic energy G) moment of inertia H) torque Answer: B, F, H Var: 1 68) A ballet dancer is spinning in the middle of a horizontal frictionless stage. Which of the following things could he change by moving parts of his body or his whole body? (There could be more than one correct choice.) A) his total kinetic energy B) his translational kinetic energy C) his rotational kinetic energy D) his angular momentum E) his moment of inertia F) the horizontal component of his linear momentum G) the location of his center of mass (or center of gravity) Answer: A, B, C, D, E, G Var: 1

69) A spinning ice skater on extremely smooth ice is able to control the rate at which she rotates by pulling in her arms. Which of the following statements are true about the skater during this process? (There could be more than one correct choice.) A) Her angular momentum remains constant. B) Her moment of inertia remains constant. C) Her kinetic energy remains constant. D) She is subject to a constant non-zero torque. Answer: A Var: 1 70) When is the angular momentum of a system constant? A) Only when its total kinetic energy is constant. B) Only when no net external force acts on the system. C) Only when the linear momentum and the energy are constant. D) Only when no net external torque acts on the system. E) Only when the moment of inertia is constant. Answer: D Var: 1 10.2 Problems 1) How much work would a child do while pulling a 12-kg wagon a distance of force? A) 95 J B) 52 J C) 67 J D) 109 J Answer: A Var: 33

with a

2) A child does 350 J of work while pulling a box from the ground up to his tree house at a steady speed with a light rope. The tree house is above the ground. What is the mass of the box? A) 8.9 kg B) 5.3 kg C) 6.7 kg D) 8.0 kg Answer: A Var: 50+

3) You carry a 7.0-kg bag of groceries above the ground at constant speed across a room. How much work do you do on the bag in the process? A) 0.00 J B) 82 J C) 185 J D) 157 J Answer: A Var: 50+ 4) It requires 0.30 kJ of work to fully drive a stake into the ground. If the average resistive force on the stake by the ground is how long is the stake? A) 0.36 m B) 0.23 m C) 0.31 m D) 0.41 m Answer: A Var: 50+ 5) A crane lifts a 425 kg steel beam vertically upward a distance of How much work does 2 the crane do on the beam if the beam accelerates upward at 1.8 m/s ? Neglect frictional forces. A) 4.7 × 105 J B) 2.7 × 105J C) 3.2 × 105 J D) 4.0 × 105 J Answer: A Var: 50+ 6) A traveler pulls on a suitcase strap at an angle 36° above the horizontal. If of work are done by the strap while moving the suitcase a horizontal distance of what is the tension in the strap? A) 46 N B) 37 N C) 52 N D) 56 N Answer: A Var: 50+ 7) A 500-kg elevator is pulled upward with a constant force of 5500 N for a distance of 50.0 m. (a) What is the work done by the 5500-N force? (b) What is the work done by gravity? (c) What is the net work done on the elevator? Answer: (a) 275 Kj (b) -245 kJ (c) 30.0 kJ Var: 1

8) A 30-N box is pulled upward 6.0 m along the surface of a ramp that rises at 37° above the horizontal. How much work does gravity do on the box during this process? A) -1100 J B) -110 J C) -140 J D) -180 J E) 120 J Answer: B Var: 3 9) Matthew pulls his little sister Sarah along the horizontal ground in a wagon. He exerts a force on the wagon of 60.0 N at an angle of 37.0° above the horizontal. If he pulls her a distance of 12.0 m, how much work does Matthew do? A) 185 J B) 433 J C) 575 J D) 720 J Answer: C Var: 1 10) Find the net work done by friction on a box that moves in a complete circle of radius on a uniform horizontal floor. The coefficient of kinetic friction between the floor and the box is 0.25, and the box weighs A) 190 J B) 0 J C) 1800 J D) 370 J Answer: A Var: 50+ 11) A 2.0-kg object is lifted vertically through 3.00 m by a 150-N force. How much work is done on the object by gravity during this process? Answer: -59 J Var: 1

12) A person carries a 25.0-N rock through the path shown in the figure, starting at point A and ending at point B. The total time from A to B is 1.50 min. How much work did gravity do on the rock between A and B?

A) 625 J B) 20.0 J C) 275 J D) 75 J E) 0 J Answer: E Var: 1 13) A person carries a 2.00-N pebble through the path shown in the figure, starting at point A and ending at point B. The total time from A to B is 6.75 min. How much work did gravity do on the rock between A and B?

A) 30.0 J B) -30.0 J C) -56.0 J D) 56.0 J E) -36.0 J Answer: B Var: 1 14) A stone with a mass of 1.0 kg is tied to the end of a light string which keeps it moving in a circle with a constant speed of 4.0 m/s on a perfectly smooth horizontal tabletop. The radius of the path is 0.60 m. How much work does the tension in the string do on the stone as it makes one-half of a complete circle? A) 100 J B) 3.8 J C) 0 J D) 40 J E) 80 J Answer: C Var: 1 23 Copyright © 2019 Pearson Education, Inc.

15) How fast must a 6.0-kg cat run to have a kinetic energy of 150 J? Answer: 7.1 m/s Var: 1 16) How much kinetic energy does a 0.30-kg stone have if it is thrown at A) 290 J B) 580 J C) 440 J D) 510 J Answer: A Var: 19 17) An object hits a wall and bounces back with half of its original speed. What is the ratio of the final kinetic energy to the initial kinetic energy of the object? A) 1/2 B) 1/4 C) 1/8 D) 1/16 Answer: B Var: 1 18) A 1000-kg car is moving at 15 km/h. If a 2000-kg truck has 23 times the kinetic energy of the car, how fast is the truck moving? A) 51 km/h B) 72 km/h C) 61 km/h D) 41 km/h Answer: A Var: 50+ 19) What is the minimum energy needed to change the speed of a 1600-kg sport utility vehicle from 15.0 m/s to 40.0 m/s? A) 1.10 MJ B) 10.0 kJ C) 20.0 kJ D) 40.0 kJ E) 0.960 MJ Answer: A Var: 1

20) A 1.0-kg object moving in a certain direction has a kinetic energy of 2.0 J. It hits a wall and comes back with half its original speed. What is the kinetic energy of this object at this point? A) 2.0 J B) 1.0 J C) 0.50 J D) 0.25 J E) 4.0 J Answer: C Var: 1 21) How much work must be done by frictional forces in slowing a 1000-kg car from rest? A) 3.41 × 105 J B) 2.73 × 105 J C) 4.09 × 105 J D) 4.77 × 105 J Answer: A Var: 50+

22) When a car of mass accelerates from 10.0 m/s to some final speed, 4.00 × 105 J of work are done. Find this final speed. A) 28.0 m/s B) 22.4 m/s C) 25.2 m/s D) 30.8 m/s Answer: A Var: 50+ 23) A 10-kg dog is runnng with a speed of 5.0 m/s. What is the minimum work required to stop the dog in 2.40 s? A) 50 J B) 75 J C) 100 J D) 125 J Answer: D Var: 4 24) How large a net force is required to accelerate a 1600-kg SUV from rest to a speed of 25 m/s in a distance of 200 m? A) 1600 N B) 0 N C) 200 N D) 400 N E) 2500 N Answer: E Var: 1 25 Copyright © 2019 Pearson Education, Inc.

25) A 100-N force has a horizontal component of 80 N and a vertical component of 60 N. The force is applied to a cart on a level frictionless floor. The cart starts from rest and moves 2.0 m horizontally along the floor due to this force. What is the cart's final kinetic energy? A) 200 J B) 160 J C) 120 J D) zero Answer: B Var: 1 26) A 1000-kg car experiences a net force of 9500 N while slowing down from 30 m/s to How far does it travel while slowing down? A) 34 m B) 31 m C) 37 m D) 41 m Answer: A Var: 50+ 27) A stone initially moving at 8.0 m/s on a level surface comes to rest due to friction after it travels 11 m. What is the coefficient of kinetic friction between the stone and the surface? A) 0.13 B) 0.25 C) 0.30 D) 0.43 E) 0.80 Answer: C Var: 1 28) A sled having a certain initial speed on a horizontal surface comes to rest after traveling 10 m. If the coefficient of kinetic friction between the object and the surface is 0.20, what was the initial speed of the object? A) 9.8 m/s B) 6.3 m/s C) 3.6 m/s D) 7.2 m/s E) 8.9 m/s Answer: B Var: 5

29) On an alien planet, an object moving at 4.0 m/s on the horizontal ground comes to rest after traveling a distance of 10 m. If the coefficient of kinetic friction between the object and the surface is 0.20, what is the value of g on that planet? A) 4.0 m/s2 B) 6.0 m/s2 C) 8.0 m/s2 D) 10 m/s2 E) 12 m/s2 Answer: A Var: 1 30) A driver, traveling at 22 m/s, slows down her 2000 kg truck to stop for a red light. What work is done on the truck by the friction force of the road? A) -2.2 × 104 J B) -4.4 × 104 J C) -4.8 × 105 J D) -9.7 × 105 J Answer: C Var: 1 31) The kinetic friction force that a horizontal surface exerts on a 60.0-kg object is 50.0 N. If the initial speed of the object is 25.0 m/s, what distance will it slide before coming to a stop? A) 15.0 m B) 30.0 m C) 375 m D) 750 m Answer: C Var: 1 32) A stone is moving on a rough level surface. It has 24 J of kinetic energy, and the friction force on it is a constant 0.50 N. What is the maximum distance it can slide? A) 2.0 m B) 12 m C) 24 m D) 48 m Answer: D Var: 1

33) In a ballistics test, a 28-g bullet pierces a sand bag that is thick. If the initial bullet velocity was and it emerged from the sandbag moving at what was the magnitude of the friction force (assuming it to be constant) that the bullet experienced while it traveled through the bag? A) 130 N B) 38 N C) 13 N D) 1.3 N Answer: A Var: 50+ 34) A certain car traveling at 34.0 mph skids to a stop in 29 meters from the point where the brakes were applied. In approximately what distance would the car have stopped had it been going 105.4 mph? A) 279 m B) 158 m C) 90 m D) 51 m E) 29 m Answer: A Var: 50+ 35) How high a hill would a 75-kg hiker have to climb to increase her gravitational potential energy by 10,000 J? Answer: 14 m Var: 1 36) You do 116 J of work while pulling your sister back on a fritctionless swing, whose chain is long, until the swing makes an angle of 32.0° with the vertical. What is your sister's mass? A) 15.3 kg B) 13.0 kg C) 17.6 kg D) 19.0 kg Answer: A Var: 50+ 37) A tennis ball bounces on the floor three times, and each time it loses 23.0% of its energy due to heating. How high does it bounce after the third time, if we released it from the floor? A) 180 cm B) 18 cm C) 180 mm D) 240 cm Answer: A Var: 50+

38) A 10-kg mass, hung by an ideal spring, causes the spring to stretch 2.0 cm. What is the spring constant (force constant) for this spring? A) 5.0 N/cm B) 49 N/cm C) 0.20 N/cm D) 20 N/m E) 0.0020 N/cm Answer: B Var: 1 39) An ideal spring stretches by 21.0 cm when a 135-N object is hung from it. If instead you hang a fish from this spring, what is the weight of a fish that would stretch the spring by A) 199 N B) 91 N C) 145 N D) 279 N Answer: A Var: 50+ 40) An ideal spring has a spring constant (force constant) of 2500 N/m. is stretched 4.0 cm. How much work is required to stretch the spring by 4.0 cm? A) 4.0 J B) 0.00 J C) 1.0 J D) 3.0 J E) 2.0 J Answer: E Var: 1 41) You want to store 1,000 J of energy in an ideal spring when it is compressed by only 2.5 cm. What should be the force constant (spring constant) of this spring? Answer: 3.2 × 106 m/m Var: 1 42) If 4.0 J of work are performed in stretching an ideal spring with a spring constant (force constant) of 2500 N/m, by what distance is the spring stretched? A) 3.2 cm B) 3.2 m C) 0.3 cm D) 5.7 m E) 5.7 cm Answer: E Var: 1

43) If the work done to stretch an ideal spring by 4.0 cm is 6.0 J, what is the spring constant (force constant) of this spring? A) 300 N/m B) 3000 N/m C) 3500 N/m D) 7500 N/m E) 6000 N/m Answer: D Var: 1 44) An ideal spring has a spring constant (force constant) of 60 N/m. How much energy does it store when it is stretched by 1.0 cm? A) 0.0030 J B) 0.30 J C) 60 J D) 600 J Answer: A Var: 1 45) How much work is required to stretch an ideal spring of spring constant (force constant) 40 N/m from x = 0.20 m to x = 0.25 m if the unstretched position is at x = 0.00 m? A) 0.45 J B) 0.80 J C) 1.3 J D) 0.050 J Answer: A Var: 1 46) An ideal spring with a force constant (spring constant) of 15 N/m is initially compressed by 3.0 cm from its uncompressed position. How much work is required to compress the spring an additional 4.0 cm? A) 0.0068 J B) 0.012 J C) 0.024 J D) 0.030 J Answer: D Var: 1 47) It takes 87 J of work to stretch an ideal spring from 1.4 m to 2.9 m from equilibrium. What is the value of the spring constant (force constant) of this spring? A) 27 N/m B) 77 N/m C) 52 N/m D) 39 N/m Answer: A Var: 50+ 30 Copyright © 2019 Pearson Education, Inc.

48) An ideal spring with a spring constant (force constant) of equilibrium to 2.9 m. How much work is done in the process? A) 93 J B) 186 J C) 47 J D) 121 J Answer: A Var: 14

is stretched from

49) A rock falls from a vertical cliff that is 4.0 m tall and experiences no significant air resistance as it falls. At what speed will its gravitational potential energy (relative to the base of the cliff) be equal to its kinetic energy? A) 3.1 m/s B) 4.4 m/s C) 6.3 m/s D) 8.9 m/s E) 13 m/s Answer: C Var: 1 50) A block slides down a frictionless inclined ramp and experiences no significant air resistance. If the ramp angle is 17.0° above the horizontal and the length of the surface of the ramp is find the speed of the block as it reaches the bottom of the ramp, assuming it started sliding from rest at the top. A) 10.7 m/s B) 114 m/s C) 7.57 m/s D) 19.6 m/s Answer: A Var: 50+ 51) A prankster drops a water balloon from the top of a building. If the balloon is traveling at 29.1 m/s when it strikes a window ledge that is 1.5 m above the ground, how tall is the building? Neglect air resistance. A) 45 m B) 43 m C) 46 m D) 47 m Answer: A Var: 1

52) A spring-loaded dart gun is used to shoot a dart straight up into the air, and the dart reaches a maximum height of 24 meters. The same dart is shot up a second time from the same gun, but this time the spring is compressed only half as far (compared to the first shot). How far up does the dart go this time (neglect all friction and assume the spring is ideal)? A) 6.0 m B) 12 m C) 3.0 m D) 48 m Answer: A Var: 1 53) A bead is moving with a speed of 20 m/s at position A on the track shown in the figure. This track is friction-free, and there is no appreciable air resistance. What is the speed of the bead at point C?

A) 0 m/s B) 34 m/s C) 69 m/s D) 20 m/s E) We cannot solve this problem without knowing the mass of the bead. Answer: B Var: 1 54) A frictionless simple pendulum, with a small but dense 4.4-kg mass at the end and a length of 75 cm, is released from rest at an angle of 50° with the vertical. (a) To what height above its lowest point does the mass swing on the other side? (b) What is the speed of the mass at the bottom of the swing? Answer: (a) 27 cm (b) 2.3 m/s Var: 1

55) The figure shows a famous roller coaster ride. You can ignore friction. If the roller coaster leaves point Q from rest, what is its speed at the top of the 25-m peak (point S)?

A) 10 m/s B) 22 m/s C) 44 m/s D) 62 m/s E) 120 m/s Answer: B Var: 1 56) What is the minimum energy needed to lift a 1.0-kg rocket to a height of 200 km and to give it a speed of 8.0 km/s at that height? (Neglect air resistance and the small decrease in g over that distance.) A) 34 TJ B) 34 kJ C) 34 MJ D) 34 GJ E) 34 J Answer: C Var: 1 57) Assuming negligible friction, what spring constant (force constant) would be needed by the spring in a "B-B gun" to fire a 10-g pellet to a height of 100 m if the spring is initially compressed by 0.10 m? A) 20 N/cm B) 200 N/m C) 2000 N/cm D) 0.0020 N/m Answer: A Var: 1 58) If a spring-operated gun can shoot a pellet to a maximum height of 100 m on Earth, how high could the pellet rise if fired on the Moon, where g = 1.6 m/s2? A) 17 m B) 160 m C) 3.6 km D) 100 m E) 610 m Answer: E Var: 1 33 Copyright © 2019 Pearson Education, Inc.

59) A 60-kg skier pushes off the top of a frictionless hill with an initial speed of 4.0 m/s. How fast will she be moving after dropping 10 m in elevation? Air resistance is negligible. A) 0.20 km/s B) 15 m/s C) 10 m/s D) 0.15 km/s E) 49 m/s Answer: B Var: 1 60) A toy rocket that weighs 10 N blasts straight up from ground level with an initial kinetic energy of 40 J. At the exact top of its trajectory, its total mechanical energy is 140 J. To what vertical height above the ground does it rise, assuming no air resistance? A) 1.0 m B) 10 m C) 14 m D) 24 m Answer: B Var: 1 61) A 5.0-N projectile leaves the ground with a kinetic energy of 220 J. At the highest point in its trajectory, its kinetic energy is 120 J. To what vertical height, relative to its launch point, did it rise if there was no air resistance? A) 44 m B) 24 m C) 20 m D) 10 m E) It is impossible to determine the height without knowing the angle of launch. Answer: C Var: 1 62) In the figure, a ball hangs by a very light string. What is the minimum speed of the ball at the bottom of its swing (point B) in order for it to reach point A, which is 1.0 m above the bottom of the swing?

63) A 1500-kg car moving at 25 m/s hits an initially uncompressed horizontal ideal spring with spring constant (force constant) of 2.0 × 106 N/m. What is the maximum distance the spring compresses? A) 0.17 m B) 0.34 m C) 0.51 m D) 0.68 m Answer: D Var: 1 64) A small but dense 2.0-kg stone is attached to one end of a very light rod that is 1.2 m long. The other end of the rod is attached to a frictionless pivot. The rod is raised until it is vertical, with the stone above the pivot. The rod is released and the stone moves in a vertical circle with no air resistance. What is the tension in the rod as the stone moves through the bottom of the circle? A) 20 N B) 40 N C) 60 N D) 80 N E) 100 N Answer: E Var: 1 65) In a museum exhibit of a simple pendulum, a very small but dense 6.0-kg ball swings from a very light 2.5-m wire. The ball is released from rest when the pendulum wire makes a 65° angle with the vertical, and it swings in a circular arc with no appreciable friction or air resistance. What is the tension in the wire just as the ball swings through its lowest position? A) 11 N B) 59 N C) 68 N D) 130 N E) 0 N Answer: D Var: 1 66) A roller coaster starting from rest descends 35 meters in its initial drop and then rises 23 meters when it goes over the first hill, which has a circular shape over the top. If a passenger at the top of the hill feels an apparent weight equal to one-half of her normal weight, what is the radius of curvature of the first hill? Neglect any frictional losses. Answer: 48 m Var: 1

67) A roller coaster starts from rest at a height h at the left side of a loop-the-loop, as shown in the figure. It is not attached to the track in anyway, and there is no friction from the track or from air resistance. If the radius of the loop is R = 6.0 m, what is the minimum height h for which the roller coaster will not fall off the track at the top of the loop?

A) 21 m B) 18 m C) 15 m D) 12 m E) 8.5 m Answer: C Var: 1 68) A stone is released from rest at a height h at the left side of a loop-the-loop, as shown in the figure. There is no appreciable friction from the track or from air resistance. If the radius of the loop is R, what is the minimum height h for which the stone will not fall off the track at the top of the loop?

A) 3.5 R B) 2.5 R C) 2.0 R D) R E) 3.0 R Answer: B Var: 1

69) A small 1.4-N stone slides down a frictionless bowl, starting from rest at the rim. The bowl itself is a hemisphere of radius 75 cm. Just as the stone reaches the bottom of the bowl, how hard is the bowl pushing on it? A) 0.70 N B) 1.4 N C) 2.8 N D) 4.2 N E) 5.6 N Answer: D Var: 1 70) A 30-N stone is dropped from a height of 10 m and strikes the ground with a speed of 13 m/s. What average force of air friction acted on the stone as it fell? A) 4.1 N B) 2.9 N C) 0.13 kN D) 7.2 N E) 1.2 N Answer: A Var: 1 71) A 60-kg skier starts from rest from the top of a 50-m high slope. If the work done by friction is -6.0 kJ, what is the speed of the skier on reaching the bottom of the slope? A) 17 m/s B) 24 m/s C) 28 m/s D) 31 m/s Answer: C Var: 1 72) A 7.5-kg otter slides down a hill, starting from rest at the top. The sloping surface of the hill is 8.8 m long, and the top is 6.5 m above the base. If the speed of the otter at the bottom of the hill is 9.2 m/s, how much energy was lost to nonconservative forces on the hill? Answer: 160 J Var: 1

73) An object with a mass of 10 kg is initially at rest at the top of a frictionless inclined plane that rises at 30° above the horizontal. At the top, the object is initially 8.0 m from the bottom of the incline, as shown in the figure. When the object is released from this position, it eventually stops at a distance d from the bottom of the inclined plane along a horizontal surface, as shown. The coefficient of kinetic friction between the horizontal surface and the object is 0.20, and air resistance is negligible. Find the distance d.

A) 5.0 m B) 10 m C) 15 m D) 20 m E) 25 m Answer: D Var: 1 74) On a planet where g = 10.0 m/s2 and air resistance is negligible, a sled is at rest on a rough inclined hill rising at 30° as shown in the figure. The object is allowed to move and it stops on a rough horizontal surface, at a distance of 4.0 m from the bottom of the hill. The coefficient of kinetic friction on the hill is 0.40. What is the coefficient of kinetic friction between the horizontal surface and the sled?

A) 0.10 B) 0.20 C) 0.31 D) 0.40 E) 0.60 Answer: C Var: 1

75) A 0.12-kg block is held in place against the spring by a 35-N horizontal external force. The external force is removed, and the block is projected with a velocity when it separates from the spring, as shown in the figure. The block descends a ramp and has a velocity at the bottom of the ramp. The track is frictionless between points A and B. The block enters a rough section at B, extending to E. The coefficient of kinetic friction between the block and the rough surface is 0.26. The block moves on to D, where it stops. By how many centimeters was the spring initially compressed?

A) 0.49 cm B) 0.26 cm C) 0.18 cm D) 0.99 cm E) 0.67 cm Answer: A Var: 50+ 76) As shown in the figure, a 1.45-kg block is held in place against the spring by a 21-N horizontal external force. The external force is removed, and the block is projected with a velocity as it separates from the spring. The block descends a ramp and has a velocity at the bottom. The track is frictionless between points A and B. The block enters a rough section at B, extending to E. The coefficient of kinetic friction between the block and the rough surface is 0.29. The velocity of the block is at C. The block moves on to D, where it stops. How much work is done by friction between points B and C?

77) A 0.46-kg block is held in place against the spring by a 30-N horizontal external force. The external force is removed, and the block is projected with a velocity upon separation from the spring, as shown in the figure. The block descends a ramp and has a velocity at the bottom. The track is frictionless between points A and B. The block enters a rough section at point B, extending to E. The coefficient of kinetic friction between the block and the rough surface is 0.38. The velocity of the block is at point C. The block moves on to D, where it stops. What distance does the block travel between points B and D?

A) 0.30 m B) 0.039 m C) 0.26 m D) 0.40 m E) 0.60 m Answer: A Var: 50+ 78) A sled is moving along a horizontal surface with a speed of 5.7 m/s. It then slides up a rough hill having a slope of 11° above the horizontal. The coefficient of kinetic friction between the sled and the surface of the hill is 0.26. How far along the surface does the block travel up the incline? Answer: 3.7 m Var: 1 79) The figure shows two crates, each of mass m = 24 kg, that are connected by a very light wire. The coefficient of kinetic friction between the crate on the inclined surface and the surface itself is 0.31. Find the speed of the crates after they have moved 1.6 m starting from rest.

Answer: 1.9 m/s Var: 1

80) As shown in the figure, a 4.0-kg block is moving at 5.0 m/s along a horizontal frictionless surface toward an ideal spring that is attached to a wall. After the block collides with the spring, the spring is compressed a maximum distance of 0.68 m. What is the speed of the block when the spring is compressed to only one-half of the maximum distance?

Answer: 4.3 m/s Var: 1 81) How many joules of energy are used by a 2.0 hp motor that runs for 1.0 hour? (1 hp = 746 W) Answer: 5.4 MJ Var: 1 82) A child pulls on a wagon with a force of If the wagon moves a total of what is the average power delivered by the child? A) 17 W B) 21 W C) 22 W D) 26 W Answer: A Var: 29

83) How many joules of energy are used by a 1.0-hp motor that runs for 1.0 hour? (1 hp = 746 W) A) 3.6 kJ B) 2.7 MJ C) 45 kJ D) 4.8 J Answer: B Var: 1 84) A 1500-kg car accelerates from rest to 25 m/s in 7.0 s. What is the average power delivered by the engine? (1 hp = 746 W) A) 60 hp B) 70 hp C) 80 hp D) 90 hp Answer: D Var: 1

85) At what minimum rate is a 60.0-kg boy using energy when, in 8.00 s, he runs up a flight of stairs that is 10.0-m high? A) 75.0 W B) 735 W C) 4.80 kW D) 48.0 W Answer: B Var: 1 86) If electricity costs 7.06¢/kW∙h, how much would it cost you to run a per day for A) $0.95 B) $0.14 C) $1.62 D) $2.66 Answer: A Var: 50+

stereo system

87) A 1321-kg car climbs a 5.0° slope at a constant speed of Assuming that air resistance may be neglected, at what rate (in kW) must the engine deliver energy to the drive wheels of the car? A) 25 kW B) 287 kW C) 38 kW D) 48 kW Answer: A Var: 50+ 88) A typical incandescent light bulb consumes 75 W of power and has a mass of 30 g. You want to save electrical energy by dropping the bulb from a height great enough so that the kinetic energy of the bulb when it reaches the floor will be the same as the energy it took to keep the bulb on for 1.0 hour. From what height should you drop the bulb, assuming no air resistance and constant g? Answer: 920 km Var: 1 89) What is the net power needed to change the speed of a 1600-kg sport utility vehicle from 15.0 m/s to 40.0 m/s in 4.00 seconds? A) 100 kW B) 10.0 kW C) 140 kW D) 14.0 kW E) 275 kW Answer: E Var: 1

90) Water flows over a waterfall that is 20 m high at the rate of 4.0 × 104 kg/s. If this water powers an electric generator with a 40% efficiency, how many watts of electric power can be supplied? Answer: 3.1 MW Var: 1 91) A certain battery charger uses 12 W of power. At 6.0 cents per kilowatt-hour, how much does it cost to charge batteries for a full day? A) 28¢ B) 1.4¢ C) 75¢ D) 1.7¢ E) 2.3¢ Answer: D Var: 1 92) A family goes on vacation for one week but forgets to turn off an electric fan that consumes electricity at the rate of 200 W. If the cost of electricity is 12.0¢/kW∙h how much does it cost (to the nearest penny) to run the fan for the week? Answer: $4.03 Var: 1 93) Suppose you left five 100-W light bulbs burning in the basement for two weeks. If electricity costs 10.0¢/kW∙h, (a) how much did the electricity cost (to the nearest dollar) to leave those bulbs on, and (b) how many joules of electrical energy did they consume? Answer: (a) $17 (b) 6.05 × 108 J Var: 1 94) Rita raises a 10kg package to a height of 2.5 m in 2.0 s. (a) How much work did she do on the package? (b) How much power was expended on the package? (c) If she were to raise the package in 1.0 s rather than 2.0 s, how do the work and power change? Answer: (a) 0.25 Kj (b) 0.12 kW (c) the same work, but the power doubles Var: 1 95) In a physical fitness program, a woman who weighs 510 N runs up four flights of stairs in 22 s. Each flight rises 3.1 m. (1 hp = 746 W) (a) What is her total change in potential energy? (b) What was the minimum average power (in watts) that she expended during the 22 s? (c) What horsepower motor would be required to generate the same power? Answer: (a) 6.3 kJ (b) 290 W (c) 0.39 hp Var: 1

96) A sand mover at a quarry lifts 2,000 kg of sand per minute a vertical distance of 12 m. The sand is initially at rest and is discharged at the top of the sand mover with speed 5.0 m/s into a loading chute. What minimum power must be supplied to this machine? A) 520 W B) 3.9 kW C) 6.7 kW D) 4.3 kW E) 1.1 kW Answer: D Var: 1 97) A 100%-efficient engine is being used to raise a 89-kg crate vertically upward at a steady rate. If the power output of the engine is 1620 W, how long does it take the engine to lift the crate a vertical distance of 18.7 m? Friction in the system is negligible. Answer: 10 s Var: 1 98) A block of mass m = 4.4 kg, moving on frictionless surface with a speed makes a sudden perfectly elastic collision with a second block of mass M, as shown in the figure. The second block is originally at rest. Just after the collision, the 4.4-kg block recoils with a speed of What is the mass M of the second block?

A) 7.7 kg B) 0 kg C) 0 kg D) 0 kg E) 0 kg Answer: A Var: 50+

99) A block of mass m = 3.6 kg, moving on a frictionless surface with a speed makes a sudden perfectly elastic collision with a stationary block of mass M, as shown in the figure. Just after the collision, the 3.6-kg block recoils with a speed of What is the speed V of the other block?

A) 6.6 m/s B) 8.0 m/s C) 9.3 m/s D) 10.7 m/s E) 12.0 m/s Answer: A Var: 50+ 100) A 320-g air track cart traveling at 1.25 m/s suddenly collides elastically with a stationary 270-g cart. What is the speed of the 270-g cart just after the collision? A) 0.678 m/s B) 0.106 m/s C) 1.36 m/s D) 1.14 m/s E) 2.72 m/s Answer: C Var: 1 101) A 320-g air track cart traveling at 1.25 m/s suddenly collides elastically with a stationary 270-g cart. What is the speed of the 320-g cart just after the collision? A) 0.68 m/s B) 0.11 m/s C) 0.21 m/s D) 1.4 m/s E) 1.1 m/s Answer: B Var: 1 102) A 550-g ball traveling at 8.0 m/s undergoes a sudden head-on elastic collision with a 250-g ball traveling toward it also at 8.0 m/s. What is the speed of the 250-g mass just after the collision? A) 15 m/s B) 8.0 m/s C) 4.0 m/s D) 14 m/s E) 0 m/s Answer: D Var: 6 45 Copyright © 2019 Pearson Education, Inc.

103) A 340-g air track cart traveling at 1.25 m/s suddenly collides elastically with a stationary 300-g cart. What is the speed of the 300-g cart just after the collision? A) 0.0781 m/s B) 1.33 m/s C) 0.625 m/s D) 1.25 m/s E) 0.664 m/s Answer: B Var: 1 104) A proton of mass m is at rest when it is suddenly struck head-on by an alpha particle (which consists of 2 protons and 2 neutrons) moving at speed v. If the collision is perfectly elastic, what speed will the alpha particle have after the collision? (Assume the neutron's mass is equal to the proton's mass.) A) zero B) 2v/3 C) 3v/5 D) 5v/3 Answer: C Var: 1 105) A 50-g ball moving at 10 m/s in the +x direction suddenly collides head-on with a stationary ball of mass 100 g. If the collision is perfectly elastic, what is the velocity of each ball immediately after the collision? A) -3.3 m/s, +6.7 m/s B) +3.3 m/s, -6.7 m/s C) -6.7 m/s, +3.3 m/s D) +6.7 m/s, -3.3 m/s Answer: A Var: 1 106) In a perfectly elastic collision, a 400-g ball moving toward the east at 3.7 m/s suddenly collides head-on with a 200 g ball sitting at rest. (a) Determine the velocity of the first ball just after the collision. (b) Determine the velocity of the second ball just after the collision. (c) Is kinetic energy conserved in this collision? How do you know? Answer: (a) 1.2 m/s toward the east (b) 4.9 m/s toward the east (c) Yes, it is an elastic collision. Var: 1

107) A 0.140-kg baseball is dropped from rest from a height of 2.20 m above the ground and experiences negligible air resistance as it falls. It rebounds to a height of 1.60 m. What change in the ball's momentum occurs as it rebounds from the ground? A) 0.117 kg ∙ m/s upwards B) 0.117 kg ∙ m/s downwards C) 1.70 kg ∙ m/s upwards D) 0.350 kg ∙ m/s upwards E) 0.350 kg ∙ m/s downwards Answer: C Var: 5 108) A 0.32-kg ball is moving horizontally at 30 m/s just before suddenly bouncing off a wall Just after the bounce, it is moving horizontally at 25 m/s but in the opposite direction. (a) What is the magnitude of the change in momentum of the ball during the bounce? (b) What percentage of the ball's original kinetic energy was lost in the collision? Answer: (a) 18 N ∙ s (b) 31% Var: 1 109) In a police ballistics test, a 2.00-g bullet suddenly hits and becomes embedded in a 5.00-kg wood block which is hanging from a 1.20-m long string. This causes the block to swing through an arc of 3.50°. What was the speed of the bullet just before it hit the block? A) 16.7 m/s B) 524 m/s C) 25.3 m/s D) 262 m/s E) 789 m/s Answer: B Var: 5 110) A block of mass m = 9.0 kg and speed V and is behind a block of mass M = 27 kg and speed of as shown int the figure. The surface is frictionless, and the blocks suddenly collide and couple. After the collision, the blocks have a common speed of 0.90 m/s. How much kinetic energy of the blocks is lost due to the collision?

A) 8.6 J B) 2.0 J C) 4.6 J D) 11 J E) 31 J Answer: A Var: 50+

111) As shown in the figure, a bullet of mass 0.010 kg moving horizontally suddenly strikes a block of wood of mass 1.5 kg that is suspended as a pendulum. The bullet lodges in the wood, and together they swing upward a vertical distance of 0.40 m. The length of the string is 2.0 m. What was the speed of the bullet just before it struck the wooden block?

A) 67 m/s B) 250 m/s C) 370 m/s D) 420 m/s E) 650 m/s Answer: D Var: 1 112) An 8.0-g bullet is suddenly shot into a 4.0-kg block that is at rest on a frictionless horizontal surface, as shown in the figure. The bullet remains lodged in the block. The block then moves against a spring and compresses it by 3.7 cm. The force constant (spring constant) of the spring is What was the initial speed v of the bullet?

A) 460 m/s B) 440 m/s C) 480 m/s D) 500 m/s E) 520 m/s Answer: A Var: 50+

113) An 8.0-g bullet is suddenly shot into a 4.0-kg block, at rest on a frictionless horizontal surface, as shown in the figure. The bullet remains lodged in the block. The block then moves against a spring and compresses it by 8.9 cm. The force constant (spring constant) of the spring is What is the magnitude of the impulse on the block (including the bullet inside) due to the spring during the entire time interval during which the block compresses the spring?

A) 13 N ∙ s B) 12 N ∙ s C) 10 N ∙ s D) 8.3 N ∙ s E) 6.7 N ∙ s Answer: A Var: 50+ 114) In a police rifle test, a 15-g bullet traveling 213 m/s in a vertical direction suddenly buries itself in a 2.4-kg block of wood at rest directly above it. As a result, the bullet-block combination moves vertically upward. (a) Determine the velocity of the bullet-block combination just after the impact. (b) Determine the maximum height reached by the bullet/block combination. (c) Is kinetic energy conserved in this collision? Answer: (a) 1.3 m/s (b) 0.089 m (c) No, this is an inelastic collision. Var: 1 115) In a certain nuclear reactor, neutrons suddenly collide with deuterons, which have twice the mass of neutrons. In a head-on elastic collision with a stationary deuteron, what fraction of the initial kinetic energy of a neutron is transferred to the deuteron? A) 1/2 B) 1/3 C) 3/4 D) 5/6 E) 8/9 Answer: E Var: 1 116) In a certain nuclear reactor, neutrons suddenly collide with carbon nuclei, which have 12 times the mass of neutrons. In a head-on elastic collision with a stationary carbon nucleus, what fraction of its initial speed does the neutron have after the collision? A) 11/12 B) 1/12 C) 11/13 D) 5/6 E) 10/13 Answer: C Var: 1 49 Copyright © 2019 Pearson Education, Inc.

117) An object initially at rest suddenly explodes in two fragments of masses and that move in opposite directions. If the speed of the first fragment is find the internal energy of the explosion. A) 30 J B) 30 kJ C) 38 J D) 38 kJ Answer: A Var: 50+ 118) Two simple pendulums of equal length l = 0.45 m are suspended from the same point. The pendulum bobs are small solid steel spheres. The first bob is drawn back to make a 35° angle with the vertical, while the other one is left hanging at rest. If the first bob has a mass of 0.25 kg and the second has a mass of how high will the second bob rise above its initial position when struck elastically by the first bob after it is released? A) 3.3 cm B) 2.7 cm C) 3.9 cm D) 4.4 cm Answer: A Var: 50+ 119) On a frictionless horizontal surface, a 1.50-kg mass traveling at 3.50 m/s suddenly collides with and sticks to a 3.00-kg mass that is initially at rest, as shown in the figure. This system then runs into an ideal spring of force constant (spring constant) 50.0 N/cm. (a) What will be the maximum compression distance of the spring? (b) How much mechanical energy is lost during this process? During which parts of the process (the collision and compression of the spring) is this energy lost?

Answer: (a) 3.50 cm, (b) 6.13 J during the inelastic collision Var: 1 120) A baseball pitcher is employing a ballistic pendulum to determine the speed of his fastball. A lump of clay is suspended from a cord 2.0 m long. When the pitcher throws his fastball aimed directly at the clay, the ball suddenly becomes embedded in the clay and the two swing up to a maximum height of 0.080 m. If the mass of the baseball is 0.21 kg, find the speed of the pitched ball. Answer: 21 m/s Var: 50+

121) A 1200-kg pick-up truck traveling south at 15 m/s suddenly collides with a 750-kg car that is traveling east. The two vehicles stick together and slide along the road after colliding. A highway patrol officer investigating the accident determines that the final position of the wreckage after the collision is 25 m, at an angle of 50° south of east, from the point of impact. She also determines that the coefficient of kinetic friction between the tires and the road at that location was 0.40. What was the speed of the car just before the collision? A) 20 m/s B) 4.8 m/s C) 14 m/s D) 23 m/s E) 17 m/s Answer: D Var: 1 122) A uniform solid cylinder with a radius of 10 cm and a mass of 3.0 kg is rotating about its center with an angular speed of 33.4 rpm. What is its kinetic energy? A) 0.18 J B) 0.092 J C) 0.96 J D) 1.1 J E) 17 J Answer: B Var: 1 123) What is the kinetic energy of a 120-cm thin uniform rod with a mass of 450 g that is rotating about its center at 3.60 rad/s? A) 0.350 J B) 4.20 J C) 0.700 J D) 0.960 J E) 2.10 J Answer: A Var: 1 124) To drive a typical car at 40 mph on a level road for one hour requires about 3.2 × 107 J of energy. Suppose we tried to store this much energy in a spinning, solid, uniform, cylindrical flywheel. A large flywheel cannot be spun too fast or it will fracture. If we used a flywheel of diameter 1.2 m and mass 400 kg, what angular speed would be required to store 3.2 × 107 J? A) 1800 rad/s B) 3600 rad/s C) 940 rad/s D) 530 rad/s E) 5500 rad/s Answer: C Var: 1

125) The L-shaped object shown in the figure consists of three small masses connected by extremely light rods. Assume that the masses shown are accurate to three significant figures. How much work must be done to accelerate the object from rest to an angular speed of 3.25 rad/s (a) about the x-axis, (b) about the y-axis?

Answer: (a) 34.2 J Var: 1

(b) 173 J

126) The L-shaped object shown in the figure consists of three small masses connected by thin uniform rods, each rod of mass 3.00 kg. Assume that the masses shown are accurate to three significant figures. How much work must be done to accelerate the object from rest to an angular speed of 3.25 rad/s about the y-axis?

Answer: 403 J Var: 1 127) A futuristic design for a car is to have a large flywheel within the car to store kinetic energy. The flywheel is a solid uniform disk of mass 370 kg with a radius of 0.50 m, and it can rotate up to Assuming all of this stored kinetic energy could be transferred to the linear speed of the car, find the maximum attainable speed of the car. Answer: 221 m/s Var: 50+ 128) A small ball is tied to one end of a light 2.5-m wire, and the other end of the wire is hooked to the ceiling. A person pulls the ball to the side until the wire makes an angle of 35° with the plane of the ceiling and then gently releases it. What is the angular speed of the ball, in rad/s, as it swings through its lowest point? Answer: 1.8 rad/s Var: 1

129) While spinning down from 500 rpm to rest, a flywheel does of work. This flywheel is in the shape of a solid uniform disk of radius 1.2 m. What is the mass of this flywheel? A) 4.0 kg B) 3.4 kg C) 4.6 kg D) 5.2 kg Answer: A Var: 50+ 130) A solid uniform sphere of mass 120 kg and radius 1.7 m starts from rest and rolls without slipping down an inclined plane of vertical height 5.3 m. What is the angular speed of the sphere at the bottom of the inclined plane? A) 5.1 rad/s B) 8.7 rad/s C) 9.7 rad/s D) 6.1 rad/s Answer: A Var: 1 131) A solid uniform disk of diameter 3.20 m and mass 42 kg rolls without slipping to the bottom of a hill, starting from rest. If the angular speed of the disk is 4.27 rad/s at the bottom, how high did it start on the hill? A) 3.57 m B) 2.68 m C) 3.14 m D) 4.28 m Answer: A Var: 1 132) A wheel having a moment of inertia of 5.00 kg ∙ m2 starts from rest and accelerates under a constant torque of 3.00 N ∙ m for 8.00 s. What is the wheel's rotational kinetic energy at the end of 8.00 s? A) 57.6 J B) 64.0 J C) 78.8 J D) 122 J Answer: A Var: 1

133) As shown in the figure, two blocks are connected by a light string that passes over a frictionless pulley having a moment of inertia of 0.0040 kg ∙ m2 and diameter 10 cm. The coefficient of kinetic friction between the table top and the upper block is 0.30. The blocks are released from rest, and the string does not slip on the pulley. How fast is the upper block moving when the lower one has fallen 0.60 m?

A) 1.2 m/s B) 5.4 m/s C) 3.2 m/s D) 2.0 m/s E) 1.4 m/s Answer: E Var: 1 134) A solid uniform ball with a mass of 125 g is rolling without slipping along the horizontal surface of a table with a speed of 4.5 m/s when it rolls off the edge and falls towards the floor, 1.1 m below. What is the rotational kinetic energy of the ball just before it hits the floor? A) 0.51 J B) 0.73 J C) 1.1 J D) 2.6 J E) This question cannot be answered without knowing the radius of the ball. Answer: A Var: 1 135) A string is wrapped tightly around a fixed pulley that has a moment of inertia of 0.0352 kg ∙ m2 and a radius of 12.5 cm. A mass of 423 g is attached to the free end of the string. With the string vertical and taut, the mass is gently released so it can descend under the influence of gravity. As the mass descends, the string unwinds and causes the pulley to rotate, but does not slip on the pulley. What is the speed of the mass after it has fallen through 1.25 m? A) 2.00 m/s B) 2.28 m/s C) 1.97 m/s D) 3.94 m/s E) 4.95 m/s Answer: C Var: 1

136) A string is wrapped tightly around a fixed frictionless pulley that has a moment of inertia of 0.0352 kg ∙ m2 and a radius of 12.5 cm. The string is pulled away from the pulley with a constant force of 5.00 N, causing the pulley to rotate. What is the speed of the string after it has unwound 1.25 m if the string does not slip on the pulley? A) 2.09 m/s B) 2.36 m/s C) 1.18m/s D) 3.18 m/s E) 4.95 m/s Answer: B Var: 1 137) An Atwood machine consists of a mass of 3.5 kg connected by a light string to a mass of 6.0 kg over a frictionless pulley with a moment of inertia of 0.0352 kg ∙ m2 and a radius of 12.5 cm. If the system is released from rest, what is the speed of the masses after they have moved through 1.25 m if the string does not slip on the pulley? A) 2.0 m/s B) 2.3 m/s C) 4.0 m/s D) 5.0 m/s E) 6.0 m/s Answer: B Var: 1 138) The figure shows two blocks connected by a light cord over a pulley. This apparatus is known as an Atwood's machine. There is no slipping between the cord and the surface of the pulley. The pulley itself has negligible friction and it has a radius of 0.12 m and a mass of 10.3 kg. We can model this pulley as a solid uniform disk. At the instant that the heavier block has descended 1.5 m starting from rest, what is the speed of the lighter block?

Answer: 2.4 m/s Var: 1

139) A pencil that is 15.7 cm long is released from a vertical position with the eraser end resting on a table. The eraser does not slip as it tips over. Treat the pencil like a uniform rod. What is the angular speed of the pencil just before it hits the table? A) 13.7 rad/s B) 7.23 rad/s C) 3.70 rad/s D) 24.5 rad/s E) 16.8 rad/s Answer: A Var: 1 140) A uniform solid disk is released from rest and rolls without slipping down an inclined plane that makes an angle of 25° with the horizontal. What is the forward speed of the disk after it has rolled 3.0 m, measured along the plane? A) 2.0 m/s B) 3.5 m/s C) 4.1 m/s D) 5.7 m/s E) 6.3 m/s Answer: C Var: 1 141) A solid uniform disk is rolling without slipping along a horizontal surface with a speed of 4.5 m/s when it starts up a ramp that makes an angle of 25° with the horizontal. What is the speed of the disk after it has rolled 3.0 m up as measured along the surface of the ramp? A) 4.0 m/s B) 1.9 m/s C) 2.1 m/s D) 6.8 m/s E) 8.0 m/s Answer: B Var: 1 142) A solid uniform sphere is rolling without slipping along a horizontal surface with a speed of 5.5 m/s when it starts up a ramp that makes an angle of 25° with the horizontal. What is the speed of the sphere after it has rolled 3.0 m up as measured along the surface of the ramp? A) 4.0 m/s B) 8.0 m/s C) 1.9 m/s D) 2.2 m/s E) 3.5 m/s Answer: E Var: 1

143) A hoop is rolling without slipping along a horizontal surface with a forward speed of 5.50 m/s when it starts up a ramp that makes an angle of 25.0° with the horizontal. What is the speed of the hoop after it has rolled 3.00 m up as measured along the surface of the ramp? A) 4.22 m/s B) 1.91 m/s C) 2.06 m/s D) 3.79 m/s E) 8.02 m/s Answer: A Var: 5 144) A hoop with a mass of 2.75 kg is rolling without slipping along a horizontal surface with a speed of 4.5 m/s when it starts down a ramp that makes an angle of 25° below the horizontal. What is the forward speed of the hoop after it has rolled 3.0 m down as measured along the surface of the ramp? A) 4.9 m/s B) 6.3 m/s C) 5.2 m/s D) 5.7 m/s E) 8.0 m/s Answer: D Var: 1 145) A hoop with a mass of 2.75 kg is rolling without slipping along a horizontal surface with a speed of 4.5 m/s when it starts down a ramp that makes an angle of 25° below the horizontal. What is the rotational kinetic energy of the hoop after it has rolled 3.0 m down as measured along the surface of the ramp? A) 34 J B) 22 J C) 45 J D) 62 J E) This question cannot be answered without knowing the radius of the hoop. Answer: C Var: 1 146) A solid uniform 3.33-kg disk has thin string of negligible mass wrapped around its rim, with one end of the string tied to the ceiling, as shown in the figure. The disk is released from rest, and as it falls, it turns as the string unwraps. At the instant its center has fallen 2.25 m, (a) how fast is the center moving, and (b) how much rotational kinetic energy does the disk have?

147) A solid uniform ball of mass 1.0 kg and radius 1.0 cm starts from rest and rolls down a 1.0m high ramp. There is enough friction on the ramp to prevent the ball from slipping as it rolls down. (a) What is the forward speed of the ball when it reaches the bottom of the ramp? (b) What would be the forward speed of the ball if there were no friction on the ramp? (c) Since the ball starts from the same height in both cases, why is the speed different? Answer: (a) 3.7 m/s (b) 4.4 m/s (c) With friction, some of the initial potential energy goes into rotational kinetic energy, leaving less for translational kinetic energy. Without friction, the ball does not rotate, so all the initial potential energy goes into translational kinetic energy. Var: 1 148) A solid ball of mass 1.0 kg and radius 10 cm rolls with a forward speed of 10 m/s when it comes to a hill. There is enough friction on the hill to keep the ball from slipping as it rolls up. (a) How high vertically up the hill can the ball roll before coming to rest? (b) How high vertically could the ball go if the hill were totally frictionless? (c) How is it that the ball can go higher with friction than without friction? Answer: (a) 7.1 m (b) 5.1 m (c) With friction, all the initial kinetic energy (translational and rotational) goes into potential energy. Without friction, only the translational kinetic energy goes into potential energy; the ball keeps spinning at the same rate as it goes up, even at the top. Var: 1 149) A ball in the shape of a uniform spherical shell (like a soccer ball) of mass 1.5 kg and radius 15 cm rolls down a 35° incline that is 6.0 m high, measured vertically. The ball starts from rest, and there is enough friction on the incline to prevent slipping of the ball. (a) How fast is the ball moving forward when it reaches the bottom of the incline, and what is its angular speed at that instant? (b) If there were no friction on the incline, how fast would the ball be moving forward and what would be its angular speed at the bottom? Answer: (a) 8.4 m/s, 56 rad/s (b) 11 m/s, 0 rad/s Var: 1 150) A solid uniform cylinder is rolling without slipping. What fraction of its kinetic energy is rotational? A) 1/3 B) 2/3 C) 1/2 D) 1/4 E) 3/4 Answer: A Var: 1

151) NASA puts a satellite into space that consists of two small 32-kg balls connected by a 12-m long light cable, as shown in the figure. The entire system is initially rotating at 4.0 rpm about an axis perpendicular to the cable at the center of mass. Motors in each mass reel out more cable so that the masses double their separation to 24 m. (a) What is the final rotational speed (in rpm) of the balls? (b) If the initial rotational kinetic energy of the system was K, what is the final rotational kinetic energy in terms of K?

Answer: (a) 1.0 rpm Var: 1

(b) K/4

152) A uniform ball with diameter of 10 cm rolls without slipping on a horizontal tabletop. The moment of inertia of the ball about an axis through its center is 2.2 × 10-3 kg ∙ m2, and the translational speed of its center is 0.45 m/s. (a) What is its angular speed of the ball about its center of mass? (b) What is the rotational kinetic energy of the ball? (c) What is the ball's angular momentum about its center of mass? Answer: (a) 9.0 rad/s (b) 0.089 J (c) 0.020 kg ∙ m2/s Var: 1 153) A solid wooden door, 90 cm wide by 2.0 m tall, has a mass of 35 kg. It is open and at rest. A small 500-g ball is thrown perpendicular to the door with a speed of 20 m/s and hits the door 60 cm from the hinged side, causing it to begin turning. The ball rebounds along the same line with a speed of 16.0 m/s relative to the ground. How much energy is lost during this collision? A) 30 J B) 16 J C) 15 J D) 13 J E) 4.8 J Answer: A Var: 1

College Physics: A Strategic Approach, 4e (Knight) Chapter 11 Using Energy 11.1 Conceptual Questions 1) Which two temperature changes are equivalent? A) 1 K = 1 F° B) 1 F° = 1 C° C) 1 C° = 1 K D) none of the above Answer: C Var: 1 2) The temperature in your classroom is closest to A) 68 K. B) 68°C. C) 50°C. D) 295 K. Answer: D Var: 1 3) A 10-L flask and a 1-L flask each contain two moles of ideal diatomic gas (but not the same gas) at 25°C. Which of the following statements about these gases must be true? (There could be more than one correct choice.) A) The internal (thermal) energy of the gas in both flasks is the same. B) The internal (thermal) energy of the gas in the larger flask is greater than the internal (thermal) energy of the gas in the smaller flask. C) The internal (thermal) energy of the gas in the smaller flask is greater than the internal (thermal) energy of the gas in the larger flask. D) The molecules in the larger flask have the same root-mean-square speed as those in the smaller flask. E) The molecules in the smaller flask have the same average kinetic energy per molecule as those in the larger flask. Answer: A, E Var: 1 4) A certain gas is compressed adiabatically. The amount of work done on the gas is 800 J. What is the change in the internal (thermal) energy of the gas? A) 800 J B) -800 J C) 400 J D) 0 J E) More information is needed to answer this question. Answer: A Var: 1

5) A cyclic process is carried out on an ideal gas such that it returns to its initial state at the end of a cycle, as shown in the pV diagram in the figure. If the process is carried out in a clockwise sense around the enclosed area, as shown on the figure, then the change of internal energy over the full cycle

A) is positive. B) is negative. C) is zero. D) cannot be determined from the information given. Answer: C Var: 1 6) A cyclic process is carried out on an ideal gas such that it returns to its initial state at the end of a cycle, as shown in the pV diagram in the figure. If the process is carried out in a clockwise sense around the enclosed area, as shown on the figure, then the magnitude of the enclosed area represents

A) the heat that flows out of the gas. B) the work done on the gas. C) the heat added to the gas. D) the work done by the gas. Answer: D Var: 1

7) A cyclic process is carried out on an ideal gas such that it returns to its initial state at the end of a cycle, as shown in the pV diagram in the figure. If the process is carried out in a counterclockwise sense around the enclosed area, as shown on the figure, then the magnitude of the enclosed area represents

A) the heat that flows out of the gas. B) the work done on the gas. C) the heat added to the gas. D) the work done by the gas. Answer: B Var: 1 8) Which one of the following is a true statement? A) The second law of thermodynamics is a consequence of the first law of thermodynamics. B) It is possible for heat to flow spontaneously from a hot body to a cold one or from a cold one to a hot one, depending on whether or not the process is reversible or irreversible. C) It is not possible to convert work entirely into heat. D) It is impossible to transfer heat from a cooler to a hotter body. E) All of these statements are false. Answer: E Var: 1 9) The second law of thermodynamics leads us to conclude that A) the total energy of the universe is constant. B) disorder in the universe is increasing with the passage of time. C) it is theoretically possible to convert heat into work with 100% efficiency. D) the average temperature of the universe is increasing with the passage of time. E) the entropy of the universe remains constant. Answer: B Var: 1 10) If the efficiency of a Carnot engine were to be 100%, the heat sink would have to be A) at absolute zero. B) at 0°C. C) at 100°C. D) infinitely hot. Answer: A Var: 1

11) A Carnot cycle consists of A) two adiabats and two isobars. B) two isobars and two isotherms. C) four isotherms. D) two adiabats and two isotherms. E) four adiabats. Answer: D Var: 1 12) An important feature of the Carnot cycle is that A) its efficiency can be 100%. B) its efficiency depends only on the absolute temperature of the hot reservoir used. C) its efficiency is determined by the temperatures of the hot and cold reservoirs between which it works and by the properties of the working substance used, and on nothing else. D) it is an example of an irreversible process that can be analyzed exactly without approximations. E) no engine can be more efficient than a Carnot engine operating between the same two temperatures. Answer: E Var: 1 13) Which of the following is a false statement? A) Entropy is a quantitative measure of disorder. B) The total entropy change in one cycle of a Carnot engine is zero. C) The entropy of an isolated system must be conserved (it remains constant). D) Entropy can be measured in units of J/K. Answer: C Var: 1 14) An ideal gas undergoes an isothermal expansion. During this process, its entropy A) decreases. B) remains unchanged. C) increases. D) cannot be predicted from the data given. Answer: C Var: 1 15) When water at 0°C freezes, the entropy of the water A) increases. B) decreases. C) remains constant. D) could either increase or decrease; it depends on other factors. Answer: B Var: 1

11.2 Problems 1) Express a body temperature 98.6°F in Celsius degrees. A) 37.0°C B) 45.5°C C) 66.6°C D) 72.6°C Answer: A Var: 1 2) Express -40°C in °F. A) -72°F B) -54°F C) -40°F D) 4.4°F Answer: C Var: 1 3) The temperature changes from 35°F during the night to 75°F during the day. What is the temperature change on the Celsius scale? A) 72 C° B) 40 C° C) 32 C° D) 22 C° Answer: D Var: 1 4) A temperature change of 20 C° corresponds to a Fahrenheit temperature change of A) 68 F°. B) 11 F°. C) 36 F°. D) 18 F°. Answer: C Var: 1 5) At what, if any, temperature are the numerical readings on the Fahrenheit and Celsius scales the same? A) -30° B) -40° C) -50° D) -60° E) They can never read the same because they are based on different zeroes. Answer: B Var: 1

6) Oxygen condenses into a liquid at approximately 90 K. What temperature, in degrees Fahrenheit, does this correspond to? A) -193°F B) -217°F C) -265°F D) -297°F Answer: D Var: 2 7) What is absolute zero on the (a) Celsius scale and (b) on the Fahrenheit scale? Answer: (a) -273°C (b) -460°F Var: 1 8) Nitrogen boils at -196°C. What is the corresponding temperature in the Fahrenheit scale? A) -315°F B) -196°F C) -346°F D) -290°F E) -321°F Answer: E Var: 1 9) The weather outside is frightful. The temperature is -22°F. What is the corresponding temperature in the Celsius scale? A) -35°C B) -30°C C) -22°C D) -20°C E) -12°C Answer: B Var: 1 10) Platinum melts at 3215°F. What is the corresponding temperature in the Kelvin scale? A) 2041 K B) 2135 K C) 2207 K D) 2296 K E) 3215 K Answer: A Var: 1

11) At room temperature, a typical person loses energy to the surroundings at the rate of 62 W. If this energy loss has to be made up by an equivalent food intake, how many kilocalories (food calories) does this person need to consume every day just to make up this heat loss? (1 cal = 4.186 J) A) 1000 kcal B) 1100 kcal C) 1300 kcal D) 1500 kcal E) 1600 kcal Answer: C Var: 1 12) A person running in place on an exercise machine for 10 min uses up 17 kcal (food calories). Another person exercises by repeatedly lifting two 2.5-kg weights a distance of 50 cm. How many repetitions of this exercise are equivalent to 10 minutes of running in place? Assume that the person uses negligible energy in letting down the weights after each lift. (1 cal = 4.186 J) A) 730 B) 1450 C) 1500 D) 2200 E) 2900 Answer: E Var: 1 13) A person consumes a snack containing 14 food calories (14 kcal). What is the power this food produces if it is to be "burned off" due to exercise in 6 hours? (1 cal = 4.186 J) A) 2.7 W B) 9763 W C) 0.6 W D) 0.0027 W Answer: A Var: 9 14) A monatomic ideal gas undergoes an isothermal expansion at 300 K, as the volume increased from to The final pressure is What is the change in the internal (thermal) energy of the gas during this process? (R = 8.31 J/mol ∙ K) A) 0.0 kJ B) 3.6 kJ C) 7.2 kJ D) -3.6 kJ E) -7.2 kJ Answer: A Var: 50+

15) The figure shows a pV diagram for a gas going through a cycle from A to B to C and back to A. From point A to point B, the gas absorbs 50 J of heat and finds its internal (thermal) energy has increased by 20 J. Going from B to C, the internal (thermal) energy decreases by 5.0 J. (a) How much work was done by the gas from A to B? (b) How much heat was absorbed by the gas from B to C? (c) How much work was done by the gas going from B to C?

Answer: (a) 30 J Var: 1

(b) -5.0 (i.e. released 5.0 J)

16) During an isothermal process, 5.0 J of heat is removed from an ideal gas. What is the change in internal (thermal) energy of the gas? A) 0 J B) 2.5 J C) 5.0 J D) 10 J Answer: A Var: 1 17) During an isothermal process, 5.0 J of heat is removed from an ideal gas. What is the work done by the gas in the process? A) 0 J B) 5.0 J C) -5.0 J D) -10 J Answer: C Var: 1 18) The work done on an ideal gas system in an isothermal process is -400 J. What is the change in internal (thermal) energy of the gas? A) 0 J B) -400 J C) 400 J D) 200 J Answer: A Var: 1

19) In an adiabatic compression, 200 J of work is done on a gas. What is the change in internal (thermal) energy of the gas during this compression? A) 0 J B) 100 J C) 200 J D) -200 J Answer: C Var: 1 20) An ideal gas undergoes an adiabatic process while doing 25 J of work. What is the change in the internal (thermal) energy of the gas? A) 0 J B) 25 J C) -25 J D) 50 J E) -50 J Answer: C Var: 1 21) In an isochoric process, the internal (thermal) energy of a gas decreases by 50 J. How much work is done by the gas during this process? A) 0 J B) 50 J C) -50 J D) 25 J E) -25 J Answer: A Var: 1 22) During an isochoric process, the internal (thermal) energy of a gas decreases by 50 J. How much heat is added to the gas during this process? A) 0 J B) 50 J C) -50 J D) 25 J E) -25 J Answer: C Var: 1

23) A fixed amount of an ideal monatomic gas is maintained at constant volume as it is cooled by 50 K. This feat is accomplished by removing 400 J of energy from the gas. How much work is done by the gas during this process? A) 0 J B) 400 J C) -400 J D) -200 J E) 200 J Answer: A Var: 1 24) An external heat source supplies heat to a system at a rate of 187 W as the system does work at a rate of 131 W. At what rate is the internal (thermal) energy of the system changing? A) -56 W B) 320 W C) 56 W D) 190 W E) -320 W Answer: C Var: 1 25) The gas in a perfectly insulated but flexible container does work at a rate of rate is the internal (thermal) energy of the gas changing? A) -13 W B) 13 W C) 0 W D) 6.5 W Answer: A Var: 50+

At what

26) A fluid in an insulated, flexible bottle is heated by a high resistance wire and expands. If of heat is applied to the system and it does of work, how much does the internal (thermal) energy of the fluid change? A) 4.0 kJ B) 14 kJ C) -4.0 kJ D) 45 kJ Answer: A Var: 50+

27) The figure shows a pV diagram of a gas for a complete cycle. During part bc of the cycle, 1190 J of heat flows into a system, and at the same time the system expands against a constant external pressure of as its volume increases from to Calculate the change in internal (thermal) energy of the system during part bc of the cycle. If the change is nonzero, be sure to indicate whether the change is positive or negative.

Answer: -3010 J Var: 50+ 28) An athlete doing push-ups performs 650 kJ of work and loses 425 kJ of heat. What is the change in the internal (thermal) energy of the athlete? A) -225 kJ B) -1075 kJ C) 1075 kJ D) 225 kJ E) 276 kJ Answer: B Var: 1 29) An ideal gas undergoes the process a→b→c→a shown in the pV diagram. The heat gained by the gas in process a→b is 546 J, while in process the gas loses 62.0 J of heat. In process a→b the gas performs of work, while in process c→a 223 J of work is done on the gas. How much heat is gained by the gas in process c→a?

A) -397 J B) -62 J C) 223 J D) 18 J E) -236 J Answer: A Var: 5

30) An ideal gas undergoes the process a→b→c→a shown in the pV diagram. In the figure, Pa = Pc = 240 kPa, Vb = Vc = 40 L, Va = 15 L, and Pb = 400 kPa. How much heat is gained by the gas in this a→b→c→a process?

A) 1000 J B) 1500 J C) 2000 J D) 2500 J E) 3000 J Answer: C Var: 1 31) A 40.0-L container is divided into two equal parts by a rubber membrane. One half of the container has 1.50 moles of an ideal monatomic gas at 250 K, and the other half is a vacuum. The container is well insulated, so there is no exchange of heat with the surroundings. The membrane breaks, and eventually the gas reaches a new equilibrium condition occupying the entire volume. What is the final temperature of the gas? A) 100 K B) 125 K C) 157 K D) 180 K E) 250 K Answer: E Var: 5 32) A cylinder contains 8.8 moles of ideal gas, initially at a temperature of 126°C. The cylinder is provided with a frictionless piston, which maintains a constant pressure of on the gas. The gas is cooled until its temperature has decreased to For the gas The ideal gas constant is R = 8.314 J/mol ∙ K. For this process, calculate: (a) the work done by gas (b) the net change in the internal (thermal) energy of the gas (c) the heat transferred to the gas. Answer: (a) -7200 J (b) -12,000 J (c) -19,000 J Var: 50+

33) An expandable container holds 2.30 mole of helium, He, gas with an initial pressure of 770 kPa and an initial volume of 2.10 L. The gas expands isothermally to a final pressure of 350 kPa. How much heat is gained by the gas during this process? (R = 8.31 J/mol ∙ K) A) 1280 J B) 792 J C) 685 J D) 1370 J E) 1700 J Answer: A Var: 5 34) A compression, at a constant pressure of 140 kPa, is performed on 4.0 moles of an ideal monatomic gas for which CV = 3/2 R. The compression reduces the volume of the gas from to What is the change in the internal (thermal) energy of the gas during this process? (R = 8.31 J/mol ∙ K) A) -29 kJ B) -49 kJ C) 29 kJ D) 49 kJ E) 0 kJ Answer: A Var: 50+ 35) An expansion process on an ideal diatomic ideal gas for which CV = 5/2 R has a linear path between the initial and final coordinates on a pV diagram. The coordinates of the initial state are: the pressure is the volume is and the temperature is The final pressure is and the final temperature is What is the change in the internal (thermal) energy of the gas, during this process? (R = 8.31 J/mol ∙ K) A) -2900 J B) -1700 J C) 2900 J D) 1700 J E) 0 J Answer: A Var: 50+ 36) A cylinder contains 1.50 moles of an ideal monatomic gas that is initially at a temperature of 317 K. If the gas gains 2730 J of heat and performs 780 J of work, what is its final temperature? (R = 8.31 J/mol ∙ K) A) 359 K B) 421 K C) 526 K D) 687 K E) 756 K Answer: B Var: 5 13 Copyright © 2019 Pearson Education, Inc.

37) A cylinder contains 10 moles of an ideal gas at a temperature of 300 K. The gas is compressed at constant pressure until the final volume equals 0.77 times the initial volume. The molar heat capacity at constant volume of the gas is 24.0 J/mol ∙ K and R = 8.31 J/mol ∙ K . How much heat is absorbed by the gas during this process? (R = 8.31 J/mol ∙ K) A) -22 kJ B) -17 kJ C) 22 kJ D) 17 kJ E) -5.7 kJ Answer: A Var: 50+ 38) A cylinder contains 13 moles of an ideal gas at a temperature of 300 K. The gas is compressed at constant pressure until the final volume equal 0.70 times the initial volume. The molar heat capacity at constant volume of the gas is 24.0 J/mol ∙ K. What is the change in the internal (thermal) energy of the gas during this process? (R = 8.31 J/mol ∙ K) A) -28 kJ B) -38 kJ C) 28 kJ D) 38 kJ E) -9.7 kJ Answer: A Var: 50+ 39) A sealed rigid tank contains 29 moles of an ideal gas, at an initial temperature of The pressure of the gas is increased until the final pressure equals 1.90 times the initial pressure. The heat capacity at constant pressure of the gas is How much heat is absorbed by the gas during this process? (R = 8.31 J/mol ∙ K) A) 110 kJ B) 170 kJ C) 230 kJ D) -52 kJ E) 7.0 kJ Answer: A Var: 50+ 40) A sealed rigitd tank contains 30 moles of an ideal gas, at an initial temperature of The pressure of the gas is increased until the final pressure equals 1.40 times the initial pressure. The heat capacity at constant pressure of the gas is What is the change in the internal (thermal) energy of the gas during this process? (R = 8.31 J/mol ∙ K) A) 77 kJ B) 100 kJ C) 130 kJ D) -50 kJ E) -23 kJ Answer: A Var: 50+ 14 Copyright © 2019 Pearson Education, Inc.

41) A heat engine receives 7000 J of heat and loses 3000 J in each cycle. What is the efficiency of this engine? A) 57% B) 30% C) 70% D) 43% Answer: A Var: 3 42) A certain heat engine extracts 1.30 kJ of heat from a hot temperature reservoir and discharges 0.70 kJ of heat to a cold temperature reservoir. What is the efficiency of this engine? A) 46% B) 54% C) 86% D) 27% E) 13% Answer: A Var: 1 43) A heat engine with an efficiency of 30% performs 2500 J of work. How much heat is discharged to the lower temperature reservoir? A) 5800 J B) 8300 J C) 750 J D) 1400 J E) 7100 J Answer: A Var: 1 44) A heat engine has an efficiency of 35.0% and receives 150 J of heat per cycle. (a) How much work does it do in each cycle? (b) How much heat does it "waste" in each cycle? Answer: (a) 52.5 J (b) 97.5 J Var: 1 45) A heat engine absorbs 64 kcal of heat each cycle and exhausts 42 kcal. (a) What is the efficiency of this engine? (b) How much work does this engine do per cycle? Answer: (a) 34% (b) 22 kcal Var: 1 46) A certain automobile engine takes in 4.00 kJ of heat and performs 1.10 kJ of mechanical work in each cycle. (a) Calculate the engine's efficiency. (b) How much heat is "wasted" in each cycle? Answer: (a) 27.5% (b) 2.90 kJ Var: 1 15 Copyright © 2019 Pearson Education, Inc.

47) During each cycle, a heat engine takes in 4.0 J of heat, does 1.0 J of work, and expels 3.0 J of heat. What is its efficiency? Answer: 25% Var: 1 48) A heat engine absorbs 85.6 kJ of heat each cycle and exhausts 61.8 kJ. (a) What is the efficiency of the engine? (b) How much work does it do each cycle? Answer: (a) 27.8% (b) 23.8 kJ Var: 1 49) A heat engine has an efficiency of 31.4% and receives 8.72 kJ of heat per cycle. (a) How much work does it perform in each cycle? (b) How much heat does it exhaust in each cycle? Answer: (a) 2.74 Kj (b) 5.98 kJ Var: 1 50) A nuclear power plant has an actual efficiency of 33%. If of energy are released from fission, how much electric power does the power plant produce? A) 0.063 MW B) 6.3 MW C) 25 MW D) 0.25 MW Answer: A Var: 50+ 51) The figure shows a pV diagram for a cycle of a heat engine for which QH = 59 J. What is the thermal efficiency of the engine?

A) 17% B) 34% C) 8.5% D) 14% Answer: A Var: 50+

52) A gas follows the pV trajectory shown in Figure 16.2. How much work is done per cycle by the gas if The gas in a heat engine follows the cycle shown in the pV diagram. How much work does this engine do each cycle if p0 =

A) 220 J B) 440 J C) 870 J D) 1100 J Answer: A Var: 50+ 53) An ideal Carnot heat engine operates between reservoirs at 1740 K and In each cycle, 260 J of heat energy is rejected to the low temperature reservoir. In each cycle, how much mechanical work W is performed by the engine? Answer: 2760 J Var: 50+ 54) An ideal Carnot engine is operated between a hot and a cold reservoir. The temperature difference between the two reservoirs is 284°C. If the efficiency of this ideal engine is 24.0%, find the temperature of the cold reservoir in degrees Celsius. Answer: 626°C Var: 50+ 55) An ideal Carnot heat engine operates between A) 0.38 B) 0.62 C) 0.61 D) 1.61 Answer: A Var: 50+

and

What is its efficiency?

56) An ideal Carnot heat engine has an efficiency of 0.600. If it operates between a deep lake with a constant temperature of and a hot reservoir, what is the temperature of the hot reservoir? A) 735 K B) 490 K C) 470 K D) 784 K Answer: A Var: 50+ 57) An ideal Carnot engine extracts 529 J of heat from a high-temperature reservoir during each cycle, and rejects of heat to a low-temperature reservoir during the same cycle. What is the efficiency of the engine? A) 0.57 B) 1.35 C) 2.35 D) 0.7 Answer: A Var: 50+ 58) A heat engine having the maximum possible efficiency has an efficiency of 35.0% when operating between two heat reservoirs. If the temperature of the hot reservoir is 700 K, what is the temperature of the cold reservoir? A) 200 K B) 245 K C) 350 K D) 455 K E) 600 K Answer: D Var: 1 59) A heat engine having the maximum possible efficiency has an efficiency of 25% when operating between two heat reservoirs. If the temperature of the cold reservoir is 300 K, what is the temperature of the hot reservoir? A) 350 K B) 375 K C) 400 K D) 450 K E) 500 K Answer: C Var: 1

60) The ocean thermal energy conversion project uses the surface water near tropical islands with a temperature of 20°C as the hot temperature reservoir, and the water at some depth, with a temperature of 5.0°C, as the cold temperature reservoir for a heat engine. What is the maximum possible efficiency of an engine running between those two temperatures? A) 4.7% B) 5.1% C) 7.9% D) 15% E) 30% Answer: B Var: 1 61) For a certain ideal Carnot engine, the hot reservoir is 35 C° higher than the cold reservoir. If this engine is to have an efficiency of 20%, what must be the temperature of the hot reservoir? A) 70.0 K B) 140 K C) 175 K D) 210 K E) 245 K Answer: C Var: 1 62) An ideal Carnot engine has an efficiency of 83.0% and performs 4500 J of work every cycle. How much energy is discharged to the lower temperature reservoir every cycle? A) 920 J B) 830 J C) 740 J D) 3700 J E) 5400 J Answer: A Var: 1 63) One of the most efficient engines built so far has the following characteristics: The combustion chamber temperature is 1900°C, the exhaust temperature = 430°C, 7.0 × 109 cal of fuel produces 1.4 × 1010 J of work in one hour. (1 cal = 4.186 J) (a) What is the actual efficiency of this engine? (b) What is the power output of this engine? (c) What would be the maximum possible efficiency for an engine using the same temperature extremes? Answer: (a) 48% (b) 3.9 MW (c) 68% Var: 1

64) A coal-fired plant generates 600 MW of electric power. The plant uses 4.8 × 106 kg of coal each day, and the heat of combustion of coal is 3.3 × 107 J/kg. The steam that drives the turbines is at a temperature of 300°C, and the exhaust water is at 37°C. (a) What is the overall efficiency of the plant for generating electric power? (b) How much thermal energy is exhausted each day? (c) Using the same heat reservoirs, what is the maximum possible efficiency for a heat engine? Answer: (a) 33% (b) 1.1 × 1014 J (c) 46% Var: 1 65) Two ideal Carnot heat engines have the same efficiency. One operates between 5.0 × 102 K and 3.0 × 102 K, and the other between 4.0 × 102 K and some lower temperature. What is the lower temperature? A) 200 K B) 220 K C) 240 K D) 260 K E) 280 K Answer: C Var: 1 66) An ideal Carnot engine operates between a high temperature reservoir at and a river with water at If it absorbs of heat each cycle, how much work per cycle does it perform? A) 1642 J B) 2358 J C) 1483 J D) 2517 J Answer: A Var: 50+ 67) A real (non-Carnot) heat engine, operating between heat reservoirs at temperatures of 450 K and 270 K, performs 3.3 kJ of net work, and rejects 8.2 kJ of heat in a single cycle. (a) What is the thermal efficiency of this heat engine? (b) What is the maximum efficiency it could possibly have? Answer: (a) 0.29 (b) 0.40 Var: 1 68) An ideal Carnot engine operating between a warm reservoir of unknown temperature and a cold reservoir at has an efficiency of What is the temperature of the warm reservoir? A) 2.93 K B) 0.0500 K C) 106 K D) 0.0400 K Answer: A Var: 16 20 Copyright © 2019 Pearson Education, Inc.

69) An ideal Carnot engine operates between a warm reservoir at 233 K and a colder reservoir. During each cycle, this engine extracts of heat from the warm reservoir and does of work. What is the temperature of the colder reservoir? A) 171 K B) 62 K C) 47 K D) 67 K Answer: A Var: 50+ 70) What is the efficiency of an ideal Carnot engine operating between a reservoir in which ice and water coexist, and a reservoir in which water and steam coexist? The pressure is constant at 1.0 atm for both reservoirs. A) 27% B) 0.27% C) 100% D) 1.0% E) 15% Answer: A Var: 1 71) An ideal Carnot engine operating between a warm reservoir of unknown temperature and a cold reservoir at has an efficiency of What is the temperature of the warm reservoir? A) 1.98 K B) 0.180 K C) 157 K D) 0.160 K Answer: A Var: 16 72) The "hot shot" heat engine operating between 40°C and 380°C has an efficiency that is 60% of that of an ideal Carnot engine operating between the same temperatures. If the "hot shot" engine absorbs heat at a rate of 60 kW, at what rate does it exhaust heat? A) 36 kW B) 41 kW C) 57 kW D) 60 kW Answer: B Var: 1 73) An inventor tries to sell you his new heat engine that takes in 40 J of heat at 87°C on each cycle, expels 30 J at 27°C, and does 10 J of work. Would it be wise to invest in this engine? Back up your conclusion with numerical calculations. Answer: Save your money! He has claimed an efficiency of 25%, but the greatest possible efficiency for an engine operating between these temperatures is only 17%, for a Carnot engine. Var: 1 21 Copyright © 2019 Pearson Education, Inc.

74) A Carnot engine operates between two reservoirs with unknown temperatures. If the Carnot engine operates at efficiency, what is the ratio of the absolute temperatures of the reservoirs, Tc/Th? A) 0.33 B) 0.0012 C) 0.0025 D) 0.67 Answer: A Var: 42 75) A refrigerator has a performance coefficient (COP) of 1.15, and it extracts 7.95 J of heat from the cold reservoir during each cycle. (a) How much work is done on the gas in each cycle? (b) How much heat is exhausted into the hot reservoir in each cycle? Answer: (a) 6.91 J (b) 14.9 J Var: 1 76) During each cycle, a refrigerator removes 20.0 kJ of heat from the freezing compartment and ejects 24.0 kJ into a room. (a) How much work per cycle is required each cycle to run this refrigerator? (b) What is the coefficient of performance of this refrigerator? Answer: (a) 4.0 kJ (b) 5.0 Var: 1 77) Suppose that the Department of Energy develops a new reversible engine that has a coefficient of performance (COP) of 4.0 when operated as a refrigerator and a COP of 5.0 when operated as a heat pump. What is its thermal efficiency when operated as a heat engine doing work? A) 10% B) 20% C) 25% D) 45% E) 80% Answer: B Var: 1 78) During each cycle of operation, a refrigerator absorbs 230 J of heat from the freezer and expels 356 J of heat to the room. How much work input is required in each cycle? A) 712 J B) 586 J C) 460 J D) 126 J Answer: D Var: 1

79) A reversible engine takes in heat at a rate of 555 W and exhausts heat at 482 W. (a) How much power does it produce? (b) What is its efficiency? (c) If operated in reverse as a refrigerator, what would be its performance coefficient (COP)? Answer: (a) 73 W (b) 13.2% (c) 6.6 Var: 6 80) If the efficiency of a reversible engine is 28%, what is its COP (performance coefficient) operated (a) as a refrigerator, and (b) as a heat pump? Answer: (a) 2.6 (b) 3.6 Var: 6 81) A refrigerator has a coefficient of performance equal to 4.2. How much work must be done on the operating gas in the refrigerator in order to remove 250 J of heat from the interior compartment? A) 60 J B) 120 J C) 250 J D) 480 J E) 1050 J Answer: A Var: 1 82) An air conditioner with a coefficient of performance of 3.50 uses 30.0 kW of power to operate. What power is it discharging to the outdoors? A) 30.0 kW B) 75.0 kW C) 105 kW D) 135 kW E) 210 kW Answer: D Var: 1 83) An ideal reversible heat pump is taking heat from the outside air at -10.0°C and discharging it into the house at 18.0°C. What is the coefficient of performance of this heat pump? A) 10.4 B) 9.44 C) 0.644 D) 0.533 E) 0.0962 Answer: A Var: 1

84) An ideal Carnot air conditioner operates between an indoor temperature of 20°C and an outdoor temperature of 39°C. How much energy does it use to remove 2000 J of heat from the interior of the house? A) 105 J B) 130 J C) 780 J D) 520 J E) 340 J Answer: B Var: 1 85) During each cycle, the compressor in a certain ideal Carnot refrigerator performs 480 J of work to remove 150 J of heat from the interior of the refrigerator. How much heat do the coils behind the refrigerator discharge into the kitchen each cycle? A) 110 J B) 150 J C) 330 J D) 480 J E) 630 J Answer: E Var: 1 86) A Carnot air conditioner has a coefficient of performance of 17.0 and removes 72.0 MJ of heat from the interior of a house every hour. How much power does it consume? A) 1180 W B) 1320 W C) 520 kW D) 3.14 MW E) 1.25 MW Answer: A Var: 5 87) An ideal Carnot engine is operated as an air conditioner to cool a house in the summer. The air conditioner removes of heat per second from the house, and maintains the inside temperature at while the outside temperature is The power required to run the air conditioner under these operating conditions is closest to A) 3600 W. B) 4400 W. C) 5100 W. D) 5800 W. E) 6600 W. Answer: A Var: 50+

88) An ideal Carnot engine is operated as a heat pump to heat a room in the winter. The heat pump delivers heat to the room at the rate of 47 kJ per second and maintains the room at a temperature of 293 K when the outside temperature is 237 K. The power requirement to run the heat pump under these operating conditions is closest to A) 9000 W. B) 7100 W. C) 20,000 W. D) 15,000 W. E) 11,000 W. Answer: A Var: 1 89) An ideal Carnot refrigerator with a performance coefficient (COP) of 5.0 cools items inside of it to What is the high temperature needed to operate this refrigerator? A) 61° C B) 1395° C C) 6° C D) 30° C Answer: A Var: 50+ 90) A heat pump with a performance coefficient (COP) of 4.9 absorbs heat from the atmosphere at a rate of At what rate is work being done to run this heat pump? A) 6 kW B) 142 kW C) 113 kW D) 35 kW Answer: A Var: 50+ 91) A heat pump absorbs heat from the atmosphere at a rate of 30 kW. If work is being done to run this heat pump at a rate of 7.7 kW, what is the coefficient of performance (COP) of the heat pump? A) 3.9 B) 4.9 C) 2.9 D) 0.26 E) 22 Answer: B Var: 1

College Physics: A Strategic Approach, 4e (Knight) Chapter 12 Thermal Properties of Matter 12.1 Conceptual Questions 1) As shown in the figure, a bimetallic strip, consisting of metal G on the top and metal H on the bottom, is rigidly attached to a wall at the left. The coefficient of linear thermal expansion for metal G is greater than that of metal H. If the strip is uniformly heated, it will

A) curve upward. B) curve downward. C) remain horizontal, but get longer. D) remain horizontal, but get shorter. E) bend in the middle. Answer: B Var: 1 2) Consider a flat steel plate with a hole through its center as shown in the figure. When the temperature of the plate is increased, the hole will

A) expand only if it takes up more than half the plate's surface area. B) contract if it takes up less than half the plate's surface area. C) always contract as the plate expands into it. D) always expand with the plate. E) remain the same size as the plate expands around it. Answer: D Var: 1 3) The coefficient of linear expansion for aluminum is 1.8 × 10-6 K-1. What is its coefficient of volume expansion? A) 9.0 × 10-6 K-1 B) 5.8 × 10-18 K-1 C) 5.4 × 10-6 K-1 D) 3.6 × 10-6 K-1 E) 0.60 × 10-6 K-1 Answer: C Var: 1

4) Two metal spheres are made of the same material and have the same diameter, but one is solid and the other is hollow. If their temperature is increased by the same amount, A) the solid sphere becomes bigger than the hollow one. B) the hollow sphere becomes bigger than the solid one. C) the two spheres remain of equal size. D) the solid sphere becomes denser and the hollow one less dense. E) the solid sphere becomes less dense and the hollow one denser. Answer: C Var: 1 5) If you wanted to know how much the temperature of a particular piece of material would rise when a known amount of heat was added to it, which of the following quantities would be most helpful to know? A) initial temperature B) specific heat C) density D) coefficient of linear expansion E) thermal conductivity Answer: B Var: 1 6) A thermally isolated system is made up of a hot piece of aluminum and a cold piece of copper, with the aluminum and the copper in thermal contact. The specific heat capacity of aluminum is more than double that of copper. Which object experiences the greater magnitude gain or loss of heat during the time the system takes to reach thermal equilibrium? A) the aluminum B) the copper C) Neither one; both of them experience the same size gain or loss of heat. D) It is impossible to tell without knowing the masses. E) It is impossible to tell without knowing the volumes. Answer: C Var: 1 7) A thermally isolated system is made up of a hot piece of aluminum and a cold piece of copper, with the aluminum and the copper in thermal contact. The specific heat capacity of aluminum is more than double that of copper. Which object experiences the greater temperature change during the time the system takes to reach thermal equilibrium? A) the copper B) the aluminum C) Neither one; both of them experience the same size temperature change. D) It is impossible to tell without knowing the masses. E) It is impossible to tell without knowing the volumes. Answer: D Var: 1

8) Which one of the following quantities is the smallest unit of heat energy? A) calorie B) kilocalorie C) Btu D) joule Answer: D Var: 1 9) Object 1 has three times the specific heat capacity and four times the mass of Object 2. The two objects are given the same amount of heat. If the temperature of Object 1 changes by an amount ΔT, the change in temperature of Object 2 will be A) ΔT. B) ΔT. C) ΔT. D) 6ΔT. E) 12ΔT. Answer: E Var: 1 10) Object 1 has three times the specific heat capacity and four times the mass of Object 2. The two objects are heated from the same initial temperature, T0, to the same final temperature Tf. During this process, if Object 1 absorbs heat Q, the amount of heat absorbed by Object 2 will be A) 12Q. B) 6Q. C) Q. D) Q. E)

Answer: E Var: 1

11) The figure shows a graph of the temperature of a pure substance as a function of time as heat is added to it at a constant rate in a closed container. If LF is the latent heat of fusion of this substance and LV is its latent heat of vaporization, what is the value of the ratio LV/LF?

A) 5.0 B) 4.5 C) 7.2 D) 3.5 E) 1.5 Answer: D Var: 1 12) A solid cylindrical bar conducts heat at a rate of 25 W from a hot to a cold reservoir under steady state conditions. If both the length and the diameter of this bar are doubled, the rate at which it will conduct heat between these reservoirs will be A) 200 W B) 100 W C) 50 W D) 25 W E) 12.5 W Answer: C Var: 1 13) Two metal rods are to be used to conduct heat from a region at 100°C to a region at 0°C as shown in the figure. The rods can be placed in parallel, as shown on the left, or in series, as on the right. When steady state flow is established, the heat conducted in the series arrangement is

A) greater than the heat conducted with the rods in parallel. B) the same as the heat conducted with the rods in parallel. C) less than the heat conducted with the rods in parallel. Answer: C Var: 1 4 Copyright © 2019 Pearson Education, Inc.

14) An architect is interested in estimating the rate of heat loss, ΔQ/Δt, through a sheet of insulating material as a function of the thickness of the sheet. Assuming fixed temperatures on the two faces of the sheet and steady state heat flow, which one of the graphs shown in the figure best represents the rate of heat transfer as a function of the thickness of the insulating sheet?

A) A B) B C) C D) D E) E Answer: C Var: 1 15) On a cold day, a piece of metal feels much colder to the touch than a piece of wood. This is due to the difference in which one of the following physical properties of these materials? A) density B) specific heat C) emissivity D) thermal conductivity E) mass Answer: D Var: 1 16) If, with steady state heat flow established, you double the thickness of a wall built from solid uniform material, the rate of heat loss for a given temperature difference across the thickness will A) become one-half its original value. B) also double. C) become one-fourth its original value. D) become 1/ of its original value. E) become four times its original value. Answer: A Var: 1

17) The process in which heat flows by the mass movement of molecules from one place to another is known as A) conduction. B) convection. C) radiation. Answer: B Var: 1 18) An object having a fixed emissivity of 0.725 radiates heat at a rate of 10 W when it is at an absolute temperature T. If its temperature is doubled to 2T, at what rate will it now radiate? A) 20 W B) 40 W C) 80 W D) 160 W E) 320 W Answer: D Var: 1 19) If the absolute temperature of an object is tripled, the thermal power radiated by this object (assuming that its emissivity and size are not affected by the temperature change) will A) increase by a factor of 3. B) increase by a factor of 9. C) increase by a factor of 18. D) increase by a factor of 27. E) increase by a factor of 81. Answer: E Var: 1 20) By what primary heat transfer mechanism does the sun warm the earth? A) convection B) conduction C) radiation D) All of the above processes are equally important in combination. Answer: C Var: 1

21) Two containers of equal volume each hold samples of the same ideal gas. Container A has twice as many molecules as container B. If the gas pressure is the same in the two containers, the correct statement regarding the absolute temperatures TA and TB in containers A and B, respectively, is A) TA = TB. B) TA = 2TB. C) TA = TB. D) TA =

TB.

E) TA = TB. Answer: C Var: 1 22) Consider two equal-volume flasks of gas at the same temperature and pressure. One gas, oxygen, has a molecular mass of 32. The other gas, nitrogen, has a molecular mass of 28. What is the ratio of the number of oxygen molecules to the number of nitrogen molecules in these flasks? A) B) C) D) E) Answer: E Var: 1 23) An ideal gas is held in a container of volume V at pressure p. The rms speed of a gas molecule under these conditions is v. If now the volume and pressure are changed to 2V and 2p, the rms speed of a molecule will be A) v/2 B) v C) 2v D) 4v E) v/4 Answer: C Var: 1

24) A mole of diatomic oxygen molecules and a mole of diatomic nitrogen molecules are at STP. Which statements are true about these molecules? (There could be more than one correct choice.) A) Both gases have the same average molecular speeds. B) Both gases have the same number of molecules. C) Both gases have the same average kinetic energy per molecule. D) Both gases have the same average momentum per molecule. Answer: B, C Var: 1 25) The root-mean-square speed of the molecules of an ideal gas is v. The gas is now slowly compressed to one-half its original volume with no change in temperature. What is the rootmean-square speed of the molecules now? A) 4v B) 2v C) v/ D) v E) v/2 Answer: D Var: 1 26) A sample of an ideal gas is heated and its Kelvin temperature doubles. If the root-meansquare speed of its molecules was originally v, what is the new root-mean-square speed? A) 4v B) 2v C) v D) v/ E) v/4 Answer: C Var: 1 27) The absolute temperature of an ideal gas is directly proportional to which of the following quantities? A) the average speed of its molecules B) the average momentum of its molecules C) the average kinetic energy of its molecules D) the mass of its molecules E) It is proportional to all of the above quantities. Answer: C Var: 1

28) The absolute temperature of a gas is T. In order to double the rms speed of its molecules, what should be the new absolute temperature? A) 4T B) 2T C) T D) 8T E) 16T Answer: A Var: 1 29) Oxygen molecules are 16 times more massive than hydrogen molecules. At a given temperature, the average molecular kinetic energy of oxygen molecules, compared to that of hydrogen molecules, A) is greater. B) is less. C) is the same. D) cannot be determined without knowing the pressure and volume. Answer: C Var: 1 30) Oxygen molecules are 16 times more massive than hydrogen molecules. At a given temperature, how do their average molecular speeds compare? The oxygen molecules are moving A) four times faster than the hydrogen molecules. B) at 1/4 the speed of the hydrogen molecules. C) sixteen times faster than the hydrogen molecules. D) at 1/16 the speed of the hydrogen molecules. E) at 1/ the speed of the hydrogen molecules. Answer: B Var: 1 31) A fixed container holds oxygen and helium gases at the same temperature. Which of the following statements are correct? (There could be more than one correct choice.) A) The oxygen molecules have the greater average kinetic energy. B) The helium molecules have the greater average kinetic energy. C) The oxygen molecules have the greater speed. D) The helium molecules have the greater speed. E) The helium molecules have the same average kinetic as the oxygen molecules. Answer: D, E Var: 1

32) For an ideal gas, A) CP = CV for all ideal gases. B) CP > CV for all ideal gases. C) CP < CV for all ideal gases. D) it depends on whether the gas is monatomic or diatomic. Answer: B Var: 1 33) For an ideal gas, A)

= 1 for all ideal gases.

< 1 for all monatomic and diatomic gases.

> 1 for all monatomic and diatomic gases.

< 1 only for a monatomic gas.

< 1 only for a diatomic gas.

Answer: C Var: 1 34) A certain ideal gas has a molar specific heat at constant volume 7R/2. What is its molar specific heat at constant pressure? A) 5R/2 B) 3R/2 C) 8R D) 9R/2 E) 6R Answer: D Var: 1 35) A certain ideal gas has a molar specific heat at constant pressure of 7R/2. What is its molar specific heat at constant volume? A) 5R/2 B) 3R/2 C) 8R D) 9R/2 E) 6R Answer: A Var: 1

36) A certain ideal gas has a molar specific heat at constant pressure of 33.2 J/mol ∙ K. Its molar specific heat at constant volume is closest to which of the following values? (R = 8.31J/mol ∙ K) A) 41.9 J/mol ∙ K B) 16.6 J/mol ∙ K C) 25.1 J/mol ∙ K D) 24.9 J/mol ∙ K E) 49.8 J/mol ∙ K Answer: D Var: 1 37) When a gas expands adiabatically, A) the internal (thermal) energy of the gas decreases. B) the internal (thermal) energy of the gas increases. C) it does no work. D) work is done on the gas. E) the temperature of the gas remains constant. Answer: A Var: 1 38) An ideal gas is compressed isothermally to one-third of its initial volume. The resulting pressure will be A) three times as large as the initial value. B) less than three times as large as the initial value. C) more than three times as large as the initial value. D) equal to the initial value. E) impossible to predict on the basis of this data. Answer: A Var: 1 39) An ideal gas is compressed isobarically to one-third of its initial volume. The resulting pressure will be A) three times as large as the initial value. B) equal to the initial value. C) more than three times as large as the initial value. D) impossible to predict on the basis of this data. Answer: B Var: 1 40) In a given reversible process, the temperature of an ideal gas is kept constant as the gas is compressed to a smaller volume. Which one of the following statements about the gas is correct? A) The gas must absorb heat from its surroundings. B) The gas must release heat to its surroundings. C) The pressure of the gas also stays constant. D) The process is adiabatic. E) It is impossible to predict on the basis of this data. Answer: B Var: 1 11 Copyright © 2019 Pearson Education, Inc.

41) The process shown on the TV graph in the figure is an

A) adiabatic compression. B) isothermal compression. C) isochoric compression. D) isobaric compression. Answer: B Var: 1 42) The process shown on the pV diagram in the figure is an

A) adiabatic expansion. B) isothermal expansion. C) isometric expansion. D) isobaric expansion. Answer: D Var: 1 43) The process shown on the pV diagram in the figure is

A) adiabatic. B) isothermal. C) isochoric. D) isobaric. Answer: C Var: 1

44) Two processes are shown on the pV diagram in the figure. One of them is an adiabat and the other one is an isotherm. Which process is the isotherm?

A) process A B) process B C) The processes shown are neither isotherms nor adiabats. D) It is not possible to tell without knowing if the gas is monatomic or diatomic. Answer: A Var: 1 45) A gas is taken through the cycle shown in the pV diagram in the figure. During one cycle, how much work is done by the gas?

A) p0V0 B) 2 p0V0 C) 3 p0V0 D) 4 p0V0 Answer: C Var: 1

12.2 Problems 1) The coefficient of linear expansion of steel is 12 × 10-6 K-1. What is the change in length of a 25-m steel bridge span when it undergoes a temperature change of 40 K from winter to summer? A) 1.2 cm B) 1.4 cm C) 1.6 cm D) 1.8 cm E) 2.0 cm Answer: A Var: 1 2) A steel bridge is 1000 m long at -20°C in winter. What is the change in length when the temperature rises to 40°C in summer? The average coefficient of linear expansion of this steel is 11 × 10-6 K-1. A) 0.33 m B) 0.44 m C) 0.55 m D) 0.66 m Answer: D Var: 1 3) An aluminum rod 17.400 cm long at 20°C is heated to 100°C. What is its new length? Aluminum has a linear expansion coefficient of 25 × 10-6 K-1. A) 17.435 cm B) 17.365 cm C) 0.348 cm D) 0.0348 cm Answer: A Var: 1 4) By what length will a slab of concrete that is originally 18 m long contract when the temperature drops from 24°C to -16°C? The coefficient of linear thermal expansion for this concrete is 1.0 × 10-5 K-1. A) 0.50 cm B) 0.72 cm C) 1.2 cm D) 1.5 cm Answer: B Var: 1

5) A hole in a brass plate has a diameter of 1.200 cm at 20°C. What is the diameter of the hole when the plate is heated to 220°C? The coefficient of linear thermal expansion for brass is 19 × 10-6 K-1. A) 1.205 cm B) 1.195 cm C) 1.200 cm D) 1.210 cm Answer: A Var: 1 6) A quantity of mercury occupies 400.0 cm3 at 0°C. What volume will it occupy when heated to 50°C? Mercury has a volume expansion coefficient of 180 × 10-6 K-1. A) 450 cm3 B) 409.7 cm3 C) 403.6 cm3 D) 401.8 cm3 Answer: C Var: 1 7) A large vat contains 1.000 L of water at 20°C. What volume will this water occupy when it is heated up to 80°C? Water has a volume expansion coefficient of 210 × 10-6 K-1. A) 1.600 L B) 1.013 L C) 0.987 L D) 0.9987 L Answer: B Var: 1 8) The volume coefficient of thermal expansion for gasoline is 950 × 10-6 K-1. By how many cubic centimeters does the volume of 1.00 L of gasoline change when the temperature rises from 30°C to 50°C? A) 6.0 cm3 B) 12 cm3 C) 19 cm3 D) 37 cm3 Answer: C Var: 1

9) For the mercury in a thermometer to expand from 4.00 cm3 to 4.10 cm3, what change in temperature is necessary? The mercury has a volume expansion coefficient of 1.80 × 10-4 K-1. A) 400 C° B) 140 C° C) 14 C° D) 8.2 C° Answer: B Var: 1 10) A mercury thermometer has a glass bulb of interior volume 0.100 cm3 at 10°C. The glass capillary tube above the bulb has an inner cross-sectional area of 0.012 mm2. The coefficient of volume expansion of mercury is 1.8 × 10-4 K-1. If the expansion of the glass is negligible, how much will the mercury rise in the capillary tube when the temperature rises from 5°C to 35°C if the bulb was full at 5°C? A) 0.45 mm B) 4.5 mm C) 45 mm D) 45 cm Answer: C Var: 1 11) The coefficient of linear expansion of copper is 17 × 10-6 K-1. A sheet of copper has a round hole with a radius of 3.0 m cut out of it. If the sheet is heated and undergoes a change in temperature of 80 K, what is the change in the radius of the hole? A) It decreases by 4.1 mm. B) It increases by 4.1 mm. C) It decreases by 8.2 mm. D) It increases by 8.2 mm. E) It does not change. Answer: B Var: 1 12) Suppose that a rigid aluminum wire were to be strung out in a loop that just fits snugly around the equator (assuming a perfectly spherical Earth with a radius of 6.37 × 106 m). If the temperature of the wire is increased by 0.50°C, and the increase in length is distributed equally over the entire length, how far off the ground will the wire loop be if it remained centered on the earth? The coefficient of linear expansion of aluminum is 24 × 10-6 K-1. A) 7.6 mm B) 76 mm C) 76 cm D) 76 m E) 760 m Answer: D Var: 1

13) The coefficient of linear expansion of copper is 17 × 10-6 K-1. A block of copper 30 cm wide, 45 cm long, and 10 cm thick is heated from 0°C to 100°C What is the change in the volume of the block? A) 2.3 × 10-5 m3 B) 4.6 × 10-5 m3 C) 5.2 × 10-5 m3 D) 6.9 × 10-5 m3 E) 14 × 10-5 m3 Answer: D Var: 1 14) The coefficient of linear expansion of aluminum is 24 × 10-6 K-1 and the coefficient of volume expansion of olive oil is 0.68 × 10-3 K-1. A novice cook, in preparation of some pesto, fills a 1.00-L aluminum pot to the brim and heats the oil and the pot from an initial temperature of 15°C to 190°C. To his consternation some olive oil spills over the top. How much? A) 0.11 L B) 0.12 L C) 0.13 L D) 0.14 L E) 0.15 L Answer: A Var: 1 15) The coefficient of volume expansion of a certain olive oil is 0.68 × 10-3 K-1. A 1.0-L glass beaker is filled to the brim with olive oil at room temperature. The beaker is placed on a range and the temperature of the oil and beaker increases by 25 C°. As a result, 0.0167 L of olive oil spills over the top of the beaker. Which of the following values is closest to the coefficient of linear expansion of the glass from which the beaker is made? A) 1 × 10-6 K-1 B) 4 × 10-6 K-1 C) 1 × 10-5 K-1 D) 2 × 10-5 K-1 E) 3 × 10-5 K-1 Answer: B Var: 1

16) The coefficient of linear expansion of aluminum is 24.0 × 10-6 K-1, and the density of aluminum at 0°C is 2.70 × 103 kg/m3. What is the density of aluminum at 300°C? A) 3.93 × 103 kg/m3 B) 2.73 × 103 kg/m3 C) 2.70 × 103 kg/m3 D) 2.67 × 103 kg/m3 E) 2.64 × 103 kg/m3 Answer: E Var: 1 17) The density of water at 0°C is 999.84 kg/m3 and at 4°C it is 999.96 kg/m3. A 1.0-L container, full to the brim with water at 4.0°C is placed in the refrigerator. By the time that the temperature of the water reaches 0.0°C, what volume of water has spilled from the container, assuming that the contraction of the container is negligible? A) 1.1 × 10-7 m3 B) 1.2 × 10-7 m3 C) 1.3 × 10-7 m3 D) 1.4 × 10-7 m3 E) 1.5 × 10-7 m3 Answer: B Var: 1 18) The coefficient of linear expansion of copper is 17 × 10-6 K-1 and that of steel is 12 × 10-6 K-1. At 12°C a steel rod has a diameter of 2.540 cm and a copper pipe has a diameter of 2.536 cm. Which one of the following quantities is closest to the temperature to which the copper pipe must be heated in order for the unheated steel rod to fit snugly in the copper pipe? A) 53°C B) 81°C C) 93°C D) 105°C E) 143°C Answer: D Var: 1 19) The coefficient of linear expansion of copper is 17 × 10-6 K-1 and that of steel is 12 × 10-6 K-1. At 12°C a steel rod has a diameter of 2.540 cm and a copper pipe has a diameter of 2.536 cm. If they are heated together to a higher temperature, which one of the following quantities is closest to the common temperature at which the steel rod will fit snugly in the copper pipe? A) 310°C B) 330°C C) 340°C D) 350°C E) 380°C Answer: B Var: 1 18 Copyright © 2019 Pearson Education, Inc.

20) A steel pipe 36.0 m long, installed when the temperature was is used to transport superheated steam at a temperature of Steel's coefficient of linear expansion is . The pipe is allowed to expand freely when the steam is transported. What is the increase in the length of the pipe when it is used with the superheated steam? A) 60 mm B) 57 mm C) 54 mm D) 64 mm E) 67 mm Answer: A Var: 50+ 21) An aluminum rod is 10.0 cm long and a steel rod is 80.0 cm long when both rods are at a temperature of 15°C. Both rods have the same diameter. The rods are now joined end-to-end to form a rod 90.0 cm long. If the temperature is now raised from 15°C to 90°C, what is the increase in the length of the joined rod? The coefficient of linear expansion of aluminum is 2.4 × 10-5 K-1 and that of steel is 1.2 × 10-5 K-1. A) 0.90 mm B) 0.81 mm C) 0.72 mm D) 0.63 mm E) 0.99 mm Answer: A Var: 1 22) A brass rod is 69.5 cm long and an aluminum rod is 49.3 cm long when both rods are at an initial temperature of 0° C. The rods are placed in line with a gap of 1.2 cm between them, as shown in the figure. The distance between the far ends of the rods is maintained at 120.0 cm throughout. The temperature of both rods is raised equally until they are barely in contact. At what temperature does contact occur? The coefficients of linear expansion of brass and aluminum are 2.0 ×10-5 K-1 (brass) and 2.4 × 10-5 K-1 (aluminum).

A) 470°C B) 440°C C) 420°C D) 490°C E) 510°C Answer: A Var: 1

23) A glass flask has a volume of 500 mL at a temperature of 20° C. The flask contains 492 mL of mercury at an equilibrium temperature of 20°C. The temperature is raised until the mercury reaches the 500 mL reference mark. At what temperature does this occur? The coefficients of volume expansion of mercury and glass are 18 ×10-5 K-1 (mercury) and 2.0 ×10-5 K-1 (glass). A) 120°C B) 110°C C) 100°C D) 140°C E) 130°C Answer: A Var: 1 24) A solid object has a volume density ρ0 at a temperature of 315 K. The coefficient of volume expansion for the material of which it is made is 7.00 × 10-5 K-1. What will be its density (in terms of ρ0 at a temperature of 425 K, assuming that it does not melt and that its thermal properties do not change with temperature? Answer: 0.992 ρ0 Var: 1 25) How much heat is required to raise the temperature of a 225-g lead ball from 15.0°C to 25.0°C? The specific heat of lead is 128 J/kg ∙ K. A) 725 J B) 576 J C) 145 J D) 217 J E) 288 J Answer: E Var: 1 26) A 4.0-kg aluminum block is originally at 10°C. If 160 kJ of heat is added to the block, what is its final temperature? The specific heat capacity of aluminum is 910 J/kg ∙ K. A) 24°C B) 34°C C) 44°C D) 54°C Answer: D Var: 3 27) If 150 kcal of heat raises the temperature of 2.0 kg of a material by 400 F°, what is the specific heat capacity of the material? A) 1.35 kcal/kg ∙ C° B) 0.75 kcal/kg ∙ C° C) 0.34 kcal/kg ∙ C° D) 0.19 kcal/kg ∙ C° Answer: C Var: 1 20 Copyright © 2019 Pearson Education, Inc.

28) A machine part consists of 0.10 kg of iron (of specific heat 470 J/kg ∙ K ) and 0.16 kg of copper (of specific heat 390 J/kg ∙ K). How much heat must be added to the gear to raise its temperature from 18°C to 53°C? A) 910 J B) 3800 J C) 4000 J D) 4400 J Answer: B Var: 1 29) An aluminum electric tea kettle with a mass of 500 g is heated with a 500-W heating coil. How long will it take to heat up 1.0 kg of water from 18°C to 98°C in the tea kettle? The specific heat of aluminum is 900 J/kg ∙ K and that of water is 4186 J/kg ∙ K. A) 5.0 minutes B) 7.0 minutes C) 12 minutes D) 15 minutes E) 18 minutes Answer: C Var: 1 30) A carpenter is driving a 15.0-g steel nail into a board. His 1.00-kg hammer is moving at 8.50 m/s when it strikes the nail. Half of the kinetic energy of the hammer is transformed into heat in the nail and does not flow out of the nail. What is the increase in temperature of the nail after the three blows that the carpenter needs to drive the nail in completely? The specific heat of steel is 448 J/kg ∙ K. A) 8.1 K B) 3.6 K C) 1.8 K D) 2.7 K E) 7.7 K Answer: A Var: 1 31) A 5.00-g lead BB moving at 44.0 m/s penetrates a wood block and comes to rest inside the block. If half of its kinetic energy is absorbed by the BB, what is the change in the temperature of the BB? The specific heat of lead is 128 J/kg ∙ K. A) 0.940 K B) 1.10 K C) 1.26 K D) 2.78 K E) 3.78 K Answer: E Var: 1

32) It is necessary to determine the specific heat of an unknown object. The mass of the object is It is determined experimentally that it takes to raise the temperature What is the specific heat of the object? A) 7.46 J/kg ∙ K B) 1500 J/kg ∙ K C) 0.00130 J/kg ∙ K D) 3,020,000 J/kg ∙ K Answer: A Var: 50+ 33) A 920-g empty iron kettle is put on a stove. How much heat in joules must it absorb to raise its temperature form to The specific heat for iron is 113 cal/kg ∙ C°, and 1 cal = 4.186 J. A) 33,900 J B) 40,500 J C) 8110 J D) 40,100 J Answer: A Var: 50+ 34) A container of 114.0 g of water is heated using of power, with perfect efficiency. How long will it take to raise the temperature of the water from to The specific heat capacity of the container is negligible, and the specific heat capacity of water is 4.186 × 103 J/kg ∙ C. A) 71 s B) 4.1 s C) 17 s D) 320,000 s Answer: A Var: 50+ 35) A 6.5-g iron meteor hits the earth at a speed of 295 m/s. If its kinetic energy is entirely converted to heat in the meteor, by how much will its temperature rise? The specific heat of iron is 113 cal/kg ∙ C°, and 1 cal = 4.186 J. A) 92.0 C° B) 57,100 C° C) 0.147 C° D) 384 C° Answer: A Var: 1

36) A glass beaker of unknown mass contains of water. The system absorbs of heat and the temperature rises as a result. What is the mass of the beaker? The specific heat of glass is 0.18 cal/g ∙ °C, and that of water is 1.0 cal/g ∙ C°. A) 140 g B) 560 g C) 540 g D) 270,000 g Answer: A Var: 37 37) On his honeymoon, James Joule attempted to explore the relationships between various forms of energy by measuring the rise of temperature of water which had fallen down a waterfall on Mount Blanc. What maximum temperature rise would one expect for a waterfall with a vertical drop of 20 m? The specific heat of water is 4186 J/kg ∙ K. A) 0.047 C° B) 0.053 C° C) 0.064 C° D) 0.071 C° Answer: A Var: 1 38) The water flowing over Niagara Falls drops a distance of 50 m. If all the gravitational potential energy is converted to thermal energy, by what temperature does the water rise? The specific heat of water is 4186 J/kg ∙ K. A) 0.10 C° B) 0.12 C° C) 0.37 C° D) 0.42 C° Answer: B Var: 1 39) In a flask, 114.0 g of water is heated using of power, with perfect efficiency. How long will it take to raise the temperature of the water from to The specific heat of water is 4186 J/kg ∙ K. A) 71 s B) 4.1 s C) 17 s D) 320,000 s Answer: A Var: 50+

40) A 200-L electric water heater uses 2.0 kW. Assuming no heat loss, how many hours would it take to heat the water in this tank from 23°C to 75°C? The specific heat of water is 4186 J/kg ∙ K and its density is 1000 kg/m3. A) 5.0. hours B) 6.0 hours C) 7.0 hours D) 8.0 hours Answer: B Var: 1 41) In grinding a steel knife, the metal can get as hot as 400°C. If the blade has a mass of 80 g, what is the minimum amount of water needed at 20°C if the water is to remain liquid and not rise above 100°C when the hot blade is quenched in it? The specific heat of the steel is 0.11 cal/g ∙ C° and the specific heat of water is 1.0 cal/g ∙ C°. A) 22 g B) 33 g C) 44 g D) 55 g Answer: B Var: 1 42) How much heat must be removed from 456 g of water at 25.0°C to change it into ice at 10.0°C? The specific heat of ice is 2090 J/kg ∙ K, the latent heat of fusion of water is 33.5 × 104 J/kg, and the specific heat of water is 4186 J/kg ∙ K. A) 105 kJ B) 153 kJ C) 57.3 kJ D) 47.7 kJ E) 210 kJ Answer: E Var: 1 43) A runner generates 1260 W of thermal energy. If this heat has to be removed only by evaporation, how much water does this runner lose in 15 minutes of running? The latent heat of vaporization of water is 22.6 × 105 J/kg. A) 50 g B) 500 g C) 35 g D) 350 g E) 40 g Answer: B Var: 1

44) If you add 700 kJ of heat to 700 g of water originally at 70.0°C, how much water is left in the container? The latent heat of vaporization of water is 22.6 × J/kg, and its specific heat capacity is 4186 J/kg ∙ K. A) 429 g B) 258 g C) 340 g D) 600 g E) none Answer: A Var: 5 45) If you add 1.33 MJ of heat to 500 g of water at 50°C in a sealed container, what is the final temperature of the steam? The latent heat of vaporization of water is 22.6 × 105 J/kg, the specific heat of steam is 2010 J/kg ∙ K, and the specific heat of water is 4186 J/kg ∙ K. A) 100°C B) 112°C C) 123°C D) 147°C E) 195°C Answer: E Var: 5 46) A 2294-kg sample of water at 0° C is cooled to and freezes in the process. How much heat is liberated? For water LF = 334,000 J/kg and LV = 2.256 × 106 J/kg. The specific heat of ice is 2050 J/kg ∙ K. A) 935,000 kJ B) 597,000 kJ C) 1,110,000 kJ D) 334,000 kJ Answer: A Var: 50+ 47) The melting point of aluminum is 660°C, its latent heat of fusion is 4.00 × 105 J/kg, and its specific heat is 900J/kg ∙ K. How much heat must be added to 500 g of aluminum originally at 27°C to completely melt it? A) 485 kJ B) 395 kJ C) 273 kJ D) 147 kJ E) 14 kJ Answer: A Var: 1

48) A metal has a latent heat of fusion of 2.32 × 104 J/kg, a specific heat of 128 J/kg ∙ K, and a melting point of 228°C. A 30-g pellet of this metal at 16°C hits a solid wall and comes to a complete stop. What would the speed of the pellet have to be in order for it to melt completely when it hits the wall, assuming that all of its kinetic energy is transformed into heat within the pellet? A) 207 m/s B) 215 m/s C) 232 m/s D) 273 m/s E) 317 m/s Answer: E Var: 1 49) Solar houses use a variety of energy storage devices to retain the heat absorbed during the day so that it can be released during the night. Suppose that you were to use a device of this kind to produce steam at 100°C during the day, and then allow the steam to cool to 0°C and freeze during the night. How many kilograms of water would be needed to store 20.0 kWh of energy in this way? The latent heat of vaporization of water is 22.6 × 105 J/kg, the latent heat of fusion of water is 33.5 × 104 J/kg, and the specific heat capacity of water is 4186 J/kg ∙ K. A) 12.4 kg B) 23.9 kg C) 35.7 kg D) 42.6 kg E) 54.2 kg Answer: B Var: 1 50) A beaker of negligible heat capacity contains 456 g of ice at -25.0°C. A lab technician begins to supply heat to the container at the rate of 1000 J/min. How long after starting will the ice begin to melt, assuming all of the ice has the same temperature? The specific heat of ice is 2090 J/kg ∙ K and the latent heat of fusion of water is 33.5 × 104 J/kg. Answer: 23.8 min Var: 1 51) A beaker of negligible heat capacity contains 456 g of ice at -25.0°C. A lab technician begins to supply heat to the container at the rate of 1000 J/min. How long after starting will it take before the temperature starts to rise above 0°C? The specific heat of ice is 2090 J/kg ∙ K and the latent heat of fusion of water is 33.5 × 104 J/kg. Answer: 177 min Var: 1

52) The melting point of aluminum is 660°C, its latent heat of fusion is 4.00 × 105 J/kg, and its specific heat is 900 J/kg ∙ K. If 300 kJ of heat are added to 442 g of aluminum at 100°C, what is the final state of the system? That is, how much is liquid, how much is solid, and what is its temperature? Answer: The system will be at 660°C, with 249 g of solid and 193 g of liquid aluminum. Var: 1 53) A 45.0-kg sample of ice is at 0.00° C. How much heat is needed to melt it? For water LF = 334,000 J/kg and LV = 2.256 × 106 J/kg. A) 1.50 × 104 kJ B) 4.10 × 106 kJ C) 0.00 kJ D) 1.02 × 105 kJ Answer: A Var: 45 54) Heat is added to a 3.0 kg piece of ice at a rate of How long will it take for the ice at 0.0° C to melt? For water LF = 334,000 J/kg and LV = 2.246 × 106 J/kg. A) 1.6 s B) 640,000 s C) 0.0 s D) 1000 s Answer: A Var: 50+ 55) A .20-kg ice cube at 0.0°C has sufficient heat added to it to cause total melting, and the resulting water is heated to How much heat is added? For water LF = 334,000 J/kg, LV = 2.256 × 106 J/kg, the c = 4.186 x 103 J/kg ∙ C. A) 130 kJ B) 14,000 kJ C) 81 kJ D) 59 kJ Answer: A Var: 50+ 56) How much heat must be added to a 8.0-kg block of ice at -8°C to change it to water at The specific heat of ice is 2050 J/kg ∙ C°, the specific heat of water is 4186 J/kg ∙ C°, the latent heat of fusion of ice is 334,000 J/kg, and 1 cal = 4.186 J. A) 780 kcal B) 140 kcal C) 180 kcal D) 810 kcal E) 730 kcal Answer: A Var: 50+ 27 Copyright © 2019 Pearson Education, Inc.

57) When a sample of water at 0.0°C is cooled to –36.0°C and freezes in the process, 935,000 kJ of heat is liberated. What is the mass of this sample of water? For water LF = 334,000 J/kg, LV = 2.256 × 106 J/kg, and the specific heat of ice is 2050 J/kg ∙ C°. A) 2290 kg B) 1145 kg C) 2800 kg D) 12,700 kg Answer: A Var: 1 58) A 771.0-kg copper bar is put into a smelter for melting. The initial temperature of the copper is 300.0 K. How much heat must the smelter produce to completely melt the copper bar? The specific heat for copper is 386 J/kg∙K, the heat of fusion for copper is 205,000 J/kg, and its melting point is 1357 K. A) 4.73 × 105 kJ B) 3.15 × 1011 kJ C) 3.15 × 108 kJ D) 5.62 × 105 kJ Answer: A Var: 50+ 59) A substance has a melting point of 20°C and a heat of fusion of 3.4 × J/kg. The boiling point is and the heat of vaporization is at a pressure of one atmosphere. The specific heats for the solid, liquid, and gaseous phases are 600 J/kg ∙ K (solid), 1000 J/kg ∙ K (liquid), and 400 J/kg ∙ K (gaseous). How much heat is required to raise the temperature of of this substance from to at a pressure of one atmosphere? A) 260 kJ B) 190 kJ C) 230 kJ D) 92 kJ E) 320 kJ Answer: A Var: 50+

60) A substance has a melting point of 20°C and a heat of fusion of The boiling point is and the heat of vaporization is at a pressure of one atmosphere. The specific heats for the solid, liquid, and gaseous phases are 600 J/kg ∙ K (solid), 1000 J/kg ∙ K (liquid), and 400 J/kg ∙ K (gaseous). How much heat is given up by of this substance when it is cooled from 170°C to 86°C at a pressure of one atmosphere? A) 400 kJ B) 200 kJ C) 300 kJ D) 440 kJ E) 640 kJ Answer: A Var: 50+ 61) A person tries to heat up her bath water by adding 5.0 L of water at 80°C to 60 L of water at 30°C. What is the final temperature of the bath water? A) 34°C B) 36°C C) 38°C D) 40°C Answer: A Var: 1 62) If 50 g of lead (of specific heat 0.11 kcal/kg ∙ C°) at 100°C is put into 75 g of water (of specific heat 1.0 kcal/kg ∙ C°) at 0°C. What is the final temperature of the mixture? A) 2.0°C B) 6.8°C C) 25°C D) 50°C Answer: B Var: 1 63) A lab assistant pours 330 g of water at 45°C into an 855-g aluminum container that is at an initial temperature of 10°C. The specific heat of aluminum is and that of water is 4186 J/kg ∙ K. What is the final temperature of the system, assuming no heat is exchanged with the surroundings? A) 28°C B) 32°C C) 31°C D) 33°C E) 35°C Answer: B Var: 5

64) A 90-g aluminum calorimeter contains 390 g of water at an equilibrium temperature of A piece of metal, initially at is added to the calorimeter. The final temperature at equilibrium is 32° C. Assume there is no external heat exchange. The specific heat capacities of aluminum and water are 910 J/kg ∙ K (aluminum) and 4190 J/kg ∙ K (water). What is the specific heat capacity of the 160-g piece of metal? A) 470 J/kg ∙ K B) 430 J/kg ∙ K C) 350 J/kg ∙ K D) 310 J/kg ∙ K E) 510 J/kg ∙ K Answer: A Var: 50+ 65) A camper is about to drink his morning coffee. He pours 400 grams of coffee, initially at 75°C into a 250-g aluminum cup, initially at 16°C. What is the equilibrium temperature of the coffee-cup system, assuming no heat is lost to the surroundings? The specific heat of aluminum is 900 J/kg ∙ K, and the specific heat of coffee is essentially the same as that of water, which is 4186 J/kg ∙ K. A) 45°C B) 62°C C) 65°C D) 68°C E) 71°C Answer: D Var: 1 66) A lab student drops a 400.0-g piece of metal at 120.0°C into a cup containing 450.0 g of water at 15.0°C. After waiting for a few minutes, the student measures that the final temperature of the system is 40.0°C. What is the specific heat of the metal, assuming that no significant heat is exchanged with the surroundings or the cup? The specific heat of water is 4186 J/kg ∙ K. A) 1470 J/kg ∙ K B) 2830 J/kg ∙ K C) 3420 J/kg ∙ K D) 3780 J/kg ∙ K E) 4280 J/kg ∙ K Answer: A Var: 5

67) A lab assistant drops a 400.0-g piece of metal at 100.0°C into a 100.0-g aluminum cup containing 500.0 g of water at In a few minutes, she measures the final temperature of the system to be 40.0°C. What is the specific heat of the 400.0-g piece of metal, assuming that no significant heat is exchanged with the surroundings? The specific heat of this aluminum is 900.0 J/kg ∙ K and that of water is 4186 J/kg ∙ K. A) 1900 J/kg ∙ K B) 2270 J/kg ∙ K C) 3300 J/kg ∙ K D) 3800 J/kg ∙ K E) 4280 J/kg ∙ K Answer: B Var: 5 68) A jogger is running outdoors on a cold day when the temperature is -20.0°C. She is breathing at the rate of 25 breaths per minute, and each time she breathes in she inhales 0.00450 m3 of air. How much heat does she lose from breathing during 20.0 minutes of jogging if the air in her lungs is heated to her body temperature of 37.0°C before it is exhaled? The specific heat of air is 1020 J/kg ∙ K and the density of air under typical conditions is 1.29 kg/m3. A) 169 kJ B) 278 kJ C) 354 kJ D) 431 kJ E) 543 kJ Answer: A Var: 1 69) A person is walking outdoors on a cold day when the temperature is -20°C. He is breathing at the rate of 16 breaths per minute, and each time he breathes in he inhales 0.0050 m3 of air. At what rate does he lose heat from breathing if the air in his lungs is heated to body temperature (37°C) before it is exhaled? The specific heat of air is 1020 J/kg ∙ K and the density of air is 1.29 kg/m3. A) 60 W B) 90 W C) 100 W D) 150 W E) 300 W Answer: C Var: 1

70) A piece of iron of mass 0.12 kg is taken from an oven where its temperature is 336°C and quickly placed in an insulated copper can that contains 0.20 kg of water. The copper can has mass 0.50 kg, and it and the water in it are originally at a temperature of 20°C. Calculate the final temperature of the system, assuming no heat is lost to the surroundings. Use the following specific heats: 4190J/kg ∙ C° (water), 470 J/kg ∙ C° (iron), and 390 J/kg ∙ C° (copper). Answer: 36°C Var: 1 71) A 0.600-kg piece of metal X is heated to 100°C and placed in an aluminum can of mass 0.200-kg which contains 0.500 kg of water initially at 17.3°C. The final equilibrium temperature of the mixture is 20.2°C, what is the specific heat of metal X? The specific heats of water and aluminum are 4186 J/kg ∙ K (water) and 910 J/kg ∙ K (aluminum). A) 140 J/kg ∙ K B) 270 J/kg ∙ K C) 450 J/kg ∙ K D) 900 J/kg ∙ K Answer: A Var: 1 72) When 50 g of a certain material at 100°C is mixed with 100 g of water at 0°C, the final temperature is 40°C. What is the specific heat of the material? The specific heat of water is 1.00 kcal/kg ∙ C°. A) 0.33 kcal/kg ∙ C° B) 0.75 kcal/kg ∙ C° C) 1.3 kcal/kg ∙ C° D) 7.5 kcal/kg ∙ C° Answer: C Var: 1 73) A person makes iced tea by adding ice to 1.8 kg of hot tea, initially at 80°C. How many kilograms of ice, initially at 0°C, are required to bring the mixture to 10°C? The specific heat of water (and tea) is 4186 J/kg ∙ K, and the latent heat of fusion of ice is 3.34 × 105 J/kg. A) 1.0 kg B) 1.2 kg C) 1.4 kg D) 1.7 kg Answer: C Var: 1 74) A 600-g piece of iron at 100°C is dropped into a calorimeter of negligible heat capacity containing 100 g of ice at 0°C and 120 g of water, also at 0°C. What is the final temperature of the system? The specific heat of iron is 448 J/kg ∙ K, the latent heat of fusion of water is 33.5 × 104 J/kg, and the specific heat of water is 4186 J/kg ∙ K. Answer: 0°C (only some of the ice will have melted) Var: 1

75) A 35-g block of ice at -14°C is dropped into a calorimeter (of negligible heat capacity) containing 400 g of water at 0°C. When the system reaches equilibrium, how much ice is left in the calorimeter? The specific heat of ice is 2090 J/kg ∙ K, that of water is 4186 J/kg ∙ K, and the latent heat of fusion of water is 33.5 × 104 J/kg. A) 32 g B) 33 g C) 35 g D) 38 g E) 41 g Answer: D Var: 5 76) A 44.0-g block of ice at -15.0°C is dropped into a calorimeter (of negligible heat capacity) containing of water at 5.0°C. When equilibrium is reached, how much of the ice will have melted? The specific heat of ice is 2090 J/kg ∙ K, that of water is 4186 J/kg ∙ K, and the latent heat of fusion of water is 33.5 × 104 J/kg. A) 2.1 g B) 21 g C) 5.2 g D) 52 g E) 4.4 g Answer: A Var: 5 77) A 40.0-g block of ice at -15.00°C is dropped into a calorimeter (of negligible heat capacity) containing water at 15.00°C. When equilibrium is reached, the final temperature is 8.00°C. How much water did the calorimeter contain initially? The specific heat of ice is 2090 J/kg ∙ K, that of water is 4186 J/kg ∙ K, and the latent heat of fusion of water is 33.5 × 104 J/kg. A) 302 g B) 345 g C) 405 g D) 546 g E) 634 g Answer: D Var: 5

78) A 400-g block of iron at 400°C is dropped into a calorimeter (of negligible heat capacity) containing 60 g of water at 30°C. How much steam is produced? The latent heat of vaporization of water is 22.6 × 105 J/kg and its specific heat capacity is 4186 J/kg ∙ K. The average specific heat of iron over this temperature range is 560 J/kg ∙ K. A) 22 g B) 33 g C) 42 g D) 54 g E) 59 g Answer: A Var: 5 79) An 920-g piece of iron at 100°C is dropped into a calorimeter of negligible heat capacity containing 50 g of ice at 0°C and 92 g of water, also at 0°C. What is the final temperature of the system? The specific heat of iron is 448 J/kg ∙ K, that of water is 4186 J/kg ∙ K, and the latent heat of fusion of water is 33.5 × 104 J/kg. A) 0°C B) 11°C C) 14°C D) 24°C E) 32°C Answer: D Var: 5 80) A 360-g metal container, insulated on the outside, holds 180.0 g of water in thermal equilibrium at 22.0°C. A 24.0-g ice cube, at the melting point, is dropped into the water, and when thermal equilibrium is reached the temperature is 15.0°C. Assume there is no heat exchange with the surroundings. For water, the specific heat capacity is 4190 J/kg ∙ K and the heat of fusion is 3.34 × 105 J/kg. What is the specific heat capacity of the metal of the container? A) 1700 J/kg ∙ K B) 970 J/kg ∙ K C) 2300 J/kg ∙ K D) 2800 J/kg ∙ K E) 3300 J/kg ∙ K Answer: A Var: 1

81) Two experimental runs are performed to determine the calorimetric properties of an alcohol which has a melting point of -10.0° C. In the first run, a 200-g cube of frozen alcohol, at the melting point, is added to 300 g of water at 20.0°C in a styrofoam container. When thermal equilibrium is reached, the alcohol-water solution is at a temperature of 5.0°C. In the second run, an identical cube of alcohol is added to 500 g of water at 20.0°C and the temperature at thermal equilibrium is 10.0°C. The specific heat capacity of water is 4190 J/kg ∙ K. Assume no heat is exchanged with the styrofoam container and the surroundings. What is the heat of fusion of the alcohol? A) 5.5 × 104 J/kg B) 6.3 × 104 J/kg C) 7.1 × 104 J/kg D) 7.9 × 104 J/kg E) 8.7 × 104 J/kg Answer: B Var: 1 82) Two experimental runs are performed to determine the calorimetric properties of an alcohol which has a melting point of -10° C. In the first run, a 200-g cube of frozen alcohol, at the melting point, is added to 300 g of water at 20°C in a styrofoam container. When thermal equilibrium is reached, the alcohol-water solution is at a temperature of 5°C. In the second run, an identical cube of alcohol is added to 500 g of water at 20°C and the temperature at thermal equilibrium is 10°C. The specific heat capacity of water is 4190 J/kg ∙ K. Assume no heat is exchanged with the styrofoam container and the surroundings. What is the specific heat capacity of the alcohol? A) 1700 J/kg ∙ K B) 1900 J/kg ∙ K C) 2100 J/kg ∙ K D) 2300 J/kg ∙ K E) 2500 J/kg ∙ K Answer: C Var: 1 83) How many grams of ice at -17°C must be added to 741 grams of water that is initially at a temperature of to produce water at a final temperature of Assume that no heat is lost to the surroundings and that the container has negligible mass. The specific heat of liquid water is 4190 J/kg ∙ C° and of ice is 2000 J/kg ∙ C°. For water the normal melting point is 0°C and the heat of fusion is 334 × 103 J/kg. The normal boiling point is 100°C and the heat of vaporization is 2.256 × 106 J/kg. Answer: 430 g Var: 50+

84) A heat-conducting rod, 0.90 m long and wrapped in insulation, is made of an aluminum section that is 0.20 m long and a copper section that is long. Both sections have a crosssectional area of The aluminum end and the copper end are maintained at temperatures of and respectively. The thermal conductivities of aluminum and copper are 205 W/m ∙ K (aluminum) and 385 W/m ∙ K (copper). What is the temperature of the aluminum-copper junction in the rod with steady state heat flow? A) 100°C B) 93°C C) 86°C D) 80°C E) 74°C Answer: A Var: 50+ 85) A heat conducting rod, 1.60 m long and wrapped in insulation, is made of an aluminum section that is 0.90 m long and a copper section that is long. Both sections have a crosssectional area of The aluminum end and the copper end are maintained at temperatures of and respectively. The thermal conductivities of aluminum and copper are 205 W/m ∙ K (aluminum) and 385 W/m ∙ K (copper). At what rate is heat conducted in the rod under steady state conditions? A) 9.0 W B) 7.9 W C) 10 W D) 11 W E) 12 W Answer: A Var: 50+ 86) A heat-conducting rod that is wrapped in insulation is constructed with a 0.15-m length of alloy A and a 0.40-m length of alloy B, joined end-to-end. Both pieces have cross-sectional areas of 0.0020 m2. The thermal conductivity of alloy B is known to be 1.8 times as great as that for alloy A. The end of the rod in alloy A is maintained at a temperature of 10°C, and the other end of the rod is maintained at an unknown temperature. When steady state flow has been established, the temperature at the junction of the alloys is measured to be 40° C, and the rate of heat flow in the rod is measured at 56 W. What is the temperature of the end of the rod in alloy B? A) 80°C B) 84°C C) 88°C D) 92°C E) 96°C Answer: B Var: 1

87) A heat-conducting rod that is wrapped in insulation is constructed with a 0.15-m length of alloy A and a 0.40-m length of alloy B, joined end-to-end. Both pieces have cross-sectional areas of 0.0020 m2. The thermal conductivity of alloy B is known to be 1.8 times as great as that for alloy A. The end of the rod in alloy A is maintained at a temperature of 10°C, and the other end of the rod is maintained at an unknown temperature. When steady state flow has been established, the temperature at the junction of the alloys is measured to be 40° C, and the rate of heat flow in the rod is measured at 56 W. What is the thermal conductivity of alloy A? A) 120 W/m ∙ K B) 125 W/m ∙ K C) 130 W/m ∙ K D) 135 W/m ∙ K E) 140 W/m ∙ K Answer: E Var: 1 88) Some properties of a certain glass are listed here: Density 2300 kg/m3 Specific heat capacity 840 J/kg ∙ C° Coefficient of thermal expansion 8.5 × 10-6 (C°)-1 Thermal conductivity 0.80 W/m ∙ C° A glass window pane is 2.7 m high, 2.4 m wide, and 9.0 mm thick. The temperature at the inner surface of the glass is and at the outer surface 4°C. How much heat is lost each hour through the window? A) 3.1 × 107 J B) 3.1 × 104 J C) 8.6 × 103 J D) 8.6 J E) 3.1 × 105 J Answer: A Var: 50+ 89) A concrete wall of a cold storage room measures 3.0 m high, 5.0 m wide, and 20 cm thick. The inside wall is to be covered by a layer of wood in order to reduce the rate of heat flow through the wall by 90 percent. The inner surface of the wooden wall is maintained at -10°C and the outer surface of the concrete wall is at 20°C. The thermal conductivities of concrete and wood are 0.80 W/m ∙ K (concrete) and 0.040 W/m ∙ K (wood). What is the temperature difference across the layer of wood? A) 24 C° B) 25 C° C) 26 C° D) 27 C° E) 28 C° Answer: D Var: 1 37 Copyright © 2019 Pearson Education, Inc.

90) A concrete wall of a cold storage room measures 3.0 m high, 5.0 m wide, and 20 cm thick. The inside wall is to be covered by a layer of wood in order to reduce the rate of heat flow through the wall by 90 percent. The inner surface of the wooden wall is maintained at -10°C and the outer surface of the concrete wall is at 20°C. The thermal conductivities of concrete and wood are 0.80 W/m ∙ K (concrete) and 0.040 W/m ∙ K (wood). What should be the thickness of the layer of wood? A) 60 mm B) 70 mm C) 80 mm D) 90 mm E) 100 mm Answer: D Var: 1 91) A solid concrete wall has dimensions 4.0 m × 2.4 m and is 30 cm thick. The thermal conductivity of the concrete is 1.3 W/m ∙ K, and it separates a basement from the ground outside. The inner surface of the wall is at 18°C, and the outside surface is at 6°C. How much heat flows through the wall every hour? A) 1.8 MJ B) 1.8 kJ C) 500 J D) 5.0 MJ E) 5.0 kJ Answer: A Var: 1 92) A glass tea kettle containing 500 g of water is on the stove. The portion of the tea kettle that is in contact with the heating element has an area of 0.090 m2 and is 1.5 mm thick. At a certain moment, the temperature of the water is 75°C, and it is rising at the rate of 3 C° per minute. What is the temperature of the outside surface of the bottom of the tea kettle? Neglect the heat capacity of the kettle, and assume that the inner surface of the kettle is at the same temperature as the water inside. The thermal conductivity of glass is 0.840 W/m ∙ K and the specific heat of water is 4186 J/kg ∙ K. A) 39°C B) 92°C C) 120°C D) 86°C E) 77°C Answer: E Var: 1

93) A 400-g stainless steel tea kettle containing 500 g of water is on the stove. The portion of the tea kettle that is in contact with the heating element has an area of 0.090 m2 and is 2.0 mm thick. At a certain moment, the temperature of the water is 75°C, and it is rising at the rate of 3.0 C° per minute. What is the difference in temperature between the inside and the outside of the bottom of the tea kettle? Assume that the inner surface of the kettle is at the same temperature as the water inside. The thermal conductivity of stainless steel is 16.3 W/m ∙ K, the specific heat of the steel is 448 J/kg ∙ K, and the specific heat of water is 4186 J/kg . K. A) 2.2 C° B) 1.5 C° C) 1.1 C° D) 0.50 C° E) 0.15 C° Answer: E Var: 1 94) Two metal rods, one silver and the other copper, are both immersed at one end in a steam chamber at a temperature of 100°C. The other end of each one is in an ice water bath at 0°C. The rods are 5.0 cm long and have a square cross-section that is 2.0 cm on a side. No heat is exchanged between the rods and the surroundings, except at the ends. How much total heat flows through the two rods each minute? The thermal conductivity of silver is 417 W/m ∙ K, and that of copper is 395 W/m ∙ K. A) 20 kJ B) 39 kJ C) 47 kJ D) 49 kJ E) 11 kJ Answer: B Var: 1 95) Two metal rods, one silver and the other gold, are attached to each other end-to-end. The free end of the silver rod is immersed in a steam chamber at 100°C, and the free end of the gold rod in an ice water bath at 0°C. The rods are both 5.0 cm long and have a square cross-section that is 2.0 cm on a side. No heat is exchanged between the rods and their surroundings, except at the ends. How much total heat flows through the two rods each minute? The thermal conductivity of silver is 417 W/m ∙ K, and that of gold is 291 W/m ∙ K. A) 8.2 kJ B) 9.5 kJ C) 12 kJ D) 14 kJ E) 16 kJ Answer: A Var: 1

96) Two metal rods, one silver and the other gold, are attached to each other end-to-end. The free end of the silver rod is immersed in a steam chamber at 100°C, and the free end of the gold rod in an ice water bath at 0°C. The rods are both 5.0 cm long and have a square cross-section that is 2.0 cm on a side. No heat is exchanged between the rods and their surroundings, except at the ends. What is the temperature at the point where the two rods are in contact with one another? The thermal conductivity of silver is 417 W/m ∙ K, and that of gold is 291 W/m ∙ K. A) 39°C B) 41°C C) 47°C D) 53°C E) 59°C Answer: E Var: 1 97) The thermal conductivity of a certain concrete is 0.80 W/m . K and the thermal conductivity of a certain wood is 0.10 W/m ∙ K. How thick would a solid concrete wall have to be in order to have the same rate of heat flow through it as an 8.0-cm thick wall made of solid wood? Both walls have the same surface area and the same temperature difference across their faces. A) 53 cm B) 64 cm C) 71 cm D) 85 cm Answer: B Var: 1 98) The thermal conductivity of aluminum is twice that of brass. Two rods (one aluminum and the other brass) of the same length and cross-sectional area are joined together end to end. The free end of the brass rod is maintained at 0°C and the free end of the aluminum rod is maintained at 200°C. If no heat escapes from the sides of the rods, what is the temperature at the place where the two rods are joined together? A) 76°C B) 133°C C) 148°C D) 155°C Answer: B Var: 1 99) A window glass that is 0.5 cm thick has dimensions of 3 m by 1.5 m. The thermal conductivity of this glass is 0.8 W/m ∙ K. If the outside surface of the glass is at -10°C and the inside surface is at 20°C, how much heat flows through the window in every hour? A) 50 MJ B) 60 MJ C) 70 MJ D) 80 MJ Answer: D Var: 1 40 Copyright © 2019 Pearson Education, Inc.

100) A rod, with sides insulated to prevent heat loss, has one end immersed in boiling water at 100°C and the other end in a water-ice mixture at 0°C. The rod has uniform cross-sectional area and length The heat conducted by the rod melts the ice at a rate of 1.0 g every 11 seconds. What is the thermal conductivity of the rod? Recall that the heat of fusion of water is 3.34 × 105 J/kg. Answer: 370 W/m ∙ °C Var: 50+ 101) In an experiment to measure the thermal conductivity of a certain material, a slab of material 10.0 mm thick separates a steam chamber from a block of ice with a square crosssection with dimensions 8.00 cm × 8.00 cm. After 5.00 min of running the experiment, 64.0 g of ice have melted. What is the thermal conductivity of this material? The latent heat of fusion of water is 33.5 × 104 J/kg, the latent heat of vaporization of water is 2.256 × 106 J/kg, and both the ice and water are under 1.00 atm of pressure. A) 0.130 W/m ∙ K B) 0.250 W/m ∙ K C) 0.440 W/m ∙ K D) 0.620 W/m ∙ K E) 1.12 W/m ∙ K Answer: E Var: 1 102) A sphere of surface area 1.25 m2 and emissivity 1.0 is at a temperature of 100°C. At what rate does it radiate heat into empty space? (σ = 5.67 × 10-8 W/m2 ∙ K4) A) 7.1 W B) 0.71 mW C) 1.4 kW D) 9.9 mW E) 3.7 W Answer: C Var: 1 103) The cylindrical filament in a light bulb has a diameter of 0.050 mm, an emissivity of 1.0, and a temperature of 3000°C. How long should the filament be in order to radiate 60 W of power? (σ = 5.67 × 10-8 W/m2 ∙ K4) A) 11 cm B) 9.4 cm C) 8.6 cm D) 7.2 cm E) 5.9 cm Answer: E Var: 1

104) How much power does a sphere with a radius of 10 cm radiate into empty space if is has an emissivity of 1.0 and is kept at a temperature of 400 K? (σ = 5.67 × 10-8 W/m2 ∙ K4) A) 60 W B) 70 W C) 180 W D) 210 W E) 360 W Answer: C Var: 1 105) A blacksmith is flattening a steel plate having dimensions 10 cm × 15 cm × 1 mm. He has heated the plate to 900 K. If the emissivity of the plate is 0.75, at what rate does it lose energy by radiation? Ignore any heat exchange with the surroundings. (σ = 5.67 × 10-8 W/m2 ∙ K4) A) 360 W B) 760 W C) 790 W D) 850 W E) 880 W Answer: D Var: 1 106) What is the net power that a person with surface area of 1.20 m2 radiates if his emissivity is 0.895, his skin temperature is 27°C, and he is in a room that is at a temperature of 17°C? (σ = 5.67 × 10-8 W/m2 ∙ K4) A) 60.3 W B) 62.6 W C) 65.7 W D) 68.4 W E) 64.8 W Answer: B Var: 1 107) What is the net power radiated by a little animal with a surface area of 0.075 m2 if his emissivity is 0.75, his skin temperature is 315 K, and he is in a room with a temperature of 290 K? (σ = 5.67 × 10-8 W/m2 ∙ K4) A) 8.8 W B) 6.0 W C) 8.0 W D) 15 W E) 18 W Answer: A Var: 1

108) The radius of a star is 6.95 × 108 m, and its rate of radiation has been measured to be 5.32 × 1026 W. Assuming that it is a perfect emitter, what is the temperature of the surface of this star? (σ = 5.67 × 10-8 W/m2 ∙ K4) A) 6.27 × 103 K B) 8.25 × 103 K C) 8.87 × 103 K D) 3.93 × 107 K E) 5.78 × 107 K Answer: A Var: 1 109) A giant star radiates energy at the rate of 3.0 × 1030 W, and its surface temperature has been measured to be 3000 K. Assuming that it is a perfect emitter, what is the radius of this star?(σ = 5.67 × 10-8 W/m2 ∙ K4) A) 7.8 × 1010 m B) 8.7 × 1010 m C) 1.4 × 1010 m D) 1.9 × 1011 m E) 2.3 × 1011 m Answer: E Var: 1 110) Two identical objects are placed in a room with a temperature of 20°C. Object A has a temperature of 50°C, while object B has a temperature of 90°C. What is the ratio of the net power emitted by object B to the power emitted by object A? A) 1.7 B) 2.8 C) 81 D) 17 E) 21 Answer: B Var: 1 111) In an electric furnace used for refining steel, the temperature is monitored by measuring the radiant power emitted through a small hole in the wall of the furnace, of area 0.5 cm2. This hole acts like a perfect blackbody radiator having the same temperature as the interior of the furnace. If the temperature of the furnace (and therefore of the hole) is to be maintained at 1650°C, how much power will the hole radiate? A) 20 W B) 30 W C) 40 W D) 50 W Answer: C Var: 1 43 Copyright © 2019 Pearson Education, Inc.

112) Originally 2.00 mol of gas are at STP. If the temperature changes to 47.0°C and the pressure decreases to half of what it was, how many liters do the two moles now occupy? (1 atm = 101 kPa, R = 8.31 J/mol ∙ K) Answer: 105 L Var: 1 113) How many molecules are in (a) 1.0 cm3 of air at STP and (b) 1.0 cm3 of helium at STP? (R = 8.31 J/mol . K, NA = 6.022 × 1023 molecules/mol) Answer: 2.7 × 1019 molecules in both cases Var: 1 114) If a certain sample of an ideal gas has a temperature of 104°C and exerts a pressure of 2.3 × 104 Pa on the walls of its container, how many gas molecules are present in each cubic centimeter of volume? The ideal gas constant is R = 8.31 J/mol × K and Avogadro's number is NA = 6.022 × 1023 molecules/mol. Answer: 4.4 × 1018 molecules Var: 1 115) A jar holds 2.0 L of ideal nitrogen gas, N2, at STP. The atomic mass of nitrogen is 14.0 g/mol, the ideal gas constant is R = 8.31 J/mol ∙ K, Avogadro's number is NA = 6.022 × 1023 molecules/mol, and 1.00 atm = 101 kPa. (a) How many moles of nitrogen are in the jar? (b) How many nitrogen molecules are in the jar? (c) What is the mass of the nitrogen in the jar? Answer: (a) 0.089 mol (b) 5.4 × 1022 molecules (c) 2.5 g Var: 1 116) How many moles are there in 2.00 kg of copper? The atomic weight of copper is 63.5 g/mol and its density is 8.90 g/cm3. A) 15.3 B) 31.5 C) 51.3 D) 53.1 Answer: B Var: 1

117) An ideal gas has a pressure of 2.5 atm, a volume of 1.0 L at a temperature of 30°C. How many molecules are there in this gas? (R = 8.31 J/mol ∙ K,1.00 atm = 101 kPa, NA = 6.022 × 1023) A) 6.1 × 1023 B) 6.0 × 1022 C) 2.4 × 1022 D) 2.3 × 1023 Answer: B Var: 1 118) A car starts out when the air temperature is 288 K and the absolute (total) air pressure in the tires is 500 kPa. After driving a while, the temperature of the air in the tires increases to 298 K. What is the pressure in the tires at that point, assuming their volume does not change? A) 129 kPa B) 483 kPa C) 507 kPa D) 517 kPa E) 532 kPa Answer: D Var: 1 119) An ideal gas occupies 6.00 × 102 cm3 at 20°C. At what temperature will it occupy 1.20 × 103 cm3 if the pressure is held constant? A) 10°C B) 40°C C) 100°C D) 313°C Answer: D Var: 1 120) A balloon originally has a volume of 1.0 m3 when the gas in it is at 20°C and under a pressure of 1.0 atm. As it rises in the earth's atmosphere, its volume expands. What will be its new volume if its final temperature and pressure are -40°C and 0.10 atm? A) 2.0 m3 B) 4.0 m3 C) 6.0 m3 D) 8.0 m3 Answer: D Var: 1

121) A certain automobile tire has a volume of 0.0185 m3. If the absolute (or total) pressure in the tire is 500 kPa and the temperature is 298 K, how many molecules are there inside the tire? (R = 8.31 J/mol ∙ K, NA = 6.022 x 1023 molecules/mol) A) 2.25 × 1023 molecules B) 2.25 × 1024 molecules C) 3.25 × 1023 molecules D) 3.25 × 1024 molecules E) 3.25 × 1025 molecules Answer: B Var: 1 122) On a cold day, you take in 4.2 L of air into your lungs at a temperature of 0°C. If you hold your breath until the temperature of the air in your lungs reaches 37°C, what is the volume of the air in your lungs at that point, assuming the pressure does not change? A) 4.2 L B) 4.4 L C) 4.6 L D) 4.8 L E) 5.0 L Answer: D Var: 1 123) Your lungs hold 4.2 L of air at a temperature of 27°C and a pressure of 101.3 kPa. How many moles of air do your lungs hold? (R = 8.31 J/mol ∙ K) A) 0.15 moles B) 0.17 moles C) 0.19 moles D) 0.21 moles E) 0.23 moles Answer: B Var: 1 124) A 20.0-L pressure vessel holds 2.00 mol of oxygen at 30°C. What is the pressure inside the vessel? (R = 8.31 J/mol ∙ K) A) 101 Pa B) 101 kPa C) 1.01 MPa D) 2.52 MPa E) 252 kPa Answer: E Var: 1

125) A weather balloon containing 2.0 m3 of hydrogen gas rises from a location at which the temperature is 22°C and the pressure is 101 kPa to a location where the temperature is -39°C and the pressure is 20 kPa. If the balloon is free to expand so that the pressure of the gas inside is equal to the ambient pressure, what is the new volume of the balloon? A) 4.0 m3 B) 6.0 m3 C) 8.0 m3 D) 10 m3 E) 12 m3 Answer: C Var: 1 126) A laboratory vacuum pump can reduce the pressure in a chamber to 1.0 × 10-7 Pa. If the volume of the chamber is 0.500 m3 and the temperature is 27°C, how many molecules are left inside the chamber? (NA = 6.022 × 1023 molecules/mol, R = 8.31 J/mol ∙ K) A) 1.2 × 1013 B) 2.4 × 1013 C) 1.2 × 1012 D) 2.4 × 1012 E) 1.2 × 1014 Answer: A Var: 1 127) A refrigerator has an interior volume of 0.500 m3. The temperature inside the refrigerator in 282 K, and the pressure is 101 kPa. If the molecular weight of air is 29 g/mol, what is the mass of air inside the refrigerator? (R = 8.31 J/mol × K) A) 625 g B) 513 g C) 447 g D) 329 g E) 243 g Answer: A Var: 1 128) A vertical cylinder, closed at the bottom end, contains 0.0100 mol of ideal gas. It is fitted at the top with a piston that can move freely. The mass of the piston is 14.0 kg and the initial height of the piston above the bottom of the cylinder is 25 cm. What is the temperature of the gas? (R = 8.31 J/mol ∙ K) A) 290 K B) 413 K C) 3620 K D) 405 K E) 500 K Answer: B Var: 5 47 Copyright © 2019 Pearson Education, Inc.

129) A gas-filled vertical cylinder, closed at the bottom end, is fitted at the top with a piston that can move freely. The mass of the piston is 10.0 kg, and the initial height of the piston above the bottom of the cylinder is 25 cm. A mass of 8.0 kg is placed on the piston. What is the resulting height of the piston, assuming that the temperature of the ideal gas is kept constant? A) 12 cm B) 13 cm C) 14 cm D) 15 cm E) 16 cm Answer: C Var: 1 130) A quantity of an ideal gas is kept in a rigid container of constant volume. If the gas is originally at a temperature of 19°C, at what temperature will the pressure of the gas double from its original value? A) 91°C B) 38°C C) 311°C D) 273°C E) 122°C Answer: C Var: 1 131) A 5.3 L flask of ideal neon gas (which is monatomic) is at a pressure of 6.0 atm and a temperature of The atomic mass of neon is 20.2 g/mol. What is the mass of the neon gas in the flask. (R = 8.31 J/mol ∙ K, 1 atm = 101 kPa, NA = 6.022 × 1023 molecules/mol) A) 2.7 × 10-2 B) 1.6 × 10-2 C) 1.3 × 101 D) 2.7 × 101 E) 2.7 × 103 Answer: A Var: 50+ 132) A 4.2-L flask of ideal neon gas (which is monatomic) is at a pressure of 3.3 atm and a temperature of 450 K. The atomic mass of neon is 20.2 g/mol. How many neon atoms are in the flask? (R = 8.31 J/mol ∙ K, 1 atm = 101 kPa, NA = 6.022 × 1023 molecules/mol) A) 2.3 × 1023 B) 2.3 × 1022 C) 6.9 × 1023 D) 2.3 × 1025 E) 6.9 × 1022 Answer: A Var: 1 48 Copyright © 2019 Pearson Education, Inc.

133) A 3.9-L volume of ideal neon gas (monatomic) is at a pressure of 5.6 aym and a temperature of The atomic mass of neon is The temperature of the gas is now increased to 430 K and the volume is increased to What is the final pressure of the gas? A) 4.8 atm B) 4.3 atm C) 5.3 atm D) 5.8 atm E) 6.3 atm Answer: A Var: 50+ 134) A 0.40- gas tank holds 7.0 moles of ideal diatomic nitrogen gas at a temperature of The atomic mass of nitrogen is . What is the pressure of the gas? (R = 8.31 J/mol ∙ K, 1 atm = 101 kPa) A) 42 atm B) 37 atm C) 32 atm D) 27 atm E) 22 atm Answer: A Var: 50+ 135) A 24.0-L tank contains ideal helium gas at 27°C and a pressure of 22.0 atm. How many moles of gas are in the tank? (R = 8.31 J/mol ∙ K, 1 atm = 101 kPa) A) 238 mol B) 138 mol C) 17.5 mol D) 21.4 mol E) 76.0 mol Answer: D Var: 1 136) A sealed cylinder fitted with a movable piston contains ideal gas at 27°C, pressure 0.500 × 105 Pa, and volume 1.25 m3. What will be the final temperature if the gas is compressed to 0.800 m3 and the pressure rises to 0.820 × 105 Pa? A) 42°C B) 68°C C) 130°C D) 250°C E) 150°C Answer: A Var: 1

137) A sealed container holds 0.020 moles of ideal nitrogen (N2) gas, at a pressure of 1.5 atm and a temperature of 290 K. The atomic mass of nitrogen is 14.0 g/mol. How many molecules of nitrogen are in the container? (R = 8.31 J/mol ∙ K, 1 atm = 101 kPa) A) 1.5 × 1021 mol B) 3.0 × 1021 mol C) 6.0 × 1021 mol D) 1.2 × 1022 mol E) 2.4 × 1022 mol Answer: D Var: 1 138) What is the total translational kinetic energy of the gas in a classroom filled with nitrogen at at The dimensions of the classroom are The -23 Boltzmann constant is 1.3806503 × 10 J/K, R = 8.31 J/mol ∙ K, and NA = 6.022 × 1023 molecules/mol. Answer: 3.19 × 107 J Var: 50+ 139) A flask contains a mixture of argon and neon gases at a stabilized temperature. The rootmean-square speed of the argon gas is determined to be 1.21 km/s. What is the root-mean-square speed of the neon gas? The atomic mass of argon is 39.95 g/mol, and that of neon is 20.18 g/mol. Answer: 1700 m/s Var: 1 140) (a) At what Celsius temperature is the average kinetic energy of a helium gas atom equal to 6.21 × 10-21 J? The Boltzmann constant is 1.38 × 10-23 J/K . (b) What would be the temperature for radon gas? Answer: (a) 27°C (b) 27°C Var: 1 141) What is the average translational kinetic energy of an ideal gas at constant is 1.38 × 10-23 J/K. A) 1.70 x 10-20 J B) 5.65 x 10-21 J C) 1.13 x 10-17 J D) 3.77 x 10-19 J Answer: A Var: 50+

The Boltzmann

142) A sealed container holds 0.020 moles of ideal nitrogen (N2) gas, at a pressure of 1.5 atm and a temperature of 290 K. The atomic mass of nitrogen is 14.0 g/mol. What is the average translational kinetic energy of a nitrogen molecule? The Boltzmann constant is 1.38 × 10-23 J/K. A) 4.0 ×1021 J B) 6.0 ×1021 J C) 8.0 ×1021 J D) 10 ×1021 J E) 12 ×1021 J Answer: B Var: 1 143) The rms speed of a certain sample of carbon dioxide molecules, with a molecular weight of 44.0 g/mole, is 396 m/s. What is the rms speed of water vapor molecules, with a molecular weight of 18.0 g/mol, at the same temperature as the carbon dioxide? A) 253 m/s B) 387 m/s C) 421 m/s D) 506 m/s E) 619 m/s Answer: E Var: 1 144) What is the average translational kinetic energy of a nitrogen molecule in the air in a room in which the air temperature is 17°C? The Boltzmann constant is 1.38 × 10-23 J/K. A) 6.01 × 10-21 J B) 4.00 × 10-21 J C) 5.00 × 10-21 J D) 7.00 × 10-21 J E) 9.00 × 10-21 J Answer: A Var: 1 145) The molecular weight of nitrogen, N2, is 28 g/mol. What is the rms speed of nitrogen molecules in a cooler at 8.0°C? The Boltzmann constant is 1.38 × 10-23 J/K and NA = 6.022 × 1023 molecules/mol. A) 450 m/s B) 500 m/s C) 550 m/s D) 600 m/s E) 650 m/s Answer: B Var: 1

146) At what temperature is the rms speed of hydrogen molecules, H2, which have a molecular weight of 2.02 g/mole, equal to 2.0 km/s? The Boltzmann constant is 1.38 × 10-23 J/K and NA = 6.022 × 1023 molecules/mol. A) 17°C B) 34°C C) 51°C D) 68°C E) 72°C Answer: C Var: 1 147) A 0.50 gas tank holds 3.0 moles of ideal diatomic nitrogen gas at a temperature of The atomic mass of nitrogen is . What is the rms speed of the molecules? (The Boltzmann constant is 1.38 × 10-23 J/K, NA = 6.022 × 1023 molecules/mol.) A) 560 B) 790 C) 390 D) 21 E) 97 Answer: A Var: 50+ 148) At what temperature would the root mean square speed of oxygen molecules, O2, be if oxygen behaves like an ideal gas? The mass of one O2 molecule is 5.312 × 10-26 kg, and the Boltzmann constant is 1.38 × 10-23 J/K. A) 0.251 K B) 2090 K C) 6270 K D) 1.52 × 1023 K Answer: A Var: 6 149) If the temperature of a gas is increased from 20°C to 100°C, by what factor does the rms speed of an ideal molecule change? A) 1.1 B) 1.3 C) 2.2 D) 1.6 Answer: A Var: 47

150) An oxygen molecule, O2, falls in a vacuum. From what height must it fall so that its translational kinetic energy at the bottom of its fall equals the average translational kinetic energy of an oxygen molecule at 920 K? The mass of one O2 molecule is 5.312 × 10-26 kg, and the Boltzmann constant is 1.38 × 10-23 J/K. Neglect air resistance and assume that g remains constant at 9.8 m/s2 throughout the fall of the molecule. A) 49 km B) 12 km C) 24 km D) 37 km E) 5.2 km Answer: D Var: 1 151) Dust particles in a grain elevator frequently have masses of the order of 1.0 × 10-9 kg. If, to a first approximation, we model the dust particles as an ideal gas, what would be the rms speed of such a particle in air at 27°C? The Boltzmann constant is 1.38 × 10-23 J/K . A) 3.5 × 10-6 m/s B) 5.6 × 10-5 m/s C) 7.8 × 10-4 m/s D) 5.2 × 10-3 m/s E) 4.9 × 10-2 m/s Answer: A Var: 1 152) At what temperature would the root-mean-square speed of hydrogen, H2, molecules equal 11.2 km/s (the earth's escape speed)? The mass of a hydrogen atom is 1.67 × 10-27 kg, and the Boltzmann constant is 1.38 × 10-23 J/K. A) 1.01 × 102 K B) 1.01 × 104 K C) 1.01 × 106 K D) 1.01 × 108 K Answer: B Var: 1 153) If the temperature of an ideal gas is increased from 20°C to 40°C, by what percent does the speed of the molecules increase? A) 3% B) 30% C) 70% D) 100% Answer: A Var: 1

154) If an ideal gas molecule has a speed of 0.50 km/s at 20°C, what is its speed at 80°C? A) 500 m/s B) 550 m/s C) 1000 m/s D) 2000 m/s Answer: B Var: 1 155) How much heat is required to raise the temperature of 2.00 moles of an ideal monatomic gas by 10 C° at constant volume? (R = 8.31 J/mol ∙ K). A) 249 J B) 416 J C) 208 J D) 200 J E) 125 J Answer: A Var: 1 156) A rigid container is filled with 4.0 mol of air with CV = 2.5R. How much does the internal (thermal) energy of the air change if its temperature rises from to (R = 8.31 J/mol ∙ K) A) 35,800 J B) 430 J C) 3580 J D) 8940 J Answer: A Var: 50+ 157) How much heat is required to increase the temperature of 1.70 moles of an ideal monatomic gas by 23.0 K at constant pressure? (R = 8.31 J/mol ∙ K) A) 812 J B) 346 J C) 751 J D) 391 J E) 290 J Answer: A Var: 1 158) If we add 700 J of heat to 12 moles of an ideal monatomic gas at constant volume, what will be the change in temperature of the gas? (R = 8.31 J/mol ∙ K) A) 4.7 K B) 5.2 K C) 5.8 J D) 6.8 K E) 9.3 K Answer: A Var: 1 54 Copyright © 2019 Pearson Education, Inc.

159) A sealed 87- tank is filled with 6000 moles of ideal oxygen gas O2 at an initial temperature of 270 K. The gas is heated to a final temperature of 460 K. The atomic mass of oxygen is 16.0 g/mol. How much heat is transferred to the gas during this process? (R = 8.31 J/mol ∙ K) A) 24 MJ B) 28 MJ C) 19 MJ D) 14 MJ E) 9.1 MJ Answer: A Var: 50+ 160) A container with rigid walls is filled with 4.00 mol of air at 17°C with CV = 2.5R. What is the final temperature of the air if its internal energy is increased by 28 kJ? (R = 8.31 J/mol ∙ K) A) 337°C B) 354°C C) 337 K D) 354 K E) 610 K Answer: B Var: 1 161) A sample of ideal monatomic gas is cooled by 50.0 C° at constant volume by removing 831 J of energy from it. How many moles of gas are in the sample? (R = 8.31 J/mol ∙ K) A) 2.50 mol B) 1.50 mol C) 1.33 mol D) 1.00 mol Answer: C Var: 1 162) The temperature of an ideal gas in a sealed rigid 0.60- container is reduced from 460 K to The final pressure of the gas is The molar heat capacity at constant volume of the gas is 28.0 J/mol ∙ K. How much heat is absorbed by the gas during this process? (R = 8.31 J/mol ∙ K) A) -130 kJ B) -170 kJ C) 130 kJ D) 170 kJ E) 0 kJ Answer: A Var: 50+

163) The figure shows a pV diagram for 2.6 g of ideal helium gas that undergoes the process 1 → 2 → 3. Find the value of volume V3. The atomic mass of helium is 4.0 g/mol, and R = 8.31 J/mol ∙ K.

A) 25 L B) 99 L C) 50 L D) 12 L Answer: A Var: 50+ 164) The figure shows a pV diagram for 8.3 g of ideal nitrogen gas N2 in a sealed container. The temperature of state 1 is 59°C, the atomic mass of the nitrogen atom is 14 g/mol, and R = 8.31 J/mol ∙ K. What are (a) pressure p1 and (b) temperature T2?

A) (a) 81 atm, (b) 660°C B) (a) 14 atm, (b) 660°C C) (a) 81 atm, (b) 120°C D) (a) 14 atm, (b) 120°C Answer: A Var: 50+

165) The figure shows a pV diagram for 2.9 g of ideal oxygen gas O2 in a sealed container. The temperature of state 1 is 76° C, the atomic mass of the oxygen atom is 16 g/mol, and R = 8.31 J/mol ∙ K. What are the temperatures T3 and T4?

A) -11° C and 510° C B) 57° C and 170° C C) 260° C and 790° C D) 38° C and 110° C Answer: A Var: 50+ 166) The figure shows a pV diagram for 0.98 mol of ideal gas that undergoes the process 1 → 2. The gas then undergoes an isochoric heating from point 2 until the pressure is restored to the value it had at point 1. What is the final temperature of the gas? (R = 8.31 J/mol ∙ K).

A) -160°C B) 12°C C) 380°C D) 110°C Answer: A Var: 50+

167) The figure shows a pV diagram for 0.0061 mol of ideal gas that undergoes the process 1 → 2 → 3. What is the pressure p2? (R = 8.31 J/mol ∙ K)

A) 4.9 atm B) 4.9 × 105 atm C) 15 atm D) 1.5 × 106 atm Answer: A Var: 30 168) The figure shows a pV diagram for 0.0077 mol of ideal gas that undergoes the process 1 → 2 → 3. What is the volume V3? (R = 8.31 J/mol ∙ K)

the volume V3? A) 770 B) 0 C) 0 D) 400 Answer: A Var: 47 169) The temperature of an ideal gas in a sealed rigid 0.20- container is reduced from 360 K to and the final pressure of the gas is How much work is done by the gas during this process? (R = 8.31 J/mol ∙ K) A) 0 kJ B) -9.0 kJ C) -12 kJ D) 9.0 kJ E) 12 kJ Answer: A Var: 50+

170) A compression at a constant pressure of 200 kPa is performed on 8.00 moles of an ideal monatomic gas. The compression reduces the volume of the gas from to How much work was done by the gas during this process? A) -16 kJ B) 16 kJ C) -40 kJ D) 40 kJ E) 0 kJ Answer: A Var: 50+ 171) An expansion process on an ideal diatomic ideal gas has a linear path between the initial and final coordinates on a pV diagram. The coordinates of the initial state are: the pressure is 300 kPa, the volume is and the temperature is The final pressure is and the final temperature is How much work is done by the gas during this process? (R = 8.31 J/mol ∙ K) A) 13,000 J B) 6300 J C) 9400 J D) 16,000 J E) 19,000 J Answer: A Var: 50+ 172) The figure shows a pV diagram for an ideal gas that is carried around a cyclic process. How much work is done in one cycle if p0 = and L? (1.00 atm = 101 kPa)

A) 1210 J B) 485 J C) 2280 J D) 2420 J E) 4850 J Answer: A Var: 50+

173) An ideal gas undergoes the process a→b→c→a shown in the pV diagram. In this figure, Pa = Pc = 3.60 × 105 Pa, Vb = Vc = 68.00 L, Va = 35 L, and Pb = 5.60 × 105 Pa. How much work is done by the system in this process?

A) 2300 J B) 3300 J C) 2800 J D) 3800 J E) 3000 J Answer: B Var: 1 174) A gas expands from an initial volume of 30.0 L to a final volume of 65.0 L at a constant pressure of 110 kPa. How much work is done by the gas during this expansion? A) 3.85 kJ B) 10.4 kJ C) 3850 kJ D) 10.4 MJ E) 3.85 MJ Answer: A Var: 1 175) A gas expands from an initial volume of 0.040 m3 to a final volume of 0.085 m3 while its pressure increases linearly with the volume (so that the process follows a straight-line path in a pV diagram) from 110 kPa to 225 kPa. How much work is done by the gas during this expansion? A) 5.2 kJ B) 7.5 kJ C) 7.8 kJ D) 11 kJ E) 12 kJ Answer: B Var: 1

College Physics: A Strategic Approach, 4e (Knight) Chapter 13 Fluids 13.1 Conceptual Questions 1) Substance A has a density of 3 g/cm3 and substance B has a density of 4 g/cm3. In order to obtain equal masses of these two substances, what must be the ratio of the volume of A to the volume of B? A)

Answer: B Var: 1 2) A hollow sphere of negligible mass and radius R is completely filled with a liquid so that its density is ρ. You now enlarge the sphere so its radius is 2R and completely fill it with the same liquid. What is the density of the enlarged sphere? A) 8 ρ B) 4 ρ C) ρ/2 D) ρ E) ρ/8 Answer: D Var: 1 3) A styrofoam sphere of radius R has a density ρ. You now carefully compress the sphere so its radius is R/2. What is the density of the compressed sphere? A) 2 ρ B) 4 ρ C) ρ D) ρ E) 8 ρ Answer: E Var: 1

4) When a box rests on a round sheet of wood on the ground, it exerts an average pressure p on the wood. If the wood is replaced by a sheet that has half the diameter of the original piece, what is the new average pressure? A) 4p B) 2p C) p D) p/2 E) p/4 Answer: A Var: 1 5) When a heavy metal block is supported by a cylindrical vertical post of radius R, it exerts a force F on the post. If the diameter of the post is increased to 2R, what force does the block now exert on the post? A) F/4 B) F/2 C) F/ D) F E) 2F Answer: D Var: 1 6) As shown in the figure, fluid fills a container having several sections. At which of the indicated points is the pressure greatest?

A) A B) B C) C D) D E) The pressure is the same at each of the labeled points. Answer: E Var: 1

7) Consider a brick that is totally immersed in water, with the long edge of the brick vertical. The pressure on the brick is A) the same on all surfaces of the brick. B) greatest on the face with largest area. C) greatest on the top of the brick. D) greatest on the sides of the brick. E) greatest on the bottom of the brick. Answer: E Var: 1 8) An air bubble underwater has the same pressure as that of the surrounding water. As the air bubble rises toward the surface (and its temperature remains constant), the volume of the air bubble A) increases. B) decreases. C) remains constant. D) increases or decreases, depending on the rate it rises. Answer: A Var: 1

9) A cubical block of stone is lowered at a steady rate into the ocean by a crane, always keeping the top and bottom faces horizontal. Which one of the following graphs best describes the gauge pressure p on the bottom of this block as a function of time t if the block just enters the water at time t = 0 s?

Answer: A Var: 1

10) A cubical block of stone is lowered at a steady rate into the ocean by a crane, always keeping the top and bottom faces horizontal. Which one of the following graphs best describes the absolute (total) pressure p on the bottom of this block as a function of time t if the block just enters the water at time t = 0 s?

Answer: C Var: 1 11) If atmospheric pressure increases by an amount Δp, which of the following statements about the pressure in a lake is true? (There could be more than one correct choice.) A) The absolute (total) pressure does not change. B) The absolute (total) pressure increases, but by an amount less than Δp. C) The absolute (total) pressure increases by Δp. D) The gauge pressure increases by Δp. E) The gauge pressure does not change. Answer: C, E Var: 1

12) A closed cubical chamber resting on the floor contains oil and a piston. If you push down on the piston hard enough to increase the pressure just below the piston by an amount Δp, which of the following statements is correct? (There could be more than one correct choice.) A) The pressure everywhere in the oil will increase by Δp. B) The pressure at the bottom of the oil will increase by more than Δp. C) The pressure at the top of the oil will increase by less than Δp. D) The pressure on the sides of the chamber will not increase. E) The increase in the force on the top of the chamber will be the same as the increase in the force on the bottom of the chamber. Answer: A, E Var: 1 13) The water pressure to an apartment is increased by the water company. The water enters the apartment through an entrance valve at the front of the apartment. Where will the increase in the static water pressure be greatest when no water is flowing in the system? A) at a faucet close to the entrance valve B) at a faucet far from the entrance valve C) It will be the same at all faucets. D) There will be no increase in the pressure at the faucets. Answer: C Var: 1 14) A waiter fills your water glass with ice water (containing many ice cubes) such that the liquid water is perfectly level with the rim of the glass. As the ice melts, A) the liquid-water level remains flush with the rim of the glass. B) the liquid water level rises, causing water to run down the outside of the glass. C) the liquid-water level decreases. Answer: A Var: 1 15) A spherical ball of lead (density 11.3 g/cm3) is placed in a tub of mercury (density 13.6 g/cm3). Which answer best describes the result? A) The lead ball will float with about 83% of its volume above the surface of the mercury. B) The lead ball will float with its top exactly even with the surface of the mercury. C) The lead ball will float with about 17% of its volume above the surface of the mercury. D) The lead will sink to the bottom of the mercury. Answer: C Var: 1 16) A wooden block contains some nails so that its density is exactly equal to that of water. If it is placed in a tank of water and released from rest when it is completely submerged, it will A) rise to the surface. B) sink to the bottom. C) remain where it is released. Answer: C Var: 1 6 Copyright © 2019 Pearson Education, Inc.

17) A boat loaded with rocks is floating in a swimming pool. If the rocks are thrown into the pool, the water level in the pool, after the rocks have settled to the bottom, A) rises. B) falls. C) stays the same. Answer: B Var: 1 18) Salt water has greater density than fresh water. A boat floats in both fresh water and in salt water. Where is the buoyant force greater on the boat? A) in salt water B) in fresh water C) The buoyant force is the same in both cases. Answer: C Var: 1 19) Salt water is denser than fresh water. A ship floats in both fresh water and salt water. Compared to the fresh water, the volume of water displaced in the salt water is A) more. B) less. C) the same. D) Cannot be determined because we do not know the volume of the ship. Answer: B Var: 1 20) A steel ball sinks in water but floats in a pool of mercury, which is much denser than water. Where is the buoyant force on the ball greater? A) floating on the mercury B) submerged in the water C) It is the same in both cases. D) It cannot be determined from the information given. Answer: A Var: 1 21) A 10-kg piece of aluminum sits at the bottom of a lake, right next to a 10-kg piece of lead, which is much denser than aluminum. Which one has the greater buoyant force on it? A) the aluminum B) the lead C) Both have the same buoyant force. D) It cannot be determined without knowing their volumes. Answer: A Var: 1

22) A piece of iron rests on top of a piece of wood floating in a bathtub. If the iron is removed from the wood, and kept out of the water, what happens to the water level in the tub? A) It goes up. B) It goes down. C) It does not change. D) It is impossible to determine from the information given. Answer: B Var: 1 23) A piece of wood is floating in a bathtub. A second piece of wood sits on top of the first piece, and does not touch the water. If the top piece is taken off and placed in the water, what happens to the water level in the tub? A) It goes up. B) It goes down. C) It does not change. D) It cannot be determined without knowing the volumes of the two pieces of wood. Answer: C Var: 1 24) As a rock sinks deeper and deeper into water of constant density, what happens to the buoyant force on it if it started above the surface of the water? A) The buoyant force keeps increasing steadily. B) The buoyant force remains constant. C) The buoyant force first increases and then remains constant. D) The buoyant force steadily decreases. Answer: C Var: 1

25) A cubical block of stone is lowered at a steady rate into the ocean by a crane, always keeping the top and bottom faces horizontal. Which one of the following graphs best describes the buoyant force B on this block as a function of time t if the block just enters the water at time t = 0 s?

Answer: B Var: 1 26) A 50-cm3 block of wood is floating on water, and a 50-cm3 chunk of iron is totally submerged in the water. Which one has the greater buoyant force on it? A) the wood B) the iron C) Both have the same buoyant force. D) It cannot be determined without knowing their densities. Answer: B Var: 1 27) When you blow some air above a paper strip, the paper rises. This happens because A) the air above the paper moves faster and the pressure is higher. B) the air above the paper moves faster and the pressure is lower. C) the air above the paper moves faster and the pressure remains constant. D) the air above the paper moves slower and the pressure is higher. E) the air above the paper moves slower and the pressure is lower. Answer: B Var: 1 9 Copyright © 2019 Pearson Education, Inc.

28) Water flows through a pipe. The diameter of the pipe at point B is larger than at point A. Where is the water pressure greatest? A) at point A B) at point B C) It is the same at both A and B. Answer: B Var: 1 29) Two horizontal pipes are the same length, but pipe B has twice the diameter of pipe A. Water undergoes viscous flow in both pipes, subject to the same pressure difference across the lengths of the pipes. If the flow rate in pipe A is Q =

, what is the flow rate in pipe B?

A) 2Q B) 4Q C) 8Q D) 16Q E) Q Answer: D Var: 1 30) Two horizontal pipes have the same diameter, but pipe B is twice as long as pipe A. Water undergoes viscous flow in both pipes, subject to the same pressure difference across the lengths of the pipes. If the flow rate in pipe B is Q =

what is the flow rate in pipe A?

A) 2Q B) 4Q C) 8Q D) 16Q E) Q Answer: A Var: 1

13.2 Problems 1) A plastic block of dimensions 2.00 cm × 3.00 cm × 4.00 cm has a mass of 30.0 g. What is its density? A) 0.80 g/cm3 B) 1.20 g/cm3 C) 1.25 g/cm3 D) 1.60 g/cm3 Answer: C Var: 1 2) A compressed gas with a total mass of is stored in a spherical container having a radius of 0.521 m. What is the density of the compressed gas? A) 181 kg/m3 B) 110 kg/m3 C) 134 kg/m3 D) 161 kg/m3 Answer: A Var: 50+ 3) The density of material at the center of a neutron star is approximately 1.00 × 1018 kg/m3. What is the mass of a cube of this material that is on each side. (One micron is equal to 1.00 × 10-6 m.) A) 5.45 kg B) 4.74 kg C) 6.16 kg D) 6.70 kg Answer: A Var: 50+ 4) Under standard conditions, the density of air is 1.29 kg/m3. What is the mass of the air inside a room measuring 4.0 m × 3.0 m × 2.0 m? A) 0.32 kg B) 3.1 kg C) 31 kg D) 1.9 kg E) 19 kg Answer: C Var: 1

5) A round coin has a diameter of 19.55 mm, a thickness of 1.55 mm, and a mass of 2.50 g. What is its density? A) 5.37 × 103 kg/m3 B) 21.5 × 103 kg/m3 C) 1.34 × 103 kg/m3 D) 2.68 × 103 kg/m3 E) 1.86 × 10-4 kg/m3 Answer: A Var: 1 6) A 1938 nickel has a diameter of 21.21 mm, a thickness of 1.95 mm, and weighs 0.04905 N. What is its density? A) 1.37 × 10-4 kg/m3 B) 1.82 × 103 kg/m3 C) 19.3 × 103 kg/m3 D) 3.63 × 103 kg/m3 E) 7.26 × 103 kg/m3 Answer: E Var: 1 7) How many grams of ethanol (density 0.80 g/cm3) should be added to 5.0 g of chloroform (density 1.5 g/cm3) if the resulting mixture is to have a density of 1.2 g/cm3? Assume that the fluids do not change their volumes when they are mixed. A) 2.0 g B) 2.4 g C) 1.8 g D) 4.4 g E) 1.6 g Answer: A Var: 1 8) A 100-kg person sits on a 5-kg bicycle. The total weight is borne equally by the two wheels of the bicycle. The tires are 2.0 cm wide and are inflated to a gauge pressure of 8.0 × 105 Pa. What length of each tire is in contact with the ground? A) 1.6 cm B) 1.8 cm C) 3.2 cm D) 2.4 cm E) 6.4 cm Answer: C Var: 1 12 Copyright © 2019 Pearson Education, Inc.

9) The weight of a 1200-kg car is supported equally by the four tires, which are inflated to the same gauge pressure. What gauge pressure is required so the area of contact of each tire with the road is 100 cm2? A) 12 × 105 Pa B) 12 × 104 Pa C) 2.9 × 105 Pa D) 2.9 × 104 Pa Answer: C Var: 1 10) One of the dangers of tornados and hurricanes is the rapid drop in air pressure that is associated with such storms. Assume that the air pressure inside of a sealed house is 1.02 atm when a hurricane hits. The hurricane rapidly decreases the external air pressure to 0.910 atm. What net outward force is exerted on a square window of the house that is on each side? (1.00 atm = 1.01 × 105 Pa) A) 4.59 × 104 N B) 5.19 × 104 N C) 4.82 × 105 N D) 5.42 × 105 N Answer: A Var: 50+ 11) Calculate the pressure exerted on the ground due to the weight of one foot. if the bottom of the person's foot is wide and long. 4 A) 2.1 × 10 Pa B) 2.2 × 103 Pa C) 4.8 × 104 Pa D) 5.3 × 104 Pa Answer: A Var: 36

person standing on

12) A brick weighs 50.0 N, and measures 30.0 cm × 10.0 cm × 4.00 cm. What is the maximum pressure it can exert on a horizontal surface due to its weight? A) 1.25 Pa B) 12.5 Pa C) 1.25 kPa D) 12.5 kPa Answer: D Var: 1

13) A person weighing 900 N is standing on snowshoes. Each snowshoe has area 2500 cm2 and has negligible weight. What pressure does this person's weight exert on the snow? A) 0.18 N/m2 B) 0.36 N/m2 C) 1800 N/m2 D) 3600 N/m2 Answer: C Var: 1 14) A water tank is filled to a depth of 10 m, and the bottom of the tank is 20 m above ground. A water-filled hose that is 2.0 cm in diameter extends from the bottom of the tank to the ground, but no water is flowing in this hose. The water pressure at ground level in the hose is closest to which of the following values? The density of water is 1000 kg/m3. A) 3.9 × 105 N/m2 B) 2.0 × 104 N/m2 C) 9.2 N/m2 D) The question cannot be answered because the cross sectional area of the tank is needed. Answer: A Var: 1 15) The Aswan High Dam on the Nile River in Egypt is 111 m high. What is the gauge pressure in the water at the foot of the dam? The density of water is 1000 kg/m3. A) 1.09 × 106 Pa B) 1.16 × 106 Pa C) 1.09 × 103 Pa D) 1.11 × 105 Pa E) 1.11 × 102 Pa Answer: A Var: 1 16) The deepest point of the Pacific Ocean is 11,033 m, in the Mariana Trench. What is the gauge pressure in the water at that point? The density of seawater is 1025 kg/m3. A) 5.55 × 107 Pa B) 8.88 × 107 Pa C) 1.11 × 108 Pa D) 2.22 × 108 Pa E) 3.33 × 108 Pa Answer: C Var: 1 14 Copyright © 2019 Pearson Education, Inc.

17) The Tonga Trench in the Pacific Ocean is 36,000 feet deep. Assuming that sea water has an average density of 1.04 g/cm3, calculate the absolute (total) pressure at the bottom of the trench in atmospheres. (1.00 in = 2.54 cm, 1.00 atm = 1.01 × 105 Pa) A) 1.1 × 103 atm B) 1.1 × 108 atm C) 1.1 × 105 atm D) 1.1 × 106 atm E) 2.1 atm Answer: A Var: 1 18) What force does the water exert (in addition to that due to atmospheric pressure) on a submarine window of radius 44.0 cm at a depth of 9400 m in sea water? The density of sea water is 1025 kg/m3. A) 5.74 × 107 N B) 5.74 × 1011 N C) 2.87 × 1011 N D) 1.83 × 107 N E) 2.87 × 107 N Answer: A Var: 50+ 19) A cubical box 25.0 cm on each side is immersed in a fluid. The pressure at the top surface of the box is 109.40 kPa and the pressure on the bottom surface is 112.00 kPa. What is the density of the fluid? A) 1000 kg/m3 B) 1030 kg/m3 C) 1060 kg/m3 D) 1090 kg/m3 E) 1120 kg/m3 Answer: C Var: 1 20) A circular window 30 cm in diameter in a submarine can withstand a net maximum force of 5.20 × 105 N without damage. What is the maximum depth in a fresh-water lake to which the submarine can go without damaging the window? The density of fresh water is 1000 kg/m3. A) 680 m B) 740 m C) 1200 m D) 750 m Answer: D Var: 1 15 Copyright © 2019 Pearson Education, Inc.

21) A container has a vertical tube, whose inner radius is 24.00 mm, connected to it at its side, as shown in the figure. An unknown liquid reaches level A in the container and level B in the tube– level A being 5.0 cm higher than level B. The liquid supports a 20-cm high column of oil, between levels B and C, whose density is The mass of the oil is closest to

A) 210 B) 410 C) 620 D) 820 E) 1000 Answer: A Var: 50+ 22) A container has a vertical tube, whose inner radius is 12.00 mm, connected to it at its side, as shown in the figure. An unknown liquid reaches level A in the container and level B in the tube– level A being 5.0 cm higher than level B. The liquid supports a 20-cm high column of oil, between levels B and C, whose density is The gauge pressure at level B is closest to

A) 630 Pa B) 310 Pa C) 470 Pa D) 790 Pa E) 940 Pa Answer: A Var: 50+

23) A container has a vertical tube, whose inner radius is 20.00 mm, connected to it at its side, as shown in the figure. An unknown liquid reaches level A in the container and level B in the tube– level A being 5.0 cm higher than level B. The liquid supports a 20-cm high column of oil, between levels B and C, whose density is The density of the unknown liquid is closest to

A) 3600 kg/ B) 3900 kg/ C) 2800 kg/ D) 3100 kg/ E) 3300 kg/ Answer: A Var: 50+ 24) As shown in the figure, a large open tank contains a layer of oil ( density 450 kg/ ) floating on top of a layer of water (density 1000 kg/m3) that is 3.0 m thick, as shown in the sketch. What must be the thickness of the oil layer if the gauge pressure at the bottom of the tank is to be

Answer: 13 m Var: 50+ 25) A container consists of two vertical cylindrical columns of different diameter connected by a narrow horizontal section, as shown in the figure. The open faces of the two columns are closed by very light plates that can move up and down without friction. The tube diameter at A is 35.0 cm and at B it is 10.2 cm. This container is filled with oil of density 0.820 g/cm3. If a 125-kg object is placed on the larger plate at A, how much mass should be placed on the smaller plate at B to balance it?

26) A 12,000-N car is raised using a hydraulic lift, which consists of a U-tube with arms of unequal areas, filled with oil and capped at both ends with tight-fitting pistons. The wider arm of the U-tube has a radius of 18.0 cm and the narrower arm has a radius of 5.00 cm. The car rests on the piston on the wider arm of the U-tube. The pistons are initially at the same level. What is the initial force that must be applied to the smaller piston in order to start lifting the car? For purposes of this problem, neglect the weight of the pistons. A) 727 N B) 926 N C) 2.90 kN D) 3.33 kN E) 1.20 kN Answer: B Var: 1 27) A 12,000-N car is raised using a hydraulic lift, which consists of a U-tube with arms of unequal areas, filled with oil with a density of 800 kg/m3 and capped at both ends with tightfitting pistons. The wider arm of the U-tube has a radius of 18.0 cm and the narrower arm has a radius of 5.00 cm. The car rests on the piston on the wider arm of the U-tube. The pistons are initially at the same level. What is the force that must be applied to the smaller piston in order to lift the car after it has been raised 1.20 m? For purposes of this problem, neglect the weight of the pistons. A) 0.954 kN B) 1.88 kN C) 1.96 kN D) 3.67 kN E) 1.20 kN Answer: C Var: 1 28) A 500-N weight sits on the small piston of a hydraulic machine. The small piston has an area of 2.0 cm2. If the large piston has an area of 40 cm2, how much weight can the large piston support? Assume the pistons each have negligible weight. A) 25 N B) 500 N C) 10000 N D) 40000 N Answer: C Var: 1

29) In a hydraulic garage lift, the small piston has a radius of 5.0 cm and the large piston has a radius of 15 cm. What force must be applied on the small piston in order to lift a car weighing 20,000 N on the large piston? Assume the pistons each have negligible weight. A) 6.7 × 103 N B) 5.0 × 103 N C) 2.9 × 103 N D) 2.2 × 103 N Answer: D Var: 1 30) A 13,000-N vehicle is to be lifted by a 25-cm diameter hydraulic piston. What force needs to be applied to a 5.0 cm diameter piston to accomplish this? Assume the pistons each have negligible weight. A) 260 N B) 520 N C) 2600 N D) 5200 N Answer: B Var: 1 31) The small piston of a hydraulic lift has a diameter of 8.0 cm, and its large piston has a diameter of 40 cm. The lift raises a load of 15,000 N. Assume the pistons each have negligible weight. (a) Determine the force that must be applied to the small piston. (b) Determine the pressure applied to the fluid in the lift. Answer: (a) 600 N (b) 1.2 × 105 Pa Var: 1 32) A block of metal weighs 40 N in air and 30 N in water. What is the buoyant force on the block due to the water? The density of water is 1000 kg/m3. A) 10 N B) 30 N C) 40 N D) 70 N Answer: A Var: 3

33) If a ship has a mass of 10 million kilograms, what volume of fresh water must it displace in order to float? The density of water is 1000 kg/m3. A) 1010 m3 B) 1012 m3 C) 104 m3 D) 107 m3 E) 108 m3 Answer: C Var: 1 34) An object has a volume of 4.0 m3 and weighs 40,000 N. What will its apparent weight be in water of density 1000 kg/m3? A) 40,000 N B) 39,200 N C) 9,800 N D) 800 N Answer: D Var: 1 35) A 4.0-kg cylinder of solid iron is supported by a string while submerged in water. What is the tension in the string? The density of iron is 7860 kg/m3 and that of water is 1000 kg/m3. A) 2.5 N B) 20 N C) 24 N D) 34 N E) 40 N Answer: D Var: 1 36) What buoyant force does a 0.60-kg solid gold crown experience when it is immersed in water? The density of gold is 19.3 × 103 kg/m3 and that of water is 1000 kg/m3. A) 3.0 × 10-5 N B) 3.0 × 10-4 N C) 3.0 × 10-2 N D) 0.30 N Answer: D Var: 1

37) A crane lifts a steel submarine of density 7800 kg/m3 and mass 20,000 kg. What is the tension in the lifting cable (a) when the submarine is submerged in water of density 1000 kg/m3, and (b) when it is entirely out of the water? A) (a) 2.0 × 105 N (b) 1.7 × 105 N B) (a) 1.7 × 105 N (b) 2.0 × 105 N C) (a) 2.6 × 103 N (b) 2.0 × 105 N D) (a) 2.0 × 105 N (b) 2.6 × 103 N Answer: B Var: 1 38) An object weighs 7.84 N when it is in air and 6.86 N when it is immersed in water of density 1000 kg/m3. What is the density of the object? A) 6000 kg/m3 B) 7000 kg/m3 C) 8000 kg/m3 D) 9000 kg/m3 Answer: C Var: 1 39) When a container of water is placed on a laboratory scale, the scale reads 120 g. Now a 20-g piece of copper (of density 8.9 g/cm3) is suspended from a thread and lowered into the water, not touching the bottom of the container. What will the scale now read? The density of water is 1.0 g/cm3. A) 120 g B) 122 g C) 138 g D) 140 g Answer: B Var: 1 40) A piece of aluminum with a mass of 1.0 kg and density of 2700 kg/m3 is suspended from a light cord and then completely immersed in a container of water having density 1000 kg/m3. (a) Determine the volume of the piece of aluminum. (b) Determine the tension in the cord when the aluminum is immersed in the container of water. Answer: (a) 3.7 × 10-4 m3 (b) 6.2 N Var: 1

41) A cylindrical rod of length 12 cm and diameter 2.0 cm will just barely float in water of density 1000 kg/m3. What is its mass? A) 38 g B) 75 g C) 150 g D) 300 g Answer: A Var: 1 42) A rectangular box of negligible mass measures 5.0 m long, 1.0 m wide, and 0.50 m high. How many kilograms of mass can be loaded onto the box before it sinks in a lake having water of density 1000 kg/m3? A) 0.50 × 103 kg B) 1.5 × 103 kg C) 2.5 × 103 kg D) 3.5 × 103 kg Answer: C Var: 1 43) A 1.00-m3 object floats in water with 20.0% of its volume above the waterline. What does the object weigh out of the water? The density of water is 1000 kg/m3. A) 1,960 N B) 7,840 N C) 9,800 N D) 11,800 N Answer: B Var: 1 44) An object floats with half its volume beneath the surface of the water. The weight of the displaced water is 2000 N. What is the weight of the object? The density of water is 1000 kg/m3. A) 1000 N B) 2000 N C) 4000 N D) It cannot be determined because we do not know the volume of the object. Answer: B Var: 1

45) A solid object floats in water with three-fourths of its volume beneath the surface. What is the object's density? The density of water is 1000 kg/m3. A) 1333 kg/m3 B) 1000 kg/m3 C) 750 kg/m3 D) 250 kg/m3 Answer: C Var: 1 46) A 200-N object floats with three-fourths of its volume beneath the surface of the water. What is the buoyant force on the object? The density of water is 1000 kg/m3. A) 50 N B) 150 N C) 200 N D) 267 N E) It cannot be determined because we do not know the volume of the object. Answer: C Var: 1 47) A polar bear of mass 200 kg stands on an ice floe that is a uniform 1.0 m thick. What is the minimum area of the floe that will just support the bear in saltwater of density 1030 kg/m3? The density of ice is 980 kg/m3. A) 1.0 m2 B) 2.0 m2 C) 3.0 m2 D) 4.0 m2 Answer: D Var: 1 48) A wooden raft has a mass of 55 kg. When empty it floats in water (density with 64% of its volume submerged. What maximum mass of sand can be put on the raft without sinking it? Answer: 31 kg Var: 50+

49) A hollow steel ball of diameter 3.0 m just barely floats in water. What is the wall thickness of the ball? (ρFe = 7.87 g/cm3, ρwater = 1.00 g/cm3) A) 6.6 cm B) 37 cm C) 131 cm D) 79 cm Answer: A Var: 1 50) A 200-kg flat-bottomed boat floats in fresh water, which has a density of 1000 kg/m3. If the base of the boat is 1.42 m wide and 4.53 m long, to what depth is the bottom of the boat submerged when it carries three passengers whose total mass is A) 7.10 cm B) 7.53 cm C) 7.95 cm D) 8.52 cm Answer: A Var: 50+ 51) A 4.7-kg solid sphere, made of metal whose density is 4000 kg/ , hangs by a light cord. When the sphere is immersed in water, what is the tension in the cord? The density of water is 1000 kg/m3. A) 35 N B) 40 N C) 46 N D) 52 N E) 58 N Answer: A Var: 50+ 52) A solid sphere of mass 8.6 kg, made of metal whose density is 3400 kg/ , hangs by a cord. When the sphere is immersed in a liquid of unknown density, the tension in the cord is 38 N. The density of the liquid is closest to which one of the following values? A) 1900 kg/ B) 1700 kg/ C) 1600 kg/ D) 1500 kg/ E) 1400 kg/ Answer: A Var: 50+

53) A barge is 10 m wide and 60 m long and has vertical sides. The bottom of the boat is 1.2 m below the water surface. What is the weight of the barge and its cargo, if it is floating in fresh water of density 1000 kg/m3? A) 3.5 MN B) 6.4 MN C) 6.8 MN D) 7.1 MN E) 9.5 MN Answer: D Var: 1 54) A barge with vertical sides is 10 m wide and 60 m long and is floating in fresh water of density 1000 kg/m3. How much deeper into the water does the barge sink when 3.0 x 105 kg of coal are loaded on the barge? A) 25 cm B) 50 cm C) 75 cm D) 1.0 m E) 1.5 m Answer: B Var: 1 55) A hot air balloon along with its cargo has a mass of 4.0 x 105 kg, and it holds 7.0 x 105 m3 of hot air. It is floating at a constant height in air with a density of 1.29 kg/m3. What is the density of the hot air in the balloon? A) 1.4 kg/m3 B) 0.72 kg/m3 C) 0.57 kg/m3 D) 0.86 kg/m3 E) 0.43 kg/m3 Answer: B Var: 1 56) A person who weighs 550 N empties her lungs as much as possible and is then completely immersed in water of density 1000 kg/m3 while suspended from a harness. Her apparent weight is now 21.2 N. What is her density? A) 1050 kg/m3 B) 1040 kg/m3 C) 1030 kg/m3 D) 960 kg/m3 E) 56.1 kg/m3 Answer: B Var: 1

57) The bathyscaphe Trieste consists of a thin-walled but very strong cylindrical hull, 15.2 m long and 3.66 m in diameter, filled with gasoline with a density of 880 kg/m3 to make it buoyant. If it is totally submerged in seawater with a density of 1025 kg/m3 and neither rising nor sinking, what is the weight of the Trieste craft? A) 127 kN B) 227 kN C) 327 kN D) 427 kN E) 527 kN Answer: B Var: 1 58) A cylinder, semicircular in cross-section, is 10 m long and 5.0 m in radius. It is completely submerged, with its flat bottom side horizontal and 8.0 m below the water surface, as shown in the figure. What is the magnitude of the net force on the curved upper surface of the halfcylinder? Neglect atmospheric pressure.

A) 2.0 × 106 N B) 2.5 × 106 N C) 3.0 × 106 N D) 3.5 × 106 N E) 4.0 × 106 N Answer: E Var: 1 59) A rectangular wooden block measures 10.0 cm × 4.00 cm × 2.00 cm. When the block is placed in water, it floats horizontally, with its bottom face 1.65 cm below the surface. What is the density of the wood? The density of water is 1.00 g/cm3. A) 0.825 g/cm3 B) 1.21 g/cm3 C) 1.65 g/cm3 D) 0.606 g/cm3 E) 0.350 g/cm3 Answer: A Var: 1

60) Consider a very small hole in the bottom of a tank that is in diameter and filled with water to a height of Find the speed at which the water exits the tank through the hole. A) 4.20 m/s B) 17.64 m/s C) 44.1 m/s D) 48.3 m/s Answer: A Var: 50+ 61) Water flowing through a cylindrical pipe suddenly comes to a section of pipe where the diameter decreases to 86% of its previous value. If the speed of the water in the larger section of the pipe was what is its speed in this smaller section if the water behaves like an ideal incompressible fluid? A) 43 m/s B) 37 m/s C) 28 m/s D) 24 m/s Answer: A Var: 50+ 62) A pump uses a piston of 15 cm diameter that moves at 2.0 cm/s as it pushes a fluid through a pipe. What is the speed of the fluid when it enters a portion of the pipe that is 3.0 mm in diameter? Treat the fluid as ideal and incompressible. A) 50 m/s B) 50 cm/s C) 6.0 cm/s D) 22 cm/s Answer: A Var: 1 63) An incompressible ideal fluid flows steadily through a pipe that has a change in diameter. The fluid speed at a location where the pipe diameter is 8.0 cm is 1.28 m/s. What is the fluid speed at a location where the diameter has narrowed to 4.0 cm? A) 0.32 m/s B) 0.64 m/s C) 1.3 m/s D) 2.6 m/s E) 5.1 m/s Answer: E Var: 1

64) Fluid flows at 2.0 m/s through a pipe of diameter 3.0 cm. What is the volume flow rate of the fluid? A) 1.4 × 10-3 m3/s B) 5.7 × 10-3 m3/s C) 14 m3/s D) 57 m3/s Answer: A Var: 3 65) Ideal incompressible fluid flows through a 4.0-cm-diameter pipe at 1.0 m/s. There is a 2.0 cm diameter constriction in the line. What is the speed of the fluid in this constriction? A) 0.25 m/s B) 0.50 m/s C) 2.0 m/s D) 4.0 m/s Answer: D Var: 1 66) Water, which we can treat as ideal and incompressible, flows at 12 m/s in a horizontal pipe with a pressure of 3.0 × 104 Pa. If the pipe widens to twice its original radius, what is the pressure in the wider section? A) 3.0 × 104 Pa B) 4.9 × 104 Pa C) 7.4 × 104 Pa D) 9.8 × 104 Pa Answer: D Var: 1 67) A hole of radius 1.0 mm forms in the bottom of a very large water storage tank that holds water to a depth of 15 m. At what volume rate will water flow out of the hole? A) 5.4 × 10-4 m3/s B) 5.4 × 10-5 m3/s C) 5.4 × 10-6 m3/s D) 5.4 × 10-7 m3/s Answer: B Var: 1

68) Ideal incompressible water flows through a horizontal pipe of cross-sectional area 10.0 cm2 at a pressure of 0.250 atm with a volume flow rate of 1.00 × 10-3 m3/s. At a valve, the effective cross-sectional area of the pipe is reduced to 5.00 cm2. What is the pressure at the valve? A) 0.112 atm B) 0.157 atm C) 0.200 atm D) 0.235 atm Answer: D Var: 1 69) For a certain patient, the build-up of fatty tissue on the wall of an artery has decreased the arterial radius by 10%. By how much would the pressure provided by the heart have to be increased to maintain a constant volume of blood flow? Model the blood as an ideal incompressible fluid. A) 48% B) 52% C) 46% D) 54% Answer: B Var: 1 70) An ideal incompressible fluid flows at 0.252 m/s through a 44-mm diameter cylindrical pipe. The pipe widens to a square cross sectional area that is 5.5 cm on a side. Assume steady flow throughout the system. (a) What is the speed of the fluid through the square section of pipe? (b) What is the flow rate in liters per minute? Answer: (a) 0.13 m/s (b) 23 L/min Var: 1 71) Ideal incompressible water is flowing in a drainage channel of rectangular cross-section. At one point, the width of the channel is 12 m, the depth of water is 6.0 m, and the speed of the flow is 2.5 m/s. At a point downstream, the width has narrowed to 9.0 m, and the depth of water is 8.0 m. What is the speed of the flow at the second point? A) 2.0 m/s B) 2.5 m/s C) 3.0 m/s D) 3.5 m/s E) 4.0 m/s Answer: B Var: 1

72) Water is flowing in a drainage channel of rectangular cross-section. The width of the channel is 15 m, the depth of water is 8.0 m, and the speed of the flow is 2.5 m/s. What is the mass flow rate of the water? The density of water is 1000 kg/m3. A) 2.0 × 105 kg/s B) 2.0 × 103 kg/s C) 3.0 × 105 kg/s D) 3.0 × 103 kg/s E) 3.0 × 102 kg/s Answer: C Var: 1 73) In a section of horizontal pipe with a diameter of 3.0 cm, the pressure is 100 kPa and water is flowing with a speed of 1.5 m/s. The pipe narrows to 2.0 cm. What is the pressure in the narrower region? Treat the water as an ideal incompressible fluid. A) 95 kPa B) 48 kPa C) 44 kPa D) 230 kPa E) 67 kPa Answer: A Var: 1 74) Water flows through a horizontal pipe of cross-sectional area 10.0 cm2 at a pressure of 0.250 atm with a flow rate is 1.00 L/s. At a valve, the effective cross-sectional area of the pipe is reduced to 5.00 cm2. What is the pressure at the valve? The density of water is 1000 kg/m3, and treat it as an ideal incompressible fluid. A) 0.110 atm B) 0.235 atm C) 0.200 atm D) 0.157 atm E) 7700 Pa Answer: B Var: 1 75) An ideal incompressible fluid flows at 12 m/s in a horizontal pipe. If the pipe widens to twice its original radius, what is the flow speed in the wider section? A) 12 m/s B) 6.0 m/s C) 4.0 m/s D) 3.0 m/s Answer: D Var: 1

76) Water flows out of a large reservoir through an open pipe, as shown in the figure. What is the speed of the water as it comes out of the pipe?

A) 8.9 m/s B) 9.9 m/s C) 13 m/s D) 14 m/s E) 16 m/s Answer: C Var: 1 77) Water flows out of a large reservoir through 5.0-cm diameter pipe. The pipe connects to a 3.0-cm diameter pipe that is open to the atmosphere, as shown in the figure. What is the speed of the water in the 5.0-cm pipe? Treat the water as an ideal incompressible fluid.

A) 2.3 m/s B) 3.2 m/s C) 3.9 m/s D) 8.9 m/s E) 10 m/s Answer: B Var: 1

78) A pressurized cylindrical tank, 5.0 m in diameter, contains water that emerges from the pipe at point C with a speed of as shown in the figure. Point A is 10 m above point B and point C is 3.0 m above point B. The area of the pipe at point B is and the pipe narrows to an area of at point C. Assume that the water is an ideal fluid in laminar flow. The density of water is 1000 kg/m3 The mass flow rate in the pipe is closest to

A) 520 Kg/s. B) 470 Kg/s. C) 420 Kg/s. D) 360 Kg/s. E) 310 Kg/s. Answer: A Var: 50+ 79) A pressurized cylindrical tank, 5.0 m in diameter, contains water that emerges from the pipe at point C with a speed of as shown in the figure. Point A is 10 m above point B and point C is 3.0 m above point B. The area of the pipe at point B is and the pipe narrows to an area of at point C. Assume that the water is an ideal fluid in laminar flow. The density of water is 1000 kg/m3. The rate at which the water level is falling in the tank is closest to

A) 300 mm/s. B) 340 mm/s. C) 250 mm/s. D) 210 mm/s. E) 160 mm/s. Answer: A Var: 50+

80) As shown in the figure, water (density 1000 kg/ ) is flowing in a pipeline. At point 1 the water speed is Point 2 is 5.20 m above point 1. The cross-sectional area of the pipe is 0.0800 at point 1 and at point 2. What is the pressure difference between points 1 and 2? Treat the water as an ideal incompressible fluid.

Answer: 3.12 × 105 Pa Var: 50+ 81) A large cylindrical water tank 11.5 m in diameter and 13.5 m tall is supported with its base 8.75 m above the ground by a stand as shown in the figure. The water level in the tank is 10.6 m deep, and the density of the water in the tank is 1.00 g/cm3. A very small hole is formed at the base of the vertical wall of the tank, and water is squirting out of this hole horizontally. When this water hits the ground, how far has it traveled horizontally from the hole, assuming no air resistance?

Answer: 19.3 m Var: 1

82) Glycerin, with a viscosity of 1.5 N ∙ s/m2, is flowing with an average speed of 1.2 m/s through a tube that has a radius of 5.0 mm and is 25 cm long. What is the drop in pressure over the length of this pipe? A) 140 kPa B) 46 kPa C) 72 kPa D) 76 kPa E) 130 kPa Answer: A Var: 1 83) Motor oil, with a viscosity of 0.25 N ∙ s/m2, is flowing through a tube that has a radius of 3.0 mm and is 1.0 m long. The drop in pressure over the length of the tube is 200 kPa. What is the average speed of the oil? A) 0.80 m/s B) 0.90 m/s C) 1.0 m/s D) 1.1 m/s E) 1.2 m/s Answer: B Var: 1 84) Motor oil, with a viscosity of 0.25 N ∙ s/m2, is flowing through a tube that has a radius of 5.0 mm and is 25 cm long. The drop in pressure is 300 kPa. What is the volume of oil flowing through the tube per second? A) 0.00038 m3/s B) 0.025 m3/s C) 0.0012 m3/s D) 4.7 m3/s E) 7.5 m3/s Answer: C Var: 1 85) A fluid is flowing with an average speed of 1.5 m/s through a tube that has a radius of 2.0 mm and is 18 cm long. The drop in pressure is 967 Pa. What is the viscosity of the fluid? A) 0.0018 N ∙ s/m2 B) 0.0056 N ∙ s/m2 C) 0.028 N ∙ s/m2 D) 0.013 N ∙ s/m2 E) 0.0034 N ∙ s/m2 Answer: A Var: 1

College Physics: A Strategic Approach, 4e (Knight) Chapter 14 Oscillations 14.1 Conceptual Questions 1) If we double the frequency of a system undergoing simple harmonic motion, which of the following statements about that system are true? (There could be more than one correct choice.) A) The period is doubled. B) The angular frequency is doubled. C) The amplitude is doubled. D) The period is reduced to one-half of what it was. E) The angular frequency is reduced to one-half of what it was. Answer: B, D Var: 1 2) A simple harmonic oscillator oscillates with frequency f when its amplitude is A. If the amplitude is now doubled to 2A, what is the new frequency? A) 2f B) 4f C) f D) f/2 E) f/4 Answer: C Var: 1

3) The figure shows a graph of the position x as a function of time t for a system undergoing simple harmonic motion. Which one of the following graphs represents the velocity of this system as a function of time?

A) graph a B) graph b C) graph c D) graph d Answer: B Var: 1

4) The figure shows a graph of the velocity v as a function of time t for a system undergoing simple harmonic motion. Which one of the following graphs represents the acceleration of this system as a function of time?

A) graph a B) graph b C) graph c D) graph d Answer: B Var: 1

5) The figure shows a graph of the position x as a function of time t for a system undergoing simple harmonic motion. Which one of the following graphs represents the acceleration of this system as a function of time?

A) graph a B) graph b C) graph c D) graph d Answer: A Var: 1 6) In simple harmonic motion, when is the speed the greatest? (There could be more than one correct choice.) A) when the magnitude of the acceleration is a maximum B) when the displacement is a maximum C) when the magnitude of the acceleration is a minimum D) when the potential energy is a maximum E) when the potential energy is a zero Answer: C, E Var: 1

7) In simple harmonic motion, when is the magnitude of the acceleration the greatest? (There could be more than one correct choice.) A) when the speed is a maximum B) when the displacement is a zero C) when the magnitude of the displacement is a maximum D) when the potential energy is a maximum E) when the kinetic energy is a minimum Answer: C, D, E Var: 1 8) The total mechanical energy of a simple harmonic oscillating system is A) zero as it passes the equilibrium point. B) zero when it reaches the maximum displacement. C) a maximum when it passes through the equilibrium point. D) a minimum when it passes through the equilibrium point. E) a non-zero constant. Answer: E Var: 1 9) An object attached to an ideal spring executes simple harmonic motion. If you want to double its total energy, you could A) double the amplitude of vibration. B) double the force constant (spring constant) of the spring. C) double both the amplitude and force constant (spring constant). D) double the mass. E) double both the mass and amplitude of vibration. Answer: B Var: 1 10) An object that hangs from the ceiling of a stationary elevator by an ideal spring oscillates with a period T. If the elevator accelerates upward with acceleration 2g, what will be the period of oscillation of the object? A) 4T B) 2T C) T D) T/2 E) T/4 Answer: C Var: 1

11) A mass on a spring undergoes SHM. When the mass passes through the equilibrium position, which of the following statements about it are true? (There could be more than one correct choice.) A) Its acceleration is zero. B) Its speed is zero. C) Its elastic potential energy is zero. D) Its kinetic energy is a maximum. E) Its total mechanical energy is zero. Answer: A, C, D Var: 1 12) A mass on a spring undergoes SHM. When the mass is at its maximum distance from the equilibrium position, which of the following statements about it are true? (There could be more than one correct choice.) A) Its acceleration is zero. B) Its speed is zero. C) Its elastic potential energy is zero. D) Its kinetic energy is a maximum. E) Its total mechanical energy is zero. Answer: B Var: 1 13) An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object located when its kinetic energy is a minimum? A) at either A or B B) midway between A and B C) one-third of the way between A and B D) one-fourth of the way between A and B E) at none of the above points Answer: A Var: 1 14) An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object located when its kinetic energy is a maximum? A) at either A or B B) midway between A and B C) one-third of the way between A and B D) one-fourth of the way between A and B E) at none of the above points Answer: B Var: 1

15) An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object located when its elastic potential energy is a minimum? A) at either A or B B) midway between A and B C) one-third of the way between A and B D) one-fourth of the way between A and B E) at none of the above points Answer: B Var: 1 16) An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object located when its elastic potential energy is a maximum? A) at either A or B B) midway between A and B C) one-third of the way between A and B D) one-fourth of the way between A and B E) at none of the above points Answer: A Var: 1 17) Two simple pendulums, A and B, are each 3.0 m long, and the period of pendulum A is T. Pendulum A is twice as heavy as pendulum B. What is the period of pendulum B? A) T/ B) T C) T D) 2T E) T/2 Answer: B Var: 1 18) A ball swinging at the end of a massless string, as shown in the figure, undergoes simple harmonic motion. At what point (or points) is the magnitude of the instantaneous acceleration of the ball the greatest?

19) Identical balls oscillate with the same period T on Earth. Ball A is attached to an ideal spring and ball B swings back and forth to form a simple pendulum. These systems are now taken to the Moon, where g = 1.6 m/s2, and set into oscillation. Which of the following statements about these systems are true? (There could be more than one correct choice.) A) Both systems will have the same period on the Moon as on Earth. B) On the Moon, ball A will take longer to complete one cycle than ball B. C) On the Moon, ball B will take longer to complete one cycle than ball A. D) On the Moon, ball A will execute more vibrations each minute than ball B. E) On the Moon, ball B will execute more vibrations each minute than ball A. Answer: C, D Var: 1 20) Grandfather clocks are designed so they can be adjusted by moving the weight at the bottom of the pendulum up or down. Suppose you have a grandfather clock at home that runs slow. Which of the following adjustments of the weight would make it more accurate? (There could be more than one correct choice.) A) Raise the weight. B) Lower the weight. C) Add more mass to the weight. D) Remove some mass from the weight. E) Increase the amplitude of swing by a small amount. Answer: A Var: 1 21) Grandfather clocks are designed so they can be adjusted by moving the weight at the bottom of the pendulum up or down. Suppose you have a grandfather clock at home that runs fast. Which of the following adjustments of the weight would make it more accurate? (There could be more than one correct choice.) A) Raise the weight. B) Lower the weight. C) Add more mass to the weight. D) Remove some mass from the weight. E) Decrease the amplitude of swing by a small amount. Answer: B Var: 1

22) A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves upward with constant acceleration? A) The period does not change. B) The period increases. C) The period decreases. D) The period becomes zero. E) The period increases if the upward acceleration is more than g/2 but decreases if the upward acceleration is less than g/2. Answer: C Var: 1 23) A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves downward with constant acceleration? A) The period does not change. B) The period increases. C) The period decreases. D) The period becomes zero. E) The period increases if the upward acceleration is more than g/2 but decreases if the upward acceleration is less than g/2. Answer: B Var: 1 24) A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves upward with constant velocity? A) The period does not change. B) The period increases. C) The period decreases. D) The period becomes zero. E) The period increases if the upward acceleration is more than g/2 but decreases if the upward acceleration is less than g/2. Answer: A Var: 1 25) A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How would the period of the pendulum change if the supporting chain were to break, putting the elevator into freefall? A) The period does not change. B) The period increases slightly. C) The period decreases slightly. D) The period becomes zero. E) The period becomes infinite because the pendulum would not swing. Answer: E Var: 1 9 Copyright © 2019 Pearson Education, Inc.

26) A simple pendulum and a mass oscillating on an ideal spring both have period T in an elevator at rest. If the elevator now accelerates downward uniformly at 2 m/s2, what is true about the periods of these two systems? A) Both periods would remain the same. B) Both periods would increase. C) Both periods would decrease. D) The period of the pendulum would increase but the period of the spring would stay the same. E) The period of the pendulum would decrease but the period of the spring would stay the same. Answer: D Var: 1 27) A simple pendulum and a mass oscillating on an ideal spring both have period T in an elevator at rest. If the elevator now moves downward at a uniform 2 m/s, what is true about the periods of these two systems? A) Both periods would remain the same. B) Both periods would increase. C) Both periods would decrease. D) The period of the pendulum would increase but the period of the spring would stay the same. E) The period of the pendulum would decrease but the period of the spring would stay the same. Answer: A Var: 1 28) A simple pendulum that consists of a small ball of mass m and a massless wire of length L swings with a period T. Suppose now that the mass is rearranged so that mass of the ball was reduced but the mass of the wire was increased, with the total mass remaining m and the length being L. What is true about the new period of swing? (There could be more than one correct choice.) A) The new period is T because the total mass m has not changed. B) The new period is T because the length L has not changed. C) The new period is greater than T. D) The new period is less than T E) The new period is T because neither L nor m have changed. Answer: D Var: 1

14.2 Problems 1) A leaky faucet drips 40 times in A) 1.3 Hz B) 0.75 Hz C) 1.6 Hz D) 0.63 Hz Answer: A Var: 21

What is the frequency of the dripping?

2) An object is undergoing simple harmonic motion of amplitude 2.3 m. If the maximum velocity of the object is 10 m/s, what is the object's angular frequency? A) 4.3 rad/s B) 4.8 rad/s C) 3.5 rad/s D) 4.0 rad/s Answer: A Var: 1 3) If a floating log is seen to bob up and down 15 times in 1.0 min as waves pass by you, what are the frequency and period of the wave? Answer: 0.25 Hz, 4.0 s Var: 1 4) The quartz crystal in a digital watch has a frequency of 32.8 kHz. What is its period of oscillation? A) 30.5 µs B) 15.3 µs C) 95.8 µs D) 0.191 ms E) 9.71 µs Answer: A Var: 1 5) If your heart is beating at 76.0 beats per minute, what is the frequency of your heart's oscillations in hertz? A) 4560 Hz B) 1450 Hz C) 3.98 Hz D) 2.54 Hz E) 1.27 Hz Answer: E Var: 1

6) A guitar string is set into vibration with a frequency of 512 Hz. How many oscillations does it undergo each minute? A) 30,700 B) 8.53 C) 26.8 D) 1610 E) 512 Answer: A Var: 1 7) A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 1.27 cm and a frequency of 2.55 Hz. What are the (a) maximum speed and (b) maximum acceleration of the tip of the needle? Answer: (a) 20.3 cm/s (b) 326 cm/s2 Var: 1 8) A sewing machine needle moves in simple harmonic motion with a frequency of 2.5 Hz and an amplitude of 1.27 cm. (a) How long does it take the tip of the needle to move from the highest point to the lowest point in its travel? (b) How long does it take the needle tip to travel a total distance of 11.43 cm? Answer: (a) 0.20 s (b) 0.90 s Var: 1 9) If the frequency of a system undergoing simple harmonic motion doubles, by what factor does the maximum value of acceleration change? A) 4 B) 2 C) D) 2/π Answer: A Var: 1 10) If a pendulum makes 12 complete swings in 8.0 s, what are its (a) frequency and (b) period? Answer: (a) 1.5 Hz (b) 0.67 s Var: 1 11) A point on the string of a violin moves up and down in simple harmonic motion with an amplitude of 1.24 mm and a frequency of 875 Hz. (a) What is the maximum speed of that point in SI units? (b) What is the maximum acceleration of the point in SI units? Answer: (a) 6.82 m/s (b) 3.75 × 104 m/s2 Var: 1

12) The position of a cart that is oscillating on a spring is given by the equation x = (12.3 cm) cos[(1.26 s-1)t]. When t = 0.805 s, what are the (a) velocity and (b) acceleration of the cart? Answer: (a) -13.2 cm/s (b) -10.3 cm/s2 Var: 1 13) The position of an object that is oscillating on a spring is given by the equation x = (18.3 cm) cos[(2.35 s-1)t]. What are the (a) frequency, (b) amplitude, and (c) period of this motion? Answer: (a) 0.374 Hz (b) 18.3 cm (c) 2.67 s Var: 1 14) The position of an air-track cart that is oscillating on a spring is given by the equation x = (12.4 cm) cos[(6.35 s-1)t]. At what value of t after t = 0.00 s is the cart first located at x = 8.47 cm? A) 4.34 s B) 0.108 s C) 0.129 s D) 7.39 s E) 7.75 s Answer: C Var: 1 15) An air-track cart is attached to a spring and completes one oscillation every 5.67 s in simple harmonic motion. At time t = 0.00 s the cart is released at the position x = +0.250 m. What is the position of the cart when t = 29.6 s? A) x = 0.0461 m B) x = 0.210 m C) x = 0.218 m D) x = 0.342 m E) x = -0.218 m Answer: A Var: 1 16) The position of an object that is oscillating on a spring is given by the equation x = (17.4 cm) cos[(5.46 s-1)t]. What is the angular frequency for this motion? A) 0.183 rad/s B) 5.46 rad/s C) 2.34 rad/s D) 17.4 rad/s E) 0.869 rad/s Answer: B Var: 1

17) An object is oscillating on a spring with a period of 4.60 s. At time t = 0.00 s the object has zero speed and is at x = 8.30 cm. What is the acceleration of the object at t = 2.50 s? A) 1.33 cm/s2 B) 0.784 cm/s2 C) 11.5 cm/s2 D) 14.9 cm/s2 E) 0.00 cm/s2 Answer: D Var: 1 18) A package is oscillating on a spring scale with a period of 4.60 s. At time t = 0.00 s the package has zero speed and is at x = 8.30 cm. At what time after t = 0.00 s will the package first be at x = 4.15 cm? A) 0.575 s B) 0.767 s C) 1.15 s D) 1.30 s E) 1.53 s Answer: B Var: 1 19) A ball is oscillating on an ideal spring with an amplitude of 8.3 cm and a period of 4.6 s. Write an expression for its position, x, as a function of time t, if x is equal to 8.3 cm at t = 0.0 s. Use the cosine function. Answer: x = (8.3 cm) cos[2πt/(4.6 s)] or x = (8.3 cm) cos[(1.4 s-1)t] Var: 1 20) The position of an object that is oscillating on an ideal spring is given by x = (17.4 cm) cos[(5.46 s-1)t]. Write an expression for the velocity of the particle as a function of time using the sine function. Answer: v = - (95.0 cm/s) sin[(5.46 s-1)t] Var: 1 21) The position of an object that is oscillating on an ideal spring is given by x = (17.4 cm) cos[(5.46 s-1)t]. Write an expression for the acceleration of the particle as a function of time using the cosine function. Answer: a = - (519 cm/s2) cos[(5.46 s-1)t] Var: 1

22) An object oscillates such that its position x as a function of time t obeys the equation x = (0.222 m) sin(314 s-1 t), where t is in seconds. (a) In one period, what total distance does the object move? (b) What is the frequency of the motion? (c) What is the position of the object when t = 1.00 s? Answer: (a) 0.888 m (b) 50.0 Hz (c) -0.0352 m Var: 1 23) An object undergoing simple harmonic motion has a maximum displacement of at If the angular frequency of oscillation is what is the object's displacement when A) 4.8 m B) 5.6 m C) 3.7 m D) 3.1 m Answer: A Var: 50+ 24) If the frequency of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum speed of the oscillator change? A) 2 B) 4 C) It does not change. D) 1/2 E) 1/4 Answer: A Var: 1 25) If the amplitude of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum speed of the oscillator change? A) 2 B) 4 C) It does not change. D) 1/2 E) 1/4 Answer: A Var: 1 26) If the angular frequency of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum acceleration of the oscillator change? A) 2 B) 4 C) It does not change. D) 1/2 E) 1/4 Answer: B Var: 1 15 Copyright © 2019 Pearson Education, Inc.

27) The equation of motion of a particle undergoing simple harmonic motion in the y direction is y = (2.0 cm) sin(0.60 s-1 t). At time t = 0.60 s determine the particle's (a) position, (b) velocity, and (c) acceleration. Answer: (a) 0.70 cm (b) 1.1 cm/s (c) -0.25 cm/s2 Var: 1 28) A 0.25 kg harmonic oscillator has a total mechanical energy of amplitude is what is the oscillation frequency? A) 4.6 Hz B) 1.4 Hz C) 2.3 Hz D) 3.2 Hz Answer: A Var: 50+

If the oscillation

29) A 0.250-kg stone is attached to an ideal spring and undergoes simple harmonic oscillations with a period of 0.640 s. What is the force constant (spring constant) of the spring? A) 2.45 N/m B) 12.1 N/m C) 24.1 N/m D) 0.102 N/m E) 0.610 N/m Answer: C Var: 1 30) A 0.150-kg air track cart is attached to an ideal spring with a force constant (spring constant) of 3.58 N/m and undergoes simple harmonic oscillations. What is the period of the oscillations? A) 2.57 s B) 0.527 s C) 0.263 s D) 1.14 s E) 1.29 s Answer: E Var: 1 31) In a supermarket, you place a 22.3-N (around 5 lb) bag of oranges on a scale, and the scale starts to oscillate at 2.7 Hz. What is the force constant (spring constant) of the spring of the scale? A) 650 N/m B) 600 N/m C) 330 N/m D) 820 N/m E) 410 N/m Answer: A Var: 1 16 Copyright © 2019 Pearson Education, Inc.

32) When a 0.350-kg package is attached to a vertical spring and lowered slowly, the spring stretches 12.0 cm. The package is now displaced from its equilibrium position and undergoes simple harmonic oscillations when released. What is the period of the oscillations? A) 0.695 s B) 0.483 s C) 0.286 s D) 0.0769 s E) 1.44 s Answer: A Var: 1 33) A 1.15-kg beaker (including its contents) is placed on a vertical spring scale. When the system is sent into vertical vibrations, it obeys the equation y = (2.3 cm)cos(17.4 s-1 t). What is the force constant (spring constant) of the spring scale, assuming it to be ideal? Answer: 348 N/m Var: 1 34) When a laboratory sample of unknown mass is placed on a vertical spring-scale having a force constant (spring constant) of 467 N/m, the system obeys the equation y = (4.4 cm) cos(33.3 s-1 t). What is the mass of this laboratory sample? Answer: 0.421 kg Var: 1 35) A 3.42-kg stone hanging vertically from an ideal spring on the earth undergoes simple harmonic motion at a place where g = 9.80 m/s2. If the force constant (spring constant) of the spring is find the period of oscillation of this setup on a planet where g = 1.60 m/s2. A) 3.35 s B) 2.51 s C) 4.36 s D) 5.70 s Answer: A Var: 31 36) A 51.8-kg bungee jumper jumps off a bridge and undergoes simple harmonic motion. If the period of oscillation is 11.2 s, what is the spring constant (force constant) of the bungee cord? A) 16.3 N/m B) 19.6 N/m C) 26.1 N/m Answer: A Var: 50+

37) A 4.8-kg block attached to an ideal spring executes simple harmonic motion on a frictionless horizontal surface. At time t = 0.00 s, the block has a displacement of a velocity of and an acceleration of The force constant (spring constant) of the spring is closest to A) 15 N/m. B) 14 N/m. C) 13 N/m. D) 12 N/m. E) 11 N/m. Answer: A Var: 50+ 38) An object of mass m = 8.0 kg is attached to an ideal spring and allowed to hang in the earth's gravitational field. The spring stretches before it reaches its equilibrium position. If it were now allowed to oscillate by this spring, what would be its frequency? A) 3.4 Hz B) 0.28 x 10-3 Hz C) 0.52 Hz D) 1.6 Hz Answer: A Var: 50+ 39) A 2.0-kg block on a frictionless table is connected to two springs whose opposite ends are fixed to walls, as shown in the figure. The springs have force constants (spring constants) k1 and k2. What is the oscillation angular frequency of the block if and

A) 2.5 rad/s B) 3.5 rad/s C) 0.40 rad/s D) 0.56 rad/s Answer: A Var: 50+ 40) A 92-kg man climbs into a car with worn out shock absorbers, and this causes the car to drop down 4.5 cm. As he drives along he hits a bump, which starts the car oscillating at an angular frequency of 4.52 rad/s. What is the mass of the car? A) 890 kg B) 760 kg C) 920 kg D) 990 kg E) 1900 kg Answer: A Var: 1 18 Copyright © 2019 Pearson Education, Inc.

41) An object attached to an ideal spring oscillates with an angular frequency of 2.81 rad/s. The object has a maximum displacement at t = 0.00 s of 0.232 m. If the force constant (spring constant) is what is the potential energy stored in the mass-spring system when t = 1.42 s? A) 0.350 J B) 0.256 J C) 0.329 J D) 0.399 J Answer: A Var: 50+ 42) A block attached to an ideal spring of force constant (spring constant) 15 N/m executes simple harmonic motion on a frictionless horizontal surface. At time t = 0 s, the block has a displacement of -0.90 m, a velocity of -0.80 m/s, and an acceleration of +2.9 m/s2 . The mass of the block is closest to A) 2.3 kg B) 2.6 kg C) 4.7 kg D) 9.4 kg Answer: C Var: 1 43) A 0.39-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant) is The block is pulled from its equilibrium position at x = 0.000 m to a displacement x = +0.080 m and is released from rest. The block then executes simple harmonic motion along the horizontal x-axis. When the position of the block is its kinetic energy is closest to A) 0.90 J. B) 0.84 J. C) 0.95 J. D) 1.0 J. E) 1.1 J. Answer: A Var: 50+

44) A 0.16-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant) is 360 N/m. The block is pulled from its equilibrium position at x = 0.000 m to a position x = +0.080 m and is released from rest. The block then executes simple harmonic motion along the horizontal x-axis. When the position is x = -0.037 m, what is the acceleration of the block? A) 83 m/s2 B) 43 m/s2 C) 64 m/s2 D) 270 m/s2 E) 370 m/s2 Answer: A Var: 1 45) A 3.7-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant) is The block is pulled from its equilibrium position at x = 0.000 m to a position x = +0.080 m and is released from rest. The block then executes simple harmonic motion along the horizontal x-axis. The maximum elastic potential energy of the system is closest to A) 1.4 J. B) 1.3 J. C) 1.6 J. D) 1.7 J. E) 1.8 J. Answer: A Var: 50+ 46) An object of mass 6.8 kg is attached to an ideal spring of force constant (spring constant) 1720 N/m. The object is set into simple harmonic motion, with an initial velocity of and an initial displacement of Calculate the maximum speed the object raches during its motion. Answer: 4.5 m/s Var: 50+ 47) A 2.0 kg box is traveling at 5.0 m/s on a smooth horizontal surface when it collides with and sticks to a stationary 6.0 kg box. The larger box is attached to an ideal spring of force constant (spring constant) 150 N/m, as shown in the figure. Find (a) the amplitude of the resulting oscillations of this system, (b) the frequency of the oscillations and (c) the period of the oscillations.

48) A ball is attached to an ideal spring and oscillates with a period T. If the mass of the ball is doubled, what is the new period? A) 2T B) T/2 C) T D) T E) T/ Answer: D Var: 1 49) A geologist suspends a 0.30-kg stone on an ideal spring. In equilibrium the stone stretches the spring 2.0 cm downward. The stone is then pulled an additional distance of 1.0 cm down and released from rest. (a) Write down the equation for the vertical position y of the stone as a function of time t, using the cosine function. Take the origin at the equilibrium point of the stone, with the positive y direction upward. (b) How fast is the stone moving at a time equal to 1/3 of its period of motion? Answer: (a) y = -(0.010 m) cos(22 s-1 t) (b) 0.19 m/s Var: 1 50) How much mass should be attached to a vertical ideal spring having a spring constant (force constant) of 39.5 N/m so that it will oscillate at 1.00 Hz? A) 39.5 kg B) 2.00 kg C) 1.00 kg D) 1.56 kg E) 6.29 kg Answer: C Var: 1 51) A 0.50-kg box is attached to an ideal spring of force constant (spring constant) 20 N/m on a horizontal, frictionless floor. The box oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. (a) What is the amplitude of vibration? (b) At what distance from the equilibrium position are the kinetic energy and the potential energy the same? Answer: (a) 0.24 m (b) 0.17 m Var: 1

52) A 1.5-kg cart attached to an ideal spring with a force constant (spring constant) of 20 N/m oscillates on a horizontal, frictionless track. At time t = 0.00 s, the cart is released from rest at position x = 10 cm from the equilibrium position. (a) What is the frequency of the oscillations of the cart? (b) Determine the maximum speed of the cart. Where does the maximum speed occur? (c) Find the maximum acceleration of the mass. Where does the maximum acceleration occur? (d) How much total energy does this oscillating system contain? (e) Express the displacement as a function of time using a cosine function. Answer: (a) 0.58 Hz (b) 0.37 m/s, at the equilibrium position (c) 1.3 m/s2, at maximum displacement (d) 0.10 J (e) x = (0.10 m) cos (3.7 s-1 t) Var: 1 53) A 0.150-kg cart that is attached to an ideal spring with a force constant (spring constant) of 3.58 N/m undergoes simple harmonic oscillations with an amplitude of 7.50 cm. What is the total mechanical energy of the system? A) 0.0201 J B) 0.0101 J C) 0.269 J D) 0.134 J E) 0 J Answer: B Var: 1 54) A 0.50-kg object is attached to an ideal spring of spring constant (force constant) 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. What are (a) the total energy and (b) the amplitude of vibration of the system? Answer: (a) 0.56 J (b) 0.24 m Var: 1 55) A 0.50-kg object is attached to an ideal spring of spring constant (force constant) 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. At what distance from the equilibrium position are the kinetic energy and potential energy of the system the same? A) 0.017 m B) 0.029 m C) 0.12 m D) 0.17 m Answer: D Var: 1

56) A 1.53-kg piece of iron is hung by a vertical ideal spring. When perturbed slightly, the system is moves up and down in simple harmonic oscillations with a frequency of 1.95 Hz and an amplitude of 7.50 cm. If we choose the total potential energy (elastic and gravitational) to be zero at the equilibrium position of the hanging iron, what is the total mechanical energy of the system? A) 0.844 J B) 0.646 J C) 0.633 J D) 0.955 J E) 0.000 J Answer: B Var: 1 57) A 0.30-kg block of wood is suspended on a spring. In equilibrium the wood stretches the spring 2.0 cm downward. The wood is then pulled an additional distance of 1.0 cm down and released from rest. (a) How long does it take the wood to make 3 complete cycles of vibration? (b) How much total mechanical energy does this system contain if we choose the total potential energy (elastic and gravitational) to be zero at the equilibrium position of the hanging block? Answer: (a) 0.84 s (b) 7.4 mJ Var: 1 58) A ball vibrates back and forth from the free end of an ideal spring having a force constant (spring constant) of 20 N/m. If the amplitude of this motion is 0.30 m, what is the kinetic energy of the ball when it is 0.30 m from its equilibrium position? A) 0.00 J B) 0.22 J C) 0.45 J D) 0.90 J E) 1.4 J Answer: A Var: 1 59) What is the length of a simple pendulum with a period of 2.0 s? A) 20 m B) 0.99 m C) 1.2 m D) 1.6 m E) 0.87 m Answer: B Var: 1

60) A 34-kg child on an 18-kg swing set swings back and forth through small angles. If the length of the very light supporting cables for the swing is how long does it take for each complete back-and-forth swing? Assume that the child and swing set are very small compared to the length of the cables. A) 4.4 s B) 4.8 s C) 5.3 s D) 5.7 s Answer: A Var: 30 61) The period of a simple pendulum that is 1.00 m long on another planet is What is the acceleration due to gravity on this planet if the mass of the pendulum bob is 1.5 kg? A) 14.3 m/s2 B) 13.3 m/s2 C) 15.7 m/s2 D) 17.2 m/s2 Answer: A Var: 50+ 62) On the Moon, the acceleration of gravity is g/6. If a pendulum has a period T on Earth, what will its period be on the Moon? A) T B) T/ C) T/6 D) 6T E) T/3 Answer: A Var: 1 63) A simple pendulum has a period T on Earth. If it were used on Planet X, where the acceleration due to gravity is 3 times what it is on Earth, what would its period be? A) 3T B) T C) T D) T/ E) T/3 Answer: D Var: 1

64) A simple pendulum having a bob of mass M has a period T. If you double M but change nothing else, what would be the new period? A) 2T B) T C) T D) T/ E) T/2 Answer: C Var: 1 65) If both the mass of a simple pendulum and its length are doubled, the period will A) be unchanged. B) increase by a factor of 2. C) increase by a factor of 4. D) increase by a factor of . E) increase by a factor of 1/ . Answer: D Var: 1 66) A simple pendulum takes 2.00 s to make one compete swing. If we now triple the length, how long will it take for one complete swing? A) 6.00 s B) 3.46 s C) 2.00 s D) 1.15 s E) 0.667 s Answer: B Var: 1 67) Tarzan swings back and forth on a long vine. His friend Jane notices in amazement that he makes 30 complete swings in 2.4 minutes. (a) What is the frequency (in hertz) of Tarzan's swing? (b) How long is the vine he is using? Answer: (a) 0.21 Hz (b) 5.7 m Var: 1

68) As shown in the figure, a 0.23-kg ball is suspended from a string 6.87 m long and is pulled slightly to the left. As the ball swings through the lowest part of its motion it encounters a spring attached to the wall. The spring pushes against the ball and eventually the ball is returned to its original starting position. Find the time for one complete cycle of this motion if the spring constant (force constant) is (Assume that once the pendulum ball hits the spring there is no effect due to the vertical movement of the ball.)

Answer: 3.0 s Var: 50+ 69) When a certain simple pendulum is set swinging, its angular displacement θ as a function of time t obeys the equation θ = 8.5° cos(2.4 s-1t). How long is the pendulum? Answer: 1.7 m Var: 1 70) A spaceship captain lands on an unknown planet. Before venturing forth, he needs to find out the acceleration due to gravity on that planet. All he has available to him is some thin light string, a stopwatch, and a small 2.75-kg metal ball (it was a rough landing). So he lets the ball swing from a 1.5-m length of the string, starting at rest, and measures that it takes 1.9 s for it to swing from the place where he released it to the place where it first stops as it reverses direction. What is the acceleration due to gravity on this planet? Answer: 4.1 m/s2 Var: 1 71) An astronaut has landed on Planet N-40 and conducts an experiment to determine the acceleration due to gravity on that planet. She uses a simple pendulum that is 0.640 m long and measures that 10 complete oscillations 26.0 s. What is the acceleration of gravity on Planet N40? A) 4.85 m/s2 B) 1.66 m/s2 C) 3.74 m/s2 D) 2.39 m/s2 E) 9.81 m/s2 Answer: C Var: 1

72) An astronaut has landed on an asteroid and conducts an experiment to determine the acceleration of gravity on that asteroid. He uses a simple pendulum that has a period of oscillation of 2.00 s on Earth and finds that on the asteroid the period is 11.3 s. What is the acceleration of gravity on that asteroid? A) 0.307 m/s2 B) 1.66 m/s2 C) 1.74 m/s2 D) 5.51 m/s2 E) 0.0544 m/s2 Answer: A Var: 1 73) In 1851 Jean Bernard Leon Foucault demonstrated the rotation of the earth using a pendulum 11.0 m long, which was set up in the Paris Observatory. How long would it have taken for Foucault's pendulum to make one complete swing back to its starting point if g = 9.81 m/s2 at the observatory? A) 6.65 s B) 5.63 s C) 1.79 s D) 2.12 s E) 2.58 s Answer: A Var: 1 74) A pendulum that was originally erected by Foucault at the Pantheon in Paris for the Paris Exhibition in 1851 was restored in 1995. It has a 28.0-kg sphere suspended from a 67.0-m light cable. How long would it take for the bob in this pendulum to move from the position of maximum displacement down to the equilibrium point? A) 4.11 s B) 21.5 s C) 2.58 s D) 32.2 s E) 42.9 s Answer: A Var: 1 75) Suppose you want to set up a simple pendulum with a period of 2.50 s. How long should it be (a) on Earth, at a location where g = 9.80 m/s2? (b) on a planet where g is 5.00 times what it is on Earth? Answer: (a) 1.55 m (b) 7.76 m Var: 1

76) A thin hoop is supported in a vertical plane by a nail. What should the radius of the hoop be in order for it to have a period of oscillation of 1.00 s? The moment of inertia of a hoop of mass M and radius R about a point on its rim is 2MR2. A) 0.0154 m B) 0.0621 m C) 0.124 m D) 0.1876 m E) 0.248 m Answer: C Var: 1 77) A Christmas ornament made from a thin hollow glass sphere hangs from a small hook at its surface. It is observed to oscillate with a frequency of 2.50 Hz in a city where g = 9.80 m/s2. What is the radius of the ornament? The moment of inertia of a hollow sphere of mass M and radius R about a point on its edge is 5MR2/3. A) 1.84 cm B) 3.68 cm C) 2.38 cm D) 3.98 cm E) 4.69 cm Answer: C Var: 1

College Physics: A Strategic Approach, 4e (Knight) Chapter 15 Traveling Waves and Sound 15.1 Conceptual Questions 1) What is the wavelength of the wave shown in the figure?

A) 8 m. B) 4 m. C) 2 m. D) 1 m. E) It cannot be determined from the given information. Answer: E Var: 1 2) What is the frequency of the wave shown in the figure?

A) 0.5 Hz. B) 1 Hz. C) 2 Hz. D) 4 Hz. E) It cannot be determined from the given information. Answer: A Var: 1

3) Which one of the curves shown in the figure best represents the variation of wave speed v as a function of tension for transverse waves on a stretched string?

A) A B) B C) C D) D E) E Answer: B Var: 1 4) A string of mass m is under tension, and the speed of a wave in the string is v. What will be the speed of a wave in the string if the mass of the string is increased to 2m but with no change in the length or tension? A) v/2 B) v/ C) v D) 2v E) 4v Answer: B Var: 1 5) A string of length L is under tension, and the speed of a wave in the string is v. What will be the speed of a wave in the string if the length is increased to 2L but with no change in the mass or tension? A) v/2 B) v/ C) v D) 2v E) 4v Answer: C Var: 1

6) When a certain string is under tension T, the speed of a wave in the string is v. What will be the speed of a wave in the string if the tension is increased to 2T without changing the mass or length of the string? A) v/2 B) v/ C) v D) 2v E) 4v Answer: C Var: 1 7) Four waves are described by the following equations, where distances are measured in meters and times in seconds. I. y = 0.12 cos(3x - 21t) II. y = 0.15 sin(6x + 42t) III. y = 0.13 cos(6x + 21t) IV. y = -0.23 sin(3x - 42t) Which of these waves have the same speed? A) I and II B) I and III C) II and III D) III and IV E) II and IV Answer: A Var: 1 8) Four waves are described by the following equations, where distances are measured in meters and times in seconds. I. y = 0.12 cos(3x - 21t) II. y = 0.15 sin(6x + 42t) III. y = 0.13 cos(6x + 21t) IV. y = -0.23 sin(3x - 42t) Which of these waves have the same period? A) I and III, and also II and IV B) I and IV, and also II and III C) I and II, and also III and IV D) All of them have the same period. E) They all have different periods. Answer: A Var: 1

9) The intensity of the waves from a point source at a distance d from the source is I. What is the intensity at a distance 2d from the source? A) 4I B) 2I C) I/2 D) I/4 E) I/ Answer: D Var: 1 10) The intensity of the waves from a point source at a distance d from the source is I. At what distance from the sources is the intensity equal to 2I? A) d/2 B) d/ C) d/4 D) d/8 Answer: B Var: 1 11) Why does the intensity of waves from a small source decrease with the square of the distance from the source? A) The waves run out of energy as they travel. B) The waves spread out as they travel. C) The medium through which the waves travel absorbs the energy of the waves. D) The waves slow down as they travel away from the source. E) The frequency of the waves decreases as they get farther from the source. Answer: B Var: 1 12) Seven seconds after a brilliant flash of lightning, thunder shakes the house. Approximately how far was the lightning strike from the house? A) much closer than one kilometer B) about one kilometer away C) about two kilometers away D) much farther away than two kilometers E) It is impossible to say. Answer: C Var: 1 13) What characteristics of a sound wave are related to the "pitch" of a musical note? (There could be more than one correct choice.) A) amplitude B) wavelength C) frequency D) period Answer: B, C, D Var: 1 4 Copyright © 2019 Pearson Education, Inc.

14) Sound A has a high pitch and sound B has a low pitch. Which of the following statements about these two sounds are correct? (There could be more than one correct choice.) A) The wavelength of A is longer than the wavelength of B. B) The period of A is shorter than the period of B. C) The frequency of A is greater than the frequency of B. D) Sound B travels faster than sound B through air. E) The amplitude of A is larger than the amplitude of B. Answer: B, C Var: 1 15) You double your distance from a sound source that is radiating equally in all directions. What happens to the intensity of the sound? It reduces to A) one-half its original value. B) one-fourth its original value. C) one-sixteenth its original value. D) none of the above Answer: B Var: 1 16) Suppose that a sound source is emitting waves uniformly in all directions. If you move to a point twice as far away from the source, the frequency of the sound will be A) unchanged. B) half as great. C) one-fourth as great. D) twice as great. Answer: A Var: 1 17) As you are moving very quickly toward a speaker emitting a pure tone, which characteristics of the sound get larger? (There may be more than one correct choice.) A) frequency B) amplitude C) wavelength D) period E) loudness Answer: A, E Var: 1

18) In many cartoon shows, a character runs off a cliff, realizes his predicament, and lets out a scream. He continues to scream as he falls. If the physical situation is portrayed correctly, from the vantage point of an observer at the top of the cliff leaning over the edge, the pitch of the scream as he falls should be A) higher than the original pitch and constant. B) higher than the original pitch and increasing as he falls. C) lower than the original pitch and constant. D) lower than the original pitch and decreasing as he falls. E) It is impossible to predict. Answer: D Var: 1 19) In many cartoon shows, a character runs off a cliff, realizes his predicament, and lets out a scream. He continues to scream as he falls. If the physical situation is portrayed correctly, from the vantage point of an observer at the foot of the cliff, the pitch of the scream as he falls should be A) higher than the original pitch and constant. B) higher than the original pitch and increasing as he falls. C) lower than the original pitch and constant. D) lower than the original pitch and decreasing as he falls. E) It is impossible to predict. Answer: B Var: 1 15.2 Problems 1) A fisherman fishing from a pier observes that the float on his line bobs up and down, taking 2.4 s to move from its highest point to its lowest point. He also estimates that the distance between adjacent wave crests is 48 m. What is the speed of the waves going past the pier? A) 1.0 m/s B) 20 m/s C) 10 m/s D) 5.0 m/s E) 120 m/s Answer: C Var: 1 2) A tsunami, an ocean wave generated by an earthquake, propagates along the open ocean at 700 km/hr and has a wavelength of 750 km. What is the frequency of the waves in such a tsunami? A) 0.93 Hz B) 0.00026 Hz C) 1.1 Hz D) 6.8 Hz E) 0.15 Hz Answer: B Var: 1 6 Copyright © 2019 Pearson Education, Inc.

3) What is the frequency of a pressure wave of wavelength 2.5 m that is traveling at 1400 m/s? A) 178 Hz B) 1.78 kHz C) 560 Hz D) 5.6 kHz Answer: C Var: 1 4) If a wave has a speed of 362 m/s and a period of 4.17 ms, what is its wavelength? A) 1510 m B) 1.51 m C) 86.8 m D) 86,800 m E) 0.0115 m Answer: B Var: 1 5) The figure shows a "snapshot" of a wave at a given instant of time. The frequency of this wave is 120 Hz. What are the (a) amplitude, (b) wavelength, and (c) speed of this wave?

Answer: (a) 0.10 m Var: 1

(b) 0.20 m

6) The speed of sound in steel is 5000 m/s. What is the wavelength of a sound wave of frequency in steel? A) 7.58 m B) 2.41 m C) 1.21 m D) 0.829 m E) 0.132 m Answer: A Var: 50+

7) Crests of an ocean wave pass a pier every wavelength of the ocean waves? A) 56 m B) 28 m C) 64 m D) 48 m Answer: A Var: 8

If the waves are moving at

8) Transverse waves travel at in a string that is subjected to a tension of string is long, what is its mass? A) 0.515 kg B) 0.216 kg C) 0.366 kg D) 0.597 kg Answer: A Var: 50+

what is the

If the

9) A piano wire of linear mass density 0.0050 kg/m is under a tension of 1350 N. What is the wave speed in this wire? A) 130 m/s B) 260 m/s C) 520 m/s D) 1040 m/s Answer: C Var: 1 10) A wave whose wavelength is 0.500 m is traveling down a 500-m long wire whose total mass is 25 kg and is under a tension of 2000 N. (a) What is the speed of the wave on the wire? (b) Find the frequency of this wave. Answer: (a) 200 m/s (b) 400 Hz Var: 1 11) The density of aluminum is 2700 kg/m3. If transverse waves travel at wire of diameter what is the tension on the wire? A) 65 N B) 39 N C) 52 N D) 78 N Answer: A Var: 21

in an aluminum

12) A rope with a total mass of 25.0 kg is tied to a tree on one side of a 125-m wide ravine. You are pulling on the other end of the rope with a force of 415 N. If you pluck the rope at your end, how long will it take the pulse to travel across the ravine to the tree? Answer: 2.74 s Var: 1 13) A 2.31-kg rope is stretched between supports that are 10.4 m apart, and has a tension in it of 49.2 N. If one end of the rope is slightly tweaked, how long will it take for the resulting disturbance to reach the other end? A) 0.699 s B) 0.720 s C) 0.664 s D) 0.615 s Answer: A Var: 50+ 14) A 1.1-kg uniform bar of metal is 0.40 m long and has a diameter of 2.0 cm. When someone bangs one end of this bar, a 1.5 MHz shock wave is travels along the length of the bar and reaches the other end in 0.12 ms. What is the wavelength of the shock wave in the metal? A) 2.2 mm B) 2.6 mm C) 3.0 mm D) 3.4 mm E) 3.8 mm Answer: A Var: 1 15) A 10-gram wire that is 6.0 m long is under tension. When a transverse wave of frequency 280 Hz travels along the wire, its wavelength is 0.60 m,and its amplitude is 8.4 mm. How much time does it take for a crest of the transverse wave to travel the length of the wire? A) 36 ms B) 31 ms C) 40 ms D) 44 ms E) 49 ms Answer: A Var: 50+

16) A 90-gram wire that is 1.0 m long is under tension. When a transverse wave of frequency 890 Hz travels down the wire, its wavelength is 0.10 m and its amplitude is 6.5 mm. What is the tension in the wire? A) 710 N B) 820 N C) 930 N D) 1000 N E) 1100 N Answer: A Var: 50+ 17) An earthquake generates three kinds of waves: surface waves (L-waves), which are the slowest and weakest, shear (S) waves, which are transverse waves and carry most of the energy, and pressure (P) waves, which are longitudinal waves and are the fastest. The speed of P waves is approximately 7 km/s, and that of S waves is about 4 km/s. People do not generally feel the P waves, but animals seem to be sensitive to them. If a person reports that her dog started barking 20 seconds "before the earthquake," then approximately how far was the origin of the earthquake? A) 100 km B) 200 km C) 300 km D) 400 km E) 500 km Answer: B Var: 1 18) A 15-m rope is pulled taut with a tension of 140 N. It takes 0.545 s for a wave to propagate along the rope. What is the mass of the rope? A) 1.7 kg B) 2.1 kg C) 2.8 kg D) 5.1 kg E) 3.2 kg Answer: C Var: 1 19) Two steel wires are stretched with the same tension. The first wire has a diameter of 0.610 mm and the second wire has a diameter of 0.910 mm. If the speed of waves traveling along the first wire is 54.0 m/s, what is the speed of waves traveling along the second wire? A) 24.9 m/s B) 27.2 m/s C) 36.2 m/s D) 81.0 m/s E) 100 m/s Answer: C Var: 5 10 Copyright © 2019 Pearson Education, Inc.

20) A crane lifts a 2500-kg beam at a steady rate of 15 cm/s using a steel cable whose mass per unit length is 0.65 kg/m. What is the speed of transverse waves on this cable? A) 230 m/s B) 580 m/s C) 1200 m/s D) 1900 m/s E) 190 m/s Answer: E Var: 1 21) A crane lifts a 2500-kg beam using a steel cable whose mass per unit length is 0.650 kg/m. What is the speed of transverse waves on this cable if the upward acceleration of the beam is a steady 3.00 m/s2? A) 194 m/s B) 578 m/s C) 1220 m/s D) 1880 m/s E) 222 m/s Answer: E Var: 1 22) A wire that is 1.0 m long with a mass of 90 g is under a tension of 710 N. When a transverse wave travels on the wire, its wavelength is 0.10 m and its amplitude is 6.5 mm. What is the frequency of this wave? A) 890 Hz B) 920 Hz C) 1000 Hz D) 1200 Hz E) 1500 Hz Answer: A Var: 1 23) What is the wave speed in a brass wire with a radius of 0.500 mm stretched with a tension of 125 N? The density of brass is 8.60 × 103 kg/m3. A) 0.121 m/s B) 100 m/s C) 136 m/s D) 500 m/s E) 68.8 m/s Answer: C Var: 1 24) The vertical displacement y(x,t) of a horizontal string aligned along the x-axis is given by the equation y(x,t) = (6.00 mm) cos[(3.25 m-1)x - (7.22 s-1)t]. What are the (a) wavelength and (b) period of this wave? Answer: (a) 1.93 m (b) 0.870 s Var: 1 11 Copyright © 2019 Pearson Education, Inc.

25) The vertical displacement y(x,t) of a horizontal string aligned along the x-axis is given by the equation y(x,t) = (6.00 mm) cos[(3.25 m-1)x - (7.22 s-1)t]. What are the (a) speed and (b) amplitude of this wave? Answer: (a) 2.22 m/s (b) 6.00 mm Var: 1 26) Find the speed of an ocean wave whose displacement is given by the equation where x and y are in meters and t is in seconds. A) 2.5 m/s B) 1.9 m/s C) 3.5 m/s D) 4.5 m/s Answer: A Var: 50+ 27) What are the wavelength (in meters) and frequency (in hertz) of a wave whose displacement is given by the equation y = 0.5 sin(0.20x + 120t), where x and y are in meters and t is in seconds? A) 10 m, 0.50 Hz B) 5.0 m, 10 Hz C) 19 m, 120 Hz D) 31 m, 19 Hz E) 0.20 m, 120 Hz Answer: D Var: 1 28) Light from a laser forms a 1.31-mm diameter spot on a wall. If the light intensity in the spot is what is the power output of the laser? Assume that all the light emitted by the laser hits the spot. A) 21.3 mW B) 13.2 mW C) 17.9 mW D) 24.7 mW Answer: A Var: 50+ 29) Calculate the light intensity 1.45 m from a light bulb that radiates 100 W equally in all directions. A) 3.78 W/m2 B) 4.36 W/m2 C) 47.6 W/m2 D) 54.7 W/m2 Answer: A Var: 1 12 Copyright © 2019 Pearson Education, Inc.

30) The average intensity of sunlight impinging on Earth is measured to be about 1.4 kW/m2. What is the power of sunlight emitted by the sun? (Earth-Sun distance = 1.5 × 108 km, Earth radius = 6.4 × 103 km) A) 4.0 × 1026 W B) 3.2 × 1022 W C) 7.2 × 1014 W D) 7.6 × 108 W Answer: A Var: 1 31) An elephant can hear sound with a frequency of 15 Hz. What is the wavelength of this wave if the speed of sound in air is 343 m/s? Answer: 23 m Var: 1 32) You drop a stone down a well that is 9.5 m deep. How long is it before you hear the splash? The speed of sound in air is 343 m/s and air resistance is negligible. A) 1.2 s B) 1.3 s C) 1.4 s D) 1.5 s E) 1.6 s Answer: C Var: 1 33) The speed of sound through the ground is about 6.0 km/s while the speed of sound in air is 343 m/s. A very powerful explosion occurs some distance away and you feel the ground vibrate 60 seconds before you hear the sound of the explosion. How far away is the explosion? A) 20 km B) 22 km C) 25 km D) 27 km E) 30 km Answer: B Var: 1 34) Two motors in a factory are running at slightly different rates. One runs at 825.0 rpm and the other at You hear the sound intensity increase and then decrease periodically due to wave interference. How long does it take between successive instances of the sound intensity increasing? A) 1.54 s B) 1.43 s C) 1.66 s D) 1.79 s Answer: A Var: 44 13 Copyright © 2019 Pearson Education, Inc.

35) A plucked guitar string produces a sound wave of frequency 0.44 kHz on a day when the speed of sound is 340 m/s. (a) What is the wavelength of the sound wave? (b) How much time elapses between the impacts of two adjacent compressions of the sound wave on your eardrum? Answer: (a) 0.77 m (b) 2.3 ms Var: 1 36) What is the intensity level in decibels of a sound with intensity 10-3 W/m2? The threshold of human hearing is 1.0 × 10-12 W/m2. A) 30 dB B) 60 dB C) 90 dB D) 96 dB Answer: C Var: 1 37) What is the intensity of a 70-dB sound? The threshold of human hearing is 1.0 × 10-12 W/m2. A) 10-4 W/m2 B) 10-5 W/m2 C) 10-6 W/m2 D) 10-7 W/m2 Answer: B Var: 1 38) What is the ratio of the intensities of two sounds with intensity levels of 70 dB and 40 dB? A) 10:1 B) 100:1 C) 1000:1 D) 10,000:1 Answer: C Var: 1 39) If the intensity level by 15 identical engines in a garage is 100 dB, what is the intensity level generated by each one of these engines? A) 67 dB B) 13 dB C) 44 dB D) 88 dB Answer: D Var: 1

40) The intensity at a distance of 6.0 m from a source that is radiating equally in all directions is 6.0 × 10-10 W/m2. What is the power emitted by the source? A) 2.1 × 10-8 W B) 2.7 × 10-7 W C) 2.1 × 10-6 W D) 2.7 × 10-5 W Answer: B Var: 1 41) The intensity at a distance of 6.0 m from a source that is radiating equally in all directions is 6.0 × 10-10 W/m2. What is the intensity level in dB? The threshold of human hearing is 1.0 × 10-12 W/m2. A) 18 dB B) 23 dB C) 28 dB D) 32 dB Answer: C Var: 1 42) A barking dog delivers about 1.0 mW of power, which is assumed to be uniformly distributed in all directions. What is the intensity level in decibels at a distance 5.00 m from the dog? The threshold of human hearing is 1.0 × 10-12 W/m2. A) 61 dB B) 63 dB C) 65 dB D) 68 dB Answer: C Var: 1 43) The intensity level is 65 dB at a distance 5.00 m from a barking dog. What would be a reasonable estimate for the intensity level if two identical dogs very close to each other were barking? You can ignore any interference effects. A) 65 dB B) 68 dB C) 130 dB D) 136 dB Answer: B Var: 1

44) At a distance of 15.0 m from a sound source, the intensity level is 60.0 dB. What is the intensity level (in decibels) at a point 2.00 m from the source if the source radiates equally in all directions? A) 55.7 dB B) 57.5 dB C) 75.5 dB D) 77.5 dB Answer: D Var: 1 45) The sound intensity level 5.0 m from a point source is 95 dB. At what distance will it be 75 dB? A) 25 m B) 50 m C) 75 m D) 225 m Answer: B Var: 1 46) A certain siren radiates sound uniformly in all directions. At a distance of 17 m from the siren, the intensity level is 49 db. How many watts of power does this siren put out? The threshold of human hearing is 1.0 × 10-12 W/m2. Answer: 2.9 × 10-4 W Var: 50+ 47) You double your distance from a sound source that is radiating equally in all directions. What happens to the intensity level of the sound? It drops by A) 2 dB. B) 3 dB. C) 6 dB. D) 8 dB. Answer: C Var: 1 48) By how many decibels does the intensity level of a sound decrease when you triple your distance from a source of sound? A) 9.5 dB B) 4.8 dB C) 6.0 dB D) 12 dB E) 3.0 dB Answer: A Var: 1

49) A certain factory whistle can be heard up to a distance of 2.5 km. Assuming that the acoustic output of the whistle is uniform in all directions, how much acoustic power is emitted by the whistle? The threshold of human hearing is 1.0 × 10-12 W/m2. A) 0.079 mW B) 0.026 mW C) 0.26 mW D) 0.79 mW E) 2.6 mW Answer: A Var: 50+ 50) A certain factory whistle can be heard up to a distance of 9.8 km. Assuming that the acoustic output of the whistle is uniform in all directions, at what distance from the factory is the intensity level of the whistle sound equal to 25 dB? The threshold of human hearing is 1.0 × 10-12 W/m2. A) 550 m B) 660 m C) 830 m D) 940 m E) 1100 m Answer: A Var: 50+ 51) By how many decibels does the intensity level of a sound increase when you triple the intensity of a source of sound? A) 9.5 dB B) 4.8 dB C) 6.0 dB D) 3.0 dB E) 12 dB Answer: B Var: 1 52) A sound of 40 decibels is A) twice as intense as a sound of 20 decibels. B) four times as intense as a sound of 20 decibels. C) 10 times as intense as a sound of 20 decibels. D) 100 times as intense as a sound of 20 decibels. E) 1000 times as intense as a sound of 20 decibels. Answer: D Var: 1 53) A long-term exposure to the sound of a riveting machine can cause your threshold of hearing to shift from 0 dB to 30 dB. What is the sound intensity of a 30-dB sound? The normal lowest detectable intensity is 1.0 × 10-12 W/m2. Answer: 1.0 × 10-9 W/m2 Var: 1 17 Copyright © 2019 Pearson Education, Inc.

54) A certain glass window reduces the intensity level of the sound from 72 dB to 47 dB. By what factor is the acoustic power reduced by this glass window? A) 3.2 × 10-3 B) 2.2 × 10-2 C) 5.6 × 10-2 D) 1.0 × 10-1 E) 1.5 × 10-1 Answer: A Var: 50+ 55) Two people are talking at a distance of 3.0 m from where you are, and you measure the sound intensity as 1.1 × 10-7 W/m2. Another student is 4.0 m away from the talkers. Calculate a reasonable estimate for the sound intensity that the other student measures. A) 6.2 × 10-8 W/m2 B) 1.5 × 10-7 W/m2 C) 8.3 × 10-8 W/m2 D) 7.8 × 10-7 W/m2 E) 2.5 × 10-8 W/m2 Answer: A Var: 1 56) A crying baby emits sound with an intensity of 8.0 × 10-8 W/m2. Calculate a reasonable estimate for the intensity level from a set of quintuplets (five babies), all crying simultaneously at the same place? The lowest detectable intensity is 1.0 × 10-12 W/m2. A) 79 dB B) 69 dB C) 56 dB D) 49 dB E) 36 dB Answer: C Var: 1 57) If the intensity level of one trombone is 70 dB, calculate a reasonable estimate for the intensity level of 76 trombones all playing simultaneously in the same place? A) 146 dB B) 89 dB C) 70 dB D) 76 dB E) 82 dB Answer: B Var: 1

58) As shown in the figure, a man is traveling on a bicycle along a straight road that runs parallel to and right next to some railroad tracks. While moving at 10 m/s, he hears the whistle of a train that is behind him, as shown in the figure. The frequency emitted by the train's whistle is but the frequency the man hears is The speed of sound is 340 m/s. (a) What frequency is heard by a stationary observer located between the train and the bicycle? (b) What is the speed of the train, and is the train traveling away from or toward the bicycle?

Answer: a) 797 Hz Var: 50+

b) 9.8 m/s, away from the bicycle

59) A factory siren indicating the end of a shift has a frequency of 80 Hz where the speed of sound in air is 343 m/s. What frequency is perceived by the occupant of a car that is traveling at 30 m/s (a) towards the factory and (b) away from the factory? Answer: (a) 87 Hz (b) 73 Hz Var: 1 60) A car approaches you at a constant speed, sounding its horn, and you hear a frequency of 76 Hz. After the car goes by, you hear a frequency of 65 Hz. What is the frequency of the sound emitted by the horn? The speed of sound in the air is 343 m/s. A) 68 Hz B) 69 Hz C) 70 Hz D) 71 Hz E) 72 Hz Answer: C Var: 1 61) As you stand by the side of the road, a car approaches you at a constant speed, sounding its horn, and you hear a frequency of 76 Hz. After the car goes by, you hear a frequency of 65 Hz. What is the speed of the car? The speed of sound in the air is 343 m/s. A) 26 m/s B) 27 m/s C) 28 m/s D) 29 m/s E) 30 m/s Answer: B Var: 1

62) You are driving along a highway at 35.0 m/s when you hear the siren of a police car approaching you from behind at constant speed and you perceive the frequency as . You are relieved that he is in pursuit of a different driver when he continues past you, but now you perceive the frequency as What is the speed of the police car? The speed of sound in air is A) 38.4 m/s B) 30 m/s C) 39.2 m/s D) 40.1 m/s E) 41.7 m/s Answer: D Var: 5 63) You are driving along a highway at 35.0 m/s when you hear the siren of a police car approaching you from behind at constant speed and you perceive the frequency as 1310 Hz. You are relieved that he is in pursuit of a different driver when he continues past you, but now you perceive the frequency as 1240 Hz. What is the frequency of the siren in the police car? The speed of sound in air is 343 m/s. A) 1300 Hz B) 1320 Hz C) 1270 Hz D) 1360 Hz E) 1370 Hz Answer: C Var: 5 64) You are driving along a highway at 25 m/s when you hear the siren of an emergency vehicle traveling at constant speed in the opposite direction on the other side of the highway. When the vehicle is approaching you, you hear the frequency of the siren as 2380 Hz, but when it is past you the frequency becomes 1680 Hz. What is the speed of the vehicle? The speed of sound in air is 343 m/s. A) 35 m/s B) 32 m/s C) 30 m/s D) 41 m/s E) 50 m/s Answer: A Var: 5

65) You are driving along a highway at 25.0 m/s when you hear the siren of an emergency vehicle traveling at constant speed in the opposite direction on the other side of the highway. When the vehicle is approaching you, you hear the frequency of the siren as 2380 Hz, but when it is past you the frequency becomes 1680 Hz. What is the frequency of the siren? The speed of sound in air is 343 m/s. A) 1850 Hz B) 2000 Hz C) 2050 Hz D) 2010 Hz E) 1980 Hz Answer: B Var: 5 66) A whistle produces sound of frequency of 1.00 kHz. If a listener moves with a speed of 30 m/s away from the whistle, what frequency does this person hear if the sound speed is 340 m/s? A) 912 Hz B) 919 Hz C) 1000 Hz D) 1090 Hz Answer: A Var: 1 67) A police car has an 800-Hz siren. It is traveling at 35.0 m/s on a day when the speed of sound through air is 340 m/s. The car approaches and passes an observer who is standing along the roadside. What change of frequency does the observer hear? A) 0 Hz B) 82 HZ C) 166 Hz D) 249 Hz Answer: C Var: 1 68) What is the frequency does a stationary observer hear when a train approaches her with a speed of 30 m/s. The frequency of the train horn is 0.600 kHz and the speed of sound is 340 m/s. A) 551 Hz B) 600 Hz C) 653 Hz D) 658 Hz Answer: D Var: 1

69) You are moving at 120 km/h toward a stationary train. The train blows its 0.400-kHz whistle. Take the speed of sound to be 340 m/s. What frequency do you hear? A) 444 Hz B) 439 Hz C) 364 Hz D) 361 Hz Answer: B Var: 1 70) A train is traveling away from you at 120 km/h. It blows its whistle, and you hear a tone of 0.400 kHz. Take the speed of sound to be 340 m/s. What frequency does the whistle actually produce? A) 444 Hz B) 439 Hz C) 364 Hz D) 361 Hz Answer: B Var: 1 71) Sonar is used to determine the speed of an object. A 40.0-kHz signal is sent out, and a 42.0kHz signal is returned. If the speed of sound is 345 m/s, how fast is the object moving? A) 6.9 m/s B) 8.4 m/s C) 331 m/s D) 347 m/s Answer: B Var: 1 72) A bat emits a sound at a frequency of 39.0 kHz as it approaches a wall. The bat detects beats with a frequency of 827 Hz between the sound it emits and the echo bouncing from the wall. What is the speed of the bat if the speed of sound in air is 343 m/s? A) 2.7 m/s B) 3.0 m/s C) 3.6 m/s D) 5.4 m/s E) 9.0 m/s Answer: C Var: 5

73) Two in-phase loudspeakers are some distance apart. They emit sound with a frequency of 536 Hz. A microphone is moved between the speakers along the line joining the two speakers with a constant speed of 1.60 m/s. What beat frequency is observed? The speed of sound in air is 343 m/s. A) 5.00 Hz B) 6.00 Hz C) 7.00 Hz D) 8.00 Hz E) 9.00 Hz Answer: A Var: 1 74) A siren emitting sound of frequency 1000 Hz approaches a stationary observer at one-half the speed of sound. The observer hears a frequency of A) 1000 Hz B) 2000 Hz. C) 500 Hz. D) 1500 Hz. E) none of the above. Answer: B Var: 1 75) The sound from the whistle of a truck moving at 17.0 m/s toward a cliff reflects from the cliff and is heard by the driver of the truck. When it is parked at the side of the road, the whistle from the truck produces sound of frequency 2.267 kHz. As observed by the driver of the truck, what is the change in frequency the sound from the whistle due to the reflection? The speed of sound is 343 m/s. A) 236 Hz B) 228 Hz C) 207 Hz D) 118 Hz E) 472 Hz Answer: A Var: 1

College Physics: A Strategic Approach, 4e (Knight) Chapter 16 Superposition and Standing Waves 16.1 Conceptual Questions 1) When a guitar is tuned to adjust its pitch, what is it that is changed? A) The wavelength of the fundamental. B) The frequency of the fundamental. C) The amplitude of the fundamental. Answer: B Var: 1 2) If a guitar string has a fundamental frequency of 500 Hz, which one of the following frequencies can set the string into resonant vibration? A) 250 Hz B) 750 Hz C) 1500 Hz D) 1750 Hz Answer: C Var: 1 3) A stretched string is observed to have four equal segments in a standing wave driven at a frequency of 480 Hz. What driving frequency will set up a standing wave with five equal segments? A) 600 Hz B) 360 Hz C) 240 Hz D) 120 Hz Answer: A Var: 1 4) If a string fixed at both ends resonates in its fundamental mode with a frequency of 150 Hz, at which of the following frequencies will it not resonate? (There could be more than one correct choice.) A) 75 Hz B) 300 Hz C) 450 Hz D) 500 Hz E) 600 Hz Answer: A, D Var: 1

5) A string fixed at both ends is vibrating in one of its harmonics. If we now increase only the frequency at which the string is vibrating, which of the following characteristics do we also increase? (There could be more than one correct choice.) A) the speed of the traveling waves on the string B) the period of the traveling waves on the string C) the wavelength of the traveling waves on the string D) the amplitude of the traveling waves on the string E) none of the above Answer: E Var: 1 6) An organ pipe of length L that is open at one end resonates in its third harmonic with a wavelength of 2L/3. Is the other end of the pipe closed or open? A) closed B) open C) We cannot tell from the information provided. Answer: B Var: 1 7) In a resonating pipe that is open at both ends, there A) are displacement nodes at each end. B) are displacement antinodes at each end. C) is a displacement node at one end and a displacement antinode at the other end. D) None of the above choices are correct. Answer: B Var: 1 8) In a resonating pipe that is open at one end and closed at the other end, there A) are displacement nodes at each end. B) are displacement antinodes at each end. C) is a displacement node at the open end and a displacement antinode at the closed end. D) is a displacement node at the closed end and a displacement antinode at the open end. Answer: D Var: 1 9) The lowest tone to resonate in pipe of length L that is open at both ends is 200 Hz. Which one of the following frequencies will not resonate in the same pipe? A) 200 Hz B) 400 Hz C) 600 Hz D) 800 Hz E) 900 Hz Answer: E Var: 1

10) The lowest tone to resonate in a pipe of length L that is closed at one end but open at the other end is 200 Hz. Which one of the following frequencies will not resonate in that pipe? A) 200 Hz B) 400 Hz C) 600 Hz D) 1000 Hz E) 1400 Hz Answer: B Var: 1 11) Consider the standing wave on a guitar string and the sound wave generated by the string as a result of this vibration. What do these two waves have in common? (There may be more than one correct choice.) A) They have the same wavelength. B) They have the same speed. C) They have the same frequency. D) They have the same amplitude. E) They have the same period. Answer: C, E Var: 1 12) Consider a pipe of length L that is open at both ends. What are the wavelengths of the three lowest-pitch tones produced by this pipe? A) 4L, 2L, L B) 2L, L, L/2 C) 2L, L, 2L/3 D) 4L, 4L/3, 4L/5 Answer: C Var: 1 13) An pipe of length L that is open at both ends is resonating at its fundamental frequency. Which statement about the sound is correct? A) The wavelength is 2L and there is a displacement node at the pipe's midpoint. B) The wavelength is 2L and there is a displacement antinode at the pipe's midpoint. C) The wavelength is L and there is a displacement node at the pipe's midpoint. D) The wavelength is L and there is a displacement antinode at the pipe's midpoint. Answer: A Var: 1 14) In a resonating pipe that is open at one end and closed at the other, there A) are displacement nodes at each end. B) are displacement antinodes at each end. C) is a displacement node at the open end and a displacement antinode at the closed end. D) is a displacement node at the closed end and a displacement antinode at the open end. Answer: D Var: 1 3 Copyright © 2019 Pearson Education, Inc.

15) Consider a pipe of length L that is open at one end and closed at the other end. What are the wavelengths of the three lowest-pitch tones produced by this pipe? A) 4L, 2L, L B) 2L, L, L/2 C) 2L, L, 2 L/3 D) 4L, 4L/3, 4L/5 Answer: D Var: 1 16) A pipe of length L that is closed at one end and open at the other end is resonating at its fundamental frequency. Which statement about the sound is correct? A) The wavelength is 4L and there is a displacement node at the pipe's open end. B) The wavelength is 4L and there is a displacement antinode at the pipe's open end. C) The wavelength is L and there is a displacement node at the pipe's open end. D) The wavelength is L and there is a displacement antinode at the pipe's open end. Answer: B Var: 1 17) Two tuning forks have frequencies of 440 and 522 Hz. What is the beat frequency if both are sounding simultaneously? A) 962 Hz B) 481 Hz C) 82 Hz D) 55 Hz E) 41 Hz Answer: C Var: 1 18) Two strings both vibrate at exactly 819 Hz. The tension in one of them is then increased slightly. As a result, six beats per second are heard when both strings vibrate. What is the new frequency of the string that was tightened? A) 825 Hz B) 813 Hz C) 822 Hz D) 816 Hz Answer: A Var: 50+ 19) Two pure tones are sounded together and a particular beat frequency is heard. What happens to the beat frequency if the frequency of one of the tones is increased? A) It increases. B) It decreases. C) It does not change. D) It could either increase or decrease. Answer: D Var: 1 4 Copyright © 2019 Pearson Education, Inc.

20) A music tuner uses a 554-Hz C# tuning fork to tune the frequency of a musical instrument. If the tuner hears a beat frequency of 2 Hz, what is the frequency of the instrument? A) It must be 556 Hz. B) It must be 552 Hz. C) It could be either 556 Hz or 552 Hz. D) It could be either 553 Hz or 555 Hz. E) It is neither 556 Hz or 552 Hz. Answer: C Var: 1 21) A person stands between two speakers driven by the same source. Each speaker produces a tone with a frequency of 200 Hz on a day when the speed of sound is 330 m/s. The person is 1.65 m from one speaker and 4.95 m from the other. What type of interference does the person perceive? A) constructive B) destructive C) both constructive and destructive D) neither constructive nor destructive Answer: A Var: 1 16.2 Problems 1) A guitar string 0.65 m long has a tension of 61 N and a mass per unit length of 3.0 g/m. (a) What is the speed of waves on the string when it is plucked? (b) What is the string's fundamental frequency of vibration when plucked? (c) At what other frequencies will this string vibrate? Answer: (a) 143 m/s (b) 110 Hz (c) f = m(110 Hz), m = 2, 3, 4, Var: 1 2) Standing waves of frequency 17 Hz are produced on a string that has a mass per unit length of To what tension must the string be stretched between two supports if adjacent nodes in the standing wave are to be 0.87 m apart? Answer: 14 N Var: 50+ 3) The speed of propagation of a transverse wave on a 2.0-m long string fixed at both ends is 200 m/s. Which one of the following is not a resonant frequency of this string? A) 25 Hz B) 50 Hz C) 100 Hz D) 200 Hz Answer: A Var: 1

4) A string of linear density 1.5 g/m is under a tension of 20 N. What should be its length if its fundamental resonance frequency is 220 Hz? A) 0.26 m B) 0.96 m C) 1.1 m D) 1.2 m Answer: A Var: 1 5) Find the first three harmonics of a string of linear mass density 2.00 g/m and length 0.600 m when the tension in it is 50.0 N. A) 132 Hz, 264 Hz, 395 Hz B) 66 Hz, 132 Hz, 198 Hz C) 264 Hz, 528 Hz, 792 Hz D) none of the above Answer: A Var: 1 6) A string of length 2.5 m is fixed at both ends. When the string vibrates at a frequency of 85 Hz, a standing wave with five loops is formed. (a) Determine the distance between two adjacent nodes. (b) Determine the wavelength of the waves that travel on the string. (c) Determine the speed of traveling waves on this string. (d) Determine the fundamental frequency of this string. Answer: (a) 0.50 m (b) 1.0 m (c) 85 m/s (d) 17 Hz Var: 1 7) What is the frequency of the fundamental mode of vibration of a steel piano wire stretched to a tension of 440 N? The wire is 0.600 m long and has a mass of 5.60 g. A) 517 Hz B) 234 Hz C) 181 Hz D) 312 Hz E) 366 Hz Answer: C Var: 1 8) A 25-g string is stretched with a tension of 43 N between two fixed points 12 m apart. What is the frequency of the second harmonic? A) 6.0 Hz B) 12 Hz C) 18 Hz D) 24 Hz E) 36 Hz Answer: B Var: 1 6 Copyright © 2019 Pearson Education, Inc.

9) A 0.588-m string is tightly clamped at both ends. If the lowest standing wave frequency of the string is how fast do waves travel on this string? A) 383 m/s B) 475 m/s C) 582 m/s D) 724 m/s Answer: A Var: 50+ 10) A string that is 2.0 meters long is fixed at both ends and tightened until the wave speed is What is the frequency of the standing wave shown in the figure?

A) 27 Hz B) 54 Hz C) 81 Hz D) 110 Hz Answer: A Var: 50+ 11) A standing wave is oscillating at 950 Hz on a string, as shown in the figure. What is the wave speed?

A) 380 m/s B) 570 m/s C) 290 m/s D) 190 m/s Answer: A Var: 50+ 12) A guitar-like stringed instrument has a string that is 16 cm long. It sounds the musical note A (440 Hz) when played without fingering. By what distance should you shorten it to play the note C (523 Hz)? A) 2.5 cm B) 1.7 cm C) 3.4 cm D) 4.2 cm Answer: A Var: 50+

13) A 4.0-g string is 0.36 m long and is under tension. The string vibrates at 500 Hz in its third harmonic. What is the wavelength of the standing wave in the string? A) 0.24 m B) 0.36 m C) 0.54 m D) 0.72 m E) 0.90 m Answer: A Var: 50+ 14) A 4.0-g string is 0.39 m long and is under tension. The string vibrates at 600 Hz in its third harmonic. What is the tension in this string? A) 250 N B) 200 N C) 160 N D) 290 N E) 340 N Answer: A Var: 50+ 15) One of the harmonics of a string fixed at both ends has a frequency of 52.2 Hz and the next higher harmonic has a frequency of 60.9 Hz. What is the fundamental frequency of the string? A) 26.1 Hz B) 8.7 Hz C) 4.35 Hz D) 30.4 Hz E) 17.4 Hz Answer: B Var: 1 16) If the frequency of a violin string is to be increased by 20%, what change in tension must be applied? A) 44% B) 20% C) 4.5% D) 10% Answer: A Var: 1 17) An organ pipe that is 1.75 m long and open at both ends produces sound of frequency 303 Hz when resonating in its second overtone. What is the speed of sound in the room? Answer: 354 m/s Var: 1

18) An organ pipe closed at one end and open at the other end has two successive harmonics with frequencies of 2170 Hz and 2790 Hz. What is the fundamental frequency of the pipe? Answer: 310 Hz Var: 1 19) A pipe that is 0.92 m long and open at both ends vibrates in the second overtone with a frequency of What is the speed of sound in the air in this pipe? A) 358 m/s B) 349 m/s C) 353 m/s D) 344 m/s E) 363 m/s Answer: A Var: 50+ 20) A standing wave of the third overtone is induced in a 1.2-m pipe that is open at one end and closed at the other end. The speed of sound in the pipe is 340 m/s. (a) How many antinodes are there in the standing wave pattern? (b) What is the frequency of the sound produced by the pipe in this situation? Answer: (a) 4 (b) 500 Hz Var: 1 21) An organ pipe open at both ends has a length of 0.80 m. If the velocity of sound in air is what is the frequency of the second harmonic of this pipe? A) 213 Hz B) 425 Hz C) 638 Hz D) 850 Hz Answer: B Var: 2 22) What is the length of the shortest pipe closed on one end and open at the other end that will have a fundamental frequency of 0.060 kHz on a day when the speed of sound is 340 m/s? A) 1.24 m B) 1.42 m C) 2.14 m D) 4.12 m Answer: B Var: 1

23) Consider two pipes of the same length: one pipe is open at both ends and the other pipe is closed on one end but open at the other end. If the fundamental frequency of the totally open pipe is 300 Hz, what is the fundamental frequency of the other pipe? A) 150 Hz B) 300 Hz C) 450 Hz D) 600 Hz Answer: A Var: 1 24) One of the harmonics of a column of air in a tube that is open at one end and closed at the other has a frequency of 448 Hz, and the next higher harmonic has a frequency of 576 Hz. What is the fundamental frequency of the air column in this tube? A) 32 Hz B) 64 Hz C) 88 Hz D) 128 Hz E) 256 Hz Answer: B Var: 1 25) One of the harmonics of a column of air in a tube that is open at both ends has a frequency of 448 Hz, and the next higher harmonic has a frequency of 576 Hz. What is the fundamental frequency of the air column in this tube? A) 32 Hz B) 64 Hz C) 88 Hz D) 128 Hz E) 256 Hz Answer: D Var: 1 26) One of the harmonics of a column of air in a tube that is open at one end and closed at the other has a frequency of 448 Hz, and the next higher harmonic has a frequency of 576 Hz. How long is the tube? The speed of sound in air is 343 m/s. A) 1.34 m B) 0.670 m C) 0.335 m D) 1.00 m E) 2.68 m Answer: A Var: 1

27) A 2.0-g string that is 0.67 m long is under tension. The string vibrates at 700 Hz tone in its third harmonic, and this vibration causes a sound wave. What is the wavelength of the sound? The speed of sound in air is 344 m/s. A) 0.49 B) 0.55 C) 0.61 D) 0.67 E) 0.45 Answer: A Var: 50+ 28) A string that is 0.15 m long and fixed at both ends is vibrating in its n = 5 harmonic. The sound from this string excites a pipe that is long and open at both ends into its second overtone resonance. What is the distance between a node and an adjacent antinode, in the string? The speed of sound in air is 345 m/s. A) 15 mm B) 7.5 mm C) 23 mm D) 30 mm E) 150 mm Answer: A Var: 50+ 29) A string that is 0.26 m long is vibrating in its n = 6 harmonic. The sound from tthis string excites a pipe that is long and open at both ends into its second overtone resonance. What is the common resonant frequency of the string and the pipe? The speed of sound in air is 345 m/s. A) 590 Hz B) 390 Hz C) 490 Hz D) 690 Hz E) 760 Hz Answer: A Var: 50+ 30) A 0.13-m string, fixed at both ends and vibrating in its n = 4 harmonic, excites a pipe that is long and open at both ends, into its second overtone resonance. What is the speed of transverse waves on the string? The speed of sound in air is 345 m/s. A) 38 m/s B) 36 m/s C) 34 m/s D) 32 m/s E) 30 m/s Answer: A Var: 50+

31) A violin with string length 32 cm and string density resonates in its fundamental with the first overtone of a 2.0-m organ pipe with one end closed and one end open. What is the tension in the string if the speed of sound in air is 344 m/s? A) 1000 N B) 110 N C) 450 N D) 4100 N E) 56 N Answer: A Var: 50+ 32) Two police cars have identical sirens that produce sound of frequency of 570 Hz. A stationary listener is standing between two cars. One car is parked and the other is approaching the listener and both have their sirens on. The listener measures 9.0 beats per second. Find the speed of the approaching police car. The speed of sound is 340 m/s. Answer: 5.3 m/s Var: 50+ 33) The wavelengths of the sounds produced by two horns are 6.0 m and 7.0 m, respectively. What beat frequency is heard when the horns are sounded on a day when the speed of sound is 340 m/s? A) 5 Hz B) 6 Hz C) 7 Hz D) 8 Hz Answer: D Var: 1 34) Two taut strings of identical mass per unit length are stretched with the same tension with their ends fixed, but one string is 0.330 cm longer than the other. Waves on these strings propagate at 34.0 m/s.The fundamental frequency of the shorter string is 258 Hz. What is the beat frequency when each string is vibrating at its fundamental frequency? A) 12.3 Hz B) 9.00 Hz C) 12.0 Hz D) 12.7 Hz E) 11.3 Hz Answer: A Var: 5

35) Two taut strings of identical mass and length are stretched with their ends fixed, but the tension in one string is 1.10 times greater than in the other. Waves on the string with the lower tension propagate at 35.2 m/s. The fundamental frequency of that string is 258 Hz. What is the beat frequency when each string is vibrating at its fundamental frequency? A) 11.0 Hz B) 9.00 Hz C) 13.7 Hz D) 12.6 Hz E) 17.1 Hz Answer: D Var: 5 36) A policeman in a stationary car measures the speed of approaching cars by means of an ultrasonic device that emits a sound with a frequency of 39.6 kHz. A car is approaching him at a speed of 35.0 m/s. The wave is reflected by the car and interferes with the emitted sound producing beats. What is the frequency of the beats when the speed of sound in air is 343 m/s? A) 5000 Hz B) 4500 Hz C) 8490 Hz D) 9000 Hz E) 4250 Hz Answer: D Var: 5 37) Two in-phase loudspeakers are 3.0 m apart. They emit sound with a frequency of 490 Hz. A microphone is placed half-way between the speakers and then moved along the line joining the two speakers until the first point of constructive interference is found. At what distance from that midpoint is that first point? The speed of sound in air is 343 m/s. A) 0.18 m B) 0.35 m C) 0.50 m D) 0.70 m E) There is no point in that line where constructive interference occurs. Answer: B Var: 1 38) Two in-phase loudspeakers are placed along a wall and are separated by a distance of 4.00 m. They emit sound with a frequency of 514 Hz. A person is standing away from the wall, in front of one of the loudspeakers. What is the closest nonzero distance from the wall the person can stand and hear constructive interference? The speed of sound in air is 343 m/s. A) 0.34 m B) 0.73 m C) 1.2 m D) 1.6 m Answer: B Var: 1 13 Copyright © 2019 Pearson Education, Inc.

39) Two in-phase loudspeakers are placed along a wall and are separated by a distance of 4.00 m. They emit sound with a frequency of 514 Hz. A person is standing away from the wall, in front of one of the loudspeakers. What is the closest distance from the wall the person can stand and hear destructive interference? The speed of sound in air is 343 m/s. A) 0.34 m B) 0.37 m C) 0.73 m D) 1.2 m E) 1.6 m Answer: A Var: 1 40) Two in-phase loudspeakers that emit sound with the same frequency are placed along a wall and are separated by a distance of 5.00 m. A person is standing 12.0 m away from the wall, equidistant from the loudspeakers. When the person moves 1.00 m parallel to the wall, she experiences destructive interference for the first time. What is the frequency of the sound? The speed of sound in air is 343 m/s. A) 211 Hz B) 256 Hz C) 422 Hz D) 512 Hz E) 674 Hz Answer: C Var: 1 41) Two in-phase loudspeakers that emit sound with the same frequency are placed along a wall and are separated by a distance of 8.00 m. A person is standing 12.0 m away from the wall, equidistant from the loudspeakers. When the person moves 3.00 m parallel to the wall, she experiences destructive interference for the second time. What is the frequency of the sound? The speed of sound in air is 343 m/s. A) 278 Hz B) 422 Hz C) 452 Hz D) 562 Hz E) 694 Hz Answer: A Var: 1

42) Two loudspeakers placed 6.00 m apart are driven in phase by an audio oscillator having a frequency range from 1908 Hz to 2471 Hz. A point P is located 4.70 m from one loudspeaker and 3.60 m from the other speaker. At what frequency of the oscillator does the sound reaching point P interfere constructively? The speed of sound is 344 m/s. A) 2190 Hz B) 2420 Hz C) 2110 Hz D) 2340 Hz E) 2270 Hz Answer: A Var: 1 43) Two loudspeakers placed 6.00 m apart are driven in phase by an audio oscillator having a frequency range from 1595 Hz to 2158 Hz. A point P is located 4.70 m from one loudspeaker and 3.60 m from the other speaker. The speed of sound in the room is 344 m/s. At what frequency (or frequencies) of the oscillator does the sound reaching point P interfere destructively? (There could be more than one correct choice.) A) 2030 Hz B) 2130 Hz C) 2100 Hz D) 1720 Hz E) 1630 Hz Answer: A, D Var: 1 44) Two stereo speakers mounted 4.52 m apart on a wall emit identical sound waves. You are standing at the opposite wall of the room at a point directly between the two speakers. You walk 2.11 m parallel to the wall, to a location where you first notice that the sound intensity is essentially zero. If the wall along which you are walking is from the wall with the speakers, what is the wavelength of the sound waves? The walls are cushioned to absorb sound reflections. A) 1.71 m B) 2.05 m C) 2.57 m D) 2.91 m Answer: A Var: 50+

45) Two speakers are placed side by side and driven by the same frequency of 0.50 kHz. If the distance from a person to one speaker is 5.0 m and the person detects little or no sound, which of the following is a possible the distance from the person to the other speaker? The sound speed in the room is 340 m/s. A) 7.7 m B) 8.1 m C) 8.4 m D) 9.1 m Answer: B Var: 1

College Physics: A Strategic Approach, 4e (Knight) Chapter 17 Wave Optics 17.1 Conceptual Questions 1) A light beam has speed c in vacuum and speed v in a certain plastic. The index of refraction n of this plastic is A) n = cv. B) n = (v/c)2. C) n = v/c. D) n = c/v. E) n = (c/v)2. Answer: D Var: 1 2) If the index of refraction of a material is 2, this means that light travels A) 2 times as fast in air as it does in vacuum. B) 2 times as fast in the material as it does in air. C) 2 times as fast in vacuum as it does in the material. D) 2 times as fast in the material than it does in vacuum. E) 1/2 as fast in air as it does in the material. Answer: C Var: 1 3) When light travels from air into water, A) its velocity, wavelength and frequency all change. B) its velocity changes, but its frequency and wavelength do not change. C) its frequency changes, but its velocity and wavelength do not change. D) its velocity and wavelength change, but its frequency does not change. E) its wavelength changes, but its velocity and frequency do not change. Answer: D Var: 1 4) Monochromatic coherent light shines through a pair of slits. If the distance between these slits is decreased, which of the following statements are true of the resulting interference pattern? (There could be more than one correct choice.) A) The distance between the maxima stays the same. B) The distance between the maxima decreases. C) The distance between the minima stays the same. D) The distance between the minima increases. E) The distance between the maxima increases. Answer: D, E Var: 1

5) Monochromatic coherent light shines through a pair of slits. If the wavelength of the light is decreased, which of the following statements are true of the resulting interference pattern? (There could be more than one correct choice.) A) The distance between the maxima stays the same. B) The distance between the maxima decreases. C) The distance between the minima stays the same. D) The distance between the minima increases. E) The distance between the minima decreases. Answer: B, E Var: 1 6) A double-slit interference experiment is performed in the air. Later, the same apparatus is immersed in benzene (which has an index of refraction of 1.50), and the experiment is repeated. When the apparatus is in benzene, you observe that the interference fringes are A) more closely spaced than when the apparatus is in air. B) equally spaced as when the apparatus is in air. C) more widely spaced than when the apparatus is in air. Answer: A Var: 1 7) In a double-slit interference experiment you are asked to use laser light of different wavelengths and determine the separation between adjacent maxima. You observe that this separation is greatest when you illuminate the double slit with A) blue light. B) green light. C) yellow light. D) red light. E) The separation is the same for all wavelengths. Answer: D Var: 1 8) Two light sources are said to be coherent if they are A) of the same frequency. B) of the same frequency, and maintain a constant phase difference. C) of the same amplitude, and maintain a constant phase difference. D) of the same frequency and amplitude. Answer: B Var: 1

9) What do we mean when we say that two light rays striking a screen are in phase with each other? A) When the electric field due to one is a maximum, the electric field due to the other is also a maximum, and this relation is maintained as time passes. B) They are traveling at the same speed. C) They have the same wavelength. D) They alternately reinforce and cancel each other. Answer: A Var: 1 10) Two beams of coherent light start out at the same point in phase and travel different paths to arrive at point P. If the maximum constructive interference is to occur at point P, the two beams must travel paths that differ by A) a whole number of wavelengths. B) an odd number of half-wavelengths. C) a whole number of half-wavelengths. Answer: A Var: 1 11) Two beams of coherent light start out at the same point in phase and travel different paths to arrive at point P. If the maximum destructive interference is to occur at point P, the two beams must travel paths that differ by A) a whole number of wavelengths. B) an odd number of half-wavelengths. C) a whole number of half-wavelengths. Answer: B Var: 1 12) If a sheet containing two very thin slits is heated (without damaging it), what happens to the angular location of the first-order interference minimum? A) It moves toward the centerline. B) It moves away from the centerline. C) It doesn't change. Answer: A Var: 1 13) In a double-slit experiment, it is observed that the distance between adjacent maxima on a remote screen is 1.0 cm. What happens to the distance between adjacent maxima when the slit separation is cut in half? A) It increases to 2.0 cm. B) It increases to 4.0 cm. C) It decreases to 0.50 cm. D) It decreases to 0.25 cm. E) None of these choices are correct. Answer: A Var: 1 3 Copyright © 2019 Pearson Education, Inc.

14) In a single-slit diffraction experiment, the width of the slit through which light passes is reduced. What happens to the width of the central bright fringe in the resulting diffraction pattern? A) It stays the same. B) It becomes narrower. C) It becomes wider. Answer: C Var: 1 15) A single-slit diffraction pattern is formed on a distant screen. Assuming the angles involved are small, by what factor will the width of the central bright spot on the screen change if the wavelength of the illuminating light is doubled? A) It will be cut to one-quarter its original size. B) It will be cut in half. C) It will double. D) It will become four times as large. E) It will become eight times as large. Answer: C Var: 1 16) A single-slit diffraction pattern is formed on a distant screen. Assuming the angles involved are small, by what factor will the width of the central bright spot on the screen change if the slit width is doubled? A) It will be cut to one-quarter its original size. B) It will be cut in half. C) It will double. D) It will become four times as large. E) It will become eight times as large. Answer: B Var: 1 17) If a sheet containing a single slit is heated (without damaging it) and therefore expands, what happens to the angular location of the first-order diffraction minimum? A) It moves toward the centerline. B) It moves away from the centerline. C) It doesn't change. Answer: A Var: 1 18) If a sheet containing a single thin slit is heated (without damaging it) and therefore expands, what happens to the width of the central bright diffraction region on a distant screen? A) It gets narrower. B) It gets wider. C) It doesn't change. Answer: B Var: 1 4 Copyright © 2019 Pearson Education, Inc.

19) What principle is responsible for light spreading as it passes through a narrow slit? A) refraction B) polarization C) diffraction D) dispersion Answer: C Var: 1 20) Radio waves are diffracted by large objects such as buildings, whereas light is not noticeably diffracted. Why is this? A) Radio waves are unpolarized, whereas light is normally polarized. B) The wavelength of light is much smaller than the wavelength of radio waves. C) The wavelength of light is much greater than the wavelength of radio waves. D) Radio waves are coherent and light is usually not coherent. E) Radio waves are polarized, whereas light is usually unpolarized. Answer: B Var: 1 21) Which of the following changes would increase the separation between the bright fringes in the diffraction pattern formed by a diffraction grating? A) Increase the wavelength of the light used. B) Increase the separation between the slits. C) Immerse the apparatus in water. D) All of these. E) None of these. Answer: A Var: 1 22) Light of the same wavelength passes through two diffraction gratings. One grating has 4000 lines/cm, and the other one has 6000 lines/cm. Which grating will spread the light through a larger angle in the first-order pattern? A) the 4000-line grating B) the 6000-line grating C) Both gratings spread the light the same. Answer: B Var: 1 23) If a diffraction grating is heated (without damaging it) and therefore expands, what happens to the angular location of the first-order maximum? A) It moves toward the centerline. B) It moves away from the centerline. C) It doesn't change. Answer: A Var: 1

24) Light in a frozen block of ice reflects off the ice-air interface at the surface of the block. What phase shift does it undergo? A) 0° B) 90° C) 180° D) 270° E) It does not undergo any phase shift. Answer: A Var: 1 25) Light reflects off the surface of Lake Superior. What phase shift does it undergo? A) 0° B) 90° C) 180° D) 270° E) It does not undergo any phase shift. Answer: C Var: 1 26) When a beam of light that is traveling in glass strikes an air boundary at the surface of the glass, there is A) a 90° phase change in the reflected beam. B) no phase change in the reflected beam. C) a 180° phase change in the reflected beam. D) a 60° phase change in the reflected beam. E) a 45° phase change in the reflected beam. Answer: B Var: 1 27) When a beam of light that is traveling in air is reflected by a glass surface, there is A) a 90° phase change in the reflected beam. B) no phase change in the reflected beam. C) a 180° phase change in the reflected beam. D) a 60° phase change in the reflected beam. E) a 45° phase change in the reflected beam. Answer: C Var: 1 28) When a light wave enters into a medium of different refractive index, A) only its speed and frequency change. B) only its speed and wavelength change. C) only its frequency and wavelength change. D) its speed, frequency, and wavelength change. Answer: B Var: 1

29) When a beam of light, originally traveling in air, enters a piece of glass having an index of refraction of 3/2, its frequency A) increases by a factor of 3/2. B) is reduced to 2/3 its original value. C) is unaffected. Answer: C Var: 1 30) When a beam of light, originally traveling in air, enters a piece of glass having an index of refraction of 3/2, its wavelength A) increases by a factor of 3/2. B) is reduced to 2/3 its original value. C) is unaffected. Answer: B Var: 1 31) When a beam of light, originally traveling in air, enters a piece of glass having an index of refraction of 3/2, its speed A) increases by a factor of 3/2. B) is reduced to 2/3 its original value. C) is unaffected. Answer: B Var: 1 32) The colors on an oil slick are caused by reflection and A) diffraction. B) interference. C) refraction. D) polarization. E) ionization. Answer: B Var: 1 33) If a metal sheet containing a tiny hole is heated (without damaging it) and therefore expands, what happens to the angular location of the first-order diffraction maximum? A) It moves toward the centerline. B) It moves away from the centerline. C) It doesn't change. Answer: A Var: 1

17.2 Problems 1) Light having a speed in vacuum of 3.0 × 108 m/s enters a liquid of refractive index 2.0. In this liquid, its speed will be A) 6.0 × 108 m/s B) 3.0 × 108 m/s C) 1.5 × 108 m/s D) 0.75 × 108 m/s E) 0.67 × 108 m/s Answer: C Var: 1 2) The speed of light in a certain material is measured to be 2.2 × 108 m/s. What is the index of refraction of this material? (c = 3.0 × 108 m/s) A) 1.1 B) 1.2 C) 1.4 D) 1.6 E) 1.8 Answer: C Var: 1 3) The index of refraction of a certain glass is measured to be 1.5. What is the speed of light in that glass? (c = 3.0 × 108 m/s) A) 1.0 × 108 m/s B) 2.0 × 108 m/s C) 3.0 × 108 m/s D) 4.0 × 108 m/s E) 5.0 × 108 m/s Answer: B Var: 1 4) Red light with a wavelength of 650 nm travels from air into a liquid with an index of 1.33. What are the frequency and wavelength of the light in the liquid? (c = 3.0 × 108 m/s) Answer: 4.61 × 1014 Hz, 489 nm Var: 1 5) Light of wavelength 550 nm in air is found to travel at 1.96 × 108 m/s in a certain liquid. (c = 3.0 × 108 m/s) (a) What is the index of refraction of this liquid? (b) What is the frequency of the light in air? Answer: (a) 1.53 (b) 5.45 × 1014 Hz Var: 1 8 Copyright © 2019 Pearson Education, Inc.

6) Light of wavelength 550 nm in air is found to travel at 1.96 × 108 m/s in a certain liquid. What are the frequency and wavelength of the light in this liquid? (c = 3.0 × 108 m/s) Answer: 5.45 × 1014 Hz, 359 nm Var: 1 7) Light having a frequency in vacuum of 6.0 × 1014 Hz enters a liquid of refractive index 2.0. What is the frequency of the light in this liquid? (c = 3.0 × 108 m/s) A) 12 × 1014 Hz B) 6.0 × 1014 Hz C) 3.0 × 1014 Hz D) 1.5 × 1014 Hz E) 2.0 × 1014 Hz Answer: B Var: 1 8) Light having a wavelength in vacuum of 600 nm enters a liquid of refractive index 2.0. In this liquid, what is the wavelength of the light? (c = 3.0 × 108 m/s) A) 1200 nm B) 600 nm C) 300 nm D) 150 nm E) 200 nm Answer: C Var: 1 9) Coherent light of wavelength 519 nm passes through two slits. In the resulting interference pattern on a screen 4.6 m away, adjacent bright fringes are apart. What is the separation of the two slits? Answer: 0.60 mm Var: 50+ 10) In a double-slit experiment, the slit separation is 1.75 mm, and two coherent wavelengths of light, 425 nm and 510 nm, illuminate the slits. At what angle from the centerline on either side of the central maximum will a bright fringe from one pattern first coincide with a bright fringe from the other pattern? Answer: 0.0835° Var: 1

11) A double-slit experiment uses coherent light of wavelength 633 nm with a slit separation of 0.100 mm and a screen placed 2.0 m away. (a) How wide on the screen is the central bright fringe? (b) What is the distance on the screen between first-order and second-order bright fringes? (c) What is the angular separation (in radians) between the central maximum and the first-order maximum? Answer: (a) 1.3 cm (b) 1.3 cm (c) 6.33 mrad Var: 6 12) In a two-slit experiment, monochromatic coherent light of wavelength 600 nm passes through a pair of slits separated by 2.20 x m. At what angle away from the centerline does the first bright fringe occur? A) 1.56° B) 2.22° C) 3.12° D) 4.70° E) 6.24° Answer: A Var: 5 13) In a two-slit experiment, monochromatic coherent light of wavelength 600 nm passes through a pair of slits separated by 2.20 × 10-5 m. At what angle away from the centerline does the second dark fringe occur? A) 4.70° B) 3.51° C) 3.94° D) 1.17° E) 2.34° Answer: E Var: 1 14) In a two-slit experiment, the slit separation is 3.00 × m. The interference pattern is created on a screen that is 2.00 m away from the slits. If the 7th bright fringe on the screen is 10.0 cm away from the central fringe, what is the wavelength of the light? A) 100 nm B) 204 nm C) 214 nm D) 224 nm E) 234 nm Answer: C Var: 5

15) Coherent light of wavelength 540 nm passes through a pair of thin slits that are 3.4 × apart. At what angle away from the centerline does the second bright fringe occur? A) 1.8° B) 3.7° C) 4.3° D) 1.5° E) 5.0° Answer: A Var: 5

16) In a two-slit experiment, a third-order bright fringe is observed at an angle of 7.10° away from the centerline. If the wavelength of light is 595 nm, how far apart are the two slits? A) 1.44 × m B) 1.07 × m C) 2.12 × m D) 2.53 × m E) 3.76 × m Answer: A Var: 5 17) In a two-slit experiment using coherent light, the distance between the slits and the screen is 1.10 m, and the distance between the slits is 0.100 mm. If the first-order bright fringe is measured to be 3.40 cm from the centerline, what is the wavelength of the light? A) 354 nm B) 241 nm C) 133 nm D) 3.09 μm E) 2.11 μm Answer: D Var: 1 18) A two-slit arrangement with 60.3 μm separation between the slits is illuminated with coherent light. If a viewing screen is located 2.14 m from the slits, find the distance from the first dark fringe on one side of the central maximum to the second dark fringe on the other side. A) 52.3 mm B) 34.9 mm C) 69.7 mm D) 24.6 mm Answer: B Var: 50+

19) In a two-slit experiment using coherent light, the distance between the slits and the screen is 1.10 m, and the distance between the slits is 0.0400 mm. If the second order bright fringe is measured to be 4.20 cm from the centerline on the screen, what is the wavelength of light? A) 200 nm B) 381 nm C) 401 nm D) 620 nm E) 763 nm Answer: E Var: 1 20) The distance between two slits is 1.50 × m. A beam of coherent light of wavelength 600 nm illuminates these slits, and the distance between the slit and the screen is 2.00 m. What is the distance on the screen between the central bright fringe and the fourth-order bright fringe? A) 0.132 m B) 0.201 m C) 0.324 m D) 0.528 m E) 0.688 m Answer: C Var: 5 21) A pair of narrow slits that are 1.8 mm apart is illuminated by a monochromatic coherent light source. A fringe pattern is observed on a screen 4.8 m from the slits. If there are 5.0 bright fringes/cm on the screen, what is the wavelength of the monochromatic light? A) 550 nm B) 600 nm C) 650 nm D) 700 nm E) 750 nm Answer: E Var: 1 22) A pair of narrow slits that are 1.8 mm apart is illuminated by a monochromatic coherent light source. A fringe pattern is observed on a screen 4.8 m from the slits. If the wavelength of the monochromatic light is 450 nm, what is the angular separation between adjacent dark fringes on the screen, measured in milliradians? A) 0.15 mrad B) 0.20 mrad C) 0.25 mrad D) 0.30 mrad E) 0.36 mrad Answer: C Var: 1

23) A double slit that is illuminated with coherent light of wavelength 644 nm produces a pattern of bright and dark fringes on a screen 6.00 cm from the slits. If the slits are 2783 nm apart, what is the distance on the screen between the 4th and the 2nd bright fringes on one side of the central maximum? A) 23.0 cm B) 17.6 cm C) 11.5 cm D) 3.13 cm E) 14.7 cm Answer: D Var: 1 24) An optical engineer needs to ensure that the bright fringes from a double-slit are 15.7 mm apart on a detector that is from the slits. If the slits are illuminated with coherent light of wavelength 633 nm, how far apart should the slits be? A) 68.5 μm B) 74.0 μm C) 79.5 μm D) 63.0 μm Answer: A Var: 50+ 25) A two-slit arrangement with 60.3 μm separation between the slits is illuminated with 537.0nm wavelength light. If a viewing screen is located 2.14 m from the slits, find the distance on the screen from the first dark fringe on one side of the central maximum to the second dark fringe on the other side. A) 57.2 mm B) 38.1 mm C) 76.3 mm D) 26.9 mm Answer: B Var: 1 26) Two thin slits are 6.00 μm apart. Monochromatic coherent light falls on these slits, and produces a fifth-order bright interference fringe at an angle of 32.3° away from the centerline. What is the wavelength of the light? A) 164 nm B) 416 nm C) 614 nm D) 641 nm Answer: D Var: 3

27) Coherent light of wavelength 575 nm falls on a double-slit and the third-order bright fringe is seen at an angle of 6.5° away from the centerline. How far apart are the double slits? A) 5.0 μm B) 10 μm C) 15 μm D) 20 μm Answer: C Var: 1 28) In a double-slit experiment, the slit separation is 2.0 mm, and two wavelengths, 750 nm and 900 nm, illuminate the slits. A screen is placed 2.0 m from the slits. At what distance from the central maximum on the screen will a bright fringe from one pattern first coincide with a bright fringe from the other? A) 1.5 mm B) 3.0 mm C) 4.5 mm D) 6.0 mm Answer: C Var: 1 29) Two radio antennas are 130 m apart on a north-south line. The two antennas radiate in phase at a frequency of 3.6 MHz. All radio measurements are made far from the antennas. What is the smallest angle, reckoned east of north from midway between the antennas, at which constructive interference of two radio waves occurs? (c = 3.00 × 108 m/s) A) 50° B) 55° C) 45° D) 40° E) 35° Answer: A Var: 50+ 30) Two radio antennas are 120 m apart on a north-south line. The two antennas radiate in phase at a frequency of 5.6 MHz. All radio measurements are made far from the antennas. What is the smallest angle, reckoned north of east from midway between the antennas, at which destructive interference of the two radio waves occurs? (c = 3.00 × 108 m/s) A) 13° B) 6.4° C) 9.7° D) 16° E) 19° Answer: A Var: 50+

31) Two radio antennas are 10 km apart on a north-south axis on high mountain tops at the seacoast. The antennas broadcast identical AM radio signals, in phase, at a frequency of 4.70 MHz. A steamship, 200 km offshore, travels toward the north at 15 km/h and passes east of the antennas. A radio on board the ship is tuned to the broadcast frequency. The reception of the radio signal on the ship is a maximum at a given instant. How much later until the next occurrence of maximum reception? (c = 3.00 × 108 m/s) A) 5.1 min B) 3.8 min C) 6.4 min D) 7.7 min E) 8.9 min Answer: A Var: 50+ 32) At most, how many bright fringes can be formed on one side of the central bright fringe (not counting the central bright fringe) when light of 625 nm falls on a pair of slits that are apart? A) 10 B) 9 C) 8 D) 11 E) 12 Answer: A Var: 50+ 33) The figure shows the resulting pattern when a single slit is illuminated by monochromatic light. The slit is 0.3 × m wide and is illuminated by light of wavelength 506 nm. A diffraction pattern is seen on a screen 2.8 m from the slit. What is the linear distance on the screen between the first two diffraction minima on either side of the central diffraction maximum?

Answer: 9.4 × 10-3 m Var: 50+ 34) A single slit, which is 0.0500 mm wide, is illuminated by light of 550 nm wavelength. What is the angular separation between the first two minima on either side of the central maximum? Answer: 0.630° Var: 1

35) Using monochromatic light of 410 nm wavelength, a single thin slit forms a diffraction pattern, with the first minimum at an angle of 40.0° from central maximum. The same slit, when illuminated by a new monochromatic light source, produces a diffraction pattern with the second minimum at a 60.0° angle from the central maximum. What is the wavelength of this new light? A) 276 nm B) 293 nm C) 309 nm D) 326 nm E) 342 nm Answer: A Var: 33 36) A single thin slit forms a diffraction pattern, with the first minimum at an angle of 40.0° from central maximum. If monochromatic light of 530.0-nm wavelength is used for the illumination, what is the width of the slit? A) 825 nm B) 791 nm C) 757 nm D) 723 nm E) 689 nm Answer: A Var: 33 37) A single slit, 1400 nm wide, forms a diffraction pattern when illuminated by monochromatic light of 490-nm wavelength. What is the largest angle from the central maximum at which the intensity of the light is zero? A) 44° B) 41° C) 38° D) 35° E) 32° Answer: A Var: 50+ 38) A single thin slit forms a diffraction pattern when illuminated with monochromatic light. The fourth minimum of the pattern occurs at an angle of 32.0° away from the central maximum. At what angle does the fifth minimum occur? A) 41.5° B) 41.0° C) 40.5° D) 42.0° E) 42.5° Answer: A Var: 40

39) A beam of monochromatic light passes through a slit that is 11.0 μm wide. If the first order dark fringe of the resulting diffraction pattern is at an angle of 4.31° away from the centerline, what is the wavelength of light? A) 827 nm B) 301 nm C) 602 nm D) 402 nm E) 201 nm Answer: A Var: 5 40) A beam of light of wavelength 610 nm passes through a slit that is 1.90 µm wide. At what the angle away from the centerline does the first dark fringe occur? A) 9.35° B) 11.4° C) 12.2° D) 39.9° E) 18.7° Answer: E Var: 1 41) A beam of light of wavelength 610 nm passes through a slit that is 1.90 µm wide. At what the angle away from the centerline does the second dark fringe occur? A) 11.4° B) 9.35° C) 12.2° D) 39.9° E) 18.7° Answer: D Var: 1 42) A beam of light of wavelength 600 nm passes through a slit that is 3.1 × 10-5 m wide, and then goes on to a screen that is 2.2 m from the slit. On the screen, how far is the second dark fringe from the center of the diffraction pattern? A) 3.9 cm B) 4.2 cm C) 6.3 cm D) 2.1 cm E) 8.5 cm Answer: E Var: 1

43) When light of wavelength 450 nm falls on a single slit of width 0.30 mm, what is the angular width of the central bright region? A) 0.086° B) 0.13° C) 0.17° D) 0.26° E) 0.35° Answer: C Var: 1 44) When a single slit that is 0.050 mm wide is illuminated by light of 550-nm wavelength, what is the angular separation between the first two minima on one side of the central maximum? A) 0.36° B) 0.47° C) 0.54° D) 0.63° E) 1.3° Answer: D Var: 1 45) Light of wavelength 687 nm passes through a single slit that is 0.75 mm wide. At what distance from the slit should a screen be placed so that the second dark fringe in the diffraction pattern is to be 1.7 mm from the center of the pattern? A) 0.39 m B) 0.93 m C) 1.1 m D) 1.5 m E) 1.9 m Answer: B Var: 1 46) Light of wavelength 610 nm is incident on a slit 0.20 mm wide and the diffraction pattern is viewed on a screen that is 1.5 m from the slit. What is the width on the screen of the central maximum? A) 0.34 cm B) 0.68 cm C) 0.92 cm D) 1.2 cm E) 1.5 cm Answer: C Var: 1

47) Light of wavelength 580 nm is incident on a slit of width 0.30 mm. An observing screen is placed 2.0 m past the slit. Find the distance on the screen of the first order dark fringe from the center of the pattern. A) 0.26 mm B) 1.5 mm C) 1.9 mm D) 3.9 mm E) 7.7 mm Answer: D Var: 1 48) A beam of light of wavelength 630 nm is incident on a slit that is 0.400 mm wide. If the distance between the slit and the screen is 1.80 m, what is the width on the screen of the central bright fringe? A) 1.94 mm B) 2.94 mm C) 3.54 mm D) 5.67 mm E) 6.94 mm Answer: D Var: 5 49) A diffraction grating is to be used to find the wavelength of the emission spectrum of a gas. The grating spacing is not known, but light of a known wavelength of 632.8 nm is deflected by 43.2° in the second order by this grating. Light of the wavelength to be measured is deflected by 34.9° in the second order. What is the wavelength of the light that is to be measured? Answer: 529 nm Var: 50+ 50) When red light illuminates a grating with 7000 lines per centimeter, its second maximum is at 62.4°. What is the wavelength of this light? Answer: 633 nm Var: 1 51) A diffraction grating has 5150 lines per centimeter ruled on it. What is the angular separation between the first- and the third-order bright spots on the same side of the central maximum when the grating is illuminated by a beam of light with wavelength 633 nm? Answer: 58.9° Var: 1 52) In a diffraction grating experiment, light of 600 nm wavelength produces a first-order maximum 0.35 mm from the central maximum on a distant screen. On the same screen, a second monochromatic source produces a third-order maximum 0.87 mm from the central maximum when it passes through the same diffraction grating. What is the wavelength of the light from the second source? Answer: 500 nm Var: 1 19 Copyright © 2019 Pearson Education, Inc.

53) Consider an experiment using a diffraction grating with 7000 lines/cm, a screen 2.50 m away, and a wavelength beam of light. (a) How many side maxima will be observed on one side of the central maximum? (b) How far apart on the screen are the first-order and second-order maxima on the same side of the central maximum? Answer: (a) 3 (b) 1.15 meters Var: 5 54) What is the angular separation of two spectral lines of wavelengths 497 nm and 251 nm formed in the third order with a diffracting grating having 587 lines per millimeter? A) 34.8° B) 24.8° C) 41.3° D) 29.4° E) 4.21° Answer: A Var: 1 55) A diffraction grating with 396 lines/mm is illuminated with light of wavelength 343 nm. What is the angular separation between the two second-order bright fringes? A) 31.5° B) 15.8° C) 32.9° Answer: A Var: 1 56) Monochromatic light of wavelength 500 nm is incident normally on a diffraction grating. If the third-order maximum of the diffraction pattern is observed at 32° from the centerline, what is the distance between the slits of the grating? A) 0.93 μm B) 1.4 μm C) 2.8 μm D) 8.5 μm Answer: C Var: 1 57) Monochromatic light of wavelength 500 nm is incident normally on a diffraction grating. If the third-order maximum of the diffraction pattern is observed at 32.0°, what is the total number of maxima can be seen? A) 5 B) 7 C) 10 D) 11 E) 8 Answer: D Var: 1 20 Copyright © 2019 Pearson Education, Inc.

58) An 18-mm-wide diffraction grating has rulings of 710 lines per millimieter. Monochromatic light of wavelength 506 nm wavelength is incident normally on the grating. What is the largest angle from the centerline at which an intensity maximum is formed? A) 46° B) 44° C) 42° D) 40° E) 38° Answer: A Var: 50+ 59) When light illuminates a diffraction grating with 7000 lines per centimeter, its second order maximum is at 62.4°. What is the wavelength of the light? A) 336 nm B) 363 nm C) 633 nm D) 752 nm Answer: C Var: 1 60) When a diffraction grating having 5000 lines/cmis illuminated by monochromatic light, the angle between the central maximum and the fourth order maximum is 47.2°. What is the wavelength of the light? A) 138 nm B) 183 nm C) 367 nm D) 637 nm Answer: C Var: 3 61) Monochromatic light is incident on a diffraction grating that is 75 mm wide and ruled with 50,000 lines. The second-order maximum is seen at 32.5°. What is the wavelength of the incident light? A) 202 nm B) 403 nm C) 605 nm D) 806 nm Answer: B Var: 1

62) A diffraction grating has 6.00 × 103 lines per centimeter ruled on it. What is the angular separation between the second and the third orders on the same side of the central order when the grating is illuminated with a beam of light of wavelength 550 nm? A) 20.5° B) 30.5° C) 40.6° D) 50.5° Answer: C Var: 1 63) A 17-mm-wide diffraction grating has rulings of 530 lines per millimeter. White light is incident normally on the grating. What is the longest wavelength that forms an intensity maximum in the fifth order? A) 377 nm B) 352 nm C) 402 nm D) 427 nm E) 452 nm Answer: A Var: 50+ 64) What is the slit spacing of a diffraction grating necessary so that 600-nm light will produce a first order principal maximum at 25.0° away from the centerline? A) 1.42 μm B) 2.01 μm C) 3.12 μm D) 4.12 μm E) 5.44 μm Answer: A Var: 1 65) A beam of light of wavelength 600 nm is incident normally on a diffraction grating with a spacing between slits of 1.70 × 10-4 cm. At what angle away from the centerline does a firstorder maximum occur? A) 10.5° B) 12.1° C) 16.4° D) 18.2° E) 20.7° Answer: E Var: 1

66) The distance between the ruled lines on a diffraction grating is 1900 nm. The grating is illuminated at normal incidence with a parallel beam of white light in the 400 nm to 700 nm wavelength band. What is the angular width of the gap between the first order spectrum and the second order spectrum? A) 3.3° B) 4.3° C) 5.3° D) 6.3° E) 2.3° Answer: A Var: 50+ 67) The distance between the ruled lines on a diffraction grating is 1770 nm. The grating is illuminated at normal incidence with a parallel beam of white light in the 400 nm to 700 nm wavelength band. What is the longest wavelength that appears in the third order spectrum? A) 590 nm B) 570 nm C) 550 nm D) 530 nm E) 610 nm Answer: A Var: 50+ 68) A metallic sheet has a large number of parallel slits, 5.0 mm wide and 20 cm apart. This sheet is used as a diffraction grating for microwaves. A wide parallel beam of microwaves is incident normally on the sheet. If the microwave wavelength is 6.0 cm, what is the largest angle from the normal, at which an intensity maximum occurs? A) 64° B) 69° C) 74° D) 79° E) 84° Answer: A Var: 1 69) A metallic sheet has a large number of parallel slits, 5.0 mm wide and 20 cm apart. This sheet is used as a diffraction grating for microwaves. A wide parallel beam of microwaves is incident normally on the sheet. What is the smallest microwave frequency for which only the central maximum will occur? (c = 3.00 × 108 m/s) A) 0.50 GHz B) 0.70 GHz C) 1.0 GHz D) 1.5 GHz E) 2.0 GHz Answer: D Var: 1 23 Copyright © 2019 Pearson Education, Inc.

70) A metallic sheet has a large number of parallel slits, 5.0 mm wide and 20 cm apart. This sheet is used as a diffraction grating for microwaves. A wide parallel beam of microwaves is incident normally on the sheet. If the intensity maxima occur 2.0° apart in the central region, what is the wavelength of the microwaves? A) 5.0 mm B) 6.0 mm C) 7.0 mm D) 8.0 mm E) 9.0 mm Answer: C Var: 1 71) A diffraction grating has 450 lines per millimeter. What is the highest order m that contains the entire visible spectrum from 400 nm to 700 nm? A) m = 2 B) m = 3 C) m = 4 D) m = 5 E) m = 6 Answer: B Var: 1 72) Light is incident perpendicularly from air onto a liquid film that is on a glass plate. The liquid film is thick, and the liquid has index of refraction 1.60. The glass has index of refraction 1.50. Calculate the longest visible wavelength (as measured in air) of the light for which there will be totally destructive interference between the rays reflected from the top and bottom surfaces of the film. Assume that the visible spectrum lies between 400 nm and 700 nm. Answer: 637 nm Var: 50+ 73) A soap bubble, when illuminated at normal incidence with light of 463 nm, appears to be especially reflective. If the index of refraction of the film is 1.35, what is the minimum thickness the soap film can be if it is surrounded by air? Answer: 85.7 nm Var: 50+ 74) Light in air of wavelength 500 nm illuminates a soap film that has an index of refraction of 1.3 and air on both sides. What is the minimum thickness of this film that will produce cancellation in the reflected light when the light is incident normally on the film? Answer: 96 nm Var: 1 75) A soap bubble with air on both sides has an index of refraction of 1.33. What minimum thickness of the wall of this bubble will ensure maximum reflectance of normally incident light having a wavelength of 530 nm? Answer: 99.6 nm Var: 1 24 Copyright © 2019 Pearson Education, Inc.

76) A glass plate that is 2.5 cm long is separated from another glass plate at one end by a strand of someone's hair that is 0.010 mm in diameter. How far apart are the adjacent interference bands when viewed with light of wavelength 600 nm? Answer: 0.75 mm Var: 1 77) The wavelength of light in a thin film is 360 nm and the wavelength of light in vacuum is 469 nm. What is the index of refraction for the film? A) 1.10 B) 1.30 C) 1.50 D) 1.70 E) 1.90 Answer: B Var: 1 78) Light has a wavelength of 600 nm in a vacuum. It passes into glass, which has an index of refraction of 1.50. What is the wavelength of the light in the glass? A) 600 nm B) 500 nm C) 400 nm D) 300 nm E) 900 nm Answer: C Var: 1 79) Light has wavelength 600 nm in a vacuum. It passes into glass, which has an index of refraction of 1.5. What is the frequency of the light inside the glass? (c = 3.0 × 108 m/s) A) 3.3 × 1014 Hz B) 5.0 × 1014 Hz C) 3.3 × 105 Hz D) 5.0 × 105 Hz Answer: B Var: 1

80) A 360-nm thick oil film floats on the surface of a pool of water water. The indices of refraction of the oil and the water are 1.5 and 1.33, respectively. When the surface of the oil is illuminated from above at normal incidence with white light, what are the two wavelengths of light between 400 nm to 800 nm wavelength that are most strongly reflected? A) 410 nm and 700 nm B) 430 nm and 720 nm C) 450 nm and 740 nm D) 470 nm and 760 nm E) 490 nm and 780 nm Answer: B Var: 1 81) A 360-nm thick oil film floats on the surface of a pool of water. The indices of refraction of the oil and the water are 1.50 and 1.33, respectively. When the surface of the oil is illuminated from above at normal incidence with white light, what is the wavelength of light between 400 nm to 800 nm wavelength that is most weakly reflected? A) 520 nm B) 540 nm C) 560 nm D) 580 nm E) 600 nm Answer: B Var: 1 82) A light beam with wavelength 500 nm is reflected constructively from a thin layer of oil having index of refraction 1.25. The oil floats on the top of water of index of refraction 1.33. What is the minimum thickness of the layer of oil? A) 100 nm B) 150 nm C) 175 nm D) 200 nm E) 225 nm Answer: D Var: 1 83) A 500-nm-wavelength beam of light illuminates a soap film with air on both sides and an index of refraction 1.33. If the beam of light is incident normally on the film, what is the minimum thickness of the film to make the reflected light enhanced in brightness? A) 47.0 nm B) 74.0 nm C) 94.0 nm D) 152 nm E) 268 nm Answer: C Var: 1

84) What is the minimum thickness of a soap bubble film with refractive index 1.38 that results in a constructive interference in the reflected light if this film is illuminated by a beam of light of wavelength 610 nm? A) 222 nm B) 111 nm C) 333 nm D) 444 nm E) 555 nm Answer: B Var: 1 85) A soap bubble has an index of refraction of 1.33. What minimum thickness of this bubble will ensure maximum reflectance of normally-incident light having a wavelength of 530 nm? A) 24.9 nm B) 76.9 nm C) 99.6 nm D) 199 nm E) 398 nm Answer: C Var: 1 86) An oil film with refractive index 1.48 and thickness 290 nm is floating on water and illuminated with white light at normal incidence. What is the wavelength of the dominant color in the reflected light? A) green (541 nm) B) blue-green (493 nm) C) violet (404 nm) D) yellow (572 nm) E) blue (470 nm) Answer: D Var: 1 87) A sodium light, having wavelength 589.3 nm, is used to view a soap film to make it look black when directed perpendicular to the film. What is the minimum thickness of the soap film if the index of refraction of soap solution is 1.38? A) 114 nm B) 194 nm C) 294 nm D) 314 nm E) 214 nm Answer: E Var: 1

88) A soap bubble film that is 106 nm thick and has an index of refraction of 1.42 results in constructive interference in the reflected light if this film is illuminated by a beam of light with a wavelength of 601 nm. What are the next three thicknesses of this film that will also result in constructive interference? A) 212 nm, 318 nm, 424 nm B) 53.0 nm, 35.3 nm, 26.5 nm C) 212 nm, 424 nm, 636 nm D) 67.0 nm, 42.4 nm, 22.3 nm E) 318 nm, 530 nm, 742 nm Answer: E Var: 1 89) A puddle of water has a thin film of gasoline floating on it. A beam of light is shining perpendicular on the film. If the wavelength of light incident on the film is 560 nm and the indices of refraction of gasoline and water are 1.40 and 1.33, respectively, what must be the minimum thickness of the film to see a bright reflection? A) 100 nm B) 200 nm C) 300 nm D) 400 nm E) 500 nm Answer: A Var: 1 90) A piece of glass has a thin film of gasoline floating on it. A beam of light is shining perpendicular on the film. If the wavelength of light incident on the film is 560 nm and the indices of refraction of gasoline and glass are 1.40 and 1.50, respectively, what is the minimum nonzero thickness of the film to see a bright reflection? A) 500 nm B) 400 nm C) 300 nm D) 200 nm E) 100 nm Answer: D Var: 1

91) Two very flat glass plates, 16 cm long, are in contact at one end and separated by 0.020 mm at the other end. The space between the plates is occupied by oil with index of refraction 1.45. The refractive index of the glass plates is 1.55. The plates are illuminated at normal incidence with monochromatic light, and fringes are observed. When the monochromatic light has a wavelength of 580 nm, how many bright fringes are visible in the pattern? A) 60 B) 70 C) 80 D) 90 E) 100 Answer: E Var: 1 92) Two very flat glass plates, 16 cm long, are in contact at one end and separated by 0.020 mm at the other end. The space between the plates is occupied by oil with index of refraction 1.45. The refractive index of the glass plates is 1.55. The plates are illuminated at normal incidence with monochromatic light, and fringes are observed. If the spacing of the dark fringes is 2.0 mm, what is the wavelength of the monochromatic light? A) 425 nm B) 475 nm C) 525 nm D) 675 nm E) 725 nm Answer: E Var: 1 93) A thin uniform film of oil that can be varied in thickness covers a sheet of glass of refractive index 1.52. The refractive index of the oil is 1.64. Light of wavelength 555 nm is shone from air at normal incidence on the film. Starting with no oil on the glass, you gradually increase the thickness of the oil film until the first interference maximum in the reflected light occurs. What is the thickness of the oil film at that instant? A) 139 nm B) 169 nm C) 183 nm D) 84.6 nm E) 91.3 nm Answer: D Var: 1 94) Light of wavelength 500 nm illuminates a round 0.50-mm-diameter hole. A screen is placed 6.0 m past the slit. What is the width of the central bright circle on the screen? A) 15 mm B) 260 μm C) 7.3 mm D) 3700 μm Answer: A Var: 50+ 29 Copyright © 2019 Pearson Education, Inc.

95) Light from a He-Ne laser of wavelength 633 nm passes through a circular aperture. The resulting pattern is observed on a screen 4.0 m behind the aperture, where the width of the central bright circle is 1.1 cm. What is the diameter of the hole? A) 560 μm B) 9.8 μm C) 32,000 μm D) 4700 μm Answer: A Var: 50+ 96) A round 0.85-mm-diameter hole is illuminated by infrared light of wavelength 2.5 μm What is the angle of the first dark fringe in the resulting pattern? A) 0.21 degrees B) 3.6 × 10-3 degrees C) 1.2 × 10-2 degrees D) 4.8 × 10-2 degrees Answer: A Var: 50+

College Physics: A Strategic Approach, 4e (Knight) Chapter 18 Ray Optics 18.1 Conceptual Questions 1) Light enters air from water. The angle of refraction will be A) greater than the angle of incidence. B) equal to the angle of incidence. C) less than the angle of incidence. Answer: A Var: 1 2) Light enters glass from air. The angle of refraction will be A) greater than the angle of incidence. B) equal to the angle of incidence. C) less than the angle of incidence. Answer: C Var: 1 3) The index of refraction of a type of glass is 1.50, and the index of refraction of water is 1.33. If light enters water from this glass, the angle of refraction will be A) greater than the angle of incidence. B) equal to the angle of incidence. C) less than the angle of incidence. Answer: A Var: 1 4) Light goes from material having a refractive index of n1 into a material with refractive index n2. If the refracted light is bent away from the normal, what can you conclude about the indices of refraction? A) n1 > n2 B) n1 ≥ n2 C) n1 < n2 D) n1 ≤ n2 E) n1 = n2 Answer: A Var: 1

5) A beam of light traveling in air strikes a glass slab at an angle of incidence less than 90°. After entering the glass slab, what does the beam of light do? (There could be more than one correct choice.) A) I follows the same path as before it struck the glass. B) It follows the normal to the glass slab. C) It bends away from the normal at the point of contact. D) It bends closer to the normal at the point of contact. E) It slows down. Answer: D, E Var: 1 6) The critical angle for a beam of light passing from water into air is 48.8°. This means that all light rays with an angle of incidence in the water that is greater than 48.8° will be A) totally absorbed by the water. B) totally reflected. C) partially reflected and partially transmitted. D) totally transmitted. Answer: B Var: 1 7) Which one of the following sets of characteristics describes the image formed by a plane mirror? A) real and inverted B) real and upright C) virtual and upright D) virtual and inverted E) virtual and larger than the object Answer: C Var: 1 8) The image formed in a plane mirror is A) at the same distance in front of the mirror as the object is in front of the mirror. B) a real image behind the mirror. C) at the same distance behind the mirror as the object is in front of the mirror. D) at a shorter distance behind the mirror than the distance the object is in front of the mirror. E) at a larger distance behind the mirror than the distance the object is in front of the mirror. Answer: C Var: 1

9) You may have seen ambulances on the street with the letters of the word AMBULANCE written on the front of them, in such a way as to appear correctly when viewed in your car's rearview mirror. (See the figure.) How do the letters appear when you look directly at the ambulance (not through the mirror)?

A) a B) b C) c D) d E) e Answer: E Var: 1 10) A lighted candle is placed a short distance from a plane mirror, as shown in the figure. At which location will the image of the flame appear to be located?

A) at A B) at B C) at C D) at M (at the mirror) Answer: C Var: 1 11) Which one of the following numbers is the correct magnification produced by a plane mirror? A) 1/2 B) 1/4 C) 2 D) 1 E) 3/2 Answer: D Var: 1

12) As you walk away from a plane mirror on a wall, the height of your image A) gets smaller. B) may or may not get smaller, depending on where the observer is positioned. C) is always a real image, no matter how far you are from the mirror. D) changes from being a virtual image to a real image as you pass the focal point. E) is always the same size. Answer: E Var: 1 13) Suppose you place an object in front of a concave mirror. Which of the following statements must be true? (There could be more than one correct choice.) A) The image of the object will always be smaller than the object. B) No matter where you place the object, a real image of the object will be formed. C) The image of the object will always be inverted. D) If you position the object between the mirror and the focal point of the mirror, its image must be upright and virtual. E) No matter where you place the object, the image of the object will always be virtual and upright. Answer: D Var: 1 14) Which statements about images are correct? (There could be more than one correct choice.) A) A virtual image cannot be formed on a screen. B) A virtual image cannot be viewed by the unaided eye. C) A virtual image cannot be photographed. D) A real image must be erect. E) Mirrors always produce real images because they reflect light. Answer: A Var: 1 15) A negative magnification for a mirror means that A) the image is inverted, and the mirror could be either concave or convex. B) the image is upright, and the mirror is convex. C) the image is inverted, and the mirror is convex. D) the image is inverted, and the mirror is concave. E) the image is upright, and the mirror could be either concave or convex. Answer: D Var: 1

16) The focal length of a concave mirror has a magnitude of 20 cm. What is its radius of curvature? A) 10 cm B) 40 cm C) -40 cm D) 20 cm E) -20 cm Answer: B Var: 1 17) The focal length of a convex mirror is has a magnitude of 20 cm. What is its radius of curvature? A) -10 cm B) 40 cm C) -40 cm D) -20 cm E) 20 cm Answer: C Var: 1 18) If a spherical concave mirror has a radius of curvature R, its focal length is A) R/4. B) R/2. C) R. D) 2R. E) 4R. Answer: B Var: 1 19) If a spherical convex mirror has a radius of curvature R, the magnitude of its focal length is A) R/2. B) R/4. C) R. D) 2R. E) 4R. Answer: A Var: 1 20) Which of the following statements about spherical mirrors is correct? (There could be more than one correct choice.) A) A concave mirror always produces a real image. B) A convex mirror always produces a virtual image. C) A concave mirror always produces a virtual image. D) A convex mirror always produces a real image. E) A convex mirror always produces an upright image. Answer: B, E Var: 1 5 Copyright © 2019 Pearson Education, Inc.

21) An object is placed to the left of a spherical mirror in front of the mirror. If the image of the object is formed on the right side of the mirror, which of the following statements must be true? (There could be more than one correct choice.) A) The image is upright and the mirror must be convex. B) The image is inverted and real, and the mirror must be convex. C) The image is upright and the mirror must be concave. D) The image is upright and virtual. E) The mirror could be either concave or convex. Answer: D, E Var: 1 22) An object is placed in front of a convex mirror at a distance larger than twice the magnitude of the focal length of the mirror. The image will appear A) in front of the mirror. B) inverted and reduced. C) inverted and enlarged. D) upright and reduced. E) upright and enlarged. Answer: D Var: 1 23) A convex mirror has a focal length of magnitude f. An object is placed in front of this mirror at a point f from the face of the mirror. The image will appear A) behind the mirror. B) upright and reduced. C) upright and enlarged. D) inverted and reduced. E) inverted and enlarged. Answer: B Var: 1 24) If an object is placed at the center of curvature of concave mirror, the image formed by the mirror is located A) out beyond the center of curvature. B) at the center of curvature. C) between the center of curvature and the focal point. D) at the focal point. E) at infinity. Answer: B Var: 1

25) If you stand in front of a convex mirror, at the same distance from it as its radius of curvature, A) you won't see your image because there is none. B) you won't see your image because it is focused at infinity. C) you will see your image and you will appear smaller than you. D) you will see your image and you will appear larger than you. E) you will see your image and it will be the same size as you except upside down. Answer: C Var: 1 26) If you stand in front of a convex mirror, at the same distance from it as its focal length, A) you won't see your image because there is none. B) you won't see your image because it is focused at infinity. C) you will see your image and you will appear smaller than you. D) you will see your image and you will appear larger than you. E) you will see your image and it will be the same size as you except upside down. Answer: C Var: 1 27) Sometimes when you look into a curved mirror you see a magnified image (a great big you) and sometimes you see a diminished image (a little you). If you look at the bottom (convex) side of a shiny spoon, what will you see? A) You won't see an image of yourself because no image will be formed. B) You will see a little you, upside down. C) You will see a little you, right side up. D) You will see a little you, but whether you are right side up or upside down depends on how near you are to the spoon. E) You will either see a little you or a great big you, depending on how near you are to the spoon. Answer: C Var: 1 28) Single concave spherical mirrors produce images that A) are always smaller than the actual object. B) are always larger than the actual object. C) are always the same size as the actual object. D) could be smaller than, larger than, or the same size as the actual object, depending on the placement of the object. E) are always real. Answer: D Var: 1

29) Single convex spherical mirrors produce images that A) are always smaller than the actual object. B) are always larger than the actual object. C) are always the same size as the actual object. D) could be larger than, smaller than, or the same size as the actual object, depending on the placement of the object. E) are sometimes real. Answer: A Var: 1 30) A beam of light that is parallel to the principal axis strikes a concave mirror. What happens to the reflected beam of light? A) It also is parallel to the principal axis. B) It is perpendicular to the principal axis. C) It passes through the center of curvature of the mirror. D) It passes through the focal point of the mirror. E) It passes between the focal point and the center of curvature of the mirror. Answer: D Var: 1 31) A beam of light that is parallel to the principal axis strikes a convex mirror. What happens to the reflected beam of light? A) It also is parallel to the principal axis. B) It is perpendicular to the principal axis. C) It appears to be coming from the focal point on the other side of the mirror. D) It appears to be coming from the center of curvature of the mirror. E) It appears to be coming from a point between the focal point and the center of curvature of the mirror. Answer: C Var: 1 32) An upright object is 50 cm from a concave mirror of radius 60 cm. The character of the image is A) real and upright B) real and inverted C) virtual and upright D) virtual and inverted Answer: B Var: 1

33) Suppose you wanted to start a fire using a mirror to focus sunlight. Which of the following statements is most accurate? A) It would be best to use a plane mirror. B) It would be best to use a convex mirror. C) It would be best to use a concave mirror, with the object to be ignited positioned at the center of curvature of the mirror. D) It would be best to use a concave mirror, with the object to be ignited positioned halfway between the mirror and its center of curvature. E) One cannot start a fire using a mirror, since mirrors form only virtual images. Answer: D Var: 1 34) A thin lens projects an image of a man as shown in the figure. Rays marked A, B, and C travel to the lens from the man's ear. Draw the paths of these three rays after they have passed through the lens. Note that A is parallel to the principal axis, B goes through the center of the lens, C goes through the focal point on the left, and the point marked f is the focal point on the right of the lens.

Answer:

Var: 1 35) Which of the following terms describe lenses that are thinner at the center than at the edges? (There could be more than one correct choice.) A) converging lenses B) diverging lenses C) concave lenses D) convex lenses Answer: B, C Var: 1

36) Which of the following terms describe lenses that are thicker at the center than at the edges? (There could be more than one correct choice.) A) converging lenses B) diverging lenses C) concave lenses D) convex lenses Answer: A, D Var: 1 37) A convex lens has focal length f. If an object is located at "infinity" (very far away), the image formed is located at a distance from the lens A) of 2f. B) between f and 2f. C) of f. D) between the lens and f. E) of infinity. Answer: C Var: 1 38) A convex lens has focal length f. If an object is placed at a distance of 2f from the lens on the principal axis, the image is located at a distance from the lens A) of 2f. B) between f and 2f. C) of f. D) between the lens and f. E) of infinity. Answer: A Var: 1 39) A convex lens has focal length f. If an object is placed at a distance between f and 2f from the lens on the principal axis, the image is located at a distance from the lens A) of 2f. B) between f and 2f. C) of f. D) that is greater than 2f. E) of infinity. Answer: D Var: 1

40) A convex lens has focal length f. If an object is placed at a distance beyond 2f from the lens on the principal axis, the image is located at a distance from the lens A) of 2f. B) between f and 2f. C) of f. D) between the lens and f. E) of infinity. Answer: B Var: 1 41) If a object is placed between a convex lens and its focal point, the image formed is A) virtual and upright. B) virtual and inverted. C) real and upright. D) real and inverted. Answer: A Var: 1 42) Starting from very far away, an object is moved closer and closer to a converging lens, eventually reaching the lens. What happens to its image formed by that lens? (There could be more than one correct choice.) A) The image gets closer and closer to the lens. B) The image gets farther and farther from the lens. C) The image eventually changes from virtual to real. D) The image eventually changes from real to virtual. E) The image keeps getting larger and larger. Answer: D Var: 1 43) Starting from very far away, an object is moved closer and closer to a diverging lens, eventually reaching the lens. What happens to its image formed by that lens? (There could be more than one correct choice.) A) The image gets closer and closer to the lens. B) The image gets farther and farther from the lens. C) The image always remains virtual. D) The image eventually changes from real to virtual. E) The image keeps getting larger and larger. Answer: A, C, E Var: 1

44) Which of following statements about the image formed by a single converging lens are true? (There could be more than one correct choice.) A) The image is always real. B) The image is always virtual. C) The image is always inverted. D) The image is always upright. E) None of the above choices are correct. Answer: E Var: 1 45) Which of following statements about the image formed by a single diverging lens are true? (There could be more than one correct choice.) A) The image is always real. B) The image is always virtual. C) The image is always inverted. D) The image is always upright. E) The image is always smaller than the object. Answer: B, D Var: 1 46) If the magnification of a mirror or lens is negative, it means that A) the image is smaller than the object. B) the image is inverted and smaller than the object. C) the image is inverted. D) the object is farther from the mirror (or lens) than the image. E) the image is farther from the mirror (or lens) than the object. Answer: C Var: 1 47) Is it possible to see a virtual image? A) No, since the rays that seem to emanate from a virtual image do not in fact emanate from the image. B) No, since virtual images do not really exist. C) Yes because the rays that appear to come from a virtual image can be focused by the eye just like those from an object. D) Yes, but only by using an additional lens to form a real image before the light reaches the eye. Answer: C Var: 1

48) An object is placed on the left side of a thin lens, and the image of this object is formed on the left side of the lens. Which of the following statements must be true? (There could be more than one correct choice.) A) The lens must be a diverging lens, and the image is upright. B) The lens must be a converging lens, and the image is upright. C) The image is upright and virtual. D) The lens could be either a converging or a diverging lens, and the image is upright. E) The image is inverted and real. Answer: C, D Var: 1 49) If a single lens forms a virtual image of an object, then A) the lens must be a diverging lens. B) the lens must be a converging lens. C) the lens could be either a diverging or a converging lens. D) the image must be inverted. E) the object must be between the lens and its focal point. Answer: C Var: 1 50) Which statement about a single thin lens is correct? A) A converging lens always produces a real inverted image. B) A diverging lens always produces a virtual inverted image. C) A converging lens sometimes produces a real upright image. D) A diverging lens always produces a virtual upright image. E) A diverging lens produces a virtual upright image only if the object is located between the lens and its focal point. Answer: D Var: 1 51) An object is placed in front of a thin lens. Which statements are correct in describing the image formed by the lens? (There could be more than one correct choice.) A) If the lens is convex, the image will never be virtual. B) If the image is real, then it is also inverted. C) If the image is real, then it is also upright. D) If the lens is concave, the image must be virtual. E) If the lens is convex, the image must be real. Answer: B, D Var: 1

52) The image formed by a single concave lens A) is always real. B) is always virtual. C) could be real or virtual, depending on whether the object distance is smaller or greater than the focal length. D) could be real or virtual, but is always real when the object is placed at the focal point. E) is always inverted. Answer: B Var: 1 18.2 Problems 1) A light beam having a wavelength of 470 nm in air is directed into glycerine at an angle of 75.0° with the normal in air. Glycerine has a refractive index of 1.47. (c = 3.0 × 108 m/s) (a) What are the frequency and wavelength of the light in the glycerine? (b) What angle does the light beam make with the normal in the glycerine? Answer: (a) 6.38 × 1014 Hz, 320 nm (b) 41.1° Var: 1 2) A thin laser beam traveling in air strikes the surface of a glass plate at 41.2° with the normal. In the plate, this beam makes an angle of 22.4° with the normal. What is the speed of light in this glass?(c = 3.0 × 108 m/s) Answer: 1.74 × 108 m/s Var: 1 3) A plastic cube is immersed in water having an index of refraction of 1.33. A laser beam in the plastic strikes the interface at an angle of 14.5° with the normal in the plastic. In the water, this beam makes an angle of 21.8° with the normal. What is the speed of light in the plastic cube? (c = 3.0 × 108 m/s) Answer: 1.52 × 108 m/s Var: 1 4) A ray of light (ray a) in air strikes a flat piece of glass at an angle of φ0 = 84° with respect to the normal, as shown in the figure. The index of refraction of the glass is 1.5. What is the angle θ between the reflected ray (ray b) and refracted ray (ray c) rays?

Answer: 54° Var: 50+

5) A narrow light beam in vacuum contains light of two wavelengths, 480 nm and 700 nm. It strikes a flat piece of glass at an angle of incidence of 60.000°. The index of refraction of the glass is 1.4830 at 480 nm and 1.4760 at 700 nm. Determine the angle between the two wavelengths as the light travels in the glass. Answer: 0.196° Var: 1 6) The index of refraction for a certain material is 1.399 for red light and 1.432 for blue light. Light containing both of these colors is traveling in vacuum and strikes a flat sheet of this material. Find the angle separating the two colors in the refracted light in the sheet if the angle of incidence is 60.00°. Answer: 1.03° Var: 1 7) A thin beam of light enters a thick plastic sheet from air at an angle of 32.0° with the normal and continues in the sheet at an angle of 23.0° with the normal. What is the index of refraction of the plastic? A) 0.74 B) 1.11 C) 1.28 D) 1.36 Answer: D Var: 1 8) An oil layer that is 5.0 cm thick is spread smoothly and evenly over the surface of water on a windless day. A light ray from the air above enters the oil at 45° with the normal and then goes into the water. What is the angle of refraction of this ray in the water? The index of refraction for the oil is 1.15, and for water it is 1.33. A) 27° B) 32° C) 36° D) 39° Answer: B Var: 1 9) A beam of light, traveling in air, strikes a plate of transparent material at an angle of incidence of 56.0°. It is observed that the reflected and refracted beams form an angle of 90.0°. What is the index of refraction of this material? A) 1.40 B) 1.43 C) 1.44 D) 1.48 Answer: D Var: 1

10) A beam of light traveling in air strikes a slab of transparent material. The incident beam makes an angle of 40° with the normal, and the refracted beam make an angle of 26° with the normal. What is the speed of light in the transparent material? (c = 3.0 × 108 m/s) A) 1.0 × 108 m/s B) 2.0 × 108 m/s C) 2.3 × 108 m/s D) 3.0 × 108 m/s E) 0.50 × 108 m/s Answer: B Var: 1 11) A light ray in air strikes a glass plate whose index of refraction is 1.42. Some of the light reflects off the surface of the plate, but most of it enters the glass. If the angle of refraction is one-half the angle of reflection, the angle of refraction is closest to which one of the following angles? A) 45° B) 43° C) 41° D) 39° E) 37° Answer: A Var: 50+ 12) A thin flashlight beam traveling in air strikes a glass plate at an angle of 52° with the plane of the surface of the plate. If the index of refraction of the glass is 1.4, what angle will the beam make with the normal in the glass? A) 34° B) 64° C) 26° D) 56° E) 38° Answer: C Var: 1 13) A glass plate with an index of refraction is 1.57 is immersed in an oil having a refractive index of 1.40. The surface of the glass is inclined at an angle of 54° with the vertical. A horizontal light ray in the glass strikes the interface. What is the angle that the refracted ray, in the oil, makes with the horizontal? A) 11° B) 5.6° C) 8.3° D) 14° E) 17° Answer: A Var: 50+ 16 Copyright © 2019 Pearson Education, Inc.

14) A light ray in glass arrives at the glass-water interface an an angle of θ = 48° with the normal. The refracted ray in water makes an angle φ = 72° angle with the normal, as shown in the figure.The index of refraction of water is 1.33. The angle of incidence is now changed to θ = 37°. What is the new angle of refraction φ in the water?

A) 50° B) 48° C) 46° D) 52° E) 54° Answer: B Var: 50+ 15) A light ray in glass arrives at the glass-water interface at an angle of θ = 48° with the normal. The refracted ray in water makes an angle θ = 61° with the normal, as shown in the figure. The index of refraction of water is 1.33. The angle of incidence is now changed to θ = 25°. What is the new angle of refraction φ in the water?

A) 30° B) 56° C) 54° D) 60° E) 62° Answer: A Var: 1

16) As shown in the figure, a laser positioned on a ship is used to communicate with a small research submarine resting on the bottom of a lake. The laser is positioned 12 m above the surface of the water, and it strikes the water 20 m from the side of the ship. The water is 58 m deep and has an index of refraction of 1.33. How far horizontally is the submarine from the side of the ship? (Assume all numbers are accurate to three significant figures.)

A) 69 m B) 49 m C) 89 m D) 59 m E) 79 m Answer: A Var: 1 17) A flashlight beam makes an angle of 60° with the plane of the surface of a calm lake before it enters the water. In the water what angle does the beam make with the plane of the surface? The index of refraction of water is 1.33. A) 0° B) 30° C) 60° D) 22° E) 68° Answer: E Var: 1 18) A beam of light in water (of refractive index of 1.33) enters a glass slab (of refractive index 1.50) at an angle of incidence of 60.0°. What is the angle of refraction in the glass? A) 27.5° B) 39.8° C) 60.0° D) 90.0° E) 50.2° Answer: E Var: 1

19) A beam of light in air enters a glass slab with an index of refraction of 1.40 at an angle of incidence of 30.0°. What is the angle of refraction? A) 20.9° B) 47.5° C) 51.8° D) 30.0° E) 14.9° Answer: A Var: 5 20) A light beam with wavelength 440 nm in a certain material then enters air and its wavelength becomes 577 nm. (a) What is the index of refraction for the material? (b) At what angle with the plane of the surface will the light be totally reflected back into the material? Answer: (a) 1.31 (b) 40.3° Var: 1 21) A thick slab of plastic lies at the bottom of a tank filled with water having an index of refraction of 1.33. A narrow laser beam is shone directly downward through the water on the plastic. You then gradually rotate the laser, thereby increasing the angle with respect to the normal that it strikes the plastic. You carefully note that at the instant the beam makes an angle of 66.5° with the normal in the water, no light enters the plastic, but it did enter for angles smaller than that. What is the speed of light in the plastic slab? (c = 3.00 × 108 m/s) Answer: 2.46 × 108 m/s Var: 1 22) A ray of light traveling in air makes a 63.0° angle with respect to the normal of the surface of a liquid. It travels in the liquid at a 39.2° angle with respect to the normal. Find the critical angle for total internal reflection for this interface. Answer: 45.2° Var: 50+ 23) A point source of light is positioned 20.0 m below the surface of a lake. What is the diameter of the largest circle on the surface of the water through which light can emerge into the air? The index of refraction of water is 1.33. Answer: 45.6 m Var: 1

24) A light ray enters a glass enclosed fish tank. From air it enters the glass at 20° with respect to the plane of the surface and then emerges into the water. The index for the glass is 1.50 and for water 1.33. (a) What is the angle of refraction in the glass? (b) What is the angle of refraction in the water? (c) Is there any incident angle in air for which the ray will not enter the water due to total internal reflection? If so, find it. Answer: (a) 39° (b) 45° (c) no Var: 9 25) Light in a transparent material that has an index of refraction of 1.333 strikes the boundary with another transparent material for which the index of refraction is 1.010. What is the critical angle for total internal reflection between these two materials? Answer: 49.26° Var: 1 26) The critical angle for a substance in air is measured at 53.7°. If light enters this substance from air at 45.0° with the normal, at what angle with the normal will it continue to travel? A) 34.7° B) 45.0° C) 53.7° D) It will not continue, but will be totally reflected. Answer: A Var: 1 27) Light enters a substance from air at 30.0° to the normal. It continues within the substance at 23.0° to the normal. What is the critical angle for this substance when it is surrounded by air? A) 53° B) 51.4° C) 36.7° D) 12.6° Answer: B Var: 1 28) Light travels from crown glass, with a refractive index of 1.52, into water, having a refractive index of 1.33? The critical angle for this interface is closest to which one of the following angles? A) 42° B) 48° C) 53° D) 57° E) 61° Answer: E Var: 1

29) Lucite has an index of refraction of 1.50. What is its critical angle if it is in air? A) 1.16° B) 15° C) 41.8° D) 65.2° E) 87.4° Answer: C Var: 1 30) An optic fiber is made of clear plastic with an index of refraction of 1.50. For what range of angles of incidence θ with the lateral surface of the fiber will light remain inside the plastic "guide" if it is surrounded by air? A) 21.1° < θ < 90° B) 23.4° < θ < 90° C) 38.3° < θ < 90° D) 40.3° < θ < 90° E) 41.8° < θ < 90° Answer: E Var: 1 31) A glass plate having an index of refraction is 1.66 is immersed in a certain alcohol. The surface of the glass is inclined at an angle of 44° with the vertical. When a horizontal ray in the glass strikes the interface, you observe that it is at the critical angle. What is the index of refraction of the alcohol? A) 1.15 B) 1.13 C) 1.11 D) 1.09 E) 1.17 Answer: A Var: 50+

32) During the investigation of a new type of optical fiber having an index of refraction laser beam is aimed at the flat end of a straight fiber, as shown in the figure. What is the maximum angle of incidence θ1 if the beam is not to escape from the sides of the fiber if it is surrounded by air?

A) 42.9° B) 39.8° C) 36.7° D) 33.6° E) 30.5° Answer: A Var: 30 33) A light beam is traveling inside a glass block that has an index of refraction of 1.46. As this light arrives at the surface of the block, it makes an angle of 53.0° with the normal. At what angle with the normal in the air will it leave the block? A) It will not leave. B) 59.1° C) 43.2° D) 33.2° Answer: A Var: 1 34) A scuba diver is 1.2 m beneath the surface of a still pond of water. At what angle relative to the normal at the surface must the diver shine a beam of light toward the surface in order for a person on a distant bank to be able to see it? The index of refraction for water is 1.33. A) 41° B) 48° C) 59° D) 90° E) 0° Answer: B Var: 1

35) A ray of light in glass strikes a water-glass interface at an angle of incidence equal to onehalf the critical angle for that interface. The index of refraction for water is 1.33, and for the glass it is 1.43. What angle does the refracted ray in the water make with the normal? A) 37° B) 42° C) 47° D) 32° E) 27° Answer: A Var: 50+ 36) The speed of light in a material is What is the critical angle of a light ray at the interface between the material and a vacuum? A) 24° B) 17° C) 19° D) 22° Answer: A Var: 31 37) A tank holds a layer of oil, of thickness To = 1.43 m, that floats on a layer of syrup of thickness Ts = 0.640 m, as shown in the figure. Both liquids are clear and do not mix together. A light ray, originating at the bottom of the tank at point P, crosses the oil-syrup interface at a point 0.900 m from the axis. The ray continues and arrives at the oil-air interface, 2.00 m to the right of P and at the critical angle. What is the index of refraction of the oil?

A) 1.64 B) 1.62 C) 1.60 D) 1.66 E) 1.68 Answer: A Var: 50+

38) A tank holds a layer of oil, of thickness To = 1.65 m, that floats on a layer of syrup of thickness Ts = 0.830 m, as shown in the figure. Both liquids are clear and do not mix together. A light ray, originating at the bottom of the tank at point P, crosses the oil-syrup interface at a point 0.900 m from the axis. The ray continues and arrives at the oil-air interface, 2.00 m to the right of P and at the critical angle. What is the index of refraction of the syrup?

A) 1.36 B) 1.25 C) 1.94 D) 1.75 E) 1.54 Answer: A Var: 50+ 39) David stands 2.5 m in front of a plane mirror. (a) How far from David is his image in the mirror? (b) If David moves away from the mirror at 1.5 m/s, how fast are David and his image moving apart from each other? (c) If David is 180 cm tall, how tall is his image in the mirror? Answer: (a) 5.0 cm (b) 3.0 m/s (c) 180 cm Var: 6 40) An object that is 75 cm tall is located 3.8 m in front of a plane mirror. The image formed by the mirror appears to be A) 1.9 m in front of the mirror. B) on the mirror's surface. C) 1.9 m behind the mirror's surface. D) 3.8 m in front of the mirror. E) 3.8 m behind the mirror's surface. Answer: E Var: 3 41) A laser beam strikes a plane mirror's reflecting surface with an angle of incidence of 43°. What is the angle between the incident ray and the reflected ray? A) 43° B) 86° C) 45° D) 90° E) 0° Answer: B Var: 3 24 Copyright © 2019 Pearson Education, Inc.

42) A person jogs toward a plane mirror at a speed of 3 m/s. How fast is he approaching his image in the mirror? A) 1 5 m/s B) 3 m/s C) 4 m/s D) 5 m/s E) 6 m/s Answer: E Var: 5 43) Two plane mirrors make an angle of with each other. A light ray enters the system and is reflected once off of each mirror. Through what angle is the ray turned? A) 60° B) 90° C) 120° D) 150° Answer: A Var: 50+ 44) An object that is 3.4 mm tall is placed 25 cm from the vertex of a convex spherical mirror. The radius of curvature of the mirror has magnitude 73 cm. (a) How far is the image from the vertex of the mirror? (b) What is the height of the image? Answer: (a) 15 cm (b) 2.0 mm Var: 50+ 45) A statue that is 2.3 cm tall is placed 15 cm in front of a convex mirror. The magnitude of the radius of curvature of the mirror is 18 cm. (a) Is the image real or virtual? (b) How far is the image from the mirror? (c) Is the image upright or inverted? (d) How tall is the image? Answer: (a) virtual (b) 5.6 cm (c) upright (d) 0.86 cm Var: 6 46) A stature that is 3.0 cm tall statue is 24 cm in front of a concave mirror. The magnitude of the radius of curvature of the mirror is 20 cm. (a) Is the image real or virtual? (b) How far is the image from the mirror? (c) Is the image upright or inverted? (d) How tall is the image? Answer: (a) real (b) 17 cm (c) inverted (d) 2.1 cm Var: 6

47) An object 2.0 cm tall is placed 24 cm in front of a convex mirror having a focal length of magnitude 30 cm. (a) Where is the image formed and how far is it from the mirror? (b) How tall is the image? Answer: (a) 13 cm behind the mirror (b) 1.1 cm Var: 1 48) An object that is 4.0 cm tall is placed 15 cm in front of a concave mirror of focal length 20 cm. (a) Where is the image formed and how far is it from the mirror? (b) How tall is the image? Answer: (a) 60 cm behind the mirror (b) 16 cm Var: 1 49) When an object is 12 cm in front of a concave mirror, the image is 3.0 cm in front of the mirror? What is the focal length of the mirror? A) -0.25 cm B) 15 cm C) 4.0 cm D) 2.4 cm E) -1.3 cm Answer: D Var: 3 50) An object that is 4.00 cm tall is placed 18.0 cm in front of a concave mirror having a focal length of 20.0 cm. What is the location of its image in relation to the mirror and what are its characteristics? A) 180 cm on the other side of mirror, real, 6.00 times bigger B) 10 cm on the other side of mirror, virtual, 10.0 times bigger C) 18 cm on the same side of mirror, virtual, 2.25 times bigger D) 20 cm on the same side of mirror, real, 10.0 times bigger E) 180 cm on the other side of mirror, virtual, 10.0 times bigger Answer: E Var: 5 51) An object that is 2.0 cm tall is placed at the center of curvature in front of a concave mirror. How tall is its image? A) 0.50 cm B) 1.0 cm C) 1.5 cm D) 2.0 cm E) infinite Answer: D Var: 5

52) An object is placed 50 cm in front of a concave mirror with a focal length of 25 cm. What is the magnification produced by the mirror? A) -0.50 B) -1.0 C) +1.5 D) -2.0 E) +1.0 Answer: B Var: 5 53) An object that is 10.0 cm tall is placed 37.0 cm in front of a concave mirror of focal length 18.5 cm. How tall is the image? A) 2.5 cm B) 5.0 cm C) 7.5 cm D) 20.0 cm E) 10.0 cm Answer: E Var: 5 54) Tan's face is 20 cm in front of a concave shaving mirror. If he observes his image to be twice as big and upright, what is the focal length of the mirror? A) 10 cm B) -40 cm C) -50 cm D) 40 cm E) 50 cm Answer: D Var: 1 55) Reza's face is 20 cm in front of a concave shaving mirror having a focal length of magnitude 30 cm. How large is the image of his face? A) half as large as his face B) of the same size as his face C) twice as large as his face D) three times as large as his face E) four times as large as his face Answer: D Var: 1

56) A concave mirror having a focal length of magnitude 5.0 cm forms an image 4.0 cm behind the mirror. Where is the object for this image? A) 2.2 cm in front of the mirror B) 2.2 cm behind the mirror C) 9.0 cm in front of the mirror D) 1.0 cm behind the mirror E) 20 cm behind the mirror Answer: A Var: 1 57) A concave spherical mirror with a radius of curvature of 20 cm creates a real image 30 cm from the mirror. How far is the object from the mirror? A) 20 cm B) 15 cm C) 7.5 cm D) 5.0 cm Answer: B Var: 1 58) When an object is 12 cm in front of a concave spherical mirror, the image is formed 3.0 cm in front of the mirror. What is the focal length of the mirror? A) 15 cm B) 4.0 cm C) 2.4 cm D) 1.3 cm Answer: C Var: 3 59) An object is 10 cm in front of a concave spherical mirror with a focal length of magnitude 3.0 cm. Where is the image? A) 13 cm from the mirror B) 7.0 cm from the mirror C) 4.3 cm from the mirror D) 3.3 cm from the mirror Answer: C Var: 1 60) A concave spherical mirror has a focal length of magnitude 20 cm. An object is placed 10 cm in front of the mirror on the mirror's axis. Where is the image located? A) 20 cm behind the mirror B) 20 cm in front of the mirror C) 6.7 cm behind the mirror D) 6.7 cm in front of the mirror Answer: A Var: 1

61) A concave spherical mirror has a focal length of magnitude 20 cm. An object is placed 30 cm in front of the mirror on the mirror's axis. Where is the image located? A) 12 cm behind the mirror B) 12 cm in front of the mirror C) 60 cm behind the mirror D) 60 cm in front of the mirror Answer: D Var: 1 62) An object is 5.7 cm from a spherical concave mirror. If the image is 4.7 cm tall and 10 cm from the mirror, how tall is the object? A) 12 cm B) 11 cm C) 8.2 cm D) 2.7 cm Answer: D Var: 1 63) An object is placed 15 cm from a spherical concave mirror with a focal length of magnitude 20 cm. If the object is 4.0 cm tall, how tall is the image? A) 1.0 cm B) 2.0 cm C) 8.0 cm D) 16 cm Answer: D Var: 1 64) An object that is 47.5 cm tall forms an image that is 38.6 cm tall and 14.8 cm from a spherical mirror. How far is the object from the mirror? A) 124 cm B) 47.6 cm C) 18.2 cm D) 12.0 cm Answer: C Var: 1 65) A 1.4-cm tall flower is 4.0 cm from a spherical concave mirror. If the image of the flower is 4.0 cm tall, how far is the image from the mirror? A) 11 cm B) 9.4 cm C) 1.4 cm D) 0.090 cm Answer: A Var: 1

66) A plant that is 4.0 cm tall is placed 15 cm from a concave spherical mirror having a focal length of magnitude 20 cm. Where is the image located? A) 12 cm behind the mirror B) 12 cm in front of the mirror C) 60 cm behind the mirror D) 60 cm in front of the mirror Answer: C Var: 1 67) When a person stands 40 cm in front of a cosmetic (concave) spherical mirror, the upright image is twice the size of the object. What is the focal length of the mirror? A) 27 cm B) 40 cm C) 80 cm D) 160 cm Answer: C Var: 1 68) A person's face is 30 cm in front of a concave spherical shaving mirror. If the image is an erect image that is 1.5 times as large as the object, what is the focal length mirror? A) 20 cm B) 50 cm C) 70 cm D) 90 cm Answer: D Var: 1 69) An object is in front of a concave spherical mirror, and its image is 4.0 cm behind the mirror. If the focal length of the mirror has a magnitude of 5.0 cm, where is the object? A) 2.2 cm in front of the mirror B) 2.2 cm behind the mirror C) 9.0 cm in front of the mirror D) 1.0 cm behind the mirror Answer: A Var: 1 70) A convex spherical mirror has a focal length of magnitude 20 cm. If an object is placed 10 cm in front of the mirror on the mirror's axis, where is the image located? A) 20 cm behind the mirror B) 20 cm in front of the mirror C) 6.7 cm behind the mirror D) 6.7 cm in front of the mirror Answer: C Var: 1

71) A toy is 14 cm in front of a convex spherical mirror. If the image of the toy is 5.8 cm behind the mirror, what is the focal length of the mirror? A) -4.1 cm B) +20 cm C) -9.9 cm D) -20 cm E) +9.9 cm Answer: C Var: 1 72) A cell phone that is 8.90 cm tall is placed in front of a convex mirror. The image of the phone is 7.80 cm tall and is located 14.8 cm from a mirror. What is the mirror's focal length? A) -120 cm B) -105 cm C) +16.9 cm D) -13.0 cm E) +120 cm Answer: A Var: 1 73) An object is 50 cm from a concave mirror of radius of curvature of magnitude 60 cm. How far is the image from the mirror? A) 19 cm B) 35 cm C) 60 cm D) 75 cm E) 120 cm Answer: D Var: 1 74) An object is 50 cm from a concave mirror with radius of curvature of magnitude 60 cm. What is the lateral magnification produced by the mirror? A) +0.40 B) +0.70 C) +1.5 D) -0.70 E) -1.5 Answer: E Var: 1

75) An object is placed near a concave mirror having a radius of curvature of magnitude 60 cm. How far should you place the object from the mirror so that the lateral magnification produced by the mirror will be +2.5? A) 18 cm B) 24 cm C) 30 cm D) 36 cm E) 42 cm Answer: A Var: 1 76) When an object is placed 118 cm from a thin diverging lens, its image is found to be 59 cm from the lens. The lens is removed, and replaced by a thin converging lens whose focal length has the same magnitude as the diverging lens. This second lens is at the original position of the first lens. Where is the image of the object now? Answer: at infinity Var: 50+ 77) A 3.0-cm tall statue is 48 cm in front of a convex lens having a focal length of magnitude 20 cm. (a) Is the image of the statue real or virtual? (b) How far is the image from the lens? (c) Is the image upright or inverted? (d) How tall is the image? Answer: (a) real (b) 34 cm (c) inverted (d) 2.1 cm Var: 1 78) A slide projector is set up with its lens 6.0 m from the screen. The projected image on the screen is 1.5 m square for a slide (the object) that is 2.5 cm square. (a) How far is the slide from the lens? (b) What is the focal length of the projector lens? Answer: (a) 10 cm (b) 9.8 cm Var: 1 79) A certain slide projector has a lens of focal length 15.0 cm. This lens forms an image measuring 100 cm × 100 cm on the screen when a slide whose dimensions are 50.0 mm × 50.0 mm is being magnified. How far from the lens should the screen be placed? Answer: 3.15 m Var: 1 80) How far from a converging lens of focal length 30 cm must an object be placed so the image will be virtual and 3.0 times as large as the object? Answer: 20 cm Var: 1

81) An object is placed 9.5 cm in front of a convex lens with a focal length of magnitude 24 cm. (a) Where is the image formed and how far is it from the lens? (b) What is the magnification produced by the lens? Answer: (a) 16 cm in front of the lens (b) 1.7 Var: 1 82) A 4.0-cm tall apple is 20 cm in front of a plano-convex lens of focal length 75 cm. (a) Find the location of the image of the apple. Is it a real or a virtual image? (b) How tall is the image of the apple? Is it upright or inverted? Answer: (a) 27 cm in front of the lens, virtual (b) 5.5 cm, upright Var: 1 83) A cell phone is placed 40 cm in front of a converging lens with a focal length of magnitude 20 cm. How far is the image of this phone from the lens? A) 40 cm B) 20 cm C) 13 cm D) 60 cm E) 10 cm Answer: A Var: 1 84) A coin is 12 cm in front of a converging lens with focal length of magnitude 4.0 cm. Where is the image? A) 8.0 cm behind the lens B) 6.0 cm in front of the lens C) 6.0 cm behind the lens D) 4.0 cm in front of the lens Answer: C Var: 1 85) A seed is 15 mm in front of a converging lens, and the image of the seed is 4.0 mm behind the lens. What is the focal length of the lens? A) 11 mm B) 5.5 mm C) 3.8 mm D) 3.2 mm Answer: B Var: 2

86) A 14-mm tall postage stamp is 4.0 mm from a converging lens. If the image of the stamp is 4.0 mm tall, how far is it from the lens? A) 14 mm B) 8.7 mm C) 1.4 mm D) 1.1 mm Answer: D Var: 1 87) When a flower petal is 4.0 cm in front of a converging lens, the inverted image is half the height of the petal. What is the focal length of this lens? A) 1.3 cm B) 2.0 cm C) 4.0 cm D) 5.3 cm Answer: A Var: 1 88) An image is 4.0 mm in front of a converging lens with focal length of magnitude 5.0 mm. Where is the object for this image? A) 2.2 mm in front of the lens B) 2.2 mm behind the lens C) 9.0 mm behind the lens D) 20 mm in front of the lens Answer: A Var: 1 89) A plant that is 4.1 cm tall is 10.3 cm from a converging lens. You observe that the image of this plant is virtual and 6.2 cm tall. What is the focal length of the lens? A) 6.8 cm B) -30 cm C) 16 cm D) 30 cm E) -16 cm Answer: D Var: 1 90) A lab specimen is 15.2 mm from a converging lens. The image is 4.0 mm tall and 9.0 cm from the lens. How tall is the specimen? A) 6.8 mm B) 5.4 mm C) 1.7 mm D) 0.68 mm Answer: D Var: 1

91) A wrench is placed at 30 cm in front of a diverging lens with a focal length of magnitude 10 cm. What is the magnification of the wrench? A) 0.25 B) -0.25 C) 0.67 D) -0.67 E) 4.0 Answer: A Var: 1 92) A statue that is 10.4 cm tall is placed 4.8 cm in front of a concave lens. The image is 4.0 cm from the lens. How tall is the image? A) 13 cm B) 8.7 cm C) 5.4 cm D) 1.8 cm Answer: B Var: 1 93) A cup that is 6.0 cm tall is in front of a concave lens. The image of the cup is 2.5 cm tall and 7.5 cm from the lens. What is the focal length of the lens? A) -6.0 cm B) -7.5 cm C) -13 cm D) +18 cm E) +6.0 cm Answer: C Var: 1 94) A drawing is placed 40 cm in front of a thin lens. If a virtual image forms at a distance of 50 cm from the lens, on the same side as the drawing, what is the focal length of the lens? A) -45 cm B) 75 cm C) 90 cm D) 200 cm Answer: D Var: 1 95) How far from a lens having a focal length of +50 mm must the object be placed if it is to form a virtual image that is 3.0 times the size of the object? A) 33 mm B) 42 mm C) 48 mm D) 54 mm Answer: A Var: 1 35 Copyright © 2019 Pearson Education, Inc.

96) How far from a +50-mm focal length lens, such as is used in many 35-mm cameras, must an object be placed so it will form a real image that is 3.0 times the size of the object? A) 46 mm B) 52 mm C) 58 mm D) 67 mm Answer: D Var: 1 97) An object is placed 15 cm to the left of a double-convex lens of focal length 20 cm. Where is the image of this object located? A) 60 cm to the right of the lens B) 60 cm to the left of the lens C) 8.6 cm to the right of the lens D) 8.6 cm to the left of the lens E) 30 cm to the left of the lens Answer: B Var: 1 98) A 4.0-cm tall object is placed 60 cm in front of a converging lens of focal length of magnitude 30 cm. What are the nature and location of the image? A) The image is real, 2.5 cm tall, 30 cm on the same side as object. B) The image is virtual, 2.5 cm tall, 30 cm on the other side of the lens. C) The image is virtual, 2.0 cm tall, 15 cm on the other side of the lens. D) The image is virtual, 4.0 cm tall, 60 cm on the same side as object. E) The image is real, 4.0 cm tall, 60 cm on the other side of the lens. Answer: E Var: 5 99) An object is placed 10 cm from a convex lens with a focal length of magnitude 20 cm. What is the magnification? A) 0.50 B) -2.0 C) 1.5 D) 2.0 E) -2.5 Answer: D Var: 1

100) An object is placed 60 cm from a convex lens with a focal length of magnitude 10 cm. What is the magnification? A) -0.10 B) 0.10 C) 0.15 D) 0.20 E) -0.20 Answer: E Var: 1 101) A 4.0-cm-tall object is placed 50.0 cm from a diverging lens having a focal length of magnitude 25.0 cm. What is the nature and location of the image? A) A real image, 4.0 cm tall, 20 cm other side of the object B) A virtual image, 4.0 cm tall, 20 cm other side of the object C) A virtual image, 2.0 cm tall, 10 cm other side of the object D) A virtual image, 1.3 cm tall, 16.7 cm same side as the object E) A real image, 1.3 cm tall, 16.7 cm same side as the object Answer: D Var: 5 102) An object is placed 21 cm from a concave lens having a focal length of magnitude 25 cm. What is the magnification? A) -0.54 B) 0.54 C) -0.32 D) -0.22 E) 0.22 Answer: B Var: 5 103) Two thin lenses, one a converging lens and the other a diverging lens, are separated by 1.00 m along the same principal axis, as shown in the figure. The magnitude of the focal length of the converging lens is 25 cm, while the magnitude of the focal length of the diverging lens is 40 cm. An object 8.25 cm tall is placed 35 cm to the left of the converging lens. (a) Where is the final image produced by this combination of lenses? (Give your answer relative to the diverging lens.) (b) Compared to the object, is the final image upright or inverted? Is it real or virtual?

College Physics: A Strategic Approach, 4e (Knight) Chapter 19 Optical Instruments 19.1 Conceptual Questions 1) The focal length of the lens of a simple digital camera is 40 mm, and it is originally focused on a person 25 m away. In what direction must the lens be moved to change the focus of the camera to a person 4.0 m away? A) It does not make any difference. B) sideways from the CCD sensors C) away from the CCD sensors D) towards the CCD sensors Answer: C Var: 1 2) The closest object that a typical young person with normal vision can focus on clearly is closest to A) 1 cm. B) 10 cm. C) 25 cm. D) 50 cm. E) 75 cm. Answer: C Var: 1 3) If the lens in a person's eye is too highly curved, this person is suffering from A) farsightedness. B) spherical aberration. C) astigmatism. D) chromatic aberration. E) nearsightedness. Answer: E Var: 1 4) If the back of a person's eye is too close to the lens, this person is suffering from A) nearsightedness. B) spherical aberration. C) astigmatism. D) chromatic aberration. E) farsightedness. Answer: E Var: 1

5) Nearsightedness is usually corrected with A) converging lenses. B) diverging lenses. C) convex mirrors. D) cylindrical lenses. E) concave mirrors. Answer: B Var: 1 6) Farsightedness can usually be corrected with A) converging lenses. B) diverging lenses. C) convex mirrors. D) cylindrical lenses. E) concave mirrors. Answer: A Var: 1 7) A little known fact is that both Robinson Crusoe and Friday wore eyeglasses. As it so happens, Robinson Crusoe was farsighted while Friday was nearsighted. Whose eyeglasses did they use whenever they wanted to start a fire by focusing the sun's rays? A) Robinson Crusoe's B) Friday's C) Both would work equally well. D) Both actually worked, but Friday's was a little bit better. E) Neither's worked, but fortunately they were in possession of matches. Answer: A Var: 1 8) What type of lens is used to make a magnifying glass? A) converging B) diverging C) Either type would work equally well. Answer: A Var: 1 9) In a compound microscope A) both the objective and the eyepiece form real images. B) magnification is provided by the objective lens and not by the eyepiece. The eyepiece merely increases the resolution of the image viewed. C) magnification is provided by the objective and not by the eyepiece. The eyepiece merely increases the brightness of the image viewed. D) the magnification is m1 + M2, where m1 is the lateral magnification of the objective and M2 is the angular magnification of the eyepiece. E) the image of the objective serves as the object for the eyepiece. Answer: E Var: 1 2 Copyright © 2019 Pearson Education, Inc.

10) A simple compound microscope normally uses A) a short focal length objective and a shorter focal length eyepiece. B) a short focal length objective and a longer focal length eyepiece. C) a long focal length objective and a shorter focal length eyepiece. D) a very long focal length objective and a longer focal length eyepiece. Answer: B Var: 1 11) For relaxed viewing with a microscope or a telescope, the eyepiece is adjusted to place the image at A) the near point of the eye. B) the pupil of the eye. C) the focal point of the eyepiece. D) infinity. E) the focal point of the objective lens. Answer: D Var: 1 12) Jack and Mary view the same microorganism through the same compound microscope. Mary's near point distance, NM, is twice as large as Jack's near point distance, NJ. If Mary sees the microorganism with magnification MM, with what magnification does Jack see it? A) 2 MM B) MM/2 C) 4 MM D) MM/4 E) 8 MM Answer: B Var: 1 13) You have a choice between two lenses of focal lengths fa and fb, where fb = 2fa, to use as the objective lens in building a compound microscope. If the magnification you obtain using lens a is Ma, what will be the magnification when using lens b? A) Mb = 2 Ma B) Mb = 4 Ma C) Mb = 8 Ma D) Mb = Ma/4 E) Mb = Ma/2 Answer: E Var: 1

14) Which one of the following is a characteristic of a compound microscope? A) The objective is a diverging lens. B) The eyepiece is a diverging lens. C) The final image is real. D) The image formed by the objective is virtual. E) The image formed by the objective is real. Answer: E Var: 1 15) Which one of the following statements is correct? A) The image formed by the objective of a microscope is smaller than the object. B) The image formed by the objective lens of a telescope is larger than the object. C) The image formed by the eyepiece is real for both a microscope and a telescope. D) The image formed by the objective lens of a microscope is larger than the object. Answer: D Var: 1 16) You are given two converging lenses to build a compound microscope. Lens A has focal length 0.50 cm and lens B has focal length of 3.0 cm. Which one of the two lenses would you use for the objective? A) Lens A, because it has the shorter focal length. B) Lens B, because it has the longer focal length. C) It makes no difference which lens I use for the objective. D) None, because the objective should be a diverging lens. Answer: A Var: 1 17) To maximize the magnification of a refracting telescope, what lenses should you choose? A) The objective lens and eyepiece should both have small focal lengths. B) The objective lens and eyepiece should both have large focal lengths. C) The objective lens should have a small focal length and the eyepiece should have a large focal length. D) The objective lens should have a large focal length and the eyepiece should have a small focal length. E) The objective lens should have a large focal length, but it doesn't matter what the focal length of the eyepiece is. Answer: D Var: 1 18) Which one of the following is normally not a characteristic of a simple two-lens refracting astronomical telescope? A) The angular size of the final image is larger than that of the object. B) The final image is virtual. C) The objective forms a virtual image. D) The final image is inverted. Answer: C Var: 1 4 Copyright © 2019 Pearson Education, Inc.

19) A simple refracting telescope provides large magnification by employing A) a short focal length objective and a short focal length eyepiece. B) a short focal length objective and a long focal length eyepiece. C) a long focal length objective and a short focal length eyepiece. D) a long focal length objective and a long focal length eyepiece. Answer: C Var: 1 20) You have a choice between two lenses of focal lengths fa and fb, where fb = 2fa, to use as the objective lens in building a refracting telescope. If the magnification you obtain using lens a is Ma, what will be the magnification when using lens b? A) Mb = 2 Ma B) Mb = 4 Ma C) Mb = 8 Ma D) Mb = Ma/4 E) Mb = Ma/2 Answer: A Var: 1 21) A refracting telescope has a magnification M. If the focal length of the objective lens is doubled and the eyepiece focal length is halved, what is the new magnification? A) 4M B) 2M C) M/2 D) M/4 E) M Answer: A Var: 1 22) Given perfect lenses, what is the main reason that a telescope with a large-diameter objective lens can produce a sharper image than one with a small-diameter lens? A) A larger lens can gather more light than a smaller lens. B) A larger lens can focus more accurately than a smaller lens. C) There is less diffraction with a larger lens than with a smaller lens. D) A larger lens can focus more wavelengths of light than a smaller lens. E) A larger lens has a longer focal length than a smaller lens. Answer: C Var: 1

23) With what color light would you expect to be able to see the finest detail when using a microscope? A) red, because of its long wavelength B) yellow, because of its intermediate wavelength C) blue, because of its shorter wavelength D) The color does not matter. Answer: C Var: 1 24) If the diameter of a radar dish is doubled, what happens to its resolving power assuming that all other factors remain unchanged? A) The resolving power quadruples. B) The resolving power doubles. C) The resolving power is cut in half. D) The resolving power is reduced to one-quarter its original value. Answer: B Var: 1 25) Chromatic aberration in lenses is due to the A) reflection of light by the lens. B) refraction of light by the lens. C) dispersion of light by the lens. D) polarization of light by the lens. E) None of the other choices is correct. Answer: C Var: 1 26) Spherical lenses suffer from A) both spherical and chromatic aberration. B) spherical aberration, but not chromatic aberration. C) chromatic aberration, but not spherical aberration. D) neither spherical nor chromatic aberration. Answer: A Var: 1 27) Which of the following statements are correct? (There could be more than one correct choice.) A) Spherical aberration, but not chromatic aberration, occurs for lenses. B) Chromatic aberration, but not spherical aberration, occurs for lenses. C) Both chromatic aberration and spherical aberration occur for lenses. D) Both chromatic aberration and spherical aberration occur for spherical mirrors. Answer: C Var: 1

19.2 Problems 1) A 35-mm digital camera using a standard 50.0 mm lens is focused on a 1.80 m tall person who is standing 3.25 m from the lens. You now refocus the camera on a 15.0 cm tall flower that is 75.0 cm from the lens. (a) In refocusing, by how much did you move the lens? Did you move it toward the film or away from it? (b) What is the height of the flower's image on the CCD sensor? Answer: (a) 2.79 mm, away from the film (b) 10.7 mm Var: 1 2) A slide projector needs to focus the image of a 24.0-mm × 36.0-mm slide onto a square screen 1.50 m on each side. You want to fill the screen as completely as possible without any of the image falling beyond the screen. Due to space constraints in the projector, the slide must be placed 10.5 cm from the lens. (a) What magnification does the projector produce? (b) How far from the lens should the screen be placed? (c) What focal length projector lens is needed? Answer: (a) 41.7, (b) 4.38 m, (c) 10.3 cm Var: 1 3) A 35-mm camera equipped with a 40-mm focal length lens is used to photograph a tree 17 m tall. If a 32-mm high image of the tree on the CCD sensor is required, how far should the camera lens be from the tree? A) 21 m B) 22 m C) 23 m D) 24 m E) 26 m Answer: A Var: 50+ 4) The focal length of the lens of a simple film camera is 40.0 mm. By what amount should the distance between the lens and the film be increased or decreased to change the focus from a person who is 25 m from the lens to one who is 4.0 m from the lens? A) 0.2 mm B) 0.3 mm C) 0.4 mm D) 0.5 mm E) 0.7 mm Answer: B Var: 1

5) A simple digital camera lens with focal length perfectly focuses the image of an object on a CCD sensor located a distance away from the lens. The object now moves away from the lens and the new distance between the lens and sensor is (a) By what amount did the object change its distance from the lens? (b) What is the new magnification? A) (a) 0.08 cm (b) 3.33 B) (a) 0.03 cm (b) 0.30 C) (a) 990.00 cm (b) 0.23 D) (a) 12.22 cm (b) 4.33 Answer: A Var: 50+ 6) A 35-mm single lens reflex (SLR) digital camera is using a lens of focal length 35.0 mm to photograph a person who is 1.80 m tall and located 3.60 m from the lens. (a) How far is the CCD sensor from the lens when the person is in focus? (b) How tall is the person's image on the CCD sensor? Answer: (a) 3.53 cm (b) 1.77 cm Var: 1 7) For an eye that is 2.4 cm in diameter, what must be the range of focal lengths of the lens to focus objects from the near point (25 cm) to infinity on the retina? Answer: 2.2 cm ≤ f ≤ 2.4 cm Var: 1 8) A person's near point is 25 cm, and her eye lens is 2.7 cm away from the retina. What must be the focal length of this lens for an object at the near point of the eye to focus on the retina? A) -3.4 cm B) -2.4 cm C) 2.4 cm D) 3.4 cm E) 2.6 cm Answer: C Var: 5 9) A person's eye lens is 2.8 cm from the retina, and his near point is at 25 cm. What must be the focal length of his eye lens so that an object at the far point of the eye will focus on the retina? A) -2.8 cm B) 2.8 cm C) -2.4 cm D) 2.4 cm E) 2.2 cm Answer: B Var: 5 8 Copyright © 2019 Pearson Education, Inc.

10) What power (in diopters) of corrective contact lens is required to correct the vision of a myopic eye whose far point is at 170 cm? Answer: -0.59 diopters Var: 29 11) A person is nearsighted with a far point of 75.0 cm. (a) What focal length contact lens is needed to give him normal vision? (b) What is the power of the corrective lens? Answer: (a) -75.0 cm (b) -1.33 diopters Var: 1 12) A nearsighted person has a near point of 12 cm and a far point of 17 cm. If the corrective lens is 2.0 cm from his eye, (a) what lens power will enable this person to see distant objects clearly, and (b) what then will be the new near point of his eye? Answer: (a) -6.7 diopters (b) 30 cm in front of the lens Var: 1 13) A person uses corrective glasses of power -8.5 D that are worn 2.0 cm from her eye. (a) Is she nearsighted or farsighted? (b) What is her far point without glasses? Answer: (a) nearsighted (b) 14 cm Var: 1 14) A nearsighted man wears contact lenses of -3.00 diopters. With these lenses, his corrected near point is 25.0 cm. What is his uncorrected near point? Answer: 14.3 cm Var: 1 15) A person's hyperopic (farsighted) eye can focus on objects that are 75 cm away and farther. What power and what focal length contact lenses should be prescribed so this person can see objects 25 cm and farther from the eye? Answer: 2.7 diopters, 38 cm Var: 1 16) A nearsighted person has a far point of 50 cm for his right eye and 150 cm for his left eye. For each eye, what power contact lens will allow the person to see gorgeous sunsets? Answer: -2.0 diopters (right eye), -0.67 diopters (left eye) Var: 1

17) What is the power of the lens that has a focal length of 40 cm and a diameter if 5.0 cm? A) -2.5 diopters B) +20 diopters C) +0.20 diopters D) +2.5 diopters E) +2.7 diopters Answer: D Var: 1 18) What is the power of a lens that has a focal length of -40 cm and a width of 2.0 cm? A) -2.5 diopters B) -0.50 diopters C) +4.0 diopters D) +2.5 diopters E) -50 diopters Answer: A Var: 1 19) The power of a lens is 4.0 diopters and its diameter is 5.0 cm. What is the focal length of this lens? A) 25 cm B) 55 cm C) 10 cm D) 0.25 cm E) 2.5 cm Answer: A Var: 1 20) A farsighted boy has a near point at 2.3 m and requires contact lenses to correct his vision to the normal near point. What is the correct choice of lens power for the contact lenses? A) -0.28 diopters B) +0.28 diopters C) -3.6 diopters D) +3.6 diopters E) +1.8 diopters Answer: D Var: 1

21) A farsighted girl has a near point at 2.0 m but has forgotten her glasses at home. The girl borrows eyeglasses that have a power of +2.75 diopters. With these eyeglasses, what is the near point of the girl, assuming that she wears them extremely close to her eyes? A) 28 cm B) 31 cm C) 33 cm D) 37 cm E) 40 cm Answer: B Var: 1 22) A myopic (nearsighted) child wears contact lenses that allow her to have clear distant vision. The power of the lenses of her eyeglasses is -3.00 diopters. Without the corrective lenses, what is the far point of the girl? A) 0.33 m B) 0.25 m C) 0.17 m D) 0.42 m E) 0.50 m Answer: A Var: 12 23) A machinist with normal vision has a near point at 25 cm. This machinist wears +4.25diopter eyeglasses in order to do very close work. With these eyeglasses, what is the near point of the machinist? Assume that he wears the glasses extremely close to his eyes. A) 12 cm B) 10 cm C) 7 cm D) 15 cm E) 17 cm Answer: A Var: 14 24) As a treatment for cataracts (a cloudiness of the lens of the eye), the natural lens is removed and a plastic lens is implanted. After this is done a person can see distant objects clearly, but he cannot accommodate to focus on nearby objects. If such a person wanted to read a book at a distance of 25 cm, he would have to wear contact lenses having a diopter power of A) +2.78 diopters B) +3.33 diopters C) -1.78 diopters D) +4.00 diopters E) -4.00 diopters Answer: D Var: 1

25) What is the focal length of the corrective contact lens needed by a nearsighted person whose far point is at 60 cm? A) -60 cm B) -30 cm C) +30 cm D) +60 cm E) +130 cm Answer: A Var: 5 26) The near point of a farsighted person is 65 cm. What power contact lens must he use to correct this problem and be able to read a book at a normal near point of 25 cm? A) -4.2 diopters B) -2.5 diopters C) -2.4 diopters D) +4.2 diopters E) +2.5 diopters Answer: E Var: 5 27) A nearsighted person has a far point that is 4.2 m from his eyes. What focal length lenses must he use in his contact lenses to allow him to focus on very distant mountains? A) -4.2 m B) 4.2 m C) -5.2 m D) 5.2 m E) -4.8 m Answer: A Var: 1 28) A nearsighted person has a far point that is 4.2 m from his eyes. What power contact lenses must he wear to allow him to focus on distant mountains? A) 0.48 diopters B) -0.48 diopters C) -0.36 diopters D) -0.24 diopters E) 0.24 diopters Answer: D Var: 1

29) What is the focal length of a contact lens that will allow a person with a near point of 125 cm to read a physics book held 25.0 cm from his eyes? A) -100 cm B) -31.3 cm C) 10.2 cm D) 20.8 cm E) 31.3 cm Answer: E Var: 1 30) What power contact lens should be used to correct the vision of a farsighted person whose near point is 80 cm so she can see things clearly that are 25 cm in front of her? A) +2.8 diopters B) -2.8 diopters C) -4.0 diopters D) -4.2 diopters E) +4.2 diopters Answer: A Var: 1 31) What power contact lens must be used to correct the vision of a nearsighted person whose far point is 40 cm? A) +2.5 diopters B) -2.5 diopters C) -3.6 diopters D) -4.0 diopters E) +4.0 diopters Answer: B Var: 1 32) What is the uncorrected near point of a farsighted person who can comfortably read a newspaper held 25 cm from his eyes when he wears +3.33-diopter contact lenses? A) 1.5 m B) 0.50 m C) 1.9 m D) 0.75 m E) 0.60 m Answer: A Var: 1

33) Without glasses, a person can comfortably read a magazine when it is held at 60 cm from his eyes. What should be the focal length of his contact lenses to allow him to read the magazine comfortably at a distance of 30 cm? A) -30 cm B) +30 cm C) -60 cm D) +60 cm E) +90 cm Answer: D Var: 1 34) Diego is nearsighted and cannot see things beyond 110 cm from his eyes. What is the focal length of the contact lenses that will enable him to comfortably see distant hills clearly? A) +50 cm B) -50 cm C) -110 cm D) +110 cm E) -30 cm Answer: C Var: 5 35) Olga is nearsighted and cannot see things beyond 90 cm cm from her eyes. What is the refractive power of the contact lenses that will enable her to comfortably see distant buildings clearly? A) +1.1 diopters B) -1.1 diopters C) -1.7 diopters D) -2.2 diopters E) +2.2 diopters Answer: B Var: 5 36) Mahmood is farsighted and cannot see objects clearly that are closer to his eye than 80.0 cm. What is the focal length of the contact lenses that will enable him to comfortably see objects at a distance of 25.0 cm from his eyes? A) +36.4 cm B) -36.4 cm C) -21.2 cm D) +21.2 cm E) +32.5 cm Answer: A Var: 5

37) Alice is farsighted and cannot see objects clearly that are closer to her eye than 80.0 cm. What is the refractive power of the contact lenses that will enable her to comfortably see objects at a distance of 25.0 cm from her eyes? A) +2.75 diopters B) -2.75 diopters C) -4.72 diopters D) +4.72 diopters E) +7.00 diopters Answer: A Var: 5 38) A nearsighted person cannot see objects beyond 80 cm from his eyes. Which one of the following combinations represents the correct focal length and the refractive power of the contact lenses that will enable him to comfortably see the distant objects clearly? A) +80 cm, +1.3 diopters B) -80 cm, +1.3 diopters C) +80 cm, -1.3 diopters D) -80 cm, -1.3 diopters E) -1.3 cm, +1.3 diopters Answer: D Var: 5 39) A farsighted person cannot see clearly objects that are closer to her eyes than 60.0 cm. Which one of the following combinations represents the correct focal length and the refractive power of the contact lenses that will enable her to comfortably see the objects at a distance of 25.0 cm from her eyes? A) -42.9 cm, +2.33 diopters B) -42.9 cm, -2.33 diopters C) +42.9 cm, +2.33 diopters D) +42.9 cm, -2.33 diopters E) +60 cm, +42.9 diopters Answer: C Var: 5 40) A nearsighted person has a far point of 18 cm. What power contact lenses will allow this person to comfortably see distant objects clearly? A) +5.6 diopters B) -5.6 diopters C) +0.056 diopters D) -0.056 diopters Answer: B Var: 3

41) A person cannot see clearly objects more than 70.0 cm away. What power of corrective lens should be prescribed if the glass is to be worn 1.00 cm in front of the eye? A) 1.45 diopters B) -1.45 diopters C) 0.0145 diopters D) -0.0145 diopters Answer: B Var: 1 42) A nearsighted person wears contact lenses having a power of -0.15 diopters. What is the person's uncorrected far point? A) 1.5 m B) 3.3 m C) 6.0 m D) 6.7 m Answer: D Var: 1 43) What power contact lens is needed to correct for farsightedness where the uncorrected near point is 75 cm? A) +2.7 D B) -2.7 D C) +5.3 D D) -5.3 D Answer: A Var: 2 44) The near point of a farsighted person is 100 cm. She places reading glasses very close to her eyes, and with them she can comfortably read a book at a distance of 25 cm. What is the power of the lenses in her reading glasses? A) +2.5 diopters B) +3.0 diopters C) +3.2 diopters D) -2.0 diopters Answer: B Var: 1 45) When a person with a near point at 28 cm uses a certain magnifying glass, it produces an angular magnification of 7.0 with the image very distant. What is the focal length of the lens of this magnifying glass? A) 2.0 cm B) 3.0 cm C) 4.0 cm D) 5.0 cm E) 6.0 cm Answer: C Var: 1 16 Copyright © 2019 Pearson Education, Inc.

46) The focal length of a magnifying glass is 15 cm. If the near point of a person is 25 cm, what is the angular magnification of the glass for this person when his eyes are focused at infinity? A) 1.7 B) 2.7 C) 3.7 D) 4.7 E) 5.7 Answer: A Var: 1 47) The focal length of a converging lens is 10 cm. What is the angular magnification of this lens if the image is viewed by a relaxed eye with a near point of 25 cm? A) 0.50 B) 1.5 C) 2.5 D) 3.5 E) 4.5 Answer: C Var: 1 48) What is the angular magnification of a magnifying glass of focal length 4.0 cm if the image is to be viewed by a relaxed eye having a near point of 25 cm? A) 2.0 B) 3.0 C) 3.6 D) 4.0 E) 6.3 Answer: E Var: 1 49) A lens of focal length 90 mm is used as a magnifier by a person with a near point of 25 cm. The object being viewed is 9.9 mm long, and is positioned at the focal point of the lens. What is the angle subtended by the image at infinity, in milliradians? A) 110 mrad B) 73 mrad C) 37 mrad D) 147 mrad E) 183 mrad Answer: A Var: 50+

50) A lens of focal length 40 mm is used as a magnifier. The object being viewed is 5.3 mm long, and is positioned at the focal point of the lens. The user of the magnifier has a near point at 25 cm. What is the angular magnification of the magnifier? A) 6.3 B) 5.6 C) 6.9 D) 7.5 E) 8.1 Answer: A Var: 50+ 51) A person having a near point of 25 cm uses a magnifying glass with a focal length of 10 cm. What is the angular magnification of the glass for that person when her eyes are focused at infinity? A) 1.5 B) 2.5 C) 3.5 D) 4.5 Answer: B Var: 1 52) A magnifying glass has a focal length of 7.0 cm. What is the angular magnification if the image is viewed by a person having a relaxed eye with the near point of 25 cm? A) 1.6 B) 2.6 C) 3.6 D) 4.6 Answer: C Var: 3 53) A person uses a converging lens of focal length 5.0 cm as a magnifying glass. What is the angular magnification if the person's eye is relaxed and has a near point of 25 cm? A) 4.0 B) 5.0 C) 6.0 D) 7.0 Answer: B Var: 1

54) A magnifying glass uses a converging lens with a refractive power of 20 diopters. What is the angular magnification if the image is to be viewed by a relaxed eye with a near point of 25 cm? A) 5.0 B) 3.0 C) 4.0 D) 1.0 E) 2.0 Answer: A Var: 1 55) A compound microscope consists of an objective lens of focal length f0 and an eyepiece that by itself produces an angular magnification 25.0. The microscope is designed so that the object to be viewed is on the left side of the objective lens and is focused in a plane that is 28.00 cm away from the right-hand (or inside) focal point of the objective lens. When properly adjusted, the eyepiece and the objective lens are 29.90 cm apart. The eyepiece magnification is based on an image at infinity and a near point at 25.0 cm. What is f0? Answer: 0.90 cm Var: 50+ 56) The objective lens of a microscope has a focal length of 2.4 mm and the eyepiece has an angular magnification of 15. The object is positioned 0.060 mm beyond the focal point of the objective. The focal point of the eyepiece is positioned at the real image formed by the objective. The near point of the microscope user is at 25 cm. The magnitude of the overall magnification of the microscope is closest to A) 400. B) 450. C) 500. D) 550. E) 600. Answer: E Var: 1 57) A very delicate sample is placed 0.150 cm from the objective lens of a microscope. The focal length of the objective is 0.140 cm, and that of the eyepiece is 1.0 cm. The near-point distance of the person using the microscope is 25.0 cm. The magnitude of the final magnification of the microscope is closes to A) 375. B) 300. C) 250. D) 125. E) 100. Answer: A Var: 1

58) The objective lens of a microscope has a focal length of 2.4 mm and the eyepiece has an angular magnification of 15. The object is positioned 0.060 mm beyond the focal point of the objective. The focal point of the eyepiece is positioned at the real image formed by the objective. The near point of the microscope user is at 25 cm. What is the distance between the objective lens and the eyepiece? A) 98 mm B) 102 mm C) 107 mm D) 111 mm E) 115 mm Answer: E Var: 1 59) A microscope has an objective lens of focal length 1.40 mm and an eyepiece of focal length 20.00 mm. It is adjusted for minimum eyestrain for persons with a near point of 25.0 cm. A blood sample is placed 1.50 mm from the objective. How far apart are the lenses? A) 20 mm B) 21 mm C) 23 mm D) 41 mm Answer: D Var: 1 60) A microscope has an objective lens of focal length 1.40 mm and an eyepiece of focal length 20.00 mm. It is adjusted for minimum eyestrain for persons with a near point of 25.0 cm. A blood sample is placed 1.50 mm from the objective. The magnitude of the overall magnification is closest to A) 18. B) 37. C) 180. D) 370. Answer: C Var: 1 61) A compound microscope has an objective with a focal length of 3.00 mm and an eyepiece of focal length 6.00 cm. It is adjusted for minimum eyestrain for persons with a near point of 25 cm. If the two lenses are separated by 40.0 cm, what is the total overall magnification? A) 28 B) 56 C) 470 D) 550 E) 2200 Answer: C Var: 1

62) A compound microscope has a 18-cm-long barrel and an objective lens with a focal length of 8.0 mm. What is the focal length of the eyepiece to give a total magnification of 240? It is adjusted for minimum eyestrain for persons with a near point of 25 cm. A) 1.3 m B) 1.5 cm C) 1.9 cm D) 2.1 cm E) 2.3 cm Answer: D Var: 1 63) The focal lengths of the objective lens and the eyepiece in a microscope are 2.90 mm and 2.50 cm, respectively. An object is placed 3.00 mm from the objective. The image of this object is viewed with the eyepiece adjusted for minimum eyestrain for persons with a near point of 25 cm. What is the distance between the objective and the eyepiece? A) 9.9 cm B) 9.0 cm C) 15 cm D) 11 cm E) 13 cm Answer: D Var: 1 64) The focal lengths of the objective lens and the eyepiece in a microscope are 0.29 cm and 2.50 cm, respectively. An object is placed at 0.30 cm from the objective lens and the image of this object is viewed with the eyepiece adjusted for minimum eyestrain for persons with a near point of 25 cm. The magnitude of the final overall magnification of the microscope is closest to A) 100 B) 200 C) 300 D) 410 E) 500 Answer: C Var: 1 65) The focal lengths of the objective lens and the eyepiece of a microscope are 0.50 cm and 2.0 cm, respectively, and their separation adjusted for minimum eyestrain is 6.0 cm. If the microscope is focused on a small object, what is the distance between the object and the objective lens? A) 0.31 cm B) 0.42 cm C) 0.49 cm D) 0.57 cm E) 0.73 cm Answer: D Var: 1 21 Copyright © 2019 Pearson Education, Inc.

66) The focal lengths of the objective lens and the eyepiece of a microscope are 0.50 cm and 2.0 cm, respectively, and their separation is 6.0 cm when adjusted for minimum eyestrain for a person with a near point of 25.0 cm. If the microscope is focused on a small object, the magnitude of its final overall magnification is closest to A) 50. B) 100. C) 150. D) 200. E) 250. Answer: B Var: 1 67) The distance between the object to be viewed and the eyepiece of a compound microscope is 18.0 cm. The focal length of its objective lens is 0.80 cm and the eyepiece has a focal length of 2.3 cm. The near-point distance of the person using the microscope is 25.0 cm. What is the magnitude of the total magnification of the microscope if it is designed for minimum eyestrain? A) 120 B) 184 C) 200 D) 360 E) 480 Answer: C Var: 1 68) The distance between the object to be viewed and the eyepiece of a compound microscope is 25.0 cm. The focal length of its objective lens is 0.200 cm and the eyepiece has a focal length of 2.60 cm. What is the magnitude of the total magnification of the microscope when used by the person of normal eyesight if it is designed for minimum eyestrain? A) 1070 B) 204 C) 520 D) 477 E) 772 Answer: A Var: 1 69) The objective lens and the eyepiece of a microscope have focal lengths of 4.0 mm and 25 mm, respectively. The objective produces a real image 30 times the size of the object, with the final image viewed at infinity. The near point of the microscope user is at 25 cm. What is the distance between the object and the focal point of the objective lens? A) 0.13 mm B) 0.18 mm C) 0.23 mm D) 0.28 mm E) 0.33 mm Answer: A Var: 1 22 Copyright © 2019 Pearson Education, Inc.

70) The objective lens and the eyepiece of a microscope have focal lengths of 4.0 mm and 25 mm, respectively. The objective produces a real image 30 times the size of the object, with the final image viewed at infinity. The near point of the microscope user is at 25 cm. What is the distance between the objective lens and the real image that it produces? A) 116 mm B) 120 mm C) 124 mm D) 128 mm E) 132 mm Answer: C Var: 1 71) The objective lens and the eyepiece of a microscope have focal lengths of 4.0 mm and 25 mm, respectively. The objective produces a real image 30 times the size of the object, with the final image viewed at infinity. The near point of the microscope user is at 25 cm. What is the magnitude of the overall magnification of the microscope? A) 250 B) 300 C) 350 D) 400 E) 450 Answer: B Var: 1 72) The eyepiece of a compound microscope has a focal length of 2.50 cm, and the objective has a focal length of 1.60 cm. The two lenses are separated by 14.0 cm. The microscope is used by a person with normal eyes, having a near point at 25 cm. What is the magnitude of the magnification of the microscope? A) 72 B) 88 C) 180 D) 219 E) 115 Answer: A Var: 50+ 73) A refracting telescope has an eyepiece of focal length -80 mm and an objective of focal length 36 cm. What is the magnification of this instrument? Answer: 4.5 Var: 1 74) A student wishing to build a telescope has available an eyepiece of focal length -5.0 cm. What focal length objective is needed to obtain a magnification of 10? Answer: 50 cm Var: 1 23 Copyright © 2019 Pearson Education, Inc.

75) The objective lens of a telescope has a focal length of 1.90 m. When viewed through this telescope, the Moon appears 5.25 times larger than normal. How far apart are the objective lens and the eyepiece when this instrument is focused on the Moon? Answer: 2.26 m Var: 1 76) Mary builds a simple refracting telescope using two lenses of focal length 80 cm and 5.0 cm. The respective diameters are 60 mm and 10 mm. How many degrees wide does the moon appear through the telescope if it appears only 1/2 degree wide with the "naked eye"? Answer: 8° (16 times larger) Var: 1 77) You have available lenses of focal lengths 2.0 cm, 4.0 cm, 8.0 cm, and 16.0 cm. If you could use any two of these lenses to build a telescope, what is the maximum magnification you could achieve for comfortable viewing of a planet? A) 2.0 B) 4.0 C) 6.0 D) 8.0 Answer: D Var: 1 78) You have available lenses of focal lengths 2.0 cm, 4.0 cm, 8.0 cm, and 16 cm. If you could use any two of these lenses to build a telescope, what is the lens separation for the telescope to provide the maximum magnification for comfortable viewing of a planet? A) 10.0 cm B) 12.0 cm C) 18.0 cm D) 24.0 cm Answer: C Var: 1 79) The objective lens of a telescope has a focal length of 2.0 m and its eyepiece has a focal length of 1.0 cm. What is the magnification of this telescope when viewing Jupiter? A) 0.0050 B) 0.50 C) 2.0 D) 20 E) 200 Answer: E Var: 1

80) A student constructs an astronomical telescope and wishes it to have a magnification of 10. If the telescope has an objective lens of focal length 0.50 m, what must be the focal length of the eyepiece? A) 2.5 cm B) 5.0 cm C) 10 cm D) 25 cm Answer: B Var: 1 81) A student constructs an astronomical telescope with a magnification of 10. If the telescope has an objective lens of focal length 0.50 m, what is the resulting length of the telescope? A) 53 cm B) 55 cm C) 60 cm D) 75 cm Answer: B Var: 1 82) A person is designing a telescope with a magnification of 10. If the telescope is limited to a length of 0.20 m, what is the approximate focal length of the objective? A) 16 cm B) 17 cm C) 18 cm D) 19 cm Answer: C Var: 1 83) A telescope has an angular magnification of 250 when used with a 20 mm eyepiece. What is the focal length of the objective lens? A) 5.0 cm B) 25 m C) 5000 cm D) 5.0 m E) 2.5 m Answer: D Var: 1

84) Cal is viewing the Moon with his new telescope, using a 10-mm focal length eyepiece. For greater detail, he wishes to double the magnification of his telescope. An eyepiece having which one of the following characteristics will accomplish this for him? A) 40 diopters B) 8 mm C) 12 mm D) 200 diopters E) 5 diopters Answer: D Var: 1 85) The focal length of the objective lens of a telescope is 75.0 cm, and the eyepiece has a focal length of 6.00 cm. What is the magnification of this telescope? A) 0.0800 B) 0.645 C) 450 D) 12.5 E) 200 Answer: D Var: 1 86) The length of a telescope is 2.00 m and the focal length of the objective lens is 2.0 cm. What is the focal length of the eyepiece? A) 200 cm B) 202 cm C) 101 cm D) 2.0 cm E) 198 cm Answer: E Var: 1 87) The length of a telescope is 2.20 m and the focal length of the eyepiece is 1.9 cm. What is the focal length of the objective lens? A) 41 cm B) 45 cm C) 111 cm D) 218 cm E) 16 cm Answer: D Var: 1

88) The focal length of the objective lens of a telescope is 0.20 m and the eyepiece has a focal length of 1.6 m. What is the length of this telescope? A) 8.0 m B) 1.4 m C) 0.90 m D) 1.6 m E) 1.8 m Answer: E Var: 1 89) The length of the telescope is 1.60 m, and it has a magnification of 60.0. What is the focal length of the objective lens? A) 60.0 cm B) 157 cm C) 100 cm D) 128 cm E) 96.0 cm Answer: B Var: 1 90) The length of a telescope is 1.60 m and it has a magnification of 60.0. What is the focal length of the eyepiece? A) 2.62 cm B) 60.0 cm C) 100 cm D) 1.16 cm E) 96.0 cm Answer: A Var: 1 91) The objective lens of a refracting astronomical telescope has a focal length of 60 cm, and the eyepiece has a focal length of 2.0 cm. How far apart should the lenses be placed in order to form a final image at infinity? A) 44 cm B) 58 cm C) 76 cm D) 60 cm E) 62 cm Answer: E Var: 1

92) An astronomical refracting telescope is made from two lenses. The objective lens has a focal length of and the eyepiece lens has a focal length of (a) What is the total length of the telescope? (b) What is the angular magnification of the telescope? (c) What is the magnification by turning the telescope around and looking through the objective lens first? A) (a) 131 cm (b) 6.71 (c) 0.15 B) (a) 97 cm (b) 0.15 (c) 6.71 C) (a) 262 cm (b) 0.87 (c) 1.15 D) (a) 194 cm (b) 1.18 (c) 0.85 Answer: A Var: 50+ 93) The angular magnification of a refracting telescope is 40. When the object and final image are both at infinity, the distance between the eyepiece and the objective is 143.5 cm. The telescope is used to view a distant radio tower. The real image of the tower, formed by the objective, is 6.0 mm in height. The focal point of the eyepiece is positioned at the real image. What is the focal length of the objective lens? A) 138 cm B) 139 cm C) 140 cm D) 141 cm Answer: C Var: 1 94) The angular magnification of a refracting telescope is 40. When the object and final image are both at infinity, the distance between the eyepiece and the objective is 143.5 cm. The telescope is used to view a distant radio tower. The real image of the tower, formed by the objective, is 6.0 mm in height. The focal point of the eyepiece is positioned at the real image. What is the angle subtended by the final image of the tower? A) 0.15 rad B) 0.17 rad C) 0.19 rad D) 0.21 rad E) 0.23 rad Answer: B Var: 1

95) The objective and the eyepiece of a refracting astronomical telescope have focal lengths of 320 cm and 4.0 cm, respectively. The telescope is used to view Neptune and the final image is set at infinity. The diameter of Neptune is 4.96 × 107 m, and its distance from Earth at the time of observation is 4.4 × 1012 m. What is the angle (in milliradians) subtended by the final telescopic image of Neptune? A) 0.90 mrad B) 1.1 mrad C) 1.3 mrad D) 1.5 mrad E) 1.7 mrad Answer: A Var: 1 96) Treat the pupil of your eye as a circular aperture of diameter 3.5 mm. Light of wavelength 500 nm is used to view two point sources that are 283 m distant from you. How far apart must these two point sources be if they are to be just barely resolved by your eye, assuming that the resolution is limited by diffraction? Answer: 4.9 × 10-2 m Var: 50+ 97) Even with perfect optics, what is the resolution limit (in radians) of the Hubble Space Telescope when it is focusing light of wavelength 400 nm? The mirror diameter is 2.4 m. Answer: 2.0 × 10-7 rad Var: 1 98) The world's largest refracting telescope is operated at the Yerkes Observatory in Wisconsin. It has an objective lens of diameter of 1.02 m. Suppose such an instrument were mounted on a satellite at an elevation of 300 km above the ground and used to map surface details. If the telescope is forming images with light of wavelength 550 nm, what is the minimum separation of two objects on the ground whose separation could be clearly resolved by this lens? Answer: 19.7 cm Var: 1 99) What is the minimum distance between two points on the Moon that could be just resolved by the Keck telescope in Hawaii using a wavelength of 600 nm and having perfect optics? The diameter of this telescope mirror system is 10 m, and the distance to the Moon is 380,000 km. Answer: 28 m Var: 1 100) A camera with a 20-cm diameter lens is recording images using a filter that allows only light of wavelength 600 nm to pass through. (a) What is the limit on the angular resolution (in microradians) in this case? (b) What is the diameter of the minimum-sized features that could be resolved on Mars with this camera? The distance to Mars at the time is 9.0 × 107 km. Answer: (a) 3.7 µrad (b) 330 km Var: 1 29 Copyright © 2019 Pearson Education, Inc.

101) In one particular case, the limiting angle of resolution for an eye is 1.4 × 10-4 rad. What is the minimum separation between two point sources of light that the eye can distinguish if they are at a distance of 40 m from the observer? A) 2.8 mm B) 5.6 mm C) 1.4 mm D) 8.4 mm E) 4.7 mm Answer: B Var: 1 102) A camera used for aerial mapping has a lens with a 30-cm diameter maximum aperture and a 42-cm focal length. Light of 550 nm wavelength is used to form the image. Assuming that the resolution of the camera is limited only by diffraction, what is the smallest angle (in milliradians) subtended by an object on the ground that can be resolved by this camera at maximum aperture? A) 1.6 mrad B) 2.2 mrad C) 3.2 mrad D) 4.5 mrad E) 6.3 mrad Answer: B Var: 1 103) Assuming a pupil diameter of 3 mm, what is the angular resolution of the human eye for light at the middle of the visible spectrum (550 nm)? A) 0.8° B) 0.2° C) 2 mrad D) 0.01° E) 2° Answer: D Var: 1 104) Suppose your telescope has perfect mirrors and is limited only by diffraction. If you are viewing with light of 400 nm wavelength, what diameter mirror in a space telescope would have 1.0-km resolution of objects on Mars when viewed from above the earth at a time when the Earth-Mars distance of 80 million kilometers? A) 39 km B) 3.9 m C) 3.9 km D) 39 m E) 390 m Answer: D Var: 1

105) Astronomers are proud of their telescopes and often say they can "resolve a dime at so many miles." How many miles from a telescope mirror can you place a coin of diameter 3.0 cm and just resolve the coin using light of wavelength (1 mi = 1.609 km) A) 19 mi B) 9.7 mi C) 40 mi D) 190,000,000 mi Answer: A Var: 50+ 106) A certain astronomical telescope has a diameter of 5.60 m. What is the minimum angle of resolution for this telescope when it is forming images using light of wavelength 620 nm? A) 1.11 × 10-7 rad B) 3.11 × 10-7 rad C) 2.70 × 10-7 rad D) 1.35 × 10-7 rad E) 4.05 × 10-7 rad Answer: D Var: 1 107) The two stars in a binary star system have an angular separation of 1.0 × 10-5 rad. If the wavelength of the light from the system is 500 nm, what is the smallest diameter aperture telescope that could just resolve this system to show that it contains two stars? A) 0.50 cm B) 0.61 cm C) 5.0 cm D) 6.1 cm Answer: D Var: 1 108) The pupil of a person's eye changes from a diameter of 3.5 mm to 1.5 mm as the illumination is increased. By what factor does the minimum angle of resolution change? A) 0.43 B) 0.65 C) 2.0 D) 2.3 Answer: D Var: 1

109) What is the limiting angle of resolution for a lens of radius 2.0 mm when viewing with light having a wavelength of 600 nm? A) 1.3 × 10-4 rad B) 1.5 × 10-4 rad C) 1.8 × 10-4 rad D) 1.5 × 10-7 rad E) 1.8 × 10-7 rad Answer: C Var: 1 110) A camera lens having a 50-mm focal length is set to f/4.0. What is the minimum spacing of two objects located 12 m from the lens if the objects are just barely resolved in the image using light of wavelength 500 nm? A) 1.66 mm B) 4.72 mm C) 0.024 mm D) 4.9 × 10-5 m E) 0.59 mm Answer: E Var: 1

College Physics: A Strategic Approach, 4e (Knight) Chapter 20 Electric Fields and Forces 20.1 Conceptual Questions 1) Electrically neutral objects cannot exert an electrical force on each other, but they can exert a gravitational force on each other. A) True B) False Answer: B Var: 1 2) If two objects are electrically attracted to each other, A) both objects must be negatively charged. B) both objects must be positively charged. C) one object must be negatively charged and the other object must be positively charged. D) the objects could be electrically neutral. E) None of the above statements are absolutely true. Answer: D Var: 1 3) A plastic rod is charged up by rubbing a wool cloth, and brought to an initially neutral metallic sphere that is insulated from ground. It is allowed to touch the sphere for a few seconds, and then is separated from the sphere by a small distance. After the rod is separated, the rod A) is repelled by the sphere. B) is attracted to the sphere. C) feels no force due to the sphere. Answer: A Var: 1 4) A negatively-charged plastic rod is brought close to (but does not touch) a neutral metal sphere that is connected to ground. After waiting a few seconds, the ground connection is removed (without touching the sphere), and after that the rod is also removed. The sphere is now A) negatively charged. B) positively charged. C) neutral. Answer: B Var: 1

X and Y are two initially uncharged metal spheres on insulating stands, and they are in contact with each other. A positively charged rod R is brought close to X as shown in part (a) of the figure. Sphere Y is now moved away from X, as shown in part (b). What are the final charge states of X and Y? A) Both X and Y are neutral. B) X is positive and Y is neutral. C) X is neutral and Y is positive. D) X is negative and Y is positive. E) Both X and Y are negative. Answer: D Var: 1 6) Two uncharged metal spheres, #1 and #2, are mounted on insulating support rods. A third metal sphere, carrying a positive charge, is then placed near #2. Now a copper wire is momentarily connected between #1 and #2 and then removed. Finally, sphere #3 is removed. In this final state A) spheres #1 and #2 are still uncharged. B) sphere #1 carries positive charge and #2 carries negative charge. C) sphere #1 carries negative charge and #2 carries positive charge. D) spheres #1 and #2 both carry positive charge. E) spheres #1 and #2 both carry negative charge. Answer: B Var: 1 7) A negatively-charged rod is brought close to (but does not touch) two neutral spheres that are in contact with each other but insulated from the ground. If the two spheres are then separated, what kind of charge will be on the spheres? A) The sphere near the charged rod becomes positive and the other one becomes negative. B) The sphere near the charged rod becomes negative and the other one becomes positive. C) The spheres do not get any charge. D) Both spheres become negative. E) Both spheres become positive. Answer: A Var: 1

8) Two tiny beads are 25 cm apart with no other charges or fields present. Bead A carries 10 µC of charge and bead B carries 1 µC. Which one of the following statements is true about the magnitudes of the electric forces on these beads? A) The force on A is 10 times the force on B. B) The force on B is 10 times the force on A. C) The force on A is exactly equal to the force on B. D) The force on A is 100 times the force on B. E) The force on B is 100 times the force on A. Answer: C Var: 1 9) Two very small plastic balls of equal mass are released from rest. One of them carries +10 µC of excess charge and the other one carries +1µC of charge. No other charges or fields are present. Which of the following statements are true about them as they move away from each other? (There may be more than one correct choice.) A) The acceleration of the 10-µC ball is 10 times that of the 1-µC ball. B) The acceleration of the 1-µC ball is 10 times that of the 10-µC ball. C) The balls always have accelerations of equal magnitude. D) The speed of the balls keeps increasing. E) The acceleration of the balls keeps increasing. Answer: C, D Var: 1 10) In outer space, a positive charge q is released near a positive fixed charge Q, as shown in the figure. As q moves away from Q, what is true about the motion of q? (There may be more than one correct choice.)

A) It will move with decreasing speed. B) It will move with constant acceleration. C) It will move with increasing acceleration. D) It will move with decreasing acceleration. E) It will move with increasing speed. Answer: D, E Var: 1

11) A small charged plastic ball is vertically above another charged small ball in a frictionless test tube as shown in the figure. The balls are in equilibrium a distance d apart. If the charge on each ball is doubled, the equilibrium distance between the balls in the test tube would become

A) d. B) 2d. C) 4d. D) 8d. E) d/4. Answer: B Var: 1 12) A hydrogen nucleus, which has a charge +e, is situated to the left of a carbon nucleus, which has a charge +6e. Which statement is true? A) The electrical force experienced by the hydrogen nucleus is to the left, and the magnitude is equal to the force exerted on the carbon nucleus. B) The electrical force experienced by the hydrogen nucleus is to the left, and the magnitude is greater than the force exerted on the carbon nucleus. C) The electrical force experienced by the hydrogen nucleus is to the left, and the magnitude is less than the force exerted on the carbon nucleus. D) The electrical force experienced by the hydrogen nucleus is to the right, and the magnitude is equal to the force exerted on the carbon nucleus. Answer: A Var: 1 13) Two identical small charged spheres are a certain distance apart, and each one initially experiences an electrostatic force of magnitude F due to the other. With time, charge gradually diminishes on both spheres by leaking off. When each of the spheres has lost half its initial charge, what will be the magnitude of the electrostatic force on each one? A) 1/16 F B) 1/8 F C) 1/4 F D) 1/2 F E) 1/ F Answer: C Var: 1 4 Copyright © 2019 Pearson Education, Inc.

14) Two point charges, Q1 and Q2, are separated by a distance R. If the magnitudes of both charges are doubled and their separation is also doubled, what happens to the electrical force that each charge exerts on the other one? A) It increases by a factor of 2. B) It increases by a factor of . C) It is reduced by a factor of . D) It increases by a factor of 4. E) It remains the same. Answer: E Var: 1 15) Two point charges, Q1 and Q2, are separated by a distance R. If the magnitudes of both charges are halved and their separation is also halved, what happens to the electrical force that each charge exerts on the other one? A) It increases by a factor of 16. B) It increases by a factor of 8. C) It increases by a factor of 2. D) It increases by a factor of 4. E) It remains the same. Answer: E Var: 1 16) Three equal charges +Q are at three of the corners of a square of side d. A fourth charge +Q of equal magnitude is at the center of the square as shown in the figure Which one of the arrows shown represents the net force acting on the charge at the center of the square?

A) A B) B C) C D) D Answer: B Var: 1

17) Four point charges of equal magnitudes but with varying signs are arranged on three of the corners and at the center of the square of side d as shown in the figure. Which one of the arrows shown represents the net force acting on the center charge?

A) A B) B C) C D) D Answer: A Var: 1 18) Four point charges of equal magnitude but with varying signs are arranged on three of the corners and at the center of the square of side d as shown in the figure. Which one of the arrows shown represents the net force acting on the center charge?

A) A B) B C) C D) D Answer: A Var: 1

19) Four point charges Q of equal magnitude and sign are arranged on three of the corners of the square of side d as shown in the figure Which one of the arrows shown represents the net force acting on the charge at the upper right hand corner of the square?

A) A B) B C) C D) D Answer: D Var: 1 20) Four point charges of varying magnitude and sign are arranged on the corners of the square of side d as shown in the figure. Which one of the arrows shown represents the net force acting on the point charge with a charge +Q?

Var: 1 21) An electron and a proton are released simultaneously from rest and start moving toward each other due to their electrostatic attraction, with no other forces present. Which of the following statements are true just before they are about to collide? (There could be more than one correct choice.) A) They are closer to the to the initial position of the electron that to the initial position of the proton. B) They are closer to the to the initial position of the proton that to the initial position of the electron. C) They are at the midpoint of their initial separation. D) They both have the same speed. E) The electrostatic force on the proton is greater than the electrostatic force on the electron. Answer: B Var: 1 22) Two equal and opposite charges are a small distance apart, forming an electric dipole. A positive charge +q is placed above these charges, as shown in the figure, equidistant from both of them. Which diagram below best gives the direction of the net force the dipole exerts on the charge +q?

Answer: C Var: 1

23) Two small identically charged balls are a certain distance apart. The vectors in the figure show the magnitude and direction of the electrostatic force on each ball due to the other one. Suppose that the charge on the left ball is now doubled (represented by two plus signs). Which vector diagram below best represents the forces that now act on each of the two balls?

Answer: C Var: 1 24) An electron is initially moving to the right when it enters a uniform electric field directed upwards, as shown in the figure. Which trajectory (X, Y, Z, or W) will the electron follow in the field?

A) trajectory W B) trajectory X C) trajectory Y D) trajectory Z Answer: D Var: 1

25) Four tiny charged particles (two having a charge +Q and two having a charge -Q) are distributed on the x- and y-axes as shown in the figure. Each charge is equidistant from the origin. In which direction is the net electric field at the point P on the y-axis?

A) directly up (in the +y direction) B) directly left (-x direction) C) upwards and towards the left D) upwards and towards the right E) The net field is zero, so there is no direction. Answer: C Var: 1 26) The figure shows two unequal charges, +q and -Q. Charge -Q has greater magnitude than charge +q. Point X is midway between the charges. In what section of the line will there be a point where the resultant electric field is zero?

A) VW B) WX C) XY D) YZ Answer: A Var: 1 27) The electric field at point P due to a point charge Q a distance R away from P has magnitude E. In order to double the magnitude of the field at P, you could A) double the distance to 2R. B) double the charge to 2Q. C) reduce the distance to R/2. D) reduce the distance to R/4. E) double the charge to 2Q and at the same time reduce the distance to R/2. Answer: B Var: 1

28) Three equal positive point charges +q are placed at the corners of a square of side d as shown in the figure. Which one of the arrows shown represents the direction of the net electric field at the center of the square?

A) A B) B C) C D) D Answer: A Var: 1 29) Three equal-magnitude point charges of varying signs are placed at the corners of a square of side d as shown in the figure. Which one of the arrows shown represents the direction of the net electric field at the center of the square?

A) A B) B C) C D) D Answer: A Var: 1

30) Three equal negative point charges -q are placed at three of the corners of a square of side d as shown in the figure. Which one of the arrows shown represents the direction of the net electric field at the center of the square?

A) A B) B C) C D) D Answer: C Var: 1 31) Three equal negative point charges -q are placed at three of the corners of a square of side d as shown in the figure. Which one of the arrows shown represents the direction of the net electric field at the vacant corner of the square?

A) A B) B C) C D) D Answer: B Var: 1

32) Three equal-magnitude point charges of varying signs are placed at three of the corners of a square of side d as shown in the figure. Which one of the arrows shown represents the direction of the net electric field at the vacant corner of the square?

A) A B) B C) C D) D Answer: B Var: 1 33) The figure shows electric field lines arising from two small charged particles P and Q. Consider the following two statements: (i) The charge on P is smaller than the charge on Q. (ii) The electrostatic force on P is smaller than the force on Q. Which of the above statements are true?

A) Only (i) is true. B) Only (ii) is true. C) Both (i) and (ii) are true. D) Neither (i) nor (ii) is true. Answer: A Var: 1

34) Two stationary point charges q1 and q2 are shown in the figure along with a sketch of some field lines representing the electric field produced by them. What can you deduce from the sketch?

A) q1 is negative and q2 is positive; the magnitudes are equal. B) q1 and q2 have the same sign; the magnitudes are equal. C) q1 is positive and q2 is negative; the magnitude of q1 is greater than the magnitude of q2. D) q1 is negative and q2 is positive; the magnitude of q1 is less than the magnitude of q2. E) q1 and q2 have the same sign; the magnitude of q1 is greater than the magnitude of q2. Answer: D Var: 1 35) A conductor is placed in a steady external electric field. Which of the following statements are correct for this situation? (There could be more than one correct choice.) A) The electric field is zero inside the conductor. B) All the free electrons go to the surface of the conductor. C) The surface of the conductor is neutral. D) The electric field just outside the surface of the conductor is perpendicular to the surface. E) None of the above statements are correct. Answer: A, B, D Var: 1 36) A solid aluminum cube rests on a wooden table in a region where a uniform external electric field is directed straight upward. What can we say concerning the charge on the top surface of the cube? A) The top surface is charged positively. B) The top surface is charged negatively. C) The top surface is neutral. D) The top surface's charge cannot be determined without further information. Answer: A Var: 1

37) Which one of the arrows shown in the figure best represents the direction of the electric field between the two uniformly charged metal plates?

A) A B) B C) C D) D E) None of the above Answer: A Var: 1 20.2 Problems 1) How many electrons are necessary to produce 1.0 C of negative charge? (e = 1.60 × 10-19 C) A) 6.3 × 1018 B) 6.3 × 109 C) 1.6 × 1019 D) 1.6 × 109 E) 6.0 × 1023 Answer: A Var: 1 2) A piece of plastic has a net charge of +2.00 μC. How many more protons than electrons does this piece of plastic have? (e = 1.60 × 10-19 C) A) 1.25 × 1013 B) 1.25 × 1019 C) 2.50 × 1013 D) 2.50 × 1019 E) 3.01 × 1023 Answer: A Var: 1 3) What is the charge on 1.0 kg of protons?(e = 1.60 × 10-19 C, mproton = 1.67 × 10-27 kg) A) 1.0 C B) 1000 C C) 9.6 × 107 C D) 6.0 × 1026 C E) 6.0 × 1023 C 15 Copyright © 2019 Pearson Education, Inc.

Answer: C Var: 1 4) If a charge generator builds a negative static charge of transferred to it during this process. (e = 1.60 × 10-19 C) A) 4.38 × 1013 B) 7.0 C) 1.12 × 10-18 D) 43.8 Answer: A Var: 6

how many electrons are

5) An asteroid of mass 58,000 kg carrying a negative charge of is from a second asteroid of mass carrying a negative charge of What is the magnitude of the net force the asteroids exert upon each other, assuming we can treat them as point particles? (G = 6.67 × 10-11 N ∙ m2/kg2, k = 1/4 πε0 = 8.99 × 109 N ∙ m2/C2) A) 0.000040 N B) 0.0062 N C) 570,000 N D) 510,000 N Answer: A Var: 50+ 6) Two electrons are apart at closest approach. What is the magnitude of the maximum electric force that they exert on each other? (e = 1.60 × 10-19 C, k = 1/4πε0 = 9.0 109 N ∙ m2/C2) A) 5.8 × 10-25 N B) 2.3 × 1010 N C) 2.3 N D) 5.8 × 10-27 N Answer: A Var: 10 7) The force of attraction that a -40.0 μC point charge exerts on a +108 μC point charge has magnitude 4.00 N. How far apart are these two charges? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2) A) 2.10 m B) 3.67 m C) 3.12 m D) 2.49 m E) 1.13 m Answer: C Var: 5

8) When 1.0-µC point charge is 15 m from a second point charge, the force each one experiences a force of 1.0 µN. What is the magnitude of the second charge? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) A) 25 C B) 1.0 C C) 10 nC D) 0.025 C E) 25 nC Answer: E Var: 1 9) Consider a container of 2.0 g of hydrogen, H2 (one mole). Suppose you removed all the electrons and moved them to the other side of the earth (Earth's radius is 6380 km, k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2, NA = 6.022 × 1023 molecules/mol, e = 1.60 × 10-19 C) (a) How much charge is left behind after you remove the electrons? (b) What electric force do the protons exert on the electrons after they are separated as described? Answer: (a) 1.9 × 105 C (b) 2.1 MN Var: 1 10) Two 10¢ coins (dimes) carrying identical charges are lying 2.5 m apart on a table. If each of these coins experiences an electrostatic force of magnitude 2.0 N due to the other coin, how large is the charge on each coin? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) A) 2.6 μC B) 26 μC C) 6.7 μC D) 5.2 μC E) 52 μC Answer: E Var: 1 11) Two point charges each experience a 1-N electrostatic force when they are 2 cm apart. If they are moved to a new separation of 8 cm, what is the magnitude of the electric force on each of them? A) 2 N B) 1/2 N C) 1/4 N D) 1/8 N E) 1/16 N Answer: E Var: 1

12) A proton is located at the point (x = 1.0 nm, y = 0.0 nm) and an electron is located at the point Find the magnitude of the electrostatic force that each one exerts on the other. (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2, e = 1.6 × 10-19 C) A) 1.4 × 10-11 N B) 5.3 × 10-18 N C) 5.3 × 108 N D) 5.9 × 10-15 N Answer: A Var: 9 13) The zirconium nucleus contains 40 protons, and an electron is 1.0 nm from the nucleus. What is the electric force on the electron due to the nucleus? ( e = 1.60 × 10-19 C, k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) A) 2.9 nN B) 1000 C C) 3.7 nN D) 6.8 nN E) 9.2 nN Answer: E Var: 1 14) Two tiny particles carrying like charges of the same magnitude are apart. If the electric force on one of them is what is the magnitude of the charge on each of these 9 particles?(k = 1/4πε0 = 9.0 × 10 N ∙ m2/C2) A) 2.4 × 10-2 C B) 2.4 × 10-8 C C) 4.5 × 104 C D) 2.4 × 10-5 C Answer: B Var: 50 15) How far apart should two protons be if the electrical force of repulsion on each one is equal to its weight on the earth? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2, e = 1.6 × 10-19 C, mproton = 1.67 × 10-27 kg) Answer: 12 cm Var: 1

16) Suppose you wanted to hold up an electron against the force of gravity by the attraction of a fixed proton some distance above it. How far above the electron would the proton have to be? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2, e = 1.6 × 10-19 C, mproton = 1.67 × 10-27 kg, melectron = 9.11 × 10-31 kg) A) 1.5 m B) 2.3 m C) 3.7 m D) 4.6 m E) 5.1 m Answer: E Var: 1 17) Two equally charged tiny spheres of mass 1.0 g are placed 2.0 cm apart. When released, they begin to accelerate away from each other at What is the magnitude of the charge on each sphere, assuming only that the electric force is present? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) A) 140 nC B) 120 nC C) 95 nC D) 75 nC Answer: A Var: 50+ 18) Two tiny particles having charges of +5.00 μC and +7.00 μC are placed along the x-axis. The +5.00-µC particle is at x = 0.00 cm, and the other particle is at x = 100.00 cm. Where on the xaxis must a third charged particle be placed so that it does not experience any net electrostatic force due to the other two particles? A) 4.58 cm B) 45.8 cm C) 50 cm D) 9.12 cm E) 91.2 cm Answer: B Var: 5 19) Two tiny particles having charges of +7.00 μC and -9.00 μC are placed along the y-axis. The +7.00-µC particle is at y = 0.00 cm, and the other particle is at y = 40.00 cm. Where must a third charged particle be placed along the y-axis so that it does not experience any net electric force due to the other two particles? A) 0.200 m B) 2.99 m C) -0.187 m D) -2.99 m E) 0.187 m Answer: D Var: 5 19 Copyright © 2019 Pearson Education, Inc.

20) A particle of charge +2q is placed at the origin and particle of charge -q is placed on the xaxis at x = 2a. Where on the x-axis can a third positive charge be placed so that the net electric force on it is zero? A) 3.4a B) 6.8a C) 8.6a D) 9.3a E) 1.0a Answer: B Var: 1 21) Two tiny beads, each of mass 3.2 g, carry equal-magnitude charges. When they are placed 6.4 cm apart and released in outer space, they begin to accelerate toward each other at 538 m/s2. What is the magnitude of the charge on each bead? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) A) 510 nC B) 44 nC C) 1800 nC D) 890 nC E) 1300 nC Answer: D Var: 1 22) Three point charges are located on the x-axis at the following positions: Q1 = +2.00 μC is at x = 1.00 m, Q2 = +3.00 μC is at x = 0.00, and Q3 = -5.00 μC is at x = -1.00 m. What is the magnitude of the electric force on Q2? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2) A) 0.0540 N B) 0.135 N C) 0.158 N D) 0.0810 N E) 0.189 N Answer: E Var: 1 23) Three point charges are placed on the x-axis, as follows. A charge of +2.0 μC is at the origin, a charge of -2.0 μC is at x = 50 cm, and a charge of +4.0 μC is at x = 100 cm. What are the magnitude and direction of the electrostatic force on the charge at the origin due to the other two charges? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) Answer: 0.072 N, toward the right Var: 1 24) A point charge Q1 = +6.0 nC is at the point (0.30 m, 0.00 m); a charge Q2 = -1.0 nC is at (0.00 m, 0.10 m), and a charge Q3 = +5.0 nC is at (0.00 m, 0.00 m). What are the magnitude and direction of the net force on the +5.0-nC charge due to the other two charges? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) Answer: 5.4 µN at 56° above -x-axis 20 Copyright © 2019 Pearson Education, Inc.

Var: 1 25) The three point charges +4.0 μC, -5.0 μC, and -9.0 μC are placed on the x-axis at the points x = 0 cm, x = 40 cm, and x = 120 cm, respectively. What is the x component of the electrostatic force on the -9.0 μC charge due to the other two charges? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) A) -0.55 N B) 0.55 N C) 0.64 N D) 0.41 N E) -0.41 N Answer: D Var: 5 26) One point charge +Q is placed at the center of a square, and a second point charge -Q is placed at the upper-left corner of the square. It is observed that an electrostatic force of magnitude 2.0 N acts on the positive charge at the center. Now a third charge -Q is placed at the lower-left corner of the square, as shown in the figure. What is the magnitude of the net force that acts on the center charge now?

A) 0.0 N B) 2.8 N C) 4.0 N D) 5.3 N Answer: B Var: 1 27) Three identical 3.0-µC charges are placed at the vertices of an equilateral triangle that measures 30 cm on a side. What is the magnitude of the electrostatic force on any one of the charges? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) A) 1.6 N B) 1.8 N C) 2.0 N D) 2.2 N E) 2.4 N Answer: A Var: 1

28) As shown in the figure, three charges are at the vertices of an equilateral triangle. The charge Q is 6.7 nC, and all the other quantities are accurate to two significant figures. What is the magnitude of the net electric force on the charge Q due to the other two charges? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)

A) 2.1 × 10-3 N B) 1.2 × 10-3 N C) 1.0 × 10-3 N D) 1.4 × 10-3 N Answer: A Var: 50+ 29) As shown in the figure, three charges are at corners of a rectangle. The charge in the bottom right corner is Q = - 90 nC, and all the other quantities are accurate to two significant figures. What is the magnitude of the net electrical force on Q due to the other two charges? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)

A) 3.8 × 10-2 N B) 2.8 × 10-2 N C) 5.3 × 10-2 N D) 7.1 × 10-2 N Answer: A Var: 19

30) As shown in the figure, three small charges are equally spaced on the arc of a circle that is centered at the charge Q, where Q = +23 nC and all the other quantities are accurate to two significant figures. What is the magnitude of the net electric force on the charge Q due to the other three charges? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)

A) 2.6 × 10-4 N B) 1.7 × 10-4 N C) 2.1 × 10-4 N D) 3.1 × 10-4 N Answer: A Var: 25 31) As shown in the figure, the charge Q is midway between two other charges. If what must be the charge q1 so that charge q2 remains stationary as Q and q1 are held in place?

A) 30 nC B) 15 nC C) 7.5 nC D) 60 nC Answer: A Var: 50+ 32) A point charge Q = -12 μC, and two other charges q2 and q2, are placed on x-y axes as shown in the figure. The electric force components on charge Q are Fx = +0.005 N and Fy = 0.003 N. (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2, e = 1.6 × 10-19 C) (a) How many excess electrons are there in charge Q? (b) What are the charges q1 and q2, including their signs?

Answer: (a) 7.5 × 1013 electrons

(b) q1 = +600 nC, q2 = -640 nC 23

Var: 1 33) As shown in the figure, charge q1 = 2.2 x is placed on the at

C is placed at the origin and charge Where along the x-axis can a third charge

Q = -8.30 × 10-6 C be placed so that the resultant force on Q is zero?

Answer: 0.89 m Var: 50+ 34) Two point charges q = -8.50 µC are fixed 10.0 cm apart along a horizontal bar, as shown in the figure. Their electrical forces will be used to balance the weight of a very small sphere carrying a charge 10.0 cm from each of them in a place where g = 9.80 m/s2. What is the greatest mass M this sphere can have without falling? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

Answer: 20.3 kg Var: 1 35) There is a +5.0-μC charge at three corners of a square having sides 70 mm long. What are the magnitude and direction of the net electrostatic force on +6.0 μC placed at the center of the square? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) Answer: 110 N toward the empty corner Var: 1

36) The figure shows two tiny 5.0-g spheres suspended from very light 1.0-m-long threads. The spheres repel each other after each one is given the same positive charge and hang at rest when θ = 4.1°. What is the charge on each sphere? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)

A) 22 nC B) 89 nC C) 360 nC D) 180 nC E) 45 nC Answer: B Var: 1 37) If a point charge of -30 µC experiences an electrostatic upward force of 27 mN at a certain location in the laboratory, what are the magnitude and direction of the electric field at that location? Answer: 0.90 kN/C downward Var: 1 38) A small object with a 5.0-μC charge is accelerating horizontally on a friction-free surface at 0.0050 m/s2 due only to an electric field. If the object has a mass of 2.0 g, what is the magnitude of the electric field? A) 2.0 N/C B) 4.0 N/C C) 0.0020 N/C D) 0.0040 N/C E) 1.0 N/C Answer: A Var: 1 39) A small 0.050-kg insulating sphere carries a charge of -60 μC and is hanging by a vertical silk thread from a fixed point in the ceiling. An external uniform vertical electric field is now applied. If the applied electric field has a magnitude of 3000 N/C and is directed downward, what is the tension in the silk thread? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) A) 0.19 N B) 0.31 N C) 0.41 N D) 0.52 N E) 0.71 N 25 Copyright © 2019 Pearson Education, Inc.

Answer: B Var: 1 40) A pair of charged conducting plates produces a uniform field of 12,000 N/C, directed to the right, between the plates. The separation of the plates is 40 mm. An electron is projected from plate A, directly toward plate B, with an initial speed of v0 = 2.0 × 107 m/s. What is the speed of the electron as it strikes plate B? (e = 1.6 × 10-19 C, melectron = 9.11 × 10-31 kg)

A) 1.2 × 107 m/s B) 1.5 × 107 m/s C) 1.8 × 107 m/s D) 2.1 × 107 m/s E) 2.4 × 107 m/s Answer: B Var: 1 41) An electron is projected with an initial velocity v0 = 8.4 × m/s along the y-axis, which is the centerline between a pair of charged plates, as shown in the figure. The plates are 1.0 m long and are separated by 0.10 m. A uniform electric field of magnitude E in the +x-direction is present between the plates. If the magnitude of the acceleration of the electron is measured to be what is the magnitude of the electric field between the plates? (e = 1.6 × 10-19 C, melectron = 9.11 × 10-31 kg)

A) 51,000 N/C B) 45,000 N/C C) 40,000 N/C D) 35,000 N/C E) 29,000 N/C Answer: A Var: 50+

42) What is the magnitude of a the vertical electric field that will balance the weight of a plastic sphere of mass that has been charged to -3.0 nC? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) A) 6.9 × 106 N/C B) 7.8 × 105 N/C C) 1.5 × 106 N/C D) 2.1 × 106 N/C Answer: A Var: 50+ 43) An electron is placed in a uniform electric field of 4.5 × 104 N/C that points to the right. (e = 1.6 × 10-19 C, melectron = 9.11 × 10-31 kg) (a) What are the magnitude and direction of the force on the electron? (b) If the electron is released from rest, what is its speed after 3.0 ps? Answer: (a) 7.2 × 10-15 N to the left (b) 24 km/s Var: 1 44) A proton is placed in an electric field of intensity 800 N/C. What are the magnitude and direction of the acceleration of the proton due to this field? (e = 1.60 × 10-19 C, mproton = 1.67 × 10-27 kg) A) 7.66 × m/ opposite to the electric field B) 7.66 × m/ opposite to the electric field C) 7.66 × m/ in the direction of the electric field D) 76.6 × m/ opposite to the electric field E) 76.6 × m/ in the direction of the electric field Answer: C Var: 5 45) A particle with a charge of +4.0 μC has a mass of 5.0 g. What magnitude electric field directed upward will exactly balance the weight of the particle? A) 4.1 × 104 N/C B) 8.2 × 104 N/C C) 4.4 × 104 N/C D) 1.2 × 104 N/C E) 5.1 × 104 N/C Answer: D Var: 1

46) A small styrofoam ball of mass 0.120 g is placed in an electric field of 6000 N/C pointing downward. What excess charge must be placed on the ball for it to remain suspended in the field? A) -16.0 nC B) -18.0 nC C) -57.2 nC D) -125 nC E) -196 nC Answer: E Var: 1 47) A small glass bead has been charged to 1.9 nC. What is the strength of the electric field 2.0 cm from the center of the bead? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2) A) 4.3 × 104 N/C B) 8.5 × 102 N/C C) 8.1 × 10-5 N/C D) 8.5 × 10-7 N/C Answer: A Var: 50+ 48) What is the magnitude of the electric field 2.8 cm from a tiny object that carries an excess charge of –16 nC? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) A) 180,000 N/C B) 5100 N/C C) 1.8 × 1014 N/C D) -180,000 N/C E) -5100 N/C Answer: A Var: 1 49) Two tiny particles having charges +20.0 μC and -8.00 μC are separated by a distance of 20.0 cm. What are the magnitude and direction of electric field midway between these two charges? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) A) 25.2 × N/C directed towards the negative charge B) 25.2 × N/C directed towards the positive charge C) 25.2 × N/C directed towards the negative charge D) 25.2 × N/C directed towards the positive charge E) 25.2 × N/C directed towards the negative charge Answer: A Var: 5

50) The electric field at a point 2.8 cm from a small object points toward the object with a strength of 180,000 N/C. What is the object's charge q? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2) A) -16 nC B) +16 nC C) -17 nC D) +17 nC Answer: A Var: 50+ 51) A +5.00-μC point charge is placed at the 0.0 cm mark of a meter stick and a -4.00-μC point charge is placed at the 50.0 cm mark. At what point on a line through the ends of the meter stick is the electric field equal to zero? A) 1.4 m from the 0 cm mark B) 2.5 m from the 0 cm mark C) 2.9 m from the 0 cm mark D) 3.3 m from the 0 cm mark E) 4.7 m from the 0 cm mark Answer: E Var: 1 52) A +5.0-μC point charge is placed at the 0 cm mark of a meter stick and a -4.0-μC charge is placed at the 50 cm mark. What is the net electric field at the 30 cm mark? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2) A) 4.0 × 105 N/C B) 5.0 × 105 N/C C) 9.0 × 105 N/C D) 1.4 × 106 N/C Answer: D Var: 1 53) An electric dipole consists of charges of ±6.00 µC that are 10.0 cm apart, as shown in the figure. Find the magnitude and direction of the electric field this dipole produces at point P, which is 7.00 cm from each charge. (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

Answer: 1.57 × 107 N/C, to the left parallel to the line connecting the two charges Var: 1 54) A thin spherical copper shell of radius 9.5 cm carries an excess charge of -4.2 nC. How many excess electrons are on (a) the outer surface of the shell, and (b) the inner surface? (e = 1.60 × 10-19 C) Answer: (a) 2.60 × 1010 electrons (b) zero Var: 1 29 Copyright © 2019 Pearson Education, Inc.

55) Two parallel square metal plates, 8.4 cm on each side, are 2.5 mm apart and carry equal but opposite charge uniformly distributed over their facing surfaces. How much excess charge is there on each plate if the electric field between the plates has a magnitude of 2.0 × 106 N/C? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2) Answer: 120 nC Var: 1 56) Two parallel square metal plates that are 1.5 cm apart and 22 cm on each side carry equal but opposite charges uniformly spread out over their facing surfaces. How many excess electrons are on the negative surface if the electric field between the plates has a magnitude of 18,000 N/C? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2, e = 1.6 × 10-19 C) Answer: 4.8 × 10-19 electrons Var: 1 57) A tiny 0.0250-µg oil drop containing 15 excess electrons is suspended between two horizontally closely-spaced metal plates that carry equal but opposite charges on their facing surfaces. The plates are both circular with a radius of 6.50 cm. (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2, e = 1.6 × 10-19 C) (a) How much excess charge must be on each plate to hold the oil drop steady? (b) Which plate must be positive, the upper one or the lower one? Answer: (a) 12.0 µC (b) upper plate Var: 1 58) Two large closely-spaced parallel metal plates are uniformly and oppositely charged and the electric field between them is 7.6 × 106 N/C. (a) What is the charge per unit area on each plate? (b) If the plates are now moved two times farther apart, what is the electric field between the plates? Answer: (a) ±67 µC/m 2 (b) 7.6 × 106 N/C (unchanged) Var: 1

College Physics: A Strategic Approach, 4e (Knight) Chapter 21 Electric Potential 21.1 Conceptual Questions 1) If the result of your calculation of a quantity has SI units kg ∙ m2/(s2 ∙ C), that quantity could be A) an electric field strength. B) a dielectric constant. C) an electric potential difference. D) a capacitance E) an electric potential energy. Answer: C Var: 1 2) If the result of your calculation of a quantity has SI units of kg ∙ m/(s2 ∙ C), that quantity could be A) an electric field strength. B) a dielectric constant. C) an electric potential difference. D) a capacitance E) an electric potential energy. Answer: A Var: 1 3) As a proton moves in the direction the electric field lines A) it is moving from low potential to high potential and gaining electric potential energy. B) it is moving from low potential to high potential and losing electric potential energy. C) it is moving from high potential to low potential and gaining electric potential energy. D) it is moving from high potential to low potential and losing electric potential energy. E) both its electric potential and electric potential energy remain constant. Answer: D Var: 1 4) As an electron moves in the direction the electric field lines A) it is moving from low potential to high potential and gaining electric potential energy. B) it is moving from low potential to high potential and losing electric potential energy. C) it is moving from high potential to low potential and gaining electric potential energy. D) it is moving from high potential to low potential and losing electric potential energy. E) both its electric potential and electric potential energy remain constant. Answer: C Var: 1

5) As a proton moves in a direction perpendicular to the electric field lines A) it is moving from low potential to high potential and gaining electric potential energy. B) it is moving from low potential to high potential and losing electric potential energy. C) it is moving from high potential to low potential and gaining electric potential energy. D) it is moving from high potential to low potential and losing electric potential energy. E) both its electric potential and electric potential energy remain constant. Answer: E Var: 1 6) A proton is accelerated from rest through a potential difference V0 and gains a speed v0. If it were accelerated instead through a potential difference of 2V0, what speed would it gain? A) 8v0 B) 4v0 C) 2v0 D) v0 Answer: D Var: 1 7) If the electric potential at a point in space is zero, then the electric field at that point must be A) negative. B) zero. C) uniform. D) positive. E) impossible to determine based on the information given. Answer: E Var: 1 8) The electron-volt is a unit of A) charge. B) electric potential. C) electric field. D) electric force. E) energy. Answer: E Var: 1

9) Four charged particles (two having a charge +Q and two having a charge -Q) are arranged in the xy-plane, as shown in the figure. These particles are all equidistant from the origin. The electric potential (relative to infinity) at point P on the z-axis due to these particles, is

A) zero. B) positive. C) negative. D) impossible to determine based on the information given. Answer: A Var: 1 10) The electric potential at a distance of 4 m from a certain point charge is 200 V relative to infinity. What is the potential (relative to infinity) at a distance of 2 m from the same charge? A) 200 V B) 50 V C) 400 V D) 100 V E) 600 V Answer: C Var: 1 11) The potential (relative to infinity) at the midpoint of a square is 3.0 V when a point charge of +Q is located at one of the corners of the square. What is the potential (relative to infinity) at the center when each of the other corners is also contains a point charge of +Q? A) 0 V B) 3.0 V C) 9.0 V D) 12 V Answer: D Var: 1

12) Two protons are released from rest, with only the electrostatic force acting. Which of the following statements must be true about them as they move apart? (There could be more than one correct choice.) A) Their electric potential energy keeps increasing. B) Their kinetic energy keeps increasing. C) Their electric potential energy keeps decreasing. D) Their kinetic energy keeps decreasing. E) Their acceleration keeps decreasing. Answer: B, C, E Var: 1 13) A proton and an electron are released from rest, with only the electrostatic force acting. Which of the following statements must be true about them as they move toward each other? (There could be more than one correct choice.) A) Their electric potential energy keeps increasing. B) Their kinetic energy keeps increasing. C) Their electric potential energy keeps decreasing. D) Their kinetic energy keeps decreasing. E) Their acceleration keeps decreasing. Answer: B, C Var: 1 14) Two protons are fired toward each other in a particle accelerator, with only the electrostatic force acting. Which of the following statements must be true about them as they move closer together? (There could be more than one correct choice.) A) Their electric potential energy keeps increasing. B) Their kinetic energy keeps increasing. C) Their electric potential energy keeps decreasing. D) Their kinetic energy keeps decreasing. E) Their acceleration keeps decreasing. Answer: A, D Var: 1

15) Four charged particles (two having a charge +Q and two having a charge -Q) are arranged in the xy-plane as shown in the figure. The charges are all equidistant from the origin. The amount of work required to move a positively charged particle from point P to point O (both of which are on the z-axis) is

A) zero. B) positive. C) negative. D) depends on the path in which the charged is moved. Answer: A Var: 1 16) A hydrogen atom consists of a proton and an electron. If the orbital radius of the electron increases, the electric potential energy of the electron due to the proton A) increases. B) decreases. C) remains the same. D) depends on the zero point of the potential. Answer: A Var: 1 17) A region of space contains a uniform electric field, directed toward the right, as shown in the figure. Which statement about this situation is correct?

A) The potential at all three locations is the same. B) The potentials at points A and B are equal, and the potential at point C is higher than the potential at point A. C) The potential at points A and B are equal, and the potential at point C is lower than the potential at point A. D) The potential at point A is the highest, the potential at point B is the second highest, and the potential at point C is the lowest. Answer: C Var: 1 5 Copyright © 2019 Pearson Education, Inc.

18) Which statements must be true about the surface of a charged conductor in which no charge is moving? (There could be more than one correct choice.) A) The electric field is zero at the surface. B) The electric potential of the surface is zero. C) The electric field is constant at the surface. D) The electric potential is constant over the surface. E) The electric field is perpendicular to the surface. Answer: D, E Var: 1 19) If the result of your calculations for a quantity has SI units of C2 ∙ s2/(kg ∙ m2), that quantity could be A) an electric potential difference. B) a dielectric constant. C) an electric field strength. D) a capacitance. E) an electric potential energy. Answer: D Var: 1 20) If the electric field between the plates of a given air-filled capacitor is weakened by removing charge from the plates, the capacitance of that capacitor A) increases. B) decreases. C) does not change. D) It cannot be determined from the information given. Answer: C Var: 1 21) Two ideal parallel-plate capacitors are identical in every respect except that one has twice the plate area of the other. If the smaller capacitor has capacitance C, the larger one has capacitance A) C/2. B) C. C) 2C. D) 4C. Answer: C Var: 1 22) An ideal parallel-plate capacitor has a capacitance of C. If the area of the plates is doubled and the distance between the plates is halved, what is the new capacitance? A) C/4 B) C/2 C) 2C D) 4C Answer: D Var: 1 6 Copyright © 2019 Pearson Education, Inc.

23) A battery charges a parallel-plate capacitor fully and then is removed. The plates are then slowly pulled apart. What happens to the potential difference between the plates as they are being separated? A) It increases. B) It decreases. C) It remains constant. D) It cannot be determined from the information given. Answer: A Var: 1 24) The plates of a parallel-plate capacitor are maintained with constant potential by a battery as they are pulled apart. During this process, the amount of charge on the plates A) must increase. B) must decrease. C) must remain constant. D) could either increase or decrease. There is no way to tell from the information given. Answer: B Var: 1 25) When a certain capacitor carries charges of ±10 µC on its plates, the potential difference cross the plates is 25 V. Which of the following statements about this capacitor are true? (There could be more than one correct choice.) A) If we double the charges on the plates to ±20 µC, the capacitance of the capacitor will also double. B) If we double the charges on the plates to ±20 µC, the potential difference across the plates will also double. C) If we double the charges on the plates to ±20 µC, the capacitance of the capacitor will not change. D) If we double the charges on the plates to ±20 µC, the potential difference across the plates will decrease by a factor of two. Answer: B, C Var: 1 26) An ideal parallel-plate capacitor having circular plates of diameter D that are a distance d apart stores energy U when it is connected across a fixed potential difference. If you want to triple the amount of energy stored in this capacitor by changing only the size of its plates, the diameter should be changed to A) 9D. B) 3D. C) D D) E) Answer: C Var: 1 7 Copyright © 2019 Pearson Education, Inc.

27) Which of the following will increase the capacitance of a parallel-plate capacitor? (There could be more than one correct choice.) A) a decrease in the plate area and an increase in the plate separation B) a decrease in the potential difference between the plates C) an increase in the potential difference between the plates D) an increase in the plate area and a decrease in the plate separation E) an increase in the charge on the plates Answer: D Var: 1 28) An ideal parallel-plate capacitor consists of two parallel plates of area A separated by a distance d. This capacitor is connected across a battery that maintains a constant potential difference between the plates. If the separation between the plates is now doubled, the magnitude of the charge on the plates will A) double. B) quadruple. C) be cut in half. D) be cut in fourth. E) not change. Answer: C Var: 1 29) An capacitor consists of two large parallel plates of area A separated by a very small distance d. This capacitor is connected to a battery and charged until its plates carry charges +Q and -Q, and then disconnected from the battery. If the separation between the plates is now doubled, the potential difference between the plates will A) double. B) quadruple. C) be cut in half. D) be cut in fourth. E) not change. Answer: A Var: 1 30) The plates of a parallel-plate capacitor are maintained with constant voltage by a battery as they are pulled apart. What happens to the strength of the electric field between the plates during this process? A) It increases. B) It decreases. C) It remains constant. D) It cannot be determined from the information given. Answer: B Var: 1

31) A parallel-plate capacitor is connected to a battery and becomes fully charged. The capacitor is then disconnected, and the separation between the plates is increased in such a way that no charge leaks off. As the plates are being separated, the energy stored in this capacitor A) increases. B) decreases. C) does not change. D) become zero. Answer: A Var: 1 32) Doubling the capacitance of a capacitor that is holding a constant charge causes the energy stored in that capacitor to A) quadruple. B) double. C) decrease to one-half. D) decrease to one-fourth. Answer: C Var: 1 33) Doubling the potential across a given capacitor causes the energy stored in that capacitor to A) quadruple. B) double. C) reduce to one-half. D) reduce to one-fourth. Answer: A Var: 1 34) An ideal parallel-plate capacitor consists of two parallel plates of area A separated by a distance d. This capacitor is connected to a battery that maintains a constant potential difference across the plates. If the separation between the plates is now doubled, the amount of electrical energy stored on the capacitor will A) double. B) quadruple. C) be cut in half. D) be cut in fourth. E) not change. Answer: C Var: 1

35) An ideal parallel-plate capacitor consists of two parallel plates of area A separated by a distance d. This capacitor is connected to a battery and charged until its plates carry charges +Q and -Q, and the battery is then disconnected. If the separation between the plates is now doubled, the electrical energy stored in the capacitor will A) double. B) quadruple. C) be cut in half. D) be cut in fourth. E) not change. Answer: A Var: 1 36) When a dielectric material is introduced between the plates of a parallel-plate capacitor and completely fills the space, the capacitance increases by a factor of 4. What is the dielectric constant of the material that was introduced? A) 0.4 B) 1/4 C) 2 D) 4 E) None of the other choices is correct. Answer: D Var: 1 37) A parallel-plate capacitor consists of a set of two parallel plates of area A separated by a distance d. This capacitor is connected to a battery that maintains a constant potential difference across the plates. A slab of a dielectric material is inserted in the region between the plates and completely fills it. What changes would you observe as the dielectric is inserted? (There could be more than one correct choice.) A) Only the charge on the plates of the capacitor would change. B) Only the capacitance would change. C) Both the charge on the plates of the capacitor and its capacitance would change. D) The potential difference across the plates would increase. E) Nothing would change. Answer: C Var: 1 38) Which of the following changes will increase the capacitance of a parallel-plate capacitor? (There could be more than one correct choice.) A) increase the charge on the plates B) decrease the potential between the plates C) increase the potential between the plates D) introduce a dielectric material between the plates E) decrease the separation between the plates Answer: D, E Var: 1

39) A dielectric material such as paper is inserted between the plates of a capacitor as the capacitor holds a fixed charge on its plates. What happens to the electric field between the plates as the dielectric is inserted? A) There is no change in the field. B) The field becomes stronger. C) The field becomes weaker. D) The field reduces to zero. Answer: C Var: 1 40) At a distance d from a point charge Q, the energy density in its electric field is u. If we double the charge, what is the energy density at the same point? A) 16u B) 8u C) 4u D) 2u E) u Answer: C Var: 1 41) At a distance d from a point charge Q, the energy density in its electric field is u. If we now go to a distance d/2 from the charge, what is the energy density at the new location? A) 16u B) 8u C) 4u D) 2u E) u Answer: A Var: 1

21.2 Problems 1) How much kinetic energy does a proton gain if it is accelerated, with no friction, through a potential difference of 1.00 V? The proton is 1836 times heavier than an electron, and e = 1.60 × 10-19 C. A) 1836 eV B) 1.00 eV C) 1.60 × 10-19 eV D) 1.00 J E) 1836 J Answer: B Var: 1 2) A tiny particle with charge + 5.0 μC is initially moving at 55 m/s. It is then accelerated through a potential difference of 500 V. How much kinetic energy does this particle gain during the period of acceleration? A) 1.0 × 104 J B) 2.5 × 10-3 J C) 100 J D) 2500 J Answer: B Var: 1 3) How much work must we do on an electron to move it from point A, which is at a potential of +50V, to point B, which is at a potential of -50 V, along the semicircular path shown in the figure? Assume the system is isolated from outside forces. (e = 1.60 × 10-19 C)

A) 1.6 J B) 1.60 × 10-17 J C) -1.60 × 10-17 J D) -1.6 J E) This cannot be determined because we do not know the distance traveled. Answer: B Var: 1

4) If an electron is accelerated from rest through a potential difference of 1500 V, what speed does it reach? (e = 1.60 × 10-19 C , melectron = 9.11 × 10-31 kg) A) 2.3 × 107 m/s B) 1.9 × 107 m/s C) 1.5 × 107 m/s D) 1.1 × 107 m/s Answer: A Var: 50+ 5) A proton that is initially at rest is accelerated through an electric potential difference of magnitude 500 V. How much kinetic energy does it gain? (e = 1.60 × 10-19 C) A) 500 J B) 8.0 × 10-17 J C) 1.6 × 10-19 J D) 800 J Answer: B Var: 1 6) A proton that is initially at rest is accelerated through an electric potential difference of magnitude 500 V. What speed does the proton gain? (e = 1.60 × 10-19 C , mproton = 1.67 × 1027 kg) A) 2.2 × 105 m/s B) 3.1 × 105 m/s C) 9.6 × 105 m/s D) 1.1 × 105 m/s Answer: B Var: 1 7) A proton with a speed of 2.0 x m/s accelerates through a potential difference and thereby increases its speed to 4.0 x m/s. Through what magnitude potential difference did the proton accelerate? (e = 1.60 × 10-19 C , mproton = 1.67 × 10-27 kg) A) 630 V B) 210 V C) 840 V D) 1000 V E) 100 V Answer: A Var: 24

8) After a proton with an initial speed of 1.50 × 105 m/s has increased its speed by accelerating through a potential difference of 0.100 kV, what is its final speed? (e = 1.60 × 10-19 C , mproton = 1.67 × 10-27 kg) A) 4.56 × 105 m/s B) 2.04 × 105 m/s C) 3.55 × 105 m/s D) 8.80 × 105 m/s E) 1.55 × 106 m/s Answer: B Var: 1 9) How much work is needed to carry an electron from the positive terminal to the negative terminal of a 9.0-V battery. (e = 1.60 × 10-19 C , melectron = 9.11 × 10-31 kg) A) 1.6 × 10-19 J B) 17 × 10-19 J C) 9.0 J D) 14.4 × 10-19 J E) 14.4 × 10-19 J/C Answer: D Var: 1 10) If it takes 50 J of energy to move 10 C of charge from point A to point B, what is the magnitude of the potential difference between points A and B? A) 500 V B) 50 V C) 5.0 V D) 0.50 V Answer: C Var: 4 11) A 4.0-g bead carries a charge of 20 μC. The bead is accelerated from rest through a potential difference V, and afterward the bead is moving at 2.0 m/s. What is the magnitude of the potential difference V? A) 800 kV B) 400 kV C) 800 V D) 400 V E) 200 V Answer: D Var: 1

12) If a Cu2+ ion that is initially at rest accelerates through a potential difference of 12 V without friction, how much kinetic energy will it gain? (e = 1.60 × 10-19 C) A) 3.0 eV. B) 6.0 eV. C) 12 eV. D) 24 eV. Answer: D Var: 1 13) A sphere with radius 2.0 mm carries a charge. What is the potential difference, between point B, which is from the center of the sphere, and point A, which is from the center of the sphere? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) A) 1500 V B) -1500 V C) 170 V D) -0.63 V Answer: A Var: 50+ 14) Two 3.0 μC charges lie on the x-axis, one at the origin and the other at What is the potential (relative to infinity) due to these charges at a point at on the x-axis? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) A) 11,000 V B) 9000 V C) 14,000 V D) 3400 V Answer: A Var: 30 15) A 6.9 μC negative point charge has a positively charged particle in an elliptical orbit about it. If the mass of the positively charged particle is and its distance from the point charge varies from to , what is the maximum potential difference through which the positive object moves? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) A) 12 MV B) 3.9 MV C) -5.2 MV D) 19 MV Answer: A Var: 50+

16) Two very small +3.00-μC charges are at the ends of a meter stick. Find the electric potential (relative to infinity) at the center of the meter stick. (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2) A) 0.00 V B) 2.70 × 104 V C) 5.40 × 104 V D) 1.08 × 105 V Answer: D Var: 1 17) Three point charges, -2.00 μC, +4.00 μC, and +6.00 μC, are located along the x-axis as shown in the figure. What is the electric potential (relative to infinity) at point P due to these charges? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

A) -307 kV B) +307 k V C) -154 kV D) +154 kV E) 0.00 kV Answer: B Var: 1

18) A +4.0-μC and a -4.0-μC point charge are placed as shown in the figure. What is the potential difference between points A and B? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)

A) 48 V B) 96 V C) 0 V D) 96 kV E) 48 kV Answer: D Var: 1 19) Four 2.0-µC point are at the corners of a rectangle with sides of length 3.0 cm and 4.0 cm. What is the electric potential (relative to infinity) at the midpoint of the rectangle? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) A) 1.3 MV B) 2.9 MV C) 3.5 MV D) 7.8 MV Answer: B Var: 1 20) A square is 1.0 m on a side. Point charges of +4.0 μC are placed in two diagonally opposite corners. In the other two corners are placed charges of +3.0 μC and -3.0 μC. What is the potential (relative to infinity) at the midpoint of the square? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) A) 1.0 × 104 V B) 1.0 × 105 V C) 1.0 × 106 V D) 0 V E) infinite Answer: B Var: 1

21) Two 5.0-µC point charges are 12 cm apart. What is the electric potential (relative to infinity) of this combination at the point where the electric field due to these charges is zero? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) A) 0.75 MV B) 1.5 MV C) 0.0 MV D) 25 MV E) 12.5 MV Answer: B Var: 1 22) A +5.0-µC point charge is 12 cm from a -5.0-µC point charge. What is the magnitude of the electric field they produce at the point on the line connecting them where their electric potential (relative to infinity) is zero? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) A) 0 N/C B) 12.5 MN/C C) 0.75 MN/C D) 25 MN/C E) 1.5 MN/C Answer: D Var: 1 23) The three point charges shown in the figure form an equilateral triangle with sides 4.9 cm long. What is the electric potential (relative to infinity) at the point indicated with the dot, which is equidistant from all three charges? Assume that the numbers in the figure are all accurate to two significant figures. (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)

A) 0.00 V B) 1300 V C) 640 V D) 1900 V Answer: A Var: 50+

24) Four +6.00-µC point charges are at the corners of a square 2.00 m on each side. What is the electric potential of these charges, relative to infinity, at the center of this square? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2) A) 76.4 kV B) 38.2 kV C) 306 kV D) 153 kV E) 61.0 kV Answer: D Var: 1 25) Four point charges of magnitude 6.00 μC and are at the corners of a square 2.00 m on each side. Two of the charges are positive, and two are negative. What is the electric potential at the center of this square, relative to infinity, due to these charges? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2) A) 76.4 kV B) 0 V C) 153 kV D) 61.0 kV E) 306 kV Answer: B Var: 1 26) Two +6.0-µC charges are placed at two of the vertices of an equilateral triangle having sides 2.0 m long. What is the electric potential at the third vertex, relative to infinity, due to these charges? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) A) 54 kV B) 108 V C) 0 V D) 90 kV E) 27 kV Answer: A Var: 1

27) Two point charges of +2.00 μC and +4.00 μC are at the origin and at the point x = 0.000 m, y = -0.300 m, as shown in the figure. What is the electric potential due to these charges, relative to infinity, at the point P at x = 0.400 m on the x-axis? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

A) 117 kV B) 15.7 kV C) 11.7 kV D) 56.0 kV E) 36.0 kV Answer: A Var: 1 28) Three point charges are placed at the following points in a horizontal x-y plane: is at is at and is at Calculate the electrical potential (relative to infinity) at the origin due to these three point charges. (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) Answer: 33,000 V Var: 50+ 29) Point charges +4.00 μC and +2.00 μC are placed at the opposite corners of a rectangle as shown in the figure. What is the potential at point A, relative to infinity, due to these charges? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

A) 0.899 kV B) 8.99 kV C) 89.9 kV D) 899 kV E) 8990 kV Answer: C Var: 1

30) Point charges +4.00 μC and +2.00 μC are placed at the opposite corners of a rectangle as shown in the figure. What is the potential at point B due to these charges? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

A) 8.99 kV B) 11.2 kV C) 89.9 kV D) 899 kV E) 112 kV Answer: E Var: 1 31) Point charges +4.00 μC and +2.00 μC are placed at the opposite corners of a rectangle as shown in the figure. What is the potential difference VA - VB? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

A) +203 kV B) -203 kV C) -22.5 kV D) +22.5 kV E) 0.00 kV Answer: C Var: 1 32) A very small 4.8-g particle carrying a charge of +9.9 μC is fired with an initial speed of directly toward a second small 7.8-g particle carrying a charge of + The second particle is held fixed throughout this process. If these particles are initially very far apart, what is the closest they get to each other? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) Answer: 3.0 m Var: 50+

33) Two tiny grains of sand having charges of 4.0 μC and -4.0 μC are situated along the x-axis at x1 = 2.0 m and x2 = -2.0 m. What is electric potential energy of these grains relative to infinity? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) A) -36 mJ B) 36 mJ C) 0 J D) -72 mJ E) 72 mJ Answer: A Var: 1 34) Two tiny particles having charges q1 = +56.0 nC and q2 = -46.0 nC are separated by and held in place, as shown in the figure. A third particle, having a charge of is placed at the point A, which is 0.18 m to the left of q2. How much work is needed to move the third particle from point A to point B, which is 0.40 m to the left of q1. All the points in the figure lie on the same line. (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) Answer: 8.2 × 10-5 J Var: 50+ 35) A 7.0-μC point charge and a work does it take to bring the point charge to the point A) 95 J B) 190 J C) 63 J D) 16 J Answer: A Var: 12

point charge are initially extremely far apart. How much point charge to the point , and the 9 (k = 1/4πε0 = 9.0 × 10 N ∙ m2/C2)

36) A +7.5-nC point charge is 5.0 cm from a -9.4-µC point charge in your laboratory in California. How much work would you have to do if you left the +7.5-nC charge in the lab but took the -9.4-µC charge to New York City? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) Answer: 13 mJ Var: 1

37) An alpha particle (a helium nucleus, having charge +2e and mass 6.64 × 10-27 kg) moves head-on at a fixed gold nucleus (having charge +79e). If the distance of closest approach is 2.0 × 10-10 m, what was the speed of the alpha particle when it was very far away from the gold? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2, e = 1.60 × 10-19 C) A) 2.3 × 105 m/s B) 4.6 × 105 m/s C) 2.3 × 106 m/s D) 4.6 × 106 m/s Answer: A Var: 1 38) How much energy is necessary to place three +2.0-µC point charges at the vertices of an equilateral triangle of side 2.0 cm if they started out extremely far away? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) A) 4.5 J B) 5.4 J C) 6.7 J D) 7.6 J Answer: B Var: 1 39) An electric dipole with ±5.0 μC point charges is positioned so that the positive charge is to the right of the origin and the negative charge is at the origin. How much work does it take to bring a point charge from very far away to the point x = 3.0 mm, y = 0.0 mm? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) A) 23 J B) 110 J C) 19 J D) 49 J Answer: A Var: 50+ 40) A +3.0-µC point charge is initially extremely far from a positive point charge Q. You find that it takes 41 J of work to bring the +3.0-µC charge to the point x = 3.0 mm, y = 0.0 mm and the point charge Q to the point x = -3.0 mm, y = 0.00 mm. What is Q? (k = …) A) 55 nC B) 9.1 µC C) 4.6 µC D) 27 pC Answer: B Var: 1

41) A point charge of +3.00 μC and a second charge Q are initially very far apart. If it takes of work to bring them to a final configuration in which the charge is at the point x = 1.00 mm, y = 1.00 mm, and the second charge Q is at the point x = 1.00 mm, y = 3.00 mm, find the magnitude of the charge Q. (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2) A) 2.15 μC B) 4.30 μC C) 10.74 μC D) 4.30 nC Answer: A Var: 50+ 42) A +5.0-nC charge is at the point (0.00 m, 0.00 m) and a -2.0-nC charge is at (3.0 m, 0.00 m). What work is required to bring a 1.0-nC charge from very far away to point (0.00 m, 4.0 m)? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) A) 15 nJ B) 3.6 nJ C) 11 nJ D) 7.7 nJ Answer: D Var: 1 43) In the figure, +4.0-μC and -4.0-μC point charges are located as shown. Now an additional +2.00-µC point charge is placed at point A. What is the electric potential energy of this system of three charges, relative to infinity? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

A) +264 mJ B) -264 mJ C) 0.00 J D) -26.4 mJ E) +26.4 mJ Answer: B Var: 1

44) A small 4.0-µC charge and a small 1.5-µC charge are initially very far apart. How much work does it take to bring them to a final configuration in which the 4.0-µC charge is at the point x = 1.0 mm, y = 1.0 mm, and the 1.5-µC charge is at the point x = 1.0 mm, y = 3.0 mm? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2) A) 27 J B) 13.5 kJ C) 54 J D) 13.5 J Answer: A Var: 1 45) Point charges +4.00 μC and +2.00 μC are placed at the opposite corners of a rectangle as shown in the figure. If these charges are released and are free to move with no friction, what is the maximum amount of kinetic energy they will gain? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

Answer: 80.4 mJ Var: 1 46) The figure shows a group of three particles, all of which have charge Q = 8.8 nC. How much work did it take to assemble this group of charges if they all started out extremely far from each other? (k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)

A) 5.5 × 10-5 J B) 6.2 × 10-5 J C) 5.7 × 10-5 J D) 5.9 × 10-5 J Answer: A Var: 1

47) The figure shows an arrangement of two particles each having charge Q = -6.8 nC and each separated by 5.0 mm from a proton.If the two particles are held fixed at their locations and the proton is set into motion as shown, what is the minimum speed the proton needs to totally escape from these particles? (mproton = 1.67 × 10-27 kg, e = 1.60 × 10-19 C, k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2)

A) 2.2 × 106 m/s B) 4.3 × 106 m/s C) 8.3 × 106 m/s D) 1.7 × 107 m/s Answer: A Var: 50+ 48) An electron is released from rest at a distance of 9.00 cm from a fixed proton. How fast will the electron be moving when it is 3.00 cm from the proton? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2, e = 1.60 × 10-19 C, melectron = 9.11 × 10-31 kg, mproton = 1.67 × 10-27 kg) A) 75.0 m/s B) 106 m/s C) 130 m/s D) 1.06 × 103 m/s E) 4.64 × 105 m/s Answer: B Var: 1 49) The potential difference between two square parallel plates is 4.00 V. If the plate separation is 6.00 cm and they each measure 1.5 m by 1.5 m, what is the magnitude of the electric field between the plates? Answer: 66.7 N/C Var: 1

50) In a region where the electric field is uniform and points in the +x direction, the electric potential is -2000 V at x = 8 m and is +400 V at x = 2 m. What is the magnitude of the electric field? A) 200 V/m B) 300 V/m C) 400 V/m D) 500 V/m E) 600 V/m Answer: C Var: 1 51) Two isolated copper plates, each of area 0.40 m2, carry opposite charges of magnitude 7.08 × 10-10 C. They are placed opposite each other in parallel alignment, with a spacing of 4.0 cm between them. What is the potential difference between the plates? (ε0 = 8.85 × 10-12 C2/N ∙ m2) A) 0.40 V B) 3.0 V C) 3.2 V D) 7.6 V E) 8.0 V Answer: E Var: 1 52) A space probe approaches a planet, taking measurements as it goes. If it detects a potential difference of 6000 MV between the altitudes of 253,000 km and 276,000 km above the planet's surface, what is the approximate electric field strength produced by the planet at 264,500 km above the surface? Assume the electric field strength is approximately constant at these altitudes. A) 261 N/C B) 0.261 N/C C) 561 N/C D) 493 μN/C Answer: A Var: 1 53) A spherical oil droplet with nine excess electrons is held stationary in an electric field between two large horizontal plates that are 2.25 cm apart. The field is produced by maintaining a potential difference of 0.3375 kV across the plates, and the density of the oil is 824 kg/m3. What is the radius of the oil drop? (e = 1.60 × 10-19 C) Answer: 8.61 µm Var: 1

54) A battery maintains the electrical potential difference of 6.0-V between two large parallel metal plates separated by 1.0 mm. What is the strength of the electric field between the plates? A) 6.0 V/m B) 600 V/m C) 6000 V/m D) zero Answer: C Var: 3 55) A uniform electric field, with a magnitude of 500 V/m, is points in the +x direction. If the potential at x = 5.0 m is 2500 V, what is the potential at x = 2.0 m? A) 0.50 kV B) 1.0 kV C) 2.0 kV D) 4.0 kV E) 5.0 kV Answer: D Var: 1 56) Consider a uniform horizontal electric field of 50 N/C directed toward the east. If the electric potential measured at a given point is 80 V, what is the potential at a point 1.0 m directly west of that point? A) 30 V B) 50 V C) 80 V D) 130 V Answer: D Var: 1 57) Consider a uniform horizontal electric field of 50 N/C directed toward the east. If the electric potential at a given point in the field is 80 V, what is the potential at a point 1.0 m directly east of the point? A) 15 V B) 30 V C) 90 V D) 130 V Answer: B Var: 1

58) Consider a uniform horizontal electric field of 50 N/C directed toward the east. If the electric potential at a given point in the field is 80 V, what is the potential at a point 1.0 m directly south of that point? A) 0 V B) 30 V C) 50 V D) 80 V Answer: D Var: 1 59) A proton moves 0.10 m along the direction of an electric field of magnitude 3.0 V/m. What is the change in kinetic energy of the proton? (e = 1.60 × 10-19 C) A) 4.8 × 10-20 J B) 3.2 × 10-20 J C) 1.6 × 10-20 J D) 8.0 × 10-21 J Answer: A Var: 1 60) Two very large parallel metal plates, separated by 0.20 m, are connected across a 12-V source of potential. An electron is released from rest at a location 0.10 m from the negative plate. When the electron arrives at a distance 0.050 m from the positive plate, how much kinetic energy has the electron gained? (e = 1.60 × 10-19 C) A) 2.4 × 10-19 J B) 4.8 × 10-19 J C) 7.2 × 10-19 J D) 9.6 × 10-19 J Answer: B Var: 1

61) The equipotential surfaces for two point charges are shown in the figure, with the value of potential marked on the line for each surface. (a) What is the potential difference, VG - VD, between points G and D? (b) What is the potential difference, VA - VG, between points A and G?

Answer: (a) -160 V Var: 1

(b) 320 V

62) The equipotential surfaces for two spherical conductors are shown in the figure, with the value of potential marked on the line for each surface. (a) If the distance between points A and B is 2.5 cm what is the approximate intensity of the electric field between these two points? (b) If the distance between points C and D is 2.5 cm what is the approximate intensity of the electric field between these two points?

Answer: (a) 8 V/m Var: 1

(b) 8 V/m

63) When the magnitude of the charge on each plate of an air-filled capacitor is 4 μC, the potential difference between the plates is 80 V. What is the capacitance of this capacitor? A) 0.1 µF B) 50 µF C) 100 µF D) 20 µF E) 50 nF Answer: E Var: 1 30 Copyright © 2019 Pearson Education, Inc.

64) What charge accumulates on the plates of a 2.0-μF air-filled capacitor when it is charged until the potential difference across its plates is 100 V? A) 50 μC B) 100 μC C) 150 μC D) 200 μC Answer: D Var: 3 65) The potential difference between the plates of an ideal air-filled parallel-plate capacitor with a plate separation of 6.0 cm is 60 V. What is the strength of the electric field between the plates of this capacitor? A) 60 V/m B) 500 V/m C) 1000 V/m D) 2000 V/m E) 3600 V/m Answer: C Var: 1 66) An ideal air-filled parallel plate capacitor with plate a separation of 4.0 cm has a plate area of 0.040 m2. What is the capacitance of this capacitor with air between these plates? (ε0 = 8.85 × 10-12 C2/N ∙ m2) A) 89 pF B) 8.9 pF C) 0.89 pF D) 8.9 µF E) 8.9 nF Answer: B Var: 1 67) An ideal air-filled parallel-plate capacitor with horizontal plates has a plate separation of 5.0 cm. If the potential difference between the plates is 2000 V, with the top plate at the higher potential, what are the magnitude and direction of the electric field between the plates? A) 100 N/C upward B) 100 N/C downward C) 40000 N/C upward D) 40000 N/C downward Answer: D Var: 1

68) Each plate of an ideal air-filled parallel-plate capacitor has an area of 0.0020 , and the separation of the plates is An electric field of is present between the plates. What is the surface charge density on the plates? (ε0 = 8.85 × 10-12 C2/N ∙ m2) A) 19 µC/m 2 B) 39 µC/m 2 C) 9.3 µC/m 2 D) 28 µC/m 2 E) 47 µC/m 2 Answer: A Var: 50+ 69) Each plate of an ideal air-filled parallel-plate capacitor has an area of 0.0010 , and the separation of the plates is An electric field of is present between the plates. What is the capacitance of this capacitor? (ε0 = 8.85 × 10-12 C2/N ∙ m2) A) 180 pF B) 120 pF C) 300 pF D) 240 pF E) 360 pF Answer: A Var: 50+ 70) Two large parallel plates are separated by 1.0 mm of air. If the potential difference between them is 3.0 V, what is the magnitude of their surface charge densities? (ε0 = 8.85 × 10-12 C2/N ∙ m2) A) 2.7 × 10-8 C/m2 B) 1.6 × 10-4 C/m2 C) 5.3 × 10-8 C/m2 D) 3.3 × 10-4 C/m2 Answer: A Var: 1 71) A 3.0-pFcapacitor consists of two large closely-spaced parallel plates that have surface charge densities of If the potential across the plates is with only air between them, find the surface area of each of the plates. (ε0 = 8.85 × 10-12 C2/N ∙ m2) A) 69 mm2 B) 0.014 mm2 C) 35 mm2 D) 0.0072 mm2 Answer: A Var: 50+

72) An ideal air-filled parallel-plate capacitor consists of two circular plates, each of radius How far apart should the plates be for the capacitance to be 300.0-pF? (ε0 = 8.85 × 1012 C2/N ∙ m2) A) 0.0083 μm B) 0.0042 μm C) 0.00094 μm D) 0.00047 μm Answer: A Var: 28 73) When the potential difference between the plates of an ideal air-filled parallel plate capacitor is 35 V, the electric field between the plates has a strength of 750 V/m. If the plate area is 4.0 × 10-2 m2, what is the capacitance of this capacitor? (ε0 = 8.85 × 10-12 C2/N ∙ m2) A) 7.6 × F B) 7.6 × F C) 7.6 × F D) 7.6 × F E) None of the other choices is correct. Answer: B Var: 5 74) An ideal air-filled parallel-plate capacitor consists of plates that are 1.0 mm apart and have an area of 1.5 × 10-4 m2. The capacitor is connected to a 12-V potential source (battery). (ε0 = 8.85 × 10-12 C2/N ∙ m2) (a) What is the capacitance of this capacitor? (b) How much charge is on each of its plates? (c) What is the strength of the electric field between the plates? Answer: (a) 1.3 pF (b) 16 pC (c) 12 kN/C Var: 1 75) An air-filled parallel-plate capacitor is constructed with a plate area of 0.40 m2 and a plate separation of 0.10 mm. It is then charged to a potential difference of 12 V? (ε0 = 8.85 × 10-12 C2/N ∙ m2) (a) How much charge is stored on each of its plates? (b) How much energy is stored in it? Answer: (a) 0.42 µC (b) 2.5 µJ Var: 1 76) A 12.0-V battery (potential source) is connected across a 6.00-µF air-filled capacitor. (a) How much energy can be stored this way? (b) How much excess charge is on each plate of the capacitor? Answer: (a) 432 µJ (b) 72.0 µC Var: 1

77) Measurements show that it takes 0.30 mJ of work to move 5.0-μC of charge from one plate to another of a certain air-filled capacitor while the potential difference between these plates is kept constant. What is the potential difference between the plates of this capacitor? A) 60 V B) 81 V C) 55 V D) 23 V E) 0 V Answer: A Var: 5 78) An air-filled 20-μF capacitor has a charge of 60 μC on its plates. How much energy is stored in this capacitor? A) 70 μJ B) 80 μJ C) 90 μJ D) 100 μJ E) 110 μJ Answer: C Var: 1 79) An air-filled capacitor has a potential difference between the plates of 80 V. If the charge on each of the plates of the capacitor has magnitude 8.0 μC, what is the electrical energy stored by this capacitor? A) 640 µJ B) 320 µJ C) 50 nJ D) 60 nJ E) 30 pJ Answer: B Var: 1 80) When a 4-μF capacitor has a potential drop of 20 V across its plates, how much electric potential energy is stored in this capacitor? A) 0.8 μJ B) 8 μJ C) 80 μJ D) 800 μJ E) 8000 μJ Answer: D Var: 1

81) When a 6.00-μF air-filled capacitor has a charge of ±40.0 μC on its plates, how much potential energy is stored in this capacitor? A) 103 μJ B) 113 μJ C) 123 μJ D) 133 μJ E) 143 μJ Answer: D Var: 5 82) An ideal, isolated, air-filled parallel-plate capacitor is not connected to a battery but has equal and opposite charges of 3.9 nC on its plates. The separation between the plates initially is 1.2 mm, and for this separation the capacitance is 3.1 × 10-11 F. How much work must be done to pull the plates apart until their separation becomes 7.7 mm? (ε0 = 8.85 × 10-12 C2/N ∙ m2) Answer: 1.3 µJ Var: 1 83) Two parallel circular plates, each with a radius of and carrying equal-magnitude surface charge densities of are separated by a distance of with only air between -12 2 them. How much energy is stored in these plates? (ε0 = 8.85 × 10 C /N ∙ m2) A) 78 nJ B) 25 nJ C) 7.9 nJ D) 250 nJ Answer: A Var: 36 84) Two parallel plates that are initially uncharged are separated by 1.7 mm, have only air between them, and each have surface areas of 16 cm2. How much charge must be transferred from one plate to the other if 1.9 J of energy are to be stored in the plates? (ε0 = 8.85 × 10-12 C2/N ∙ m2) A) 5.6 μC B) 4.0 μC C) 8.0 μC D) 0.60 mC Answer: A Var: 1 85) When a 12.0-V battery causes 2.00 μC of charge to flow onto the plates of an air-filled capacitor, how much work did the battery do? A) 24.0 μJ B) 12.0 μJ C) 144 μJ D) 576 J Answer: B Var: 1 35 Copyright © 2019 Pearson Education, Inc.

86) If you want to store 2.0 mJ of energy in a 10-μF capacitor, how much potential do you need to put across it? A) 5.0 V B) 10 V C) 15 V D) 20 V Answer: D Var: 1 87) A 5.0 μF capacitor has a potential difference of applied across its plates. If the potential difference across its plates is increased to how much additional energy does the capacitor store? A) 98 μJ B) 200 μJ C) 23 μJ D) 45 μJ Answer: A Var: 28 88) A 15-μF capacitor is connected to a 50-V battery and becomes fully charged. The battery is removed and a slab of dielectric, having a dielectric constant of 5.0, is inserted between the plates and completely fills the space between them. (a) What is the capacitance of the capacitor after the slab is inserted? (b) What is the potential difference across the capacitor with the dielectric inserted. Answer: (a) 75 µF (b) 10 V Var: 1 89) A 12.6-µF isolated capacitor is constructed with Teflon, having a dielectric constant of 2.1, between the plates. The capacitor is initially charged to 1.5 volts, and then the Teflon is removed. (a) How much excess charge was originally stored on the plates of the capacitor? (b) After removing the Teflon, what is the potential difference across the capacitor plates? Answer: (a) 19 µC (b) 3.2 V Var: 1 90) A parallel-plate capacitor consists of two parallel, square plates having dimensions 1.0 cm by 1.0 cm. The plates are separated by and the space between them is filled with Teflon, which has a dielectric constant of 2.1. What is the capacitance of this capacitor? (ε0 = 8.85 × 1012 C2/N ∙ m2) A) 1.9 pF B) 0.44 pF C) 2.1 pF D) 0.89 pF Answer: A Var: 5 36 Copyright © 2019 Pearson Education, Inc.

91) A parallel-plate capacitor with plate separation of 4.0 cm has a plate area of 6.0 × .What is the capacitance of this capacitor if a dielectric material with a dielectric constant of 2.4 is placed between the plates, completely filling the space? (ε0 = 8.85 × 10-12 C2/N ∙ m2) A) 3.7 × F B) 3.7 × F C) 16 × F D) 32 × F E) 32 × F Answer: E Var: 5 92) The square plates of a 5000-pF parallel-plate capacitor measure 50 mm by 50 mm and are separated by a dielectric that is thickand totally fills the region between the plates. The voltage rating (the maximum safe voltage) of the capacitor is What is the maximum energy that can be stored in this capacitor without damaging it? (ε0 = 8.85 × 10-12 C2/N ∙ m2) A) 0.40 mJ B) 0.50 mJ C) 0.60 mJ D) 0.70 mJ E) 0.80 mJ Answer: A Var: 50+ 93) The square plates of a 3000-pF parallel-plate capacitor measure 40 mm by 40 mm and are separated by a dielectric that is 0.29 mm thick and completely fills the region between the plates. What is the dielectric constant of the dielectric? (ε0 = 8.85 × 10-12 C2/N ∙ m2) A) 61 B) 56 C) 50 D) 45 E) 67 Answer: A Var: 1 94) An air-filled capacitor carries enough charge to store of potential energy. It is then accidentally filled with water in such a way as not to discharge its plates. How much energy does it continue to store after it is filled? The dielectric constant for water is 78 and for air it is 1.0006. A) 0.077 mJ B) 468 mJ C) 0.04 mJ D) 6.00 mJ Answer: A Var: 18

95) A capacitor has a voltage of applied across its plates, and then the voltage source is removed. What is the potential difference across its plates if the space between them is then filled with mica, having a dielectric constant of 5.4? A) 72 V B) 2110 V C) 641 V D) 18,675 V Answer: A Var: 50+ 96) A 6.0-μF air-filled capacitor is connected across a 100-V potential source (a battery). After the battery fully charges the capacitor, it is left connected and the capacitor is immersed in transformer oil, which has a dielectric constant of 4.5. How much additional charge flows from the battery onto the capacitor during this process? A) 1.2 mC B) 1.7 mC C) 2.1 mC D) 2.5 mC Answer: C Var: 1 97) A parallel-plate air-filled capacitor is made from two plates that are 0.070 m on each side and spaced 9.2 mm apart. What must the potential difference between the plates be to produce an energy density of in the region between them? (ε0 = 8.85 × 10-12 C2/N ∙ m2) Answer: 1100 V Var: 50+ 98) A uniform electric field has the strength of field? (ε0 = 8.85 × 10-12 C2/N ∙ m2) A) 2.2 × 10-10 J/m3 B) 3.1 × 10-11 J/m3 C) 2.8 × 1012 J/m3 D) 5.5 × 1012 J/m3 Answer: A Var: 5

What is the electric energy density of this

99) Each plate of a parallel-plate air-filled capacitor has an area of 0.0040 , and the separation of the plates is An electric field of is present between the plates. What is the energy density in the region between the plates? (ε0 = 8.85 × 10-12 C2/N ∙ m2) A) 300 J/ B) 200 J/ C) 400 J/ D) 500 J/ E) 610 J/ Answer: A Var: 50+ 100) What the electric energy density at a point 1.0 cm from a proton? (e = 1.6 × 10-19 C, ε0 = 8.85 × 10-12 C2/N ∙ m2, k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) Answer: 9.2 × 10-22 J/m3 Var: 1 101) A tiny particle carries a charge of What is the energy density in the electric field at a distance of from this charge? (ε0 = 8.85 × 10-12 C2/N ∙ m2, k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) A) 0.050 mJ/m3 B) 0.20 mJ/m3 C) 0.81 mJ/m3 D) 3.2 mJ/m3 Answer: A Var: 40 102) A -6.5-µC point charge is 8.0 cm from a -17-µC charge. What is the electric energy density at the point midway between them? (ε0 = 8.85 × 10-12 C2/N ∙ m2, k = 1/4πε0 = 9.0 × 109 N ∙ m2/C2) Answer: 1.5 × 104 J/m3 Var: 1 103) A 25.0-V potential source (a battery) is connected across the plates of a 6.66-µF air-filled parallel-plate capacitor having plates that are 1.22 mm apart. What energy density does it produce between the plates? (ε0 = 8.85 × 10-12 C2/N ∙ m2) Answer: 1.86 × J/m3 Var: 1

College Physics: A Strategic Approach, 4e (Knight) Chapter 22 Current and Resistance 22.1 Conceptual Questions 1) If a quantity you calculated has units of A ∙ s, what is that quantity? A) potential B) resistivity C) resistance D) capacitance E) charge Answer: E Var: 1 2) When current is flowing in an ordinary metal wire, the magnitude of the average velocity of the electrons is closest to A) 10 m/s. B) the speed of light. C) 1 mm/s. D) 1 km/s. E) 1 m/s. Answer: C Var: 1 3) When a current flows through a metal wire, the moving charges are A) only protons. B) only electrons. C) both protons and electrons. D) positive metal ions. E) negative metal ions. Answer: B Var: 1 4) When a current flows through an ionic liquid such as salty water, the moving charges are A) only protons. B) only electrons. C) only negative ions. D) only positive ions. E) both positive and negative ions. Answer: E Var: 1

5) If a quantity you calculated has units of Ω ∙ m what is that quantity? A) potential B) resistivity C) resistance D) capacitance E) charge Answer: A Var: 1 6) If a quantity you calculated has units of

, what is that quantity?

A) potential B) resistivity C) resistance D) capacitance E) charge Answer: A Var: 1 7) The figure shows electrons passing through a resistor. The arrow shows the direction in which the electrons are moving. Which of the following statements are correct? (There could be more than one correct choice.)

A) The electrons are moving slower at point b than at point a. B) The electric potential is higher at point b than at point a. C) The electric potential is lower at point b than at point a. D) The electrons are losing electric potential energy as they move through the resistor from a to b. E) The speed of the electrons at point b is the same as it is at point a. Answer: B, D, E Var: 1 8) The figure shows conventional current passing through a resistor. The arrow shows the direction in which this conventional current is flowing. Which of the following statements are correct? (There could be more than one correct choice.)

A) The charges are moving slower at point b than at point a. B) The electric potential is lower at point b than at point a. C) The electric potential is higher at point b than at point a. D) The current at point b is the same as the current at point a. E) The electric potential at point b is the same as it is at point a. Answer: B, D Var: 1 2 Copyright © 2019 Pearson Education, Inc.

9) For the graph shown in the figure, what physical quantity does the slope of the graph represent for ohmic material?

A) power B) resistivity C) 1/(resistivity) D) resistance E) 1/(resistance) Answer: D Var: 1 10) For the graph shown in the figure, what physical quantity does the slope of the graph represent for ohmic material?

A) power B) resistivity C) 1/(resistivity) D) resistance E) 1/(resistance) Answer: E Var: 1

11) For the graph shown in the figure, what physical quantity does the slope of the graph represent for ohmic material?

A) current B) resistivity C) 1/(current) D) power E) 1/(resistivity) Answer: A Var: 1 12) For the graph shown in the figure, what physical quantity does the slope of the graph represent for ohmic material?

A) current B) resistivity C) 1/(current) D) power E) 1/(resistivity) Answer: C Var: 1 13) You are given a copper bar of dimensions 3 cm × 5 cm × 8 cm and asked to attach leads to it in order to make a resistor. If you want to achieve the smallest possible resistance, you should attach the leads to the opposite faces that measure A) 3 cm × 5 cm. B) 3 cm × 8 cm. C) 5 cm × 8 cm. D) Any pair of faces produces the same resistance. Answer: C Var: 1

14) You are given a copper bar of dimensions 3 cm × 5 cm × 8 cm and asked to attach leads to it in order to make a resistor. If you want to achieve the largest possible resistance, you should attach the leads to the opposite faces that measure A) 3 cm × 5 cm. B) 3 cm × 8 cm. C) 5 cm × 8 cm. D) Any pair of faces produces the same resistance. Answer: A Var: 1 15) Copper wire #1 has a length L and a radius b. Copper wire #2 has a length 2L and a radius 2b. Which statement about the resistance across the ends of the wires is true? A) The resistance of wire #1 is twice as high as that of wire #2. B) The resistance of wire #1 is equal to that of wire #2. C) The resistance of wire #1 is half that of wire #2. D) The resistance of wire #1 is four times higher than that of wire #2. Answer: A Var: 1 16) The figure shows a graph of the resistance of a wire as a function of its length. What physical quantities does the slope of this graph represent?

A) the cross-sectional area of the wire B) the resistivity of the material of which the wire is made C) the product of the resistivity and the cross-sectional area of the wire D) the resistivity of the material divided by the cross-sectional area of the wire E) the reciprocal of the resistivity of the material Answer: D Var: 1 17) A wire of resistivity ρ must be replaced in a circuit by a wire of the same material but four times as long. If, however, the total resistance is to remain as before, the diameter of the new wire must A) be the same as the original diameter. B) be one-half the original diameter. C) be one-fourth the original diameter. D) be two times the original diameter. E) be four times the original diameter. Answer: D Var: 1

18) The length of a certain wire is kept same while its radius is doubled. What is the new resistance of this wire? A) It is increased by a factor of 2. B) It is increased by a factor of 4. C) It is reduced by a factor of 2. D) It is reduced by a factor of 4. E) It is reduced by a factor of 8. Answer: D Var: 1 19) The length of a certain wire is kept same while its radius is doubled. What is the new resistivity of this wire? A) It is increased by a factor of 2. B) It is increased by a factor of 4. C) It is reduced by a factor of 2. D) It is reduced by a factor of 4. E) It does not change. Answer: E Var: 1 20) The length of a certain wire is doubled while its radius is kept constant. What is the new resistance of this wire? A) It stays the same. B) It is 2 times as large. C) It is 3 times as large. D) It is 4 times as large. E) It is 1/2 as large. Answer: B Var: 1 21) The length of a certain wire is doubled and at the same time its radius is also doubled. What is the new resistance of this wire? A) It stays the same. B) It is 2 times as large. C) It is 4 times as large. D) It is 1/2 as large. E) It is 1/4 as large. Answer: D Var: 1

22) The length of a certain wire is doubled and at the same time its radius is reduced by a factor of 2. What is the new resistance of this wire? A) It is 2 times as large. B) It is 4 times as large. C) It is 6 times as large. D) It it 8 times as large. E) It is 1/2 as large. Answer: D Var: 1 23) If a quantity you calculated has units of

what is that quantity?

A) potential B) resistivity C) resistance D) capacitance E) current Answer: C Var: 1 24) If a quantity you calculated has units of

what is that quantity?

A) potential B) resistivity C) resistance D) capacitance E) current Answer: B Var: 1 25) Which one of the following quantities is equivalent to 1 Ω? A) 1 J/s B) 1 W/A C) 1 V ∙ A D) 1 V/A E) 1 A ∙ s Answer: D Var: 1

26) If the length and diameter of a wire of circular cross section are both tripled, the resistance will be A) unchanged. B) tripled. C) increased by a factor of 9. D) 1/3 of what it originally was. E) 1/9 of what it originally was. Answer: D Var: 1 27) Consider two copper wires of equal cross-sectional area. One wire has 3 times the length of the other. How do the resistivities of these two wires compare? A) Both wires have the same resistivity. B) The longer wire has 3 times the resistivity of the shorter wire. C) The longer wire has 9 times times the resistivity of the shorter wire. D) The longer wire has 27 times times the resistivity of the shorter wire. Answer: A Var: 1 28) Consider two copper wires of equal cross-sectional area. One wire has 3 times the length of the other. How do the resistances of these two wires compare? A) Both wires have the same resistance. B) The longer wire has 1/3 the resistance of the shorter wire. C) The longer wire has 3 times the resistance of the shorter wire. D) The longer wire has 9 times times the resistance of the shorter wire. E) The longer wire has 27 times times the resistance of the shorter wire. Answer: C Var: 1 29) Consider two copper wires of equal length. One wire has twice the cross-sectional area of the other. How do the resistances of these two wires compare? A) The thicker wire has twice the resistance of the thinner wire. B) The thicker wire has eight times the resistance of the thinner wire. C) The thicker wire has one-half the resistance of the thinner wire. D) The thicker wire has four times the resistance of the thinner wire. E) The thicker wire has one-fourth the resistance of the thinner wire. Answer: C Var: 1

30) Consider two copper wires with circular cross-sections and equal lengths. One wire has 3 times the diameter of the other. How do the resistances of these two wires compare? A) The thicker wire has 1/3 the resistance of the thinner wire. B) The thicker wire has 1/9 the resistance of the thinner wire. C) The thicker wire has 3 times the resistance of the thinner wire. D) The thicker wire has 9 times the resistance of the thinner wire. E) The thicker wire has times the resistance of the thinner wire. Answer: B Var: 1 31) When the current through a resistor is increased by a factor of 4, the power dissipated by the resistor A) decreases by a factor of 4. B) decreases by a factor of 16. C) increases by a factor of 16. D) increases by a factor of 4. E) increases by a factor of 2. Answer: C Var: 1 32) Which one of the following quantities is equivalent to 1 W? A) 1 V/A B) 1 Ω ∙ m C) 1 V ∙ A D) 1 V/Ω E) 1 A ∙ s Answer: C Var: 1 33) A kilowatt-hour is equivalent to A) 1000 W. B) 3600 J. C) 3,600,000 J/s. D) 3,600,000 J. E) 3600 J/s Answer: D Var: 1 34) If the resistance in a constant voltage circuit is doubled, the power dissipated by that circuit will A) increase by a factor of two. B) increase by a factor of four. C) decrease to one-half its original value. D) decrease to one-fourth its original value. Answer: C Var: 1 9 Copyright © 2019 Pearson Education, Inc.

35) If the voltage across a circuit of constant resistance is doubled, the power dissipated by that circuit will A) be four times as large. B) be two times as large. C) decrease to one-half the original power. D) decrease to one-fourth the original power. Answer: A Var: 1 36) If we double the resistance in a circuit but keep the current in it constant, the power dissipated by that circuit will A) be four times as great. B) be two times as great. C) be one-half as great. D) be one-fourth as great. Answer: B Var: 1 37) If the current flowing through a circuit of constant resistance is doubled, the power dissipated by that circuit will A) quadruple in magnitude. B) double in magnitude. C) decrease to one-half of what it was. D) decrease to one-fourth of what it was. Answer: A Var: 1 38) During a period of high power demand, the voltage output of the power company is reduced by 5.0%. By what percentage is the power in a resistor decreased? A) 2.5% B) 5.0% C) 10% D) 15% E) 90% Answer: C Var: 1

39) The figure shows a graph of the power dissipated in a resistor as a function of the resistance. What quantity does the slope of this graph represent?

A) the current in the resistor B) the potential difference across the resistor C) the reciprocal of the current in the resistor D) the square of the current in the resistor E) the resistivity of the resistor Answer: D Var: 1 40) For the graph shown in the figure, what physical quantity does the slope of the graph represent for a dc circuit?

A) resistivity B) resistance C) energy D) current E) capacitance Answer: D Var: 1

41) For the graph shown in the figure, what physical quantity does the slope of the graph represent for a dc circuit?

A) 1/(current) B) resistance C) 1/(resistance) D) current E) resistivity Answer: A Var: 1 42) For the graph shown in the figure, what physical quantity does the slope of the graph represent for a dc circuit?

A) 1/(resistance) B) resistance C) potential D) (potential)2 E) 1/(potential) Answer: C Var: 1

43) For the graph shown in the figure, what physical quantity does the slope of the graph represent for a dc circuit?

A) 1/(resistance) B) resistance C) potential D) (potential)2 E) 1/(potential) Answer: E Var: 1 22.2 Problems 1) A 10-A current flows through a wire for 2.0 min. (e = 1.60 × 10-19 C) (a) How much charge has passed through this wire? (b) How many electrons have passed any point in the wire? Answer: (a) 1200 C (b) 7.5 × 1021 Var: 1 2) If a charge of 11.4 C passes through a computer in 1.75 min, what is the average current through the computer? Answer: 0.109 A Var: 1 3) A current of 5.0 A flows through an electrical device for 10 seconds. How many electrons flow through this device during this time? (e = 1.60 × 10-19 C) A) 0.20 B) 20 C) 2.0 D) 3.1 x E) 31 x Answer: D Var: 5 4) What current is flowing in a wire if 0.67 C of charge pass a point in the wire in 0.30 s? A) 2.2 A B) 0.67 A C) 0.30 A D) 0.20 A Answer: A Var: 3 13 Copyright © 2019 Pearson Education, Inc.

5) A charge of 12 C passes through an electroplating apparatus in 2.0 min. What is the average current in the apparatus? A) 0.10 A B) 0.60 A C) 1.0 A D) 6.0 A Answer: A Var: 1 6) How much charge must pass by a point in a wire in 10 s for the current inb the wire to be 0.50 A? A) 20 C B) 2.0 C C) 5.0 C D) 0.050 C Answer: C Var: 3 7) A total of 2.0 × 1013 electrons pass a given point in a wire in 15 s. What is the current in the wire? (e = 1.60 × 10-19 C) A) 1.3 mA B) 1.3 A C) 0.21 μA D) 3.2 μA Answer: C Var: 1 8) What current is flowing in a resistor if 4.0 × 1016 electrons pass a point in the resistor in 0.50 s? (e = 1.60 × 10-19 C) A) 0.013 A B) 0.31 A C) 6.3 A D) 78 A Answer: A Var: 1 9) If 3.0 × 1015 electrons flow through a section of a wire of diameter 2.0 mm in 4.0 s, what is the current in the wire? (e = 1.60 × 10-19 C) A) 0.12 mA B) 0.24 mA C) 7.5 × 107 A D) 7.5 × 1014 A Answer: A Var: 1 14 Copyright © 2019 Pearson Education, Inc.

10) A electric heater that draws 13.5 A of dc current has been left on for 10 min. How many electrons that have passed through the heater during that time? (e = 1.60 × 10-19 C) A) 1.5 × 1022 B) 5.1 × 1022 C) 1.8 × 103 D) 8.1 × 103 E) 1.0 × 1023 Answer: B Var: 1 11) In an electroplating process, it is desired to deposit 40 mg of silver on a metal part by using a current of 2.0 A. How long must the current be allowed to run to deposit this much silver? The silver ions are singly charged, and the atomic mass of silver is 108 g/mol. (e = 1.60 × 10-19 C, NA = 6.02 × 1023 atoms/mol) A) 16 s B) 18 s C) 20 s D) 22 s Answer: B Var: 1 12) A jeweler needs to electroplate gold, having an atomic mass of 196.97 g/mol, onto a bracelet. He knows that the charge carriers in the ionic solution are singly-ionized gold ions, Au+, and has calculated that he must deposit of gold to reach the necessary thickness. How much current does he need to plate the bracelet in 3.0 hours? (e = 1.60 × 10-19 C, NA = 6.02 × 1023 atoms/mol) A) 9.1 mA B) 540 mA C) 33 A D) 1800 mA Answer: A Var: 50+ 13) What potential difference is required across an 8.0-Ω resistor to cause 2.0 A to flow through it? Answer: 16 V Var: 1 14) The current through a piece of lab equipment must be limited to 2.75 A when it is run by a 120-V dc power supply. What must be the resistance of this equipment? Answer: 43.6 Ω Var: 1

15) What potential difference is required to cause 4.00 A to flow through a resistance of 330 Ω? A) 12.1 V B) 82.5 V C) 334 V D) 1320 V Answer: D Var: 2 16) What is the voltage drop across a 5.0-Ω resistor if the current through it is 5.0 A? A) 100 V B) 25 V C) 4.0 V D) 1.0 V Answer: B Var: 2 17) A 4000-Ω resistor is connected across a 220-V power source. What current will flow through the resistor? A) 0.055 A B) 1.8 A C) 5.5 A D) 18 A Answer: A Var: 1 18) A light bulb operating at 110 V draws 1.40 A of current. What is its resistance? A) 12.7 Ω B) 78.6 Ω C) 109 Ω D) 154 Ω Answer: B Var: 1 19) A 12-V battery is connected across a 100-Ω resistor. How many electrons flow through the wire in 1.0 min? (e = 1.60 × 10-19 C) A) 1.5 × 1019 B) 2.5 × 1019 C) 3.5 × 1019 D) 4.5 × 1019 Answer: D Var: 1

20) The graph shown in the figure shows the results of measurements of the dc current through a circuit device for various potential differences across it. Assume that all the numbers shown are accurate to two significant figures. What is the resistance of this device?

Answer: 25 Ω Var: 1 21) The graph shown in the figure shows the results of measurements of the dc current through a circuit device for various potential differences across it. Assume that all the numbers shown are accurate to two significant figures. What is the resistance of this device?

Answer: 2.0 Ω Var: 1 22) When a thin copper wire that is 178 m long is connected between a 1.2-V potential difference, a current of 2.0 amps flows through the wire. What is the diameter of this wire? The resistivity of copper is 1.72 × 10-8 Ω ∙ m. Answer: 2.5 mm Var: 1 23) A 25-m wire of diameter 0.30 mm draws 0.499 A when connected across a 3.0-V potential difference. (a) What is the resistance of the wire? (b) What is the resistivity of the material from which the wire is made? Answer: (a) 6.0 Ω (b) 1.7 × 10-8 Ω ∙ m Var: 1

24) A certain metal wire has a cross-sectional area of 1.0 cm2 and a resistivity of 1.7 × 10-8 Ω ∙ m. How long would it have to be to have a resistance of 1.0 Ω? A) 5.9 × 106 m B) 5.9 m C) 5.9 × 104 m D) 590 m E) 5.9 km Answer: E Var: 1 25) What is the resistance of 1.0 m of a solid cylindrical metal cable having a diameter of 0.40 inches and a resistivity of 1.68 × 10-8 Ω ∙ m? A) 0.00012 Ω B) 0.00021 Ω C) 0.0012 Ω D) 0.0021 Ω Answer: B Var: 1 26) What is the resistance of a cylindrical metal rod 1.0 cm in diameter and 45 m long, if the resistivity of the metal is 1.4 × 10-8 Ω ∙ m? A) 0.0063 Ω B) 0.0080 Ω C) 0.80 Ω D) 6.3 Ω Answer: B Var: 1 27) A certain metal has a resistivity of 1.68 × 10-8 Ω ∙ m. You have a long spool of wire made from this metal. If this wire has a diameter of 0.15 mm, how long should you cut a segment so its resistance will be 15 Ω? A) 16 mm B) 16 cm C) 1.6 m D) 16 m Answer: D Var: 1 28) A 120-m long metal wire having a resistivity of 1.68 × 10-8 Ω ∙ m has a resistance of 6.0 Ω. What is the diameter of the wire? A) 0.065 mm B) 0.65 mm C) 0.65 cm D) 0.65 m Answer: B Var: 1 18 Copyright © 2019 Pearson Education, Inc.

29) A rod is 4.0 m long and has a square cross-section that is 1.5 cm on each side. An ohmmeter measures 0.040 Ω across its ends. What is the resistivity of the material from which this rod is made? A) 0.023 Ω ∙ m B) 0.015 Ω ∙ m C) 1.5 × 10-4 Ω ∙ m D) 2.3 × 10-6 Ω ∙ m Answer: D Var: 1 30) Calculate the current through a 10.0-m long 22-gauge nichrome wire with a radius of 0.321 mm if it is connected across a 12.0-V battery. The resistivity of the nichrome is 1.00 × 10-6 Ω ∙ m. A) 30.9 A B) 61.8 A C) 0.388 A D) 0.776 A Answer: C Var: 1 31) A metal bar is 20 cm long and has a rectangular cross-section measuring 1.0 cm × 2.0 cm. What is the voltage drop along its length when it carries a 4000-A current? The resistivity of the metal is 1.68 × 10-8 Ω ∙ m. A) 0.67 V B) 0.34 V C) 0.067 V D) 0.034 V Answer: C Var: 1 32) A 1.0-m length of nichrome wire has a radius of 0.50 mm and a resistivity of 1.0 × 10-6 Ω ∙ m. When this wire carries a current of 0.50 A, what is the voltage across its ends? A) 0.0030 V B) 0.32 V C) 0.64 V D) 1.6 V Answer: C Var: 1

33) A 1.0-mm diameter extension cord is made of metal having a resistivity of 1.68 × 10-8 Ω ∙ m. When it carries a current of 15 A, what is the potential difference between two points in the cord that are 100 m apart? A) 12 V B) 23 V C) 32 V D) 41 V Answer: C Var: 1 34) The resistivity of gold is at a temperature of 20°C. A gold wire that is 0.50 mm in diameter and 44 cm long carries a current of 380 mA. How many electrons each second pass a given cross section of the wire at 20°C? (e = 1.60 × 10-19 C) A) 2.4 × 1018 B) 2.4 × 1017 C) 1.2 × 1022 D) 2.8 × 1014 E) 6.3 × 1015 Answer: A Var: 50+ 35) How much current will be flowing through a length of copper wire with radius if it is connected to a source supplying The resistivity of the metal is 1.68 × 10-8 Ω ∙ m. A) 0 A B) 0 × 108 A C) 0 nA D) 0 A Answer: A Var: 50+ 36) When a 1.0-m length of metal wire is connected to a battery, a current of flows through it. What is the diameter of the wire? The resistivity of the metal is 2.24 × 10-8 Ω ∙ m. A) 12 μm B) 6.0 μm C) 24 μm D) 2.2 μm Answer: A Var: 38

37) The resistance of a 100-cm wire of cross sectional area 2 × resistivity of the material from which this wire is made? A) 0.80 × Ω∙m B) 8.0 × Ω∙m C) 0.80 × Ω∙m D) 0.80 × Ω∙m E) 8.0 × Ωv Answer: B Var: 5

is 400 Ω. What is the

38) The resistivity of the material of a wire is 1.76 × 10-8 Ω ∙ m. If the diameter of the wire is 2.00 mm and its length is 2.00 m, what is its resistance? A) 112 Ω B) 11.2 Ω C) 1.12 Ω D) 0.112 Ω E) 0.0112 Ω Answer: E Var: 1 39) The resistivity of a 1.0 m long copper wire is 1.72 × 10-8 Ω ∙ m and its cross sectional area is 2.0 × 10-6 m2. If the wire carries a current of 0.20 A, what is the voltage across the wire? A) 17 mV B) 0.90 mV C) 1.7 mV D) 10 mV E) 90 mV Answer: C Var: 1 40) How much current will flow through a it is connected to a power source supplying m. A) 0 A B) 0 x 108 A C) 0 nA D) 0 A Answer: A Var: 50+

length of metal wire with a radius of if The resistivity of the metal is 1.68 × 10-8 Ω ∙

41) When a potential difference is applied across a piece of wire made of metal A, a current flows. If the metal-A wire is replaced with a wire made of metal B having twice the diameter of the metal-A wire, how much current will flow through the metal-B wire? The lengths of both wires are the same, and the voltage difference remains unchanged. The resistivity of metal A is 1.68 × 10-8 Ω ∙ m, and the resistivity of metal B is 1.59 × 10-8 Ω ∙ m. A) 21 mA B) 19 mA C) 11 mA D) 5.3 mA Answer: A Var: 9 42) A tube of mercury with resistivity 9.84 × 10-7 Ω ∙ m has a uniform electric field of 23 N/C inside the mercury. How much current is flowing in the tube, if the radius of the tube is 0.495 mm? A) 18 A B) 180 A C) 29 A D) 280 A Answer: A Var: 1 43) The power rating of a 400-Ω resistor is 0.800 W. (a) What is the maximum safe voltage across this resistor? (b) What is the maximum current the resistor can safely draw? Answer: (a) 17.9 V (b) 44.7 mA Var: 1 44) A resistor operated at 120 V dc is rated at 1.40 kW. (a) What is the normal operating current through the resistor? (b) What is the resistance of the resistor? Answer: (a) 11.7 A (b) 10.3 Ω Var: 1 45) A flashlight draws 0.133 A from a 3.0-V battery pack. In 2.0 minutes (a) how much charge flows from the battery, (b) how much energy does the battery supply, and (c) how many electrons have passed any point in the circuit every second? Answer: (a) 16 C (b) 48 J (c) 8.3 × 1017 Var: 1 46) An instrument is rated at 250 W if it is connected across a 120-V dc power supply. (a) What current does it draw under normal operation? (b) What is its resistance? (c) How many kilowatt-hours does it use in a day if it is left on all the time? Answer: (a) 2.1 A (b) 58 Ω (c) 6.0 kWh Var: 1 22 Copyright © 2019 Pearson Education, Inc.

47) A 200-W light bulb is connected across a 110-V dc power supply. What current will flow through this bulb? A) 0.90 A B) 0.36 A C) 0 A D) 0.60 A E) 1.8 A Answer: E Var: 1 48) A 100-W resistance heater is connected to a 110-V dc source. What current flows through the heater? A) 1.1 A B) 2.2 A C) 3.3 A D) 4.4 A E) 0.91 A Answer: E Var: 1 49) A 100-W light bulb is operated by a 110-V dc source. What is the resistance of this bulb? A) 100 Ω B) 8.0 × 10-3 Ω C) 6.0 × 10-3 Ω D) 120 Ω E) 240 Ω Answer: D Var: 1 50) If the power rating of a 400-Ω resistor is 0.800 W, what is the maximum voltage that can safely be connected across the resistor? A) 110 V B) 17.9 V C) 170 V D) 1.80 V Answer: B Var: 1 51) If the power rating of a 400-Ω resistor is 0.80 W, what is the maximum current it can safely draw? A) 45 mA B) 18 mA C) 4.4 mA D) 2.0 mA E) 320 mA Answer: A Var: 1 23 Copyright © 2019 Pearson Education, Inc.

52) A light bulb operating at a dc voltage of 120 V has a power rating of 60 W. How much current is flowing through this bulb? A) 1.5 A B) 2.5 A C) 0.50 A D) 2.0 A E) 1.0 A Answer: C Var: 1 53) A light bulb operating at a dc voltage of 120 V has a resistance of 200 Ω. How much power is dissipated in this bulb? A) 100 W B) 60 W C) 72 W D) 14 mW E) 7.2 W Answer: C Var: 1 54) The power rating of a 400-Ω resistor is 0.25 W. What is the maximum voltage you can safely connect across its ends? A) 10 V B) 20 V C) 30 V D) 40 V E) 50 V Answer: A Var: 1 55) When 5.00 A is flowing through an 10.0-Ω device, how much power is being dissipated in the device? A) 50.0 W B) 250 W C) 500 W D) 2.50 kW Answer: B Var: 2

56) A resistance heater is rated at 1200 W when operating at 110 V dc. What current will it draw? A) 0.090 A B) 1.0 A C) 11 A D) 12 A Answer: C Var: 1 57) A 150-W light bulb is designed to operate at 110 V dc. How much current does it draw? A) 0.73 A B) 1.4 A C) 2.0 A D) 15 A Answer: B Var: 2 58) What is the resistance of a 0.100-kW light bulb designed to be used in a 120-V circuit dc? A) 12.0 Ω B) 144 Ω C) 1.2 Ω D) 0.83 Ω Answer: B Var: 1 59) A toaster is rated at 800 W when operating at 120 V dc. What is the resistance of its heating element? A) 16 Ω B) 18 Ω C) 6.7 Ω D) 0.15 Ω Answer: B Var: 1 60) A 200-Ω resistor is rated at 1/4 W. What is the maximum current it can safely draw? A) 0.035 A B) 0.35 A C) 50 A D) 0.25 A Answer: A Var: 1

61) A 25-W soldering iron runs on 110 V dc. What is its resistance? A) 0.0020 Ω B) 4.4 Ω C) 0.48 kΩ D) 2.8 kΩ Answer: C Var: 1 62) How much does it cost to operate a 25-W soldering iron for 8.0 hours if energy costs 8.0¢/kWh? A) $1.50 B) 25¢ C) 16¢ D) 1.6¢ Answer: D Var: 1 63) How much energy does a 100-W light bulb use in 8.0 hours? A) 0.0080 kWh B) 0.80 kWh C) 13 kWh D) 800 kWh Answer: B Var: 1 64) A 1500-W heater is connected to a 120-V line for 2.0 hours. How much heat energy is produced? A) 1.5 kJ B) 3.0 kJ C) 0.18 MJ D) 11 MJ Answer: D Var: 1 65) A battery is rated at 12 V and 160 A-h. How much energy does this battery store? A) 1.9 kJ B) 6.0 kJ C) 1.9 MJ D) 6.9 MJ Answer: D Var: 1

66) An electronic component with a 17-Ω resistor is rated for use at power levels not exceeding How much current can safely flow through the component? A) 0.91 A B) 1.21 A C) 238 A D) 0.22 A Answer: A Var: 50+ 67) A 100-W driveway light bulb is on 10 hours per day. If the power company charges 10¢ for each kilowatt-hour of electricity used, estimate the yearly cost to operate the bulb if it is used every day for a 365-day year. A) $3.65 B) $7.30 C) $37 D) $73 Answer: C Var: 1 68) A 400-W computer (including its monitor) is turned on for 8.0 hours per day. If electricity costs 10¢ per kWh, how much does it cost to run the computer annually for a 365-day year? A) $120 B) $1200 C) $15 D) $150 Answer: A Var: 1 69) The nichrome heating element in an electric drier operates on 240 V and generates heat at the rate of 2.0 kW. The heating element shorts out and, in repairing it, the repairman shortens the nichrome wire by 10%. (Assume the temperature is unchanged. In reality, the resistivity of the wire will depend on its temperature.) What effect will the repair have on the power dissipated in the heating element? A) The power is still 2.0 kW. B) The power increases to 2.2 kW. C) The power decreases to 1.8 kW. D) None of the given answers is correct. Answer: B Var: 1

70) When a 14.0-A current flows through an 8.00-Ω device for 24.0 hours, how much does this cost if energy costs $0.0900 per kW ∙ h? A) $0.24 B) $1.04 C) $2.16 D) $3.39 Answer: D Var: 1 71) A 9.0-V battery costs $1.49 and will run a portable CD player for 6.0 hours before running down and needing to be replaced. If this battery supplies a current of 25 mA to the player, what is the cost of the energy provided by the battery in dollars per kWh? A) $11/kWh B) $110/kWh C) $1100/kWh D) $11,000/kWh Answer: C Var: 1 72) A 200-Ω resistor is rated at 1/4 W. What is the maximum voltage that can safely be connected across it? A) 0.71 V B) 7.1 V C) 50 V D) 0.25 V Answer: B Var: 1 73) A simple circuit has a total resistance of 30 Ω. If a 2.0-A current is maintained in this circuit, how much energy is dissipated in this circuit in 4.0 seconds? A) 24 J B) 4.8 J C) 48 J D) 480 J E) 6.0 J Answer: D Var: 5

74) The resistivity of gold is at a temperature of 20°C. A gold wire, 1.8 mm in diameter and 14 cm long, carries a current of 480 mA. What power is dissipated in this wire at 20°C? A) 0.31 mW B) 0.077 mW C) 0.14 mW D) 0.19 mW E) 0.25 mW Answer: A Var: 50+ 75) A 120-Ω laboratory resistor is rated at 0.25 W. How much current can safely flow through the resistor? A) 30 A B) 2.1 mA C) 22 mA D) 46 mA Answer: D Var: 1 76) The voltage drop across a metal bar is much power does this bar dissipate? A) 50 mW B) 500 μW C) 2.5 kW D) 0.50 kW Answer: A Var: 35

while a current of

77) A battery is rated such that it provides much current can it deliver? A) 0.11 mA B) 81 kA C) 0.33 mA D) 9.1 kA Answer: A Var: 41

of power at

78) A device with a resistance of the device use? A) 0.50 mW B) 20,000 kW C) 0.050 mW D) 2000 kW Answer: A Var: 10

is connected to a

flows through it. How

when fully charged. How

battery. How much power does

79) A 6.0-V battery that can store of energy is connected to a resistor. How much charge must flow between the battery's terminals to completely drain the battery if it is fully charged? Assume that the voltage of the battery remains the same until it is totally drained. A) 83 C B) 0.010 C C) 3000 C D) 0.07 C Answer: A Var: 50 80) The heating element of a toaster is a 5.4-m length of nichrome wire of diameter 0.48 mm. The resistivity of nichrome at the operating temperature of the toaster is 1.3 × 10-6 Ω ∙ m. The toaster is designed to operate at a voltage of 120 V. How much power does it draw in normal operation? A) 370 W B) 360 W C) 380 W D) 400 W E) 410 W Answer: A Var: 50+ 81) A battery supplies 6.0 mA to a 12-Ω resistor for 1.5 h. How much electric energy does this resistor dissipate in this time? Answer: 2.3 J Var: 1 82) A 5.0-V battery storing 43.0 kJ of energy supplies of current to a circuit. How much energy does the battery have left after powering the circuit for A) 16 kJ B) 27 kJ C) 43 kJ D) 41 kJ Answer: A Var: 50+

College Physics: A Strategic Approach, 4e (Knight) Chapter 23 Circuits 23.1 Conceptual Questions 1) When two or more different capacitors are connected in series across a potential source, which of the following statements must be true? (There could be more than one correct choice.) A) The total voltage across the combination is the algebraic sum of the voltages across the individual capacitors. B) Each capacitor carries the same amount of charge. C) The equivalent capacitance of the combination is less than the capacitance of any of the capacitors. D) The potential difference across each capacitor is the same. E) The capacitor with the largest capacitance has the most charge. Answer: A, B, C Var: 1 2) Three identical capacitors are connected in series across a potential source (battery). If a charge of Q flows into this combination of capacitors, how much charge does each capacitor carry? A) 3Q B) Q C) Q/3 D) Q/9 Answer: B Var: 1 3) Three identical capacitors are connected in parallel to a potential source (battery). If a charge of Q flows into this combination, how much charge does each capacitor carry? A) 3Q B) Q C) Q/3 D) Q/9 Answer: C Var: 1 4) When two or more different capacitors are connected in parallel across a potential source (battery), which of the following statements must be true? (There could be more than one correct choice.) A) The potential difference across each capacitor is the same. B) Each capacitor carries the same amount of charge. C) The equivalent capacitance of the combination is less than the capacitance of any one of the capacitors. D) The capacitor with the largest capacitance has the largest potential difference across it. E) The capacitor with the largest capacitance has the most charge. Answer: A, E Var: 1 1 Copyright © 2019 Pearson Education, Inc.

5) A 5-µF, a 7-µF, and an unknown capacitor CX are connected in series between points a and b. What do you know about the equivalent capacitance Cab between a and b? (There could be more than one correct choice.) A) Cab > 12 µF B) 5 µF < Cab < 7 µF C) 5 µF < Cab < 12 µF D) Cab < 5 µF E) Cab < CX Answer: D, E Var: 1 6) A 5-µF, a 7-µF, and an unknown capacitor CX are connected in parallel between points a and b as shown in the figure. What do you know about the equivalent capacitance Cab between a and b? (There could be more than one correct choice.)

A) Cab > 12 µF B) Cab > CX C) 5 µF < Cab < 12 µF D) Cab < 5 µF E) Cab < CX Answer: A, B Var: 1 7) Suppose you have two capacitors and want to use them to store the maximum amount of energy by connecting them across a voltage source. You should connect them A) in series across the source. B) in parallel across the source. C) It doesn't matter because the stored energy is the same either way. Answer: B Var: 1 8) Four unequal resistors are connected in series with each other. Which one of the following statements is correct about this combination? A) The equivalent resistance is equal to that of any one of the resistors. B) The equivalent resistance is equal to average of the four resistances. C) The equivalent resistance is less than that of the smallest resistor. D) The equivalent resistance is less than that of the largest resistor. E) The equivalent resistance is more than the largest resistance. Answer: E Var: 1 2 Copyright © 2019 Pearson Education, Inc.

9) Four unequal resistors are connected in a parallel with each other. Which one of the following statements is correct about this combination? A) The equivalent resistance is less than that of the smallest resistor. B) The equivalent resistance is equal to the average of the four resistances. C) The equivalent resistance is midway between the largest and smallest resistance. D) The equivalent resistance is more than the largest resistance. E) None of the other choices is correct. Answer: A Var: 1 10) Draw a circuit with two batteries, a resistor between them, and a capacitor in parallel with the resistor. The batteries are connected negative pole to positive pole.

Answer: A Var: 1

11) Draw a circuit consisting of a battery connected to two resistors, R1 and R2, in series with each other and a capacitor C connected across the resistors.

Answer: A Var: 1

12) Draw a circuit with a battery connected to four resistors, R1, R2, R3, and R4, as follows. Resistors R1 and R2 are connected in parallel with each other, resistors R3 and R4 are connected in parallel with each other, and both parallel sets of resistors are connected in series with each other across the battery.

Answer: A Var: 1 13) When unequal resistors are connected in parallel in a circuit, A) the same current always runs through each resistor. B) the potential drop is always the same across each resistor. C) the largest resistance has the largest current through it. D) the power generated in each resistor is the same. Answer: B Var: 1

14) When unequal resistors are connected in series across an ideal battery, A) the same power is dissipated in each one. B) the potential difference across each is the same. C) the current flowing in each is the same. D) the equivalent resistance of the circuit is less than that of the smallest resistor. E) the equivalent resistance of the circuit is equal to the average of all the resistances. Answer: C Var: 1 15) You obtain a 100-W light bulb and a 50-W light bulb. Instead of connecting them in the normal way, you devise a circuit that places them in series across normal household voltage. If each one is an incandescent bulb of fixed resistance, which statement about these bulbs is correct? A) Both bulbs glow with the same brightness, but less than their normal brightness. B) Both bulbs glow with the same brightness, but more than their normal brightness. C) The 100-W bulb glows brighter than the 50-W bulb. D) The 50-W bulb glows more brightly than the 100-W bulb. Answer: D Var: 1 16) As more resistors are added in series to a constant voltage source, the power supplied by the source A) increases. B) decreases. C) does not change. D) increases for a time and then starts to decrease. Answer: B Var: 1 17) As more resistors are added in parallel across a constant voltage source, the power supplied by the source A) increases. B) decreases. C) does not change. D) increases for a time and then starts to decrease. Answer: A Var: 1

18) When different resistors are connected in parallel across an ideal battery, we can be certain that A) the same current flows in each one. B) the potential difference across each is the same. C) the power dissipated in each is the same. D) their equivalent resistance is greater than the resistance of any one of the individual resistances. E) their equivalent resistance is equal to the average of the individual resistances. Answer: B Var: 1 19) The lamps in a string of decorative lights are connected in parallel across a constant-voltage power source. What happens if one lamp burns out? (Assume negligible resistance in the wires leading to the lamps.) A) The brightness of the lamps will not change appreciably. B) The other lamps get brighter equally. C) The other lamps get brighter, but some get brighter than others. D) The other lamps get dimmer equally. E) The other lamps get dimmer, but some get dimmer than others. Answer: A Var: 1 20) A 9-V battery is hooked up to two resistors in series using wires of negligible resistance. One has a resistance of 5 Ω, and the other has a resistance of 10 Ω. Several locations along the circuit are marked with letters, as shown in the figure. Which statements about this circuit are true? (There could be more than one correct choice.)

A) The current is exactly the same at points A, B, C, and D. B) The current at A is greater than the current at B, which is equal to the current at C, which is greater than the current at D. C) The current at A is greater than the current at B, which is greater than the current at C, which is greater than the current at D. D) The potential at B is equal to the potential at C. E) The potential at D is equal to the potential at C. Answer: A, D Var: 1

21) A 9-V battery is hooked up to two resistors in series. One has a resistance of 5 Ω, and the other has a resistance of 10 Ω. Several locations along the circuit are marked with letters, as shown in the figure. Through which resistor is energy being dissipated at the higher rate?

A) the 10-Ω resistor B) the 5-Ω resistor C) Energy is being dissipated by both resistors at the same rate. Answer: A Var: 1 22) Identical light bulbs can be attached to identical ideal batteries in three different ways (A, B, or C), as shown in the figure. The ranking (from lowest to highest) of the total power produced by the battery is

A) B, A, C B) A, B, C C) C, B, A D) A, C, B E) C, A, B Answer: A Var: 1

23) Identical ideal batteries are connected in different arrangements to the same light bulb, as shown in the figure. For which arrangement will the bulb shine the brightest?

A) A B) B C) C Answer: C Var: 1 24) A resistor is made out of a wire having a length L. When the ends of the wire are attached across the terminals of an ideal battery having a constant voltage V0 across its terminals, a current I flows through the wire. If the wire were cut in half, making two wires of length L/2, and both wires were attached across the terminals of the battery (the right ends of both wires attached to one terminal, and the left ends attached to the other terminal), how much current would the battery put out? A) 4I B) 2I C) I D) I/2 E) I/4 Answer: A Var: 1

25) In the circuit shown in the figure, the resistor R has a variable resistance. As R is decreased, what happens to the currents?

A) I1 remains unchanged and I2 increases. B) I1 decreases and I2 decreases. C) I1 decreases and I2 increases. D) I1 increases and I2 decreases. E) I1 increases and I2 increases. Answer: C Var: 1 26) Kirchhoff's junction rule is a statement of A) the law of conservation of momentum. B) the law of conservation of charge. C) the law of conservation of energy. D) the law of conservation of angular momentum. E) Newton's second law. Answer: B Var: 1 27) Kirchhoff's loop rule is a statement of A) the law of conservation of momentum. B) the law of conservation of charge. C) the law of conservation of energy. D) the law of conservation of angular momentum. E) Newton's second law. Answer: C Var: 1 28) For the circuit shown in the figure, write the Kirchhoff current equation for the node labeled A. Notice the directions of the currents!

Answer: I1 - I2 + I3 = 0 Var: 1

29) For the circuit shown in the figure, write the Kirchhoff loop equation for the entire outside loop. Notice the directions of the currents!

Answer: V1 + I3R3 - V3 - I1R1 = 0 Var: 1 30) A resistor, an uncharged capacitor, a dc voltage source, and an open switch are all connected in series. The switch is closed at time t = 0 s. Which one of the following is a correct statement about this circuit? A) The charge on the capacitor after four time constants is about 98% of the maximum value. B) The charge on the capacitor after one time constant is 50% of its maximum value. C) The charge on the capacitor after one time constant is 1/e of its maximum value. D) The voltage on the capacitor after one time constant is 1/e of the maximum value. E) The voltage on this capacitor after one time constant is 100% of its maximum value. Answer: A Var: 1 31) A capacitor C is connected in series with a resistor R across a battery and an open switch. If a second capacitor of capacitance 2C is connected in parallel with the first one, the time constant of the new RC circuit will be A) the same as before. B) twice as large as before. C) three times a large as before. D) one-half as large as before. E) one-fourth as large as before. Answer: C Var: 1 32) A capacitor C is connected in series with a resistor R across a battery and an open switch. If a second capacitor of capacitance 2C is connected in series with the first one, the time constant of the new RC circuit will be A) the same as before. B) larger than before. C) smaller than before. D) variable. Answer: C Var: 1

33) A resistor, an uncharged capacitor, a dc voltage source, and an open switch are all connected in series. The switch is closed at time t = 0 s. Which one of the following is a correct statement about the circuit? A) The capacitor charges to its maximum value in one time constant. B) The capacitor charges to its maximum value in two time constants. C) The potential difference across the resistor is always equal to the potential difference across the capacitor. D) Current flows through the circuit even after the capacitor is essentially fully charged. E) Once the capacitor is essentially fully charged, there is no current in the circuit. Answer: E Var: 1 34) A charged capacitor is connected in series with a resistor and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the charge Q on the capacitor as a function of time t?

Answer: B Var: 1

35) An uncharged capacitor is connected in series with a resistor, a dc battery, and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the charge Q on the capacitor as a function of time t?

Answer: A Var: 1 36) A charged capacitor is connected in series with a resistor and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the current I through the resistor as a function of time t?

Answer: B Var: 1

37) An uncharged capacitor is connected in series with a resistor, a dc battery, and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the current I through the resistor as a function of time t?

Answer: B Var: 1 38) A charged capacitor is connected in series with a resistor and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the potential difference V across the resistor as a function of time t?

Answer: B Var: 1

39) An uncharged capacitor is connected in series with a resistor, a dc battery, and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the potential difference V across the resistor as a function of time t?

Answer: B Var: 1 40) A charged capacitor is connected in series with a resistor and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the potential difference V across the capacitor as a function of time t?

Answer: B Var: 1

41) An uncharged capacitor is connected in series with a resistor, a dc battery, and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the potential difference V across the capacitor as a function of time t?

Answer: A Var: 1 23.2 Problems 1) A 4.0-µF capacitor and an 8.0-µF capacitor are connected together. What is the equivalent capacitance of the combination if they are connected (a) in series or (b) in parallel? Answer: (a) 2.7 µF (b) 12.0 µF Var: 1 2) You have three capacitors with capacitances of 4.00 μF, 7.00 μF, and 9.00 μF. What is the equivalent capacitance if they are connected (a) in series and (b) in parallel? Answer: (a) 1.98 µF (b) 20.00 µF Var: 1 3) A network of capacitors is connected across a potential difference V0 as shown in the figure. (a) What should V0 be so that the 60.0-µF capacitor will have 18.0 µC of charge on each of its plates? (b) Under the conditions of part (a), how much total energy is stored in this network of capacitors?

Answer: (a) 1.50 V Var: 1

(b) 13.5 μJ

4) A network of capacitors is mostly inside a sealed box, but one capacitor CX is sticking out, as shown in the figure. When you connect a multimeter across points a and b, it reads 27.0 µF. What is CX?

A) 27.0 µF B) 23.0 µF C) 4.0 µF D) 2.4 µF E) 2.2 µF Answer: C Var: 1 5) A 5.0-μF capacitor and a 7.0-μF capacitor are connected in series across an 8.0-V potential source. What is the potential difference across the 5.0-μF capacitor? A) 0 V B) 8.0 V C) 2.7 V D) 3.6 V E) 4.7 V Answer: E Var: 5 6) A 2.0-μF capacitor and a 4.0-μF capacitor are connected in series across an 8.0-V potential source. What is the charge on the 2.0-μF capacitor? A) 2.0 μC B) 4.0 μC C) 12 μC D) 11 μC E) 25 μC Answer: D Var: 5

7) Three capacitors are connected as shown in the figure. What is the equivalent capacitance between points A and B?

A) 12 μF B) 4.0 μC C) 7.1 μF D) 1.7 μF E) 8.0 μF Answer: D Var: 1 8) A system of four capacitors is connected across a 90-V voltage source as shown in the figure. What is the equivalent capacitance of this system?

A) 1.5 μF B) 15 μF C) 3.6 μF D) 3.3 μF Answer: D Var: 1

9) A system of four capacitors is connected across a 90-V voltage source as shown in the figure. (a) What is the charge on the 4.0-µF capacitor? (b) What is the charge on the 2.0-µF capacitor?

Answer: (a) 120 µC Var: 1

(b) 120 µC

10) A system of four capacitors is connected across a 90-V voltage source as shown in the figure. (a) What is the potential difference across the plates of the 6.0-µF capacitor? (b) What is the charge on the 3.0-µF capacitor?

Answer: (a) 30 V Var: 1

(b) 180 µC

11) A 5.0-μF, a 14-μF, and a capacitor are connected in parallel. How much capacitance would a single capacitor need to have to replace the three capacitors? A) 40 μF B) C) 5.0 μF D) 14 μF Answer: A Var: 50+

12) A 5.0-μF, a 14-μF, and a 21-μF capacitor are connected in series. How much capacitance would a single capacitor need to have to replace the three capacitors? A) 40 μF B) 3.6 μF C) 2.0 μF D) 3.1 μF Answer: D Var: 1 13) A 5.0-μF and a 12.0-μF capacitor are connected in series, and the series arrangement is connected in parallel to a capacitor. How much capacitance would a single capacitor need to replace this combination of three capacitors? A) 33 μF B) 13 μF C) 16 μF D) 38 μF Answer: A Var: 50+ 14) Four 16-μF capacitors are connected in combination. What is the equivalent capacitance of this combination if they are connected (a) in series? (b) in parallel? (c) such that two of them are in parallel with each other and that combination is in series with the remaining two capacitors? Answer: (a) 4.0 µF (b) 64 µF (c) 6.4 µF Var: 1 15) Three capacitors of capacitance 5.00 μF, 10.0 μF, and 50.0 μF are connected in series across a 12.0-V potential difference (a battery). (a) How much charge is stored in the 5.00-μF capacitor? (b) What is the potential difference across the 10.0-µF capacitor? Answer: (a) 37.5 µC (b) 3.75 V Var: 1 16) A 1.0-µF capacitor and a 2.0-µF capacitor are connected together, and then that combination is connected across a 3.0-V potential source (a battery). What is the potential difference across the 2.0-µF capacitor if the capacitors are connected (a) in series or (b) in parallel? Answer: (a) 1.0 V (b) 3.0 V Var: 1

17) Two capacitors are connected as shown in the figure, with C1 = 4.0 µF and C2 = 7.0 µF. If a voltage source V = 90 V is applied across the combination, find the potential difference across C1.

A) 57 V B) 36 V C) 60 V D) 9.0 V Answer: A Var: 1 18) A potential difference of V = 100 V is applied across two capacitors in series, as shown in the figure. If = and the voltage drop across it is 75 V, what is the capacitance of C2?

A) 30 μF B) 2.5 μF C) 7.5 μF D) 3.3 μF Answer: A Var: 10 19) Three capacitors of equal capacitance are arranged as shown in the figure, with a voltage source across the combination. If the voltage drop across C1 is what is the voltage drop across

20) Three capacitors are arranged as shown in the figure, with a voltage source connected across the combination. C1 has a capacitance of has a capacitance of and has a capacitance of Find the potential drop across the entire arrangement if the potential drop across C2 is

A) 1500 V B) 1000 V C) 470 V D) 430 V Answer: A Var: 50+ 21) The capacitive network shown in the figure is assembled with initially uncharged capacitors. Assume that all the quantities in the figure are accurate to two significant figures. The switch S in the network is kept open throughout. What is the total energy stored in the seven capacitors?

A) 48 mJ B) 72 mJ C) 96 mJ D) 120 mJ E) 144 mJ Answer: B Var: 1

22) The network shown is assembled with uncharged capacitors X , Y, and Z, with and The switches S1 and S2 are initially open, and a potential difference Vab = 120 V is applied between points a and b. After the network is assembled, switch S1 is then closed, but switch S2 is kept open. How much energy is finally stored in capacitor X?

A) 29 mJ B) 0.48 mJ C) 0.24 mJ D) 58 mJ E) 0.96 mJ Answer: A Var: 50+ 23) The network shown is assembled with uncharged capacitors X , Y, and Z, with and The switches S1 and S2 are initially open, and a potential difference Vab = 120 V is applied between points a and b. After the network is assembled, switch S1 is then closed, but switch S2 is kept open. How much charge is finally stored in capacitor Y?

A) 110 µC B) 54 µC C) 81 µC D) 140 µC E) 160 µC Answer: A Var: 50+

24) The network shown is assembled with uncharged capacitors X , Y, and Z, with and The switches S1 and S2 are initially open, and a potential difference Vab = 120 V is applied between points a and b. After the network is assembled, switch S1 is then closed, but switch S2 is kept open. What is the final potential difference across capacitor Z?

A) 100 V B) 600 V C) 55 V D) 38 V E) 29 V Answer: A Var: 50+ 25) The network shown is assembled with uncharged capacitors X , Y, and Z, with CX = 4.0 μF, CY = 6.0 μF, and CZ = 5.0 μF. The switches S1 and S2 are initially open, and a potential difference Vab = 120 V is applied between points a and b. After the network is assembled, switch S1 is then closed, but switch S2 is kept open. What is the final potential difference across capacitor X?

A) 120 V B) 82 V C) 75 V D) 67 V E) 60 V Answer: A Var: 1 26) A group of 1.0-μF, 2.0-μF, and 3.0-μF capacitors is connected in parallel across a 24-V potential difference (a battery). How much energy is stored in this three-capacitor combination when the capacitors are fully charged? A) 1.7 mJ B) 2.1 mJ C) 4.8 mJ D) 7.1 mJ Answer: A Var: 1 24 Copyright © 2019 Pearson Education, Inc.

27) A 9.00-µF and a 12.0-µF capacitor are connected together, and this combination is connected across a 25.0-V potential difference. How much electric energy is stored in the combination if they are connected (a) in parallel or (b) in series? Answer: (a) 6.56 mJ (b) 1.61 mJ Var: 1 28) What different resistances can be obtained by using two 2.0-Ω resistors and one 4.0-Ω resistor? You must use all three of them in each possible combination. Answer: 0.80 Ω, 1.5 Ω, 2.0 Ω, 3.3 Ω, 5.0 Ω, 8.0 Ω Var: 1 29) Two resistors in series are equivalent to 9.0 Ω, and in parallel they are equivalent to 2.0 Ω. What are the resistances of these two resistors? Answer: 3.0 Ω and 6.0 Ω Var: 1 30) What resistance must be connected in parallel with a 633-Ω resistor to produce an equivalent resistance of 205 Ω? Answer: 303 Ω Var: 1 31) What is the equivalent resistance between points A and B of the network shown in the figure?

Answer: 16 Ω Var: 1 32) A combination of a 2.0-Ω resistor in series with 4.0-Ω resistor is connected in parallel with a 3.0-Ω resistor. What is the equivalent resistance of this system? A) 2.0 Ω B) 3.0 Ω C) 4.0 Ω D) 9.0 Ω Answer: A Var: 1

33) Two 4.0-Ω resistors are connected in parallel, and this combination is connected in series with 3.0 Ω. What is the equivalent resistance of this system? A) 1.2 Ω B) 5.0 Ω C) 7.0 Ω D) 11 Ω Answer: B Var: 1 34) A 2.0-Ω resistor is in series with a parallel combination of 4.0-Ω, 6.0-Ω, and 12-Ω resistors. What is the equivalent resistance of this system? A) 24 Ω B) 4.0 Ω C) 1.8 Ω D) 2.7 Ω Answer: B Var: 1 35) What is the equivalent resistance in the circuit shown in the figure?

A) 80 Ω B) 55 Ω C) 50 Ω D) 35 Ω Answer: C Var: 1 36) Each of the resistors shown in the figure has a resistance of resistance between points a and b of this combination?

What is the equivalent

37) The resistors in the circuit shown in the figure each have a resistance of equivalent resistance between points a and b of this combination?

What is the

A) 700 Ω B) 2800 Ω C) 175 Ω D) 1400 Ω Answer: A Var: 9 38) Three 2.0-Ω resistors are connected to form the sides of an equilateral triangle ABC as shown in the figure. What is the equivalent resistance between any two points, AB, BC, or AC, of this circuit?

A) 2.0 Ω B) 6.0 Ω C) 4.3 Ω D) 3.3 Ω E) 1.3 Ω Answer: E Var: 1

39) Five 2.0-Ω resistors are connected as shown in the figure. What is the equivalent resistance of this combination between points a and b?

A) 1.0 Ω B) 10.0 Ω C) 2.0 Ω D) 6.0 Ω E) 0.40 Ω Answer: A Var: 1 40) A number of resistors are connected across points A and B as shown in the figure. What is the equivalent resistance between points A and B?

A) 4 Ω B) 6 Ω C) 8 Ω D) 10 Ω E) 12 Ω Answer: C Var: 1

41) A number of resistors are connected across points A and B as shown in the figure. What is the equivalent resistance between points A and B?

A) 4 Ω B) 6 Ω C) 8 Ω D) 10 Ω E) 12 Ω Answer: C Var: 1 42) What is the equivalent resistance of the circuit shown in the figure? The battery is ideal and all resistances are accurate to 3 significant figures.

A) 950 Ω B) 450 Ω C) 392 Ω D) 257 Ω Answer: C Var: 1

43) Three light bulbs, A, B, and C, have electrical ratings as follows: Bulb A: 96.0 W, 1.70 A Bulb B: 80.0 V, 205 W Bulb C: 120 V, 0.400 A These three bulbs are connected in a circuit across a 150-V voltage power source, as shown in the figure. Assume that the filament resistances of the light bulbs are constant and independent of operating conditions. What is the equivalent resistance of this combination of bulbs between the terminals of the power source?

A) 61.5 Ω B) 15.3 Ω C) 74.0 Ω D) 86.2 Ω E) 364 Ω Answer: A Var: 1 44) Three resistors of 12 Ω, 12 Ω, and 6.0 Ω are connected together, and an ideal 12-V battery is connected across the combination. What is the current from the battery if they are connected (a) in series or (b) in parallel? Answer: (a) 0.40 A (b) 4.0 A Var: 1 45) Two resistors with resistances of 5.0 Ω and 9.0 Ω are connected in parallel. A 4.0-Ω resistor is then connected in series with this parallel combination. An ideal 6.0-V battery is then connected across the series-parallel combination. What is the current through (a) the 4.0-Ω resistor and (b) the 5.0-Ω resistor? Answer: (a) 0.83 A (b) 0.53 A Var: 1 46) Two 100-W light bulbs of fixed resistance are to be connected to an ideal 120-V source. What are the current, potential difference, and dissipated power for each bulb when they are connected (a) in parallel (the normal arrangement)? (b) in series? Answer: (a) 0.83 A in each; 120 V for each; 100 W in each (200 W total) (b) 0.42 A in each; 60 V for each; 25 W in each (50 W total) Var: 1

47) For the circuit shown in the figure, R1 = 5.6 Ω, R2 = 5.6 Ω, R3 = 14 Ω, and ε = 6.0 V, and the battery is ideal. (a) What is the equivalent resistance across the battery? (b) Find the current through each resistor.

Answer: (a) 9.6 Ω Var: 1

(b) I1 = 0.63 A, I2 = 0.45 A, I3 = 0.18 A

48) A 22-A current flows into a parallel combination of 4.0-Ω, 6.0-Ω, and 12-Ω resistors. What current flows through the 12-Ω resistor? A) 18 A B) 11 A C) 7.3 A D) 3.7 A Answer: D Var: 1 49) A 6.0-Ω and a 12-Ω resistor are connected in parallel across an ideal 36-V battery. What power is dissipated by the 6.0-Ω resistor? A) 220 W B) 48 W C) 490 W D) 24 W Answer: A Var: 1 50) The following three appliances are connected in parallel across an ideal 120-V dc power source: 1200-W toaster, 650-W coffee pot, and 600-W microwave. If all were operated at the same time what total current would they draw from the source? A) 4.0 A B) 5.0 A C) 10 A D) 20 A Answer: D Var: 1

51) A certain 20-A circuit breaker trips when the current in it equals 20 A. What is the maximum number of 100-W light bulbs you can connect in parallel in an ideal 120-V dc circuit without tripping this circuit breaker? A) 11 B) 17 C) 23 D) 27 Answer: C Var: 1 52) A15-Ω resistor is connected in parallel with a 30-Ω resistor. If this combination is now connected in series with an ideal 9.0-V battery and a 20-Ω resistor, what is the current through the 15-Ω resistor? A) 0.10 A B) 0.13 A C) 0.20 A D) 0.26 A Answer: C Var: 1 53) Three resistors of resistances 4.0 Ω, 6.0 Ω, and 10 Ω are connected in parallel. If this combination is now connected in series with an ideal 12-V battery and a 2.0-Ω resistor, what is the current through the 10-Ω resistor? A) 0.59 A B) 2.7 A C) 11 A D) 16 A Answer: A Var: 1 54) Two resistors having resistances of 5.0 Ω and 9.0 Ω are connected in parallel. A 4.0-Ω resistor is then connected in series with the parallel combination. An ideal 6.0-V battery is then connected across the series-parallel combination. What is the current through the 9.0-Ω resistor? A) 0.35 A B) 0.53 A C) 0.83 A D) 0.30 A E) 0.67 A Answer: D Var: 1

55) A 3.0-Ω resistor is connected in parallel with a 6.0-Ω resistor. This combination is then connected in series with a 4.0-Ω resistor. The resistors are connected across an ideal 12-volt battery. How much power is dissipated in the 3.0-Ω resistor? A) 2.7 W B) 5.3 W C) 6.0 W D) 12 W Answer: B Var: 1 56) Four resistors having resistances of 20 Ω, 40 Ω, 60 Ω, and 80 Ω are connected in series across an ideal dc voltage source. If the current through this circuit is 0.50 A, what is the voltage of the voltage source? A) 20 V B) 40 V C) 60 V D) 80 V E) 100 V Answer: E Var: 1 57) Four resistors having resistances of 20 Ω, 40 Ω, 60 Ω, and 80 Ω are connected in series across an ideal 50-V dc source. What is the current through each resistor? A) 0.25 A B) 0.50 A C) 0.75 A D) 2.0 A E) 4.0 A Answer: A Var: 1 58) If V = 40 V and the battery is ideal, what is the potential difference across R1 in the figure?

A) 6.7 V B) 8.0 V C) 10 V D) 20 V Answer: B Var: 1

59) If V = 20 V and the battery is ideal, what is the current through R3 in the figure?

A) 0.050 A B) 0.20 A C) 1.0 A D) 4.0 A Answer: B Var: 1 60) If 1.5 A flows through R2, what is the emf V of the ideal battery in the figure?

A) 150 V B) 75 V C) 60 V D) 30 V Answer: A Var: 1 61) If emf of the ideal battery is V = 100 V, what is the potential difference across R5 for the circuit shown in the figure?

A) 19 V B) 40 V C) 75 V D) 77 V Answer: A Var: 1

62) If emf of the ideal battery is V = 4.0 V, what is the current through R6 for the circuit shown in the figure?

A) 0.0077 A B) 0.017 A C) 0.040 A D) 4.0 A Answer: A Var: 1 63) What is the magnitude of the potential difference between points A and C for the circuit shown in the figure? The battery is ideal, and all the numbers are accurate to two significant figures.

A) 6.0 V B) 4.0 V C) 3.0 V D) 2.0 V Answer: A Var: 1

64) What is the magnitude of the potential difference between points B and C for the circuit shown in the figure? The battery is ideal, and all the numbers are accurate to two significant figures.

A) 6.0 V B) 4.0 V C) 3.0 V D) 2.0 V Answer: C Var: 1 65) What is the magnitude of the potential difference between points C and D for the circuit shown in the figure? The battery is ideal, and all the numbers are accurate to two significant figures.

A) 6.0 V B) 4.0 V C) 3.0 V D) 2.0 V Answer: B Var: 1

66) What current flows from the battery in the circuit shown in the figure? The battery is ideal, and all the numbers are accurate to two significant figures.

A) 0.35 A B) 2.0 A C) 2.5 A D) 3.0 A Answer: B Var: 1 67) What is the potential drop from point A to point B for the circuit shown in the figure? The battery is ideal, and all the numbers are accurate to two significant figures.

A) 0.35 V B) 2.0 V C) 2.5 V D) 3.0 V Answer: D Var: 1

68) A 4.0-Ω resistor is connected to a 12-Ω resistor and this combination is connected to an ideal dc power supply with voltage V as shown in the figure. If the total current in this circuit is I = 2.0 A, what is the value of voltage V?

A) 2.0 V B) 3.0 V C) 6.0 V D) 1.5 V E) 8.0 V Answer: C Var: 1 69) A 4.0-Ω resistor is connected with a 12-Ω resistor and both of these are connected across an ideal dc power supply with voltage V as shown in the figure. If the total current in this circuit is I = 2.0 A, what is the current through the 4.0-Ω resistor?

A) 2.0 A B) 2.5 A C) 0.5 A D) 3.0 A E) 1.5 A Answer: E Var: 1

70) A 4.0-Ω resistor is connected with a 12-Ω resistor and this combination is connected across an ideal dc power supply with V = 6.0 V, as shown in the figure. When a total current I flows from the power supply, what is the current through the 12-Ω resistor?

A) 1.5 A B) 2.0 A C) 2.5 A D) 3.0 A E) 0.50 A Answer: E Var: 1 71) Four resistors are connected across an ideal dc battery with voltage V, as shown in the figure. If the total current in this circuit is I = 1 A, what is the value of the voltage V?

A) 2 V B) 4 V C) 6 V D) 8 V E) 10 V Answer: B Var: 1

72) Four resistors are connected across an ideal dc battery with voltage V as shown in the figure. Assume that all quantities shown are accurate to two significant figures. If the total current through this circuit is I = 2.0 A, what is the current through the 4.0-Ω resistor?

A) 1.0 A B) 2.0 A C) 3.0 A D) 1.3 A E) 2.4 A Answer: D Var: 1 73) An ideal 100-V dc battery is applied across a series combination of four resistors having resistances of 20 Ω, 40 Ω, 60 Ω, and 80 Ω. What is the potential difference across the 40-Ω resistor? A) 20 V B) 40 V C) 60 V D) 80 V E) 100 V Answer: A Var: 1

74) Four resistors are connected across an ideal dc source of V = 8.0 V, as shown in the figure. Assume all resistances shown are accurate to two significant figures. What is the current through the 9.0-Ω resistor?

A) 1.0 A B) 0.67 A C) 0.50 A D) 0.90 A E) 2.0 A Answer: B Var: 1 75) Three resistors with resistances of 2.0 Ω, 6.0 Ω, and 12 Ω are connected across an ideal dc voltage source V as shown in the figure. If the total current through the circuit is I = 2.0 A, what is the applied voltage V?

A) 6.0 V B) 3.0 V C) 2.0 V D) 2.7 V E) 1.5 V Answer: D Var: 1

76) Three resistors with resistances of 2.0 Ω, 6.0 Ω, and 12 Ω are connected across an ideal dc voltage source V = 2.0 V, as shown in the figure. What is the total current I in this circuit?

A) 0.70 A B) 1.5 A C) 2.0 A D) 3.0 A E) 6.0 A Answer: B Var: 1 77) Three resistors with resistances of 2.0 Ω, 6.0 Ω, and 12 Ω are connected across an ideal dc voltage source V, as shown in the figure. If the total current in the circuit is I = 5.0 A, what is the current through the 12-Ω resistor?

A) 1.7 A B) 2.5 A C) 0.56 A D) 5.0 A E) 0.75 A Answer: C Var: 1

78) For the circuit shown in the figure, the ideal battery has an emf ε = 80 V. The four resistors have resistances of and Calculate the rate at which heat is being generated in the resistor R4.

Answer: 120 W Var: 50+ 79) A portion of a circuit is shown in the figure, and the batteries are ideal. What is the potential difference VA - VB if I = 5.0 A?

A) 63 V B) 35 V C) 55 V D) 45 V E) 71 V Answer: D Var: 1 80) An ideal 10.0-V dc is connected across a resistor in series with an What is the potential drop across the resistor? A) 4.1 V B) 5.9 V C) 14 V D) 7.0 V Answer: A Var: 50+

resistor.

81) For the circuit shown in the figure, the current in the 8.0-Ω resistor is 0.50A. What is the current in the 2.0-Ω resistor? All the numbers shown are accurate to two significant figures.

A) 2.25 A B) 0.75 A C) 4.5 A D) 9.5 A E) 6.4 A Answer: D Var: 1 82) For the circuit shown in the figure, what is the power dissipated in the 2.0-Ω resistor? All the numbers shown are accurate to three significant figures.

A) 5.33 W B) 8.00 W C) 6.67 W D) 2.67 W E) 3.56 W Answer: E Var: 1 83) For the circuit shown in the figure, calculate the emf's ε1 and ε3, assuming that the batteries are ideal. Note that two currents are shown.

84) In the circuit shown in the figure, R1 = R2 = 90.0 Ω, R3 = R4 = 20.0 Ω, V1 = 7.0 V, V2 = 8.0 V, and the batteries are both ideal. What current does the ammeter read?

A) 0.40 A B) 0.050 A C) 0.83 A D) 0.056 A Answer: A Var: 50+ 85) In the circuit shown in the figure, R1 = 60 Ω, R2 = 120 Ω, R3 = 180 Ω, V1 = 3.0 V, V2 = 6.0 V, and the batteries are both ideal. What is the current through R1?

A) 0.050 A B) 0.030 A C) 0.00 A D) 2.68 A Answer: A Var: 1

86) In the circuit shown in the figure, R1 = 10 Ω, R2 = 12 Ω, R3 = 20 Ω, V1 = 1.0 V, V2 = 7.0 V, and the batteries are both ideal. What is the current through R1?

A) 0.60 A B) 0.80 A C) 0.18 A D) 0.13 A Answer: A Var: 1 87) For the circuit shown in the figure, R1 = 18 Ω, R2 = 44 Ω, R3 = 33 Ω, R4 = 14 Ω, R5 = 12 Ω, V1 = 18 V, V2 = 12 V, and the batteries are ideal. Determine I1 and I2.

Answer: I1 = 0.25 A, I2 = 0.12 A Var: 1 88) For the circuit shown in the figure, R1 = 50 Ω, R2 = 20 Ω, R3 = 35 Ω, R4 = 10 Ω, R5 = 68 Ω, I1 = 0.111 A, I2 = 0.142 A, and the batteries are ideal. (a) Determine V1 and V2. (b) What is the potential difference across R4?

Answer: (a) V1 = 12 V, V2 = 15 V Var: 1

(b) 2.5 V

89) Determine the current in the 7.0-Ω resistor for the circuit shown in the figure. Assume that the batteries are ideal and that all numbers are accurate to two significant figures.

A) 0.28 A B) 1.3 A C) 1.6 A D) 2.1 A Answer: C Var: 1 90) Determine the current in the 8.0-Ω resistor for the circuit shown in the figure. Assume that the batteries are ideal and that all numbers are accurate to two significant figures.

A) 0.28 A B) 1.3 A C) 1.6 A D) 2.1 A Answer: B Var: 1 91) Determine the current in the 4.0-Ω resistor for the circuit shown in the figure. Assume that the batteries are ideal and that all numbers are accurate to two significant figures.

92) Determine the current in the 12-Ω resistor for the circuit shown in the figure assuming that the batteries are ideal.

A) 0.25 A B) 0.50 A C) 0.75 A D) 1.0 A Answer: A Var: 1 93) Determine the current in the 18-Ω resistor for the circuit shown in the figure assuming that the batteries are ideal.

A) 0.25 A B) 0.50 A C) 0.75 A D) 1.0 A Answer: B Var: 1 94) For the circuit shown in the figure, both batteries are ideal. What current flows in the solid wire connecting the upper left and lower left corners of the circuit?

A) 0.25 A B) 0.50 A C) 0.75 A D) 1.0 A Answer: C Var: 1

95) A multiloop circuit is shown in the figure. Find the current I1 if the batteries are ideal. (It is not necessary to solve the entire circuit.)

A) -2 A B) 2 A C) 6 A D) -5 A E) 0 A Answer: A Var: 1 96) A multiloop circuit is shown in the figure. Find the current I2 if the batteries are ideal. (It is not necessary to solve the entire circuit.)

A) -3 A B) 3 A C) 7 A D) -7 A E) 0 A Answer: A Var: 1

97) A multiloop circuit is shown in the figure. Find the emf ε1 if the batteries are ideal. (It is not necessary to solve the entire circuit.)

A) -4 V B) 4 V C) 44 V D) 52 V E) -52 V Answer: A Var: 1 98) A multiloop circuit is shown in the figure, but some quantities are not labeled. Find the emf ε if the batteries are ideal. (It is not necessary to solve the entire circuit.)

A) +3 V B) +19 V C) -3 V D) -10 V E) -19 V Answer: B Var: 1

99) A multiloop circuit is shown in the figure, but some quantities are not labeled. Find the current I1 if the batteries are ideal. (It is not necessary to solve the entire circuit.)

A) 0 A B) +0.2 A C) +0.4 A D) -0.2 A E) -0.4 A Answer: B Var: 1 100) A multiloop circuit is shown in the figure, but some quantities are not labeled. Find the current I2 if the batteries are ideal. (It is not necessary to solve the entire circuit.)

A) +0.1 A B) +0.3 A C) +0.5 A D) -0.1 A E) -0.3 A Answer: E Var: 1 101) A 8.0-μF uncharged capacitor is connected in series with a 6.0-kΩ resistor, an ideal 20-V dc source, and an open switch. If the switch is closed at time t = 0.0 s, what is the charge on the capacitor at t = 9.0 ms? A) 0 C B) 37% of the minimum charge C) 17% of the maximum charge D) 68% of the minimum charge E) 96% of the maximum charge Answer: C Var: 5

102) A 2.0-μF capacitor that is initially uncharged is charged through a 50-kΩ resistor. How long does it take for the capacitor to reach 90% of its full charge? A) 0.90 s B) 0.23 s C) 2.2 s D) 2.3 s Answer: B Var: 1 103) A fully charged 37-µF capacitor is discharged through a 1.0-kΩ resistor. If the voltage across the capacitor is reduced to 7.6 volts after just 20 ms, what was the original potential across the capacitor? A) 16 V B) 13 V C) 11 V D) 9.0 V E) 8.0 V Answer: B Var: 1 104) When an initially uncharged capacitor is charged through a 25-kΩ resistor by a 75-V dc ideal power source, it takes 0.23 ms for the capacitor to reach 50% of its maximum charge? What is the capacitance of this capacitor? Answer: 13 nF Var: 1 105) A 2.0-μF capacitor is charged to 12 V and then discharged through a 4.0-MΩ resistor. How long will it take for the voltage across the capacitor to drop to 3.0 V? A) 8.0 s B) 11 s C) 22 s D) 24 s Answer: B Var: 1

106) For the circuit shown in the figure, V = 60 V, C = 20 µF, R = 0.10 MΩ, and the battery is ideal. Initially the switch S is open and the capacitor is uncharged. The switch is then closed at time t = 0.00 s. What is the charge on the capacitor 8.0 s after closing the switch?

A) 1200 µC B) 940 µC C) 1400 µC D) 1600 µC E) 1900 µC Answer: A Var: 50+ 107) For the circuit shown in the figure, V = 20 V, C = 10 µF, R = 0.80 MΩ, and the battery is ideal. Initially the switch S is open and the capacitor is uncharged. The switch is then closed at time t = 0.00 s. What is the potential difference across the resistor 20 s after closing the switch?

A) 1.6 V B) 2.0 V C) 2.3 V D) 2.6 V E) 3.0 V Answer: A Var: 50+ 108) For the circuit shown in the figure, V = 60 V, C = 40 µF, R = 0.90 MΩ, and the battery is ideal. Initially the switch S is open and the capacitor is uncharged. The switch is then closed at time t = 0.00 s. At a given instant after closing the switch, the potential difference across the capacitor is twice the potential difference across the resistor. At that instant, what is the charge on the capacitor?

109) For the circuit shown in the figure, C = 12 µF and R = 8.5 MΩ. Initially the switch S is open with the capacitor charged to a voltage of 80 V. The switch is then closed at time t = 0.00 s. What is the charge on the capacitor, when the current in the circuit is 3.3 µA?

A) 350 µC B) 340 µC C) 480 µC D) 620 µC E) 700 µC Answer: B Var: 1 110) For the circuit shown in the figure, C = 13 µF and R = 7.6 MΩ. Initially the switch S is open with the capacitor charged to a voltage of 80 V. The switch is then closed at time t = 0.00 s. What is the charge on the capacitor 40 s after closing the switch?

A) 3300 µC B) 3100 µC C) 2900 µC D) 2700 µC E) 2500 µC Answer: A Var: 50+ 111) A 1.0-μF capacitor is charged until it acquires a potential difference of across its plates, and then the emf source is removed. If the capacitor is then discharged through a resistance, what is the voltage drop across the capacitor after beginning the discharge? A) 880 V B) 920 V C) 16 V D) -16 V Answer: A Var: 50+

112) The capacitor shown in the circuit in the figure is initially uncharged when the switch S is suddenly closed, and the battery is ideal. After one time constant has gone by, find (a) the current through the resistor and (b) the charge on the capacitor. Assume that the numbers shown are all accurate to two significant figures.

Answer: (a) 0.74 A Var: 1

(b) 1.3 mC

113) A circuit contains a 2.0-MΩ resistor in series with an uncharged capacitor. When this combination is connected across an ideal battery, the capacitor reaches 25% of its maximum charge in 1.5 s. What is its capacitance? Answer: 2.6 µF Var: 1 114) A series circuit consists of a 2.5-μF capacitor, a 7.6-MΩ resistor, and an ideal 6.0-V dc power source. (a) What is the time constant for charging the capacitor? (b) What is the potential difference across the capacitor 25 s after charging begins? Answer: (a) 19 s (b) 4.4 V Var: 1 115) A resistor with a resistance of 360 Ω is in a series circuit with a capacitor of capacitance 7.3 × 10-6 F. What capacitance must be placed in parallel with the original capacitance to change the capacitive time constant of the combination to three times its original value? Answer: 15 × 10-6 F Var: 1 116) In the circuit shown in the figure, all the capacitors are initially uncharged when the switch S is suddenly closed, and the battery is ideal. Find (a) the maximum reading of the ammeter and (b) the maximum charge on the 5.00-µF capacitor.

Answer: (a) 2.50 A Var: 1

(b) 458 µC

College Physics: A Strategic Approach, 4e (Knight) Chapter 24 Magnetic Fields and Forces 24.1 Conceptual Questions 1) If you were to cut a small permanent bar magnet in half, A) one piece would be a magnetic north pole and the other piece would be a south pole. B) neither piece would be magnetic. C) each piece would in itself be a smaller bar magnet with both north and south poles. D) None of these statements is true. Answer: C Var: 1 2) A straight bar magnet is initially 4 cm long, with the north pole on the right and the south pole on the left. If you cut the magnet in half, the right half will A) contain only a north pole. B) contain a north pole on the right and a south pole on the left. C) contain only a south pole. D) no longer contain any poles. Answer: B Var: 1 3) Which one of the following statements is correct? A) Earth's geographic north pole is the north pole of Earth's magnetic field. B) Earth's geographic south pole is the south pole of Earth's magnetic field. C) The north pole of a magnet points towards Earth's geographic north pole. D) The north pole of a magnet points towards Earth's geographic south pole. E) None of the above statements is correct. Answer: C Var: 1 4) A positive charge is moving to the right and experiences an upward magnetic force, as shown in the figure. In which direction must the magnetic field have a component?

A) to the right B) to the left C) upward D) out of the page E) into the page Answer: E Var: 1

5) A charged particle that is moving in a static uniform magnetic field A) will always experience a magnetic force, regardless of its direction of motion. B) may experience a magnetic force which will cause its speed to change. C) may experience a magnetic force, but its speed will not change. D) may experience a magnetic force, but its direction of motion will not change. E) None of the above statements are true. Answer: C Var: 1 6) An electron moving along the +x-axis enters a magnetic field. If the electron experiences a magnetic deflection in the -y direction, then the magnetic field must have a component A) along the +z-axis B) along the -z-axis C) along the -x-axis D) along the +y-axis E) along the -y-axis Answer: B Var: 1 7) An electron, moving south, enters a magnetic field. Because of this field, the electron curves upward. We may conclude that the magnetic field must have a component A) downward. B) towards the east. C) upward. D) towards the west. E) towards the north. Answer: D Var: 1 8) A proton, moving north, enters a magnetic field. Because of this field, the proton curves downward. We may conclude that the magnetic field must have a component A) downward. B) upward. C) towards the east. D) towards the west. E) towards the north. Answer: C Var: 1

9) An electron, moving west, enters a magnetic field. Because of this field the electron curves upward. We may conclude that the magnetic field must have a component A) towards the north. B) towards the south. C) upward. D) downward. E) towards the west. Answer: A Var: 1 10) A proton, moving west, enters a magnetic field. Because of this magnetic field the proton curves upward. We may conclude that the magnetic field must have a component A) towards the west. B) towards the east. C) towards the south. D) towards the north. E) downward. Answer: C Var: 1 11) A proton, moving east, enters a magnetic field. Because of this magnetic field the proton curves downward. We may conclude that the magnetic field must have a component A) towards the south. B) towards the north. C) towards the west. D) upward. E) downward. Answer: A Var: 1 12) An electron is moving to the right, as shown in the figure. Suddenly it encounters uniform magnetic field pointing out of the page. Which one of the three paths shown will it follow in the field?

A) path a B) path b C) path c Answer: A Var: 1

13) Three particles travel through a region of space where the magnetic field is out of the page, as shown in the figure. What are the signs of the charges of these three particles?

A) 1 is neutral, 2 is negative, and 3 is positive. B) 1 is neutral, 2 is positive, and 3 is negative. C) 1 is positive, 2 is neutral, and 3 is negative. D) 1 is positive, 2 is negative, and 3 is neutral. E) 1 is negative, 2 is neutral, and 3 is positive. Answer: E Var: 1 14) An electron moving in the +y direction, at right angles to a magnetic field, experiences a magnetic force in the -x direction. The direction of the magnetic field is in the A) -x direction. B) +x direction. C) +y direction. D) -z direction. E) +z direction. Answer: E Var: 1 15) A charged particle moving along the +x-axis enters a uniform magnetic field pointing along the +z-axis. Because of an electric field along the +y-axis, the charge particle does not change velocity. What is the sign of this particle? A) positive B) negative C) The particle could be either positive or negative. D) None of the above choices is correct. Answer: C Var: 1 16) A charged particle moving along the +x-axis enters a uniform magnetic field pointing along the +z-axis. A uniform electric field is also present. Due to the combined effect of both fields, the particle does not change its velocity. What is the direction of the electric field? A) along the -y-axis B) along the +y-axis C) along the -x-axis D) along the +x-axis E) along the -z-axis Answer: B Var: 1 4 Copyright © 2019 Pearson Education, Inc.

17) A proton is to orbit Earth at the equator using Earth's magnetic field to supply part of the necessary centripetal force. In what direction should the proton move? A) upward B) northward C) southward D) eastward E) westward Answer: E Var: 1 18) If a calculated quantity has units of

, that quantity could be

A) an electric field. B) an electric potential. C) μ0. D) a magnetic field. E) a magnetic torque. Answer: D Var: 1 19) If a calculated quantity has units of T ∙ m/A, that quantity could be A) an electric field. B) an electric potential. C) μ0. D) a magnetic field. E) a magnetic torque. Answer: C Var: 1 20) We observe that a moving charged particle experiences no magnetic force. From this we can definitely conclude that A) no magnetic field exists in that region of space. B) the particle must be moving parallel to the magnetic field. C) the particle is moving at right angles to the magnetic field. D) either no magnetic field exists or the particle is moving parallel to the field. E) either no magnetic field exists or the particle is moving perpendicular to the field. Answer: D Var: 1

21) A charged particle moves with a constant speed through a region where a uniform magnetic field is present. If the magnetic field points straight upward, the magnetic force acting on this particle will be strongest when the particle moves A) straight upward. B) straight downward. C) in a plane parallel to Earth's surface. D) upward at an angle of 45° above the horizontal. Answer: C Var: 1 22) A negatively-charged particle moves across a constant uniform magnetic field that is perpendicular to the velocity of the particle. The magnetic force on this particle A) causes the particle to speed up. B) causes the particle to slow down. C) causes the particle to accelerate. D) is in the same direction as the particle's velocity. E) is opposite the direction of the particle's velocity. Answer: C Var: 1 23) At a particular instant, a proton moves toward the east in a uniform magnetic field that is directed straight downward. The magnetic force that acts on it is A) zero. B) upward. C) toward the north. D) toward the south. E) downward. Answer: C Var: 1 24) At a particular instant, an electron moves toward the east in a uniform magnetic field that is directed straight downward. The magnetic force that acts on it is A) zero. B) upward. C) toward the north. D) toward the south. E) downward. Answer: D Var: 1

25) An electron has an initial velocity to the south but is observed to curve upward as the result of a magnetic field. This magnetic field must have a component A) to the west. B) to the east. C) upward. D) downward. E) to the north. Answer: A Var: 1 26) A proton has an initial velocity to the south but is observed to curve upward as the result of a magnetic field. This magnetic field must have a component A) to the west. B) to the east. C) upward. D) downward. E) to the north. Answer: B Var: 1 27) After landing on an unexplored Klingon planet, Spock tests for the direction of the magnetic field by firing a beam of electrons in various directions and by recording the following observations: Electrons moving upward feel a magnetic force in the northwest direction. Electrons moving horizontally toward the north are pushed downward. Electrons moving horizontally toward the southeast are pushed upward. Mr. Spock therefore concludes that the magnetic field at this landing site is in which direction? A) toward the east B) toward the northeast C) toward the southwest D) toward the southeast E) toward the west Answer: C Var: 1 28) A charged particle is injected into a uniform magnetic field such that its velocity vector is perpendicular to the magnetic field lines. Ignoring the particle's weight, the particle will A) move in a straight line. B) follow a spiral path. C) move along a parabolic path. D) follow a circular path. Answer: D Var: 1

29) A charged particle is observed traveling in a circular path of radius R in a uniform magnetic field. If the particle were traveling twice as fast, the radius of the circular path would be A) 2R. B) 4R. C) 8R. D) R/2. E) R/4. Answer: A Var: 1 30) A particle carrying a charge of +e travels in a circular path of radius R in a uniform magnetic field. If instead the particle carried a charge of +2e, the radius of the circular path would have been A) 2R. B) 4R. C) 8R. D) R/2. E) R/4. Answer: D Var: 1 31) A proton, moving in a uniform magnetic field, moves in a circle perpendicular to the field lines and takes time T for each circle. If the proton's speed tripled, what would now be its time to go around each circle? A) 9T B) 3T C) T D) T/3 E) T/9 Answer: C Var: 1 32) If a calculated quantity has units of

, that quantity could be

A) an electric field. B) an electric potential. C) μ0. D) a magnetic field. E) a magnetic torque. Answer: D Var: 1

33) A rectangular coil, with corners labeled ABCD, has length L and width w. It is placed between the poles of a magnet, as shown in the figure If there is a current I flowing through this coil in the direction shown, what is the direction of the force acting on section AB of this coil?

A) perpendicular to and into the page B) perpendicular to and out of the page C) in the direction of the magnetic field D) in the opposite direction of the magnetic field E) The force is zero. Answer: A Var: 1 34) A rectangular coil, with corners labeled ABCD, has length L and width w. It is placed between the poles of a magnet, as shown in the figure. If there is a current I flowing through this coil in the direction shown, what is the direction of the force acting on section CD of this coil?

35) A rectangular coil, with corners labeled ABCD, has length L and width w. It is placed between the poles of a magnet, as shown in the figure If there is a current I flowing through this coil in the direction shown, what is the direction of the force acting on section BC of this coil?

A) perpendicular to and into the page B) perpendicular to and out of the page C) in the direction of the magnetic field D) in the opposite direction of the magnetic field E) The force is zero. Answer: E Var: 1 36) A wire is carrying current vertically downward. What is the direction of the force on this wire due to Earth's magnetic field? A) horizontally towards the north B) horizontally towards the south C) horizontally towards the east D) horizontally towards the west E) vertically upward Answer: C Var: 1 37) When the switch is closed in the circuit shown in the figure, the wire between the poles of the horseshoe magnet deflects upward. From this you can conclude that the left end of the magnet is

A) a north magnetic pole. B) a south magnetic pole. C) There is not enough information given to answer the question. Answer: B Var: 1

38) For the horseshoe magnet shown in the figure, the left end is a north magnetic pole and the right end is a south magnetic pole. When the switch is closed in the circuit, which way will the wire between the poles of the horseshoe magnet initially deflect?

A) to the right B) to the left C) upward D) downward Answer: D Var: 1 39) The direction of the force on a current-carrying wire in a magnetic field is A) perpendicular only to the current. B) perpendicular only to the magnetic field. C) perpendicular to both the current and the magnetic field. D) in the direction opposite to the current. E) in same direction as the current. Answer: C Var: 1 40) The magnetic force on a current-carrying wire in a magnetic field is the strongest when A) the current is in the direction of the magnetic field lines. B) the current is in the direction opposite to the magnetic field lines. C) the current is at a 180° angle with respect to the magnetic field lines. D) the current is perpendicular to the magnetic field lines. E) the current is at a 0° angle with respect to the magnetic field lines. Answer: D Var: 1 41) A vertical wire carries a current straight up in a region where the magnetic field vector points toward the north. What is the direction of the magnetic force on this wire? A) downward B) toward the north C) toward the east D) toward the west E) upward F) toward the south Answer: D Var: 1

42) Two long parallel wires are placed side-by-side on a horizontal table. If the wires carry current in the same direction, A) one wire is lifted slightly while the other wire is forced downward against the table's surface. B) both wires are lifted slightly. C) the wires pull toward each other. D) the wires push away from each other. Answer: C Var: 1 43) Two long parallel wires are placed side-by-side on a horizontal table. If the wires carry current in opposite directions, A) one wire is lifted slightly while the other wire is forced downward against the table's surface. B) both wires are lifted slightly. C) the wires pull toward each other. D) the wires push away from each other. Answer: D Var: 1 44) When two long parallel wires carry unequal currents, the magnitude of the magnetic force that one wire exerts on the other is F. If the current in both wires is now doubled, what is the magnitude of the new magnetic force on each wire? A) 16F B) 8F C) 4F D) 2F E) F Answer: C Var: 1 45) Two long parallel wires are placed side-by-side on a horizontal table and carry current in the same direction. The current in one wire is 20 A, and the current in the other wire is 5 A. If the magnetic force on the 20-A wire has magnitude F, what is the magnitude of the magnetic force on the 5-A wire? No external magnetic fields are present. A) 4F B) 2F C) F D) F/2 E) F/4 Answer: C Var: 1

46) Two long, parallel wires carry currents of different magnitudes. If the current in one of the wires is doubled and the current in the other wire is halved, what happens to the magnitude of the magnetic force that each wire exerts on the other? A) It is doubled. B) It stays the same. C) It is tripled. D) It is quadrupled. E) It is reduced by a factor of two. Answer: B Var: 1 47) Two long, parallel wires carry currents of different magnitudes. If the amount of current in one of the wires is doubled, what happens to the magnitude of the force that each wire exerts on the other? A) It is increased by a factor of 8. B) It is increased by a factor of 4. C) It is increased by a factor of 3. D) It is increased by a factor of 2. E) It is increased by a factor of Answer: D Var: 1 48) A ring with a clockwise current (as viewed from above the ring) is situated with its center directly above another ring, which has a counter-clockwise current, as shown in the figure. In what direction is the net magnetic force exerted on the top ring due to the bottom ring?

A) upward B) downward C) to the left D) to the right E) The net force is zero. Answer: A Var: 1 49) An object is hung using a metal spring. If now a current is passed through the spring, what will happen to this system? A) The spring will contract, raising the weight. B) The spring will extend, lowering the weight. C) The weight will not move. D) The spring will begin to swing like a pendulum. E) None of these are true. Answer: A Var: 1 13 Copyright © 2019 Pearson Education, Inc.

50) Which of the following are units for the magnetic moment? (There could be more than one correct choice.) A) B) A ∙ m2 C) N ∙ m/T D) T/m2 Answer: B, C Var: 1 51) The maximum torque on a flat current-carrying loop occurs when the angle between the plane of the loop's area and the magnetic field vector is A) 0° B) 45° C) 90° D) 135° Answer: A Var: 1 52) A flat circular wire loop lies in a horizontal plane on a table and carries current in a counterclockwise direction when viewed from above. At this point, the earth's magnetic field points to the north and dips below the horizontal. Which side of the coil tends to lift off of the table due to the magnetic torque on the loop? A) the north side B) the east side C) the south side D) the west side E) The entire loop lifts straight up. Answer: C Var: 1 53) Two long parallel wires placed side-by-side on a horizontal table carry identical size currents in opposite directions. The wire on your right carries current directly toward you, and the wire on your left carries current directly away from you. From your point of view, the magnetic field at a point exactly midway between the two wires A) points upward. B) points downward. C) points toward you. D) points away from you. E) is zero. Answer: B Var: 1

54) Two long parallel wires placed side-by-side on a horizontal table carry identical current straight toward you. From your point of view, the magnetic field at a point exactly between the two wires A) points upward. B) points downward. C) points toward you. D) points away from you. E) is zero. Answer: E Var: 1 55) A long, straight, horizontal wire carries current toward the east. A proton moves toward the east alongside and just south of the wire. What is the direction of the magnetic force on the proton? A) toward the north B) toward the south C) upward D) downward E) toward the east Answer: A Var: 1 56) A long, straight, horizontal wire carries current toward the east. An electron moves toward the east alongside and just south of the wire. What is the direction of the magnetic force on the electron? A) toward the north B) toward the south C) upward D) downward E) toward the west Answer: B Var: 1 57) A wire lying in the plane of this page carries a current directly toward the top of the page. What is the direction of the magnetic force this current produces on an electron that is moving perpendicular to the page and outward from it on the left side of the wire? A) perpendicular to the page and towards you B) perpendicular to the page and away from you C) toward the top of the page D) toward the bottom of the page E) The force is zero. Answer: E Var: 1

58) A long, straight wire carrying a current is placed along the y-axis. If the direction of the current is in the +y direction, what is the direction of the magnetic field due to this wire as you view it in such a way that the current is coming directly toward you? A) clockwise, around the x-axis B) counterclockwise, around the x-axis C) counterclockwise, around the z-axis D) counterclockwise, around the y-axis E) clockwise, around the y-axis Answer: D Var: 1 59) A negatively charged particle -Q is moving to the right, directly above a wire having a current I flowing to the right, as shown in the figure. In what direction is the magnetic force exerted on the particle due to the current?

A) into the page B) out of the page C) downward D) upward E) The magnetic force is zero because the velocity is parallel to the current. Answer: D Var: 1 60) A wire lying in the plane of the page carries a current toward the bottom of the page, as shown in the figure. What is the direction of the magnetic force it produces on an electron that is moving to the left directly toward the wire, as shown?

A) straight into the page B) straight out of the page C) directly toward the top of the page D) directly toward the bottom of the page E) directly to the left away from the wire Answer: D Var: 1

61) A very long straight current-carrying wire produces a magnetic field of 20 mT at a distance d from the wire. To measure a field of 5 mT due to this wire, you would have to go to a distance from the wire of A) 16d. B) 8d. C) 4d. D) 2d. E) d Answer: C Var: 1 62) The magnetic field at a distance of 2 cm from a long straight current-carrying wire is 4 μT. What is the magnetic field at a distance of 4 cm from this wire? A) 2 μT B) 4 μT C) 6 μT D) 8 μT E) 10 μT Answer: A Var: 1 63) The magnetic field at a distance of 2 cm from a long straight current-carrying wire is 4 μT. What is the magnetic field at a distance of 1 cm from this wire? A) 2 μT B) 4 μT C) 6 μT D) 8 μT E) 10 μT Answer: D Var: 1

64) A long straight wire carrying a 4-A current is placed along the x-axis as shown in the figure. What is the direction of the magnetic field at a point P due to this wire?

A) into the plane of the page B) out of the plane of the page C) along the -x-axis D) along the +x-axis E) along the +y-axis Answer: B Var: 1 65) Which one of the following statements is correct? A) When a current-carrying wire is in your right hand, with your thumb in the direction of the current, your fingers point opposite to the direction of the magnetic field lines. B) When a current-carrying wire is in your right hand, with your thumb in the direction of the current, your fingers point in the direction of the magnetic field lines. C) When a current-carrying wire is in your left hand, with your thumb in the direction of the current, your fingers point in the direction of the magnetic field lines. Answer: B Var: 1 66) A vertical wire carries a current vertically downward. To the east of this wire, the magnetic field points A) north. B) east. C) south. D) down. Answer: C Var: 1 67) A horizontal wire carries a current straight toward you. From your point of view, the magnetic field caused by this current A) points directly away from you. B) points to the left. C) circles the wire in a clockwise direction. D) circles the wire in a counter-clockwise direction. Answer: D Var: 1

68) A long straight wire has a constant current flowing to the right. A rectangular metal loop is situated above the wire, and also has a constant current flowing through it, as shown in the figure. Which one of the following statements is true?

A) The net magnetic force on the rectangle is upward, and there is also a nonzero torque on the rectangle. B) The net magnetic force on the rectangle is zero, and the net torque on it is zero. C) The net magnetic force on the rectangle is downward, and there is also a nonzero torque on the rectangle. D) The net magnetic force on the rectangle is zero, but there is a nonzero torque on the rectangle. E) The net magnetic force on the rectangle is downward, and the net torque on it is zero. Answer: E Var: 1 69) A single current-carrying circular loop of radius R is placed next to a long, straight wire, as shown in the figure. The current I in the wire flows to the right. In which direction must current flow in the loop to produce a net magnetic field of zero at its center?

A) counterclockwise B) clockwise C) It could be either clockwise or counterclockwise. D) The current in the loop should be zero. Answer: B Var: 1 70) A current-carrying loop of wire lies flat on a horizontal tabletop. When viewed from above, the current moves around the loop in a counterclockwise sense. For points on the tabletop outside the loop, the magnetic field lines caused by this current A) circle the loop in a clockwise direction. B) circle the loop in a counterclockwise direction. C) point straight up. D) point straight down. Answer: D Var: 1 19 Copyright © 2019 Pearson Education, Inc.

71) A current-carrying loop of wire lies flat on a horizontal tabletop. When viewed from above, the current moves around the loop in a counterclockwise sense. For points on the tabletop inside the loop, the magnetic field lines caused by this current A) circle the loop in a clockwise direction. B) circle the loop in a counterclockwise direction. C) point straight up. D) point straight down. Answer: C Var: 1 72) Consider two current-carrying circular loops. Both are made from one strand of wire and both carry the same current, but one has twice the radius of the other. If the magnetic field strength at the center of the smaller loop is B, what is the magnetic field strength at the center of the larger loop? A) 8B B) 4B C) 2B D) B/2 E) B/4 Answer: D Var: 1 73) Consider an ideal solenoid of length L, N windings, and radius b (L is much longer than b). A current I is flowing through the wire windings. If the radius of the solenoid is doubled to 2b, but all the other quantities remain the same, the magnetic field inside the solenoid will A) remain the same. B) become twice as strong as initially. C) become one-half as strong as initially. D) become four times as strong as initially. E) become one-fourth as strong as initially. Answer: A Var: 1 74) Consider an ideal solenoid of length L, N windings, and radius b (L is much longer than b). A current I is flowing through the wire windings. If the length of the solenoid becomes twice as long (to 2L), but all other quantities remained the same, the magnetic field inside the solenoid will A) remain the same. B) become twice as strong as initially. C) become one-half as strong as initially. D) become four times as strong as initially. E) become one-fourth as strong as initially. Answer: C Var: 1

75) When you double the number of windings in an ideal solenoid while keeping all other parameters (radius, length and current) fixed, the magnetic field at the center of the solenoid will A) double. B) triple. C) quadruple. D) be reduced by a factor of one-half. E) be reduced by a factor of one-fourth. Answer: A Var: 1 76) When a ferromagnetic material is placed in an external magnetic field, the net magnetic field of its magnetic domains becomes A) smaller. B) zero. C) larger. Answer: C Var: 1 24.2 Problems 1) A proton moving at 5.0 × 104 m/s horizontally enters a region where a magnetic field of 0.12 T is present, directed vertically downward. What magnitude force acts on the proton due to this field? (e = 1.60 × 10-19 C) Answer: 9.6 × 10-16 N Var: 1 2) A geophysicist measures the magnetic force on a proton that is moving vertically downward at a point 1.996 km/s at the earth's equator. At that location, the earth's magnetic magnetic field is horizontal and has a strength of 0.40 × 10-4 T. What are the magnitude and direction of the force she will measure? (e = 1.60 × 10-19 C) Answer: 1.3 × 10-20 N, toward the east Var: 1 3) An electron moves with a speed of 5.0 × 104 m/s perpendicular to a uniform magnetic field of magnitude 0.20 T. What is the magnitude of the magnetic force on the electron? (e = 1.60 × 1019 C) A) 4.4 × 10-14 N B) 1.6 × 10-15 N C) 5 × 10-20 N D) 2.6 × 10-24 N E) zero Answer: B Var: 3 21 Copyright © 2019 Pearson Education, Inc.

4) An electron traveling toward the magnetic north with speed 400 km/s enters a region where the earth's magnetic field has the magnitude 5.0 × 10-5 T and is directed downward at 45° below horizontal. What magnitude magnetic force acts on the electron? (e = 1.60 × 10-19 C) Answer: 2.3 × 10-18 N Var: 1 5) A proton travels at a speed of 5.0 × 107 m/s through a 1.0-T magnetic field. What is the magnitude of the magnetic force on the proton if the angle between the proton's velocity and the magnetic field vector is 30°? (e = 1.60 × 10-19 C) A) 2.0 × 10-14 N B) 4.0 × 10-14 N C) 2.0 × 10-12 N D) 4.0 × 10-12 N Answer: D Var: 1 6) A proton, with mass 1.67 × 10-27 kg and charge +1.6 × 10-19 C, is sent with velocity in the +x direction into a region where there is a uniform electric field of magnitude in the +y direction. What must be the magnitude and direction of the uniform magnetic field in the region if the proton is to pass through undeflected? Assume that the magnetic field has no x component and neglect gravitational effects. Answer: 3.4 × 10-2 T, +z direction Var: 50+ 7) A proton is projected with a velocity of 7.0 km/s into a magnetic field of 0.60 T perpendicular to the motion of the proton. What is the magnitude of the magnetic force that acts on the proton? (e = 1.60 × 10-19 C) A) 0 N B) 3.4 × 10-16 N C) 4.2 × 10-16 N D) 13 × 10-16 N E) 6.7 × 10-16 N Answer: E Var: 1

8) A proton moving eastward with a velocity of 5.0 km/s enters a magnetic field of 0.20 T pointing northward. What are the magnitude and direction of the force that the magnetic field exerts on the proton? (e = 1.60 × 10-19 C) A) 0 N B) 1.6 × 10-16 N upwards C) 1.6 × 10-16 N downwards D) 1.1 × 10-16 N eastwards E) 4.4 × 10-16 N westwards Answer: B Var: 1 9) A proton moving with a velocity of 4.0 × 104 m/s enters a magnetic field of 0.20 T. If the angle between the velocity of the proton and the direction of the magnetic field is 60°, what is the magnitude of the magnetic force on the proton? (e = 1.60 × 10-19 C) A) 1.8 × 10-15 N B) 0.60 × 10-15 N C) 1.1 × 10-15 N D) 2.2 × 10-15 N E) 3.3 × 10-15 N Answer: C Var: 1 10) A proton moving with a velocity of 4.0 × 104 m/s along the +y-axis enters a magnetic field of 0.20 T directed towards the -x-axis. What is the magnitude of the magnetic force acting on the proton? (e = 1.60 × 10-19 C) A) 8.0 × 10-15 N B) 3.9 × 10-15 N C) 2.6 × 10-15 N D) 0 N E) 1.3 × 10-15 N Answer: E Var: 1 11) An electron moves with a speed of 3.0 × 104 m/s perpendicular to a uniform magnetic field of 0.40 T. What is the magnitude of the magnetic force on the electron? (e = 1.60 × 10-19 C) A) 4.8 × 10-14 N B) 1.9 × 10-15 N C) 5 × 10-20 N D) 2.2 × 10-24 N E) 0 N Answer: B Var: 3

12) An electron moves with a speed of 8.0 × 106 m/s along the +x-axis. It enters a region where there is a magnetic field of 2.5 T, directed at an angle of 60° to the +x-axis and lying in the xyplane. Calculate the magnitude of the magnetic force on the electron. (e = 1.60 × 10-19 C) A) 2.8 × 10-10 N B) 3.2 × 10-10 N C) 2.8 × 10-12 N D) 3.2 × 10-12 N E) 0 N Answer: C Var: 1 13) An electron moves with a speed of 8.0 × 106 m/s along the +x-axis. It enters a region where there is a magnetic field of 2.5 T, directed at an angle of 60° to the +x-axis and lying in the xyplane. Calculate the magnitude of the acceleration of the electron. (e = 1.60 × 10-19 C, me1 = 9.11 × 10-31 kg) A) 1.3 × 1018 m/s2 B) 3.0 × 1018 m/s2 C) 1.3 × 10-18 m/s2 D) 3.0 × 10-18 m/s2 E) 0 m/s2 Answer: B Var: 1 14) A proton is accelerated from rest through 0.50 kV. It then enters a uniform magnetic field of 0.30 T that is oriented perpendicular to its direction of motion. (a) What is the radius of the path the proton follows in the magnetic field? (b) How long does it take the proton to make one complete circle in the magnetic field?. Answer: (a) 11 mm (b) 0.22 µs Var: 1 15) In the figure, a small particle of charge -1.9 x C and mass has speed as it enters a region of uniform magnetic field. The particle is initially traveling perpendicular to the magnetic field and is observed to travel in the semicircular path shown with radius R = 5.0 cm. Find the magnitude and direction of the magnetic field in the region.

16) A proton having a speed of 3.0 × 106 m/s in a direction perpendicular to a uniform magnetic field moves in a circle of radius 0.20 m within the field. What is the magnitude of the magnetic field? (e = 1.60 × 10-19 C, mproton = 1.67 × 10-27 kg) A) 0.080 T B) 0.16 T C) 0.24 T D) 0.32 T E) 0.36 T Answer: B Var: 1 17) An electron moving perpendicular to a uniform magnetic field of 3.2 × 10-2 T moves in a circle of radius 0.40 cm. How fast is this electron moving? (e = 1.60 × 10-19 C, melectron = 9.11 × 10-31kg) A) 2.2 × 107 m/s B) 1.9 × 107 m/s C) 1.9 × 106 m/s D) 3.0 × 107 m/s E) 0.80 × 107 m/s Answer: A Var: 1 18) An electron moving perpendicular to a uniform magnetic field of 0.22 T moves in a circle with a speed of 1.5 × 107 m/s. What is the radius of the circle? (e = 1.60 × 10-19 C, melectron = 9.11 × 10-31kg) A) 1.5 mm B) 0.22 mm C) 2.2 mm D) 0.39 mm E) 3.9 mm Answer: E Var: 1 19) An electron is accelerated from rest through a potential difference of 3.75 kV. It enters a region where a uniform 4.0-mT magnetic field is perpendicular to the velocity of the electron. Calculate the radius of the path this electron will follow in the magnetic field. (e = 1.60 × 10-19 C, melectron = 9.11 × 10-31 kg) A) 1.2 cm B) 2.2 cm C) 3.2 cm D) 4.2 cm E) 5.2 cm Answer: E Var: 1 25 Copyright © 2019 Pearson Education, Inc.

20) A doubly charged ion with speed 6.9 × 106 m/s enters a uniform 0.80-T magnetic field, traveling perpendicular to the field. Once in the field, it moves in a circular arc of radius 30 cm. What is the mass of this ion? (e = 1.60 × 10-19 C) A) 11 × 10-27 kg B) 6.7 × 10-27 kg C) 3.3 × 10-27 kg D) 8.2 × 10-27 kg Answer: A Var: 1 21) A proton, starting from rest, accelerates through a potential difference of 1.0 kV and then moves into a magnetic field of 0.040 T at a right angle to the field. What is the radius of the proton's resulting orbit? (e = 1.60 × 10-19 C, mproton = 1.67 × 10-27 kg) A) 0.080 m B) 0.11 m C) 0.14 m D) 0.17 m Answer: B Var: 1 22) A charged particle of mass 0.0040 kg is subjected to a magnetic field which acts at a right angle to its motion. If the particle moves in a circle of radius at a speed of what is the magnitude of the charge on the particle? A) 0.020 C B) 50 C C) 0.00040 C D) 2500 C Answer: A Var: 50+ 23) Alpha particles, each having a charge of +2e and a mass of 6.64 ×10-27 kg, are accelerated in a uniform 0.80-T magnetic field to a final orbit radius of 0.30 m. The field is perpendicular to the velocity of the particles. How long does it take an alpha particle to make one complete circle in the final orbit? (e = 1.60 × 10-19 C) A) 0.15 μs B) 0.25 μs C) 0.33 μs D) 0.40 μs E) 0.49 μs Answer: A Var: 1

24) Alpha particles, each having a charge of +2e and a mass of 6.64 ×10-27 kg, are accelerated in a uniform magnetic field to a final orbit radius of The field is perpendicular to the velocity of the particles. What is the kinetic energy of an alpha particle in the final orbit? (1 eV = 1.60 × 10-19 J, e = 1.60 × 10-19 C) A) 3.0 MeV B) 2.6 MeV C) 3.4 MeV D) 3.9 MeV E) 4.3 MeV Answer: A Var: 50+ 25) A wire along the z-axis carries a current of 4.9 A in the +z direction. Find the magnitude and direction of the force exerted on a 3.3-cm long length of this wire by a uniform magnetic field pointing in the -x direction having a magnitude Answer: 0.070 N, -y direction Var: 50+ 26) A 2.0-m straight wire carrying a current of 0.60 A is oriented parallel to a uniform magnetic field of 0.50 T. What is the magnitude of the magnetic force on it? A) zero B) 0.15 N C) 0.30 N D) 0.60 N Answer: A Var: 2 27) A straight wire carries a current of 10 A at an angle of 30° with respect to the direction of a uniform 0.30-T magnetic field. Find the magnitude of the magnetic force on a 0.50-m length of the wire. A) 0.75 N B) 1.5 N C) 3.0 N D) 6.0 N Answer: A Var: 1 28) What is the force per meter on a straight wire carrying 5.0 A when it is placed in a magnetic field of 0.020 T so that the wire makes an angle of 27° with respect to the magnetic field lines. A) 0.022 N/m B) 0.045 N/m C) 0.17 N/m D) 0.26 N/m Answer: B Var: 1

29) A thin copper rod 1.0 m long has a mass of 0.050 kg and is in a magnetic field of 0.10 T. What minimum current in the rod is needed in order for the magnetic force to balance the weight of the rod? A) 1.2 A B) 2.5 A C) 4.9 A D) 9.8 A Answer: C Var: 1 30) A rigid rectangular loop, measuring 0.30 m by 0.40 m, carries a current of 9.9 A, as shown in the figure. A uniform external magnetic field of magnitude 1.8 T in the -x direction is present. Segment CD is in the xz-plane and forms a 19° angle with the z-axis, as shown. What is the y component of the magnetic force on segment AB of the loop?

A) +5.1 N B) -5.1 N C) +1.7 N D) -1.7 N E) 0.0 N Answer: A Var: 1 31) A straight wire that is 0.60 m and carrying a current of 2.0 A is placed at an angle with respect to the magnetic field of strength 0.30 T. If the wire experiences a force of magnitude 0.18 N, what angle does the wire make with respect to the magnetic field? A) 20° B) 25° C) 30° D) 35° E) 60° Answer: C Var: 1

32) A straight wire is carrying a current of 2.0 A. It is placed at an angle of 60° with respect to a magnetic field of strength 0.20 T. If the wire experiences a force of 0.40 N, what is the length of the wire? A) 1.0 m B) 1.2 m C) 1.4 m D) 1.6 m E) 1.8 m Answer: B Var: 1 33) A straight 1.0-m long wire is carrying a current. The wire is placed perpendicular to a magnetic field of strength 0.20 T. If the wire experiences a force of 0.60 N, what is the current in the wire? A) 2.0 A B) 1.0 A C) 3.0 A D) 4.0 A E) 5.0 A Answer: C Var: 1 34) A wire in the shape of an "M" lies in the plane of the paper. It carries a current of 2.0 A, flowing from A to E, as shown in the figure. It is placed in a uniform magnetic field of 0.75 T in the same plane, directed as shown on the right side of the figure. The figure indicates the dimensions of the wire. Note that AB is parallel to DE and to the baseline from which the magnetic field direction is measured. What are the magnitude and direction of the force acting on section AB of this wire?

A) 0.20 N perpendicular out of the page B) 0.40 N perpendicular out of the page C) 0.11 N perpendicular out of the page D) 0.20 N perpendicular into the page E) 0.11 N perpendicular into the page Answer: C Var: 5

35) A wire in the shape of an "M" lies in the plane of the paper. It carries a current of 2.0 A, flowing from A to E, as shown in the figure. It is placed in a uniform magnetic field of 0.65 T in the same plane, directed as shown on the right side of the figure. The figure indicates the dimensions of the wire. Note that AB is parallel to DE and to the baseline from which the magnetic field direction is measured. What are the magnitude and direction of the force acting on section BC of this wire?

A) 0 N B) 0.090 N perpendicular out of the page C) 0.090 N perpendicular into the page D) 0.060 N perpendicular out of the page E) none of the above Answer: A Var: 5

36) A wire in the shape of an "M" lies in the plane of the paper. It carries a current of 2.0 A, flowing from A to E, as shown in the figure. It is placed in a uniform magnetic field of 0.55 T in the same plane, directed as shown on the right side of the figure. The figure indicates the dimensions of the wire. Note that AB is parallel to DE and to the baseline from which the magnetic field direction is measured. What are the magnitude and direction of the force acting on section CD of this wire?

A) 0.066 N perpendicular into the page B) 0.40 N perpendicular out of the page C) 0.066 N perpendicular out of the page D) 0.40 N perpendicular into the page E) 0.20 N perpendicular out of the page Answer: C Var: 1

37) A wire in the shape of an "M" lies in the plane of the paper. It carries a current of 2.0 A, flowing from A to E, as shown in the figure. It is placed in a uniform magnetic field of 0.85 T in the same plane, directed as shown on the right side of the figure. The figure indicates the dimensions of the wire. Note that AB is parallel to DE and to the baseline from which the magnetic field direction is measured. What are the magnitude and direction of the force acting on section DE of this wire?

A) 0.30 N perpendicular out of the page B) 0.12 N perpendicular into the page C) 0.30 N perpendicular into the page D) 0.12 N perpendicular out of the page E) 0.20 N perpendicular out of the page Answer: B Var: 5 38) A wire in the shape of an "M" lies in the plane of the paper. It carries a current of 2.0 A, flowing from A to E. It is placed in a uniform magnetic field of 0.85 T in the same plane, directed as shown on the right side of the figure. The figure indicates the dimensions of the wire. Note that AB is parallel to DE and to the baseline from which the magnetic field direction is measured. What are the magnitude and direction of the net force acting on this wire?

A) 0.40 N perpendicular out of the page B) 0.10 N perpendicular into the page C) 0.40 N perpendicular into the page D) 0.10 N perpendicular out of the page E) 0.20 N perpendicular out of the page Answer: D Var: 5 32 Copyright © 2019 Pearson Education, Inc.

39) Two long parallel wires separated by 7.5 cm each carry 3.3 A in opposite directions. (μ0 = 4π × 10-7 T ∙ m/A) (a) What magnetic force per length acts on each of the wires? Is it attractive or repulsive? (b) Find the magnitude of the magnetic field midway between the two wires. Answer: (a) 2.9 × N/m, repulsive (b) 3.5 × T Var: 7 40) In the figure, a rectangular current loop is carrying current I1 = 7.0 A, in the direction indicated, near a long wire carrying a current Iw. The long wire is parallel to the sides of the rectangle. The rectangle loop has length 0.80 m and its sides are 0.10 m and 0.70 m from the wire. If the net force on the loop is to have magnitude and is to be directed towards the wire, what must be the magnitude and direction (from top to bottom or from bottom to top in the sketch) of the current Iw in the wire? (μ0 = 4π × 10-7 T ∙ m/A)

Answer: 0.18 A, from bottom to top Var: 50+ 41) Two parallel straight wires are 7.0 cm apart and 50 m long. Each one carries a 18-A current in the same direction. One wire is securely anchored, and the other is attached in the center to a movable cart. If the force needed to move the wire when it is not attached to the cart is negligible, with what magnitude force does the wire pull on the cart? (μ0 = 4π × 10-7 T ∙ m/A) A) 46 mN B) 37 mN C) 66 mN D) 93 mN Answer: A Var: 1

42) Two long parallel wires that are 0.30 m apart carry currents of 5.0 A and 8.0 A in the opposite direction. Find the magnitude of the force per unit length that each wire exerts on the other wire and indicate if the force is attractive or repulsive. (μ0 = 4π × 10-7 T ∙ m/A) A) 2.7 × 10-5 N repulsive B) 7.2 × 10-5 N repulsive C) 3.4 × 10-5 N attractive D) 2.7 × 10-5 N attractive E) 7.2 × 10-5 N attractive Answer: A Var: 1 43) Two long parallel wires are 0.400 m apart and carry currents of 4.00 A and 6.00 A. What is the magnitude of the force per unit length that each wire exerts on the other wire? (μ0 = 4π × 107 T ∙ m/A) A) 2.00 μN/m B) 5.00 μN/m C) 12.0 μN/m D) 16.0 μN/m E) 38.0 μN/m Answer: C Var: 5 44) A flat circular coil has 250 identical loops of very thin wire. Each loop has an area of 0.12 m2 and carries 15 mA of current. This coil is placed in a magnetic field of 0.050 T oriented at 30° to the plane of the loop. What is the magnitude of the magnetic moment of the coil? Answer: 0.45 A ∙ m2 Var: 1 45) A flat coil containing 25 identical loops carries 6.4 A of current. When it is placed in a uniform magnetic field of 0.22 T that is oriented parallel to the plane of the coil, the magnetic torque on it is 3.7 N ∙ m. (a) What is the magnetic moment of the coil? (b) What is the area of each loop? Answer: (a) 17 A ∙ m2 (b) 0.11 m2 Var: 1 46) What is the magnetic moment of a rectangular loop having 120 turns that carries 6.0 A if its dimensions are 4.0 cm × 8.0 cm? A) 0.23 A ∙ m2 B) 2.3 A ∙ m2 C) 23 A ∙ m2 D) 230 A ∙ m2 Answer: B Var: 1 34 Copyright © 2019 Pearson Education, Inc.

47) In the figure, the rectangular loop is pivoted about one side (of length 0.060 m), that coincides with the y-axis. The end (length 0.020 m) of the loop that lies in the xz-plane makes an angle of 37° with the x-axis as shown. The loop carries a current of I = 69 A in the direction shown. (In the side of the loop that is along the y-axis the current is in the +y direction.) If there is a uniform magnetic field of magnitude 9.7 T in the -x direction, find the magnitude of the torque that this magnetic field exerts on the loop.

Answer: 0.64 N ∙ m Var: 1 48) A rigid rectangular loop, measuring 0.30 m by 0.40 m, carries a current of 5.5 A, as shown in the figure. A uniform external magnetic field of magnitude 2.9 T in the -x direction is present. Segment CD is in the xz-plane and forms a 35° angle with the z-axis, as shown. What is the magnitude of the torque that the magnetic field exerts on the loop?

A) 1.1 N ∙ m B) 0.73 N ∙ m C) 1.3 N ∙ m D) 1.4 N ∙ m E) 1.6 N ∙ m Answer: A Var: 1

49) A flat rectangular loop of wire is placed between the poles of a magnet, as shown in the figure. It has dimensions w = 0.60 m and L = 1.0 m, and carries a current I = 2.0 A in the direction shown. The magnetic field due to the magnet is uniform and of magnitude 0.80 T. The loop rotates in the magnetic field and at one point the plane of the loop makes a 30° angle with the field. At that instant, what is the magnitude of the torque acting on the wire due to the magnetic field?

A) 0.30 N ∙ m B) 0.40 N ∙ m C) 0.48 N ∙ m D) 0.83 N ∙ m E) 0.96 N ∙ m Answer: C Var: 1 50) A flat rectangular loop of wire is placed between the poles of a magnet, as shown in the figure. It has dimensions w = 0.60 m and L = 1.0 m, and carries a current I = 2.0 A in the direction shown. The magnetic field due to the magnet is uniform and of magnitude 0.80 T. The loop rotates in the magnetic field and at one point the plane of the loop is parallel to the field. At that instant, what is the magnitude of the torque acting on the wire due to the magnetic field?

A) 0.00 N ∙ m B) 0.40 N ∙ m C) 0.48 N ∙ m D) 0.83 N ∙ m E) 0.96 N ∙ m Answer: E Var: 1

51) A flat rectangular loop of wire is placed between the poles of a magnet, as shown in the figure. It has dimensions w = 0.60 m and L = 1.0 m, and carries a current I = 2.0 A in the direction shown. The magnetic field due to the magnet is uniform and of magnitude 0.80 T. The loop rotates in the magnetic field and at one point the plane of the loop is perpendicular to the field. At that instant, what is the magnitude of the torque acting on the wire due to the magnetic field?

A) 0.00 N ∙ m B) 0.40 N ∙ m C) 0.48 N ∙ m D) 0.83 N ∙ m E) 0.96 N ∙ m Answer: A Var: 1 52) A flat circular coil of wire having 200 turns and diameter 6.0 cm carries a current of 7.0 A. It is placed in a magnetic field of with the plane of the coil making an angle of 30° with the magnetic field. What is the magnitude of the magnetic torque on the coil? A) 2.1 N ∙ m B) 1.2 N ∙ m C) 3.9 N ∙ m D) 5.4 N ∙ m E) 1.0 N ∙ m Answer: A Var: 50+ 53) A flat circular coil has 200 identical loops of very thin wire. Each loop has an area of 0.12 m2 and carries 0.50 A of current. This coil is placed in a magnetic field of 0.050 T oriented at 30° to the plane of the loop. What is the magnitude of the magnetic torque on the coil? A) 0.25 N ∙ m B) 0.52 N ∙ m C) 2.5 N ∙ m D) 5.2 N ∙ m Answer: B Var: 1

54) A flat circular loop carrying a current of 2.0 A is in a magnetic field of 3.5 T. The loop has an area of 0.12 m2 and its plane is oriented at a 37° angle to the field. What is the magnitude of the magnetic torque on the loop? A) 0.10 N ∙ m B) 0.51 N ∙ m C) 0.67 N ∙ m D) 46 N ∙ m Answer: C Var: 1 55) A flat circular loop of wire is in a uniform magnetic field of 0.30 T. The diameter of the loop is 1.0 m, and a 2.0-A current flows in it. What is the magnitude of the magnetic torque on the loop when the plane of the loop is parallel to the magnetic field? A) 0.00 N ∙ m B) 0.41 N ∙ m C) 0.47 N ∙ m D) 0.52 N ∙ m Answer: C Var: 1 56) A flat rectangular loop of wire carrying a 4.0-A current is placed in a uniform 0.60-T magnetic field. The magnitude of the torque acting on this loop when the plane of the loop makes a 30° angle with the field is measured to be 1.1 N ∙ m. What is the area of this loop? A) 0.20 m2 B) 0.40 m2 C) 0.26 m2 D) 0.80 m2 E) 0.53 m2 Answer: E Var: 1 57) A flat circular loop of wire of radius 0.50 m that is carrying a 2.0-A current is in a uniform magnetic field of 0.30 T. What is the magnitude of the magnetic torque on the loop when the plane of its area is perpendicular to the magnetic field? A) 0.00 N ∙ m B) 0.41 N ∙ m C) 0.47 N ∙ m D) 0.52 N ∙ m E) 0.58 N ∙ m Answer: A Var: 1

58) A flat square coil of wire measures 9.5 cm on each side and contains 175 turns of very thin wire. It carries a current of 6.3 A in a uniform 0.84-T magnetic field. What angle less than 90° should the plane of this coil make with the magnetic field direction so that the magnitude of the magnetic torque on it is 6.5 N ∙ m? Answer: 39° Var: 1 59) A flat circular wire loop of area 0.25 m2 carries a current of 5.0 A. This coil lies on a horizontal table with the current flowing in the counterclockwise direction when viewed from above. At this point, the earth's magnetic field is 1.2 × 10-5 T directed 60° below the horizontal. What is the magnitude of the torque that the earth's magnetic field exerts on this loop? A) 2.5 × 10-6 N ∙ m B) 5.0 × 10-6 N ∙ m C) 7.5 × 10-6 N ∙ m D) 1.0 × 10-5 N ∙ m Answer: C Var: 1 60) At a point 10 m away from a long straight thin wire, the magnetic field due to the wire is 0.10 mT. What current flows through the wire? (μ0 = 4π × 10-7 T ∙ m/A) Answer: 5.0 kA Var: 1 61) In the figure, the two long straight wires are separated by a distance of The currents are = 1.0 A to the right in the upper wire and = 8.0 A to the left in the lower wire. What are the magnitude and direction of the magnetic field at point P, that is a distance below the lower wire? (μ0 = 4π × 10-7 T ∙ m/A)

Answer: B = 7.7 × 10-6 T, out of the plane of the paper. Var: 50+ 62) A high power line carries a current of 1.0 kA. What is the strength of the magnetic field this line produces at the ground, 10 m away? (μ0 = 4π × 10-7 T ∙ m/A) A) 4.7 µT B) 6.4 µT C) 20 µT D) 56 µT Answer: C Var: 1 39 Copyright © 2019 Pearson Education, Inc.

63) A long wire carrying a 2.0-A current is placed along the y-axis. What is the magnitude of the magnetic field at a point that is 0.60 m from the origin along the x-axis? (μ0 = 4π × 10-7 T ∙ m/A) A) 0.67 µT B) 1.3 µT C) 0.12 µT D) 6.7 T E) 12 T Answer: A Var: 1 64) A long straight wire carrying a 4-A current is placed along the x-axis as shown in the figure. What is the magnitude of the magnetic field at a point P, located at y = 2 cm, due to the current in this wire? (μ0 = 4π × 10-7 T ∙ m/A)

A) 20 μT B) 30 μT C) 40 μT D) 50 μT E) 60 μT Answer: C Var: 1 65) At point P the magnetic field due to a long straight wire carrying a current of 2.0 A is 1.2 µT. How far is P from the wire? (μ0 = 4π × 10-7 T ∙ m/A) A) 11 cm B) 22 cm C) 33 cm D) 44 cm E) 55 cm Answer: C Var: 1

66) The magnetic field due to the current in a long, straight wire is 8.0 μT at a distance of 4.0 cm from the center of the wire. What is the current in the wire? (μ0 = 4π × 10-7 T ∙ m/A) A) 0.20 A B) 0.40 A C) 0.80 A D) 3.2 A E) 1.6 A Answer: E Var: 1 67) The magnetic field at point P due to a 2.0-A current flowing in a long, straight, thin wire is 8.0 μT. How far is point P from the wire? (μ0 = 4π × 10-7 T ∙ m/A) A) 2.0 cm B) 2.5 cm C) 4.0 cm D) 5.0 cm E) 10 cm Answer: D Var: 1 68) The magnitude of the magnetic field that a long and extremely thin current-carrying wire produces at a distance of 3.0 µm from the center of the wire is 2.0 × 10 -3 T. How much current is flowing through the wire? (μ0 = 4π × 10-7 T ∙ m/A) A) 30 mA B) 190 mA C) 19 mA D) 380 mA Answer: A Var: 1 69) A very long thin wire produces a magnetic field of at a distance of -7 the wire. What is the magnitude of the current? (μ0 = 4π × 10 T ∙ m/A) A) 1.0 mA B) 2.0 mA C) 4000 mA D) 3100 mA Answer: A Var: 27

from

70) How much current must flow through a long straight wire for the magnetic field strength to be 1.0 mT at 1.0 cm from a wire? (μ0 = 4π × 10-7 T ∙ m/A) A) 50 mA B) 9.2 A C) 16 A D) 50 A E) 5.0 mA Answer: D Var: 1 71) At what distance from a long straight wire carrying a current of 5.0 A is the magnitude of the magnetic field due to the wire equal to the strength of Earth's magnetic field of about 5.0 × 10-5 T? (μ0 = 4π × 10-7 T ∙ m/A) A) 1.0 mm B) 1.0 cm C) 2.0 cm D) 3.0 cm E) 4.0 cm Answer: C Var: 1 72) Two long parallel wires that are 0.40 m apart carry currents of 10 A in opposite directions. What is the magnetic field strength in the plane of the wires at a point that is 20 cm from one wire and 60 cm from the other? (μ0 = 4π × 10-7 T ∙ m/A) A) 3.3 µT B) 6.7 µT C) 33 µT D) 67 µT Answer: B Var: 1 73) Two long parallel wires carry currents of 20 A and 5.0 A in opposite directions. The wires are separated by 0.20 m. What is the strength of the magnetic field midway between the two wires? (μ0 = 4π × 10-7 T ∙ m/A) A) 1.0 × 10-5 T B) 2.0 × 10-5 T C) 3.0 × 10-5 T D) 4.0 × 10-5 T E) 5.0 × 10-5 T Answer: E Var: 1

74) Two long parallel wires carry currents of 20 A and 5.0 A in opposite directions. The wires are separated by 20 cm. At what point between the two wires do they produce the same strength magnetic field? A) 4.0 cm from the 20 A wire B) 8.0 cm from the 20 A wire C) 12 cm from the 20 A wire D) 16 cm from the 20 A wire E) 18 cm from the 20 A wire Answer: D Var: 1 75) Three long parallel wires each carry 2.0-A currents in the same direction. The wires are oriented vertically, and they pass through three of the corners of a horizontal square of side 4.0 cm. What is the magnitude of the magnetic field at the fourth (unoccupied) corner of the square due to these wires? (μ0 = 4π × 10-7 T ∙ m/A) A) 1.2 µT B) 2.1 µT C) 12 µT D) 21 µT E) 0 T Answer: D Var: 1 76) Three very long, straight, parallel wires each carry currents of 4.0 A, directed out of the page as shown in the figure. These wires pass through the vertices of a right isosceles triangle as shown. Assume that all the quantities shown in the figure are accurate to two significant figures. What is the magnitude of the magnetic field at point P at the midpoint of the hypotenuse of the triangle? (μ0 = 4π × 10-7 T ∙ m/A)

A) 4.4 µT B) 18 µT C) 57 µT D) 130 µT E) 1.8 µT Answer: C Var: 1

77) What is the strength of the magnetic field at the center of a circular loop of wire of diameter 8.0 cm when a current of 2.0 A flows in the wire? (μ0 = 4π × 10-7 T ∙ m/A) Answer: 31 µT Var: 1 78) A wire carrying a current is shaped in the form of a circular loop of radius 4.0 mm. If the magnetic field strength at its center is with no external magnetic fields present, what is the magnitude of the current flowing through the wire? (μ0 = 4π × 10-7 T ∙ m/A) A) 7.0 A B) 28 A C) 14 A D) 17 A Answer: A Var: 30 79) A circular metal loop of radius 10 cm and three long straight wires carry currents of and as shown in the figure. Each of the straight wires is 20 cm from the center of the loop. The axes are shown in the figure, with the +z-axis coming out of the paper. What is the y component of the resultant magnetic field at the center of the loop? (μ0 = 4π × 10-7 T ∙ m/A)

A) -54 μT B) -60 μT C) -50 μT D) +60 μT E) +50 μT Answer: A Var: 50+

80) A circular metal loop of radius 10 cm and three long straight wires carry currents of and as shown in the figure. Each of the straight wires is 20 cm from the center of the loop. The axes are shown in the figure, with the +z-axis coming out of the paper. What is the z component of the resultant magnetic field at the center of the loop? (μ0 = 4π × 10-7 T ∙ m/A)

A) -360 μT B) +360 μT C) -40 μT D) +40 μT E) -170 μT Answer: A Var: 50+ 81) A long straight wire on the z-axis carries a current of 8.0 A in the +z direction (out of the paper). A circular loop of radius 10 cm lies in the xy-plane and carries a 3.0-A current, as shown in the figure. Point P, at the center of the loop, is 25 cm from the z-axis. An electron is projected from P with a velocity of 3.0 × 106 m/s in the -x direction. What is the y component of the magnetic force on the electron? (e = 1.60 × 10-19, μ0 = 4π × 10-7 T ∙ m/A)

A) -9.0 × 10-18 N B) 9.0 × 10-18 N C) -4.5 × 10-18 N D) 4.5 × 10-18 N E) zero Answer: A Var: 1

82) A flat circular coil having 57 turns of very thin wire has a diameter of 9.5 cm and carries 7.2 A of current. (μ0 = 4π × 10-7 T ∙ m/A) (a) What is the strength of the magnetic field at the center of the coil? (b) If the same length of wire were used to make a coil with twice the original diameter, how large would the magnetic field at the center be when it carried the same current as before? Answer: (a) 5.4 mT (b) 1.4 mT Var: 1 83) An ideal solenoid having 200 turns and carrying a current of 2.0 A is 25 cm long. What is the magnitude of the magnetic field at the center of the solenoid? (μ0 = 4π × 10-7 T ∙ m/A) Answer: 2.0 mT Var: 1 84) In order to trap the starship Enterprise, the diabolical Klingons build a huge ideal solenoid 10 light-years long with a diameter of 2.0 million kilometers. Every kilometer of length of the solenoid contains 100 turns of wire. What magnetic field strength is produced near the center of the solenoid using a current of 2.00 kA? (μ0 = 4π × 10-7 T ∙ m/A) Answer: 251 µT Var: 1 85) An ideal solenoid 20 cm long is wound with 5000 turns of very thin wire. What strength magnetic field is produced at the center of the solenoid when a current of 10 A flows through it? (μ0 = 4π × 10-7 T ∙ m/A) A) 0.0063 T B) 0.20 T C) 3.2 T D) 4.8 T E) 0.31 T Answer: E Var: 1 86) An ideal solenoid having a coil density of 5000 turns per meter is 10 cm long and carries a current of 4.0 A. What is the strength of the magnetic field at its center? A) 3.1 mT B) 6.2 mT C) 13 mT D) 25 mT Answer: D Var: 1

87) An ideal solenoid of length 10 cm consists of a wire wrapped tightly around a wooden core. The magnetic field strength is inside the solenoid. If the solenoid is stretched to by applying a force to it, what does the magnetic field become? A) 1.6 T B) 10.0 T C) 20 T D) 4.0 T Answer: A Var: 50+ 88) An ideal solenoid that is 34.0 cm long is carrying a current of 2.00 A. If the magnitude of the magnetic field generated at the center of the solenoid is 9.00 mT, how many turns of wire does this solenoid contain? (μ0 = 4π × 10-7 T ∙ m/A) A) 860 B) 1590 C) 2320 D) 3180 E) 1220 Answer: E Var: 1 89) How much current must pass through a 400-turn ideal solenoid that is 4.0 cm long to generate a 1.0-T magnetic field at the center? (μ0 = 4π × 10-7 T ∙ m/A) A) 0.013 A B) 13 A C) 22 A D) 40 A E) 80 A Answer: E Var: 1 90) How many turns should a 10-cm long ideal solenoid have if it is to generate a 1.5-mT magnetic field when 1.0 A of current runs through it? (μ0 = 4π × 10-7 T ∙ m/A) A) 12 B) 15 C) 120 D) 1200 E) 3200 Answer: C Var: 1

91) An ideal solenoid with 400 turns has a radius of 0.040 m and is 40 cm long. If this solenoid carries a current of 12 A, what is the magnitude of the magnetic field at the center of the solenoid? (μ0 = 4π × 10-7 T ∙ m/A) A) 16 mT B) 4.9 mT C) 15 mT D) 6.0 mT E) 9.0 mT Answer: C Var: 5 92) An ideal solenoid is wound with 470 turns on a wooden form that is 4.0 cm in diameter and 50 cm long. The windings carry a current in the sense shown in the figure. The current produces a magnetic field of magnitude at the center of the solenoid. What is the current I in the solenoid windings? (μ0 = 4π × 10-7 T ∙ m/A)

A) 3.5 A B) 3.0 A C) 2.6 A D) 4.3 A E) 3.9 A Answer: A Var: 50+

College Physics: A Strategic Approach, 4e (Knight) Chapter 25 EM Induction and EM Waves 25.1 Conceptual Questions 1) An object having a fixed emissivity of 0.725 radiates heat at a rate of 10 W when it is at an absolute temperature T. If its temperature is doubled to 2T, at what rate will it now radiate? A) 20 W B) 40 W C) 80 W D) 160 W E) 320 W Answer: D Var: 1 2) If the absolute temperature of an object is tripled, the thermal power radiated by this object (assuming that its emissivity and size are not affected by the temperature change) will A) increase by a factor of 3. B) increase by a factor of 9. C) increase by a factor of 18. D) increase by a factor of 27. E) increase by a factor of 81. Answer: E Var: 1 3) By what primary heat transfer mechanism does the sun warm the earth? A) convection B) conduction C) radiation D) All of the above processes are equally important in combination. Answer: C Var: 1 4) A flat coil is in a uniform magnetic field. The magnetic flux through the coil is greatest when the plane of its area is A) parallel to the magnetic field. B) at 45° with the magnetic field. C) perpendicular to the magnetic field. Answer: C Var: 1 5) According to Faraday's law, a coil in a strong magnetic field must have a greater induced emf in it than a coil in a weak magnetic field. A) True B) False Answer: B Var: 1 1 Copyright © 2019 Pearson Education, Inc.

6) At a certain instant, coil A is in a 10-T external magnetic field and coil B is in a 1-T external magnetic field. Both coils have the same area and are oriented at right angles to the field. Which coil will have a greater emf induced in it? A) coil A B) coil B C) It is impossible to know without more information about the fields. Answer: C Var: 1 7) A coil of wire containing N turns is in an external magnetic field that is perpendicular to the plane of the coil and it steadily changing. Under these circumstances, an emf ε is induced in the coil. If the rate of change of the magnetic field and the number of turns in the coil are now doubled (but nothing else changes), what will be the induced emf in the coil? A) 2ε B) ε/2 C) 4ε D) ε/4 E) ε Answer: C Var: 1 8) According to Lenz's law, the induced current in a circuit always flows to oppose the external magnetic flux through the circuit. A) True B) False Answer: B Var: 1 9) According to Lenz's law, the induced current in a circuit always flows to oppose the external magnetic field through the circuit. A) True B) False Answer: B Var: 1 10) A coil lies flat on a tabletop in a region where the magnetic field vector points straight up. The magnetic field vanishes suddenly. When viewed from above, what is the sense of the induced current in this coil as the field fades? A) The induced current flows counterclockwise. B) The induced current flows clockwise. C) There is no induced current in this coil. D) The current flows clockwise initially, and then it flows counterclockwise before stopping. Answer: A Var: 1

11) A coil lies flat on a level tabletop in a region where the magnetic field vector points straight up. The magnetic field suddenly grows stronger. When viewed from above, what is the direction of the induced current in this coil as the field increases? A) counterclockwise B) clockwise C) clockwise initially, then counterclockwise before stopping D) There is no induced current in this coil. Answer: B Var: 1 12) A coil lies flat on a horizontal tabletop in a region where the magnetic field points straight down. The magnetic field disappears suddenly. When viewed from above, what is the direction of the induced current in this coil as the field disappears? A) counterclockwise B) clockwise C) clockwise initially, then counterclockwise before stopping D) There is no induced current in this coil. Answer: B Var: 1 13) Two solenoids are close to each other, as shown in the figure, with the switch S open. When the switch is suddenly closed, which way will the induced current flow through the galvanometer in the left-hand solenoid?

A) from left to right B) from right to left C) There will be no induced current through the galvanometer. Answer: B Var: 1

14) An outer metal ring surrounds an inner metal ring, as shown in the figure. The current in the outer ring is counterclockwise and decreasing. What is the direction of the induced current in the inner ring?

A) clockwise B) counterclockwise C) There is no induced current in the inner ring. Answer: B Var: 1 15) A long straight wire lies on a horizontal table and carries an ever-increasing current toward the north. Two coils of wire lie flat on the table, one on either side of the wire. When viewed from above, the direction of the induced current in these coils is A) clockwise in both coils. B) counterclockwise in both coils. C) clockwise in the east coil and counterclockwise in the west coil. D) counterclockwise in the east coil and clockwise in the west coil. Answer: D Var: 1 16) A circular coil lies flat on a horizontal surface. A bar magnet is held fixed above the center of the coil with its north pole pointing downward. What is the direction of the induced current in the coil, as viewed from above? A) clockwise B) counterclockwise C) There is no current in the coil. Answer: C Var: 1 17) A circular coil of copper wire is lying flat on a horizontal table. A bar magnet is held above the center of the coil with its south pole downward. The magnet is released from rest and falls toward the coil. As viewed from above, what is the direction of the current induced in the coil as the magnet approaches the coil? A) counterclockwise B) clockwise C) No current is induced in the coil. D) An emf but no current is induced in the coil. Answer: B Var: 1

18) A circular coil of copper wire is lying flat on a horizontal table. A bar magnet is held above the center of the coil with its south pole downward. The magnet and the coil are now both raised upward with the same velocities. As viewed from above, what is the direction of the current induced in the coil as the magnet approaches the coil? A) counterclockwise B) clockwise C) No current is induced in the coil. D) An emf but no current is induced in the coil. Answer: C Var: 1 19) A circular coil lies flat on a horizontal surface. A bar magnet is held above the center of the coil with its north pole pointing down. If the magnet is dropped from this position what is the direction of the induced current in the coil, as viewed from above? A) counterclockwise B) clockwise C) An emf but no current is induced in the coil. D) There is no current in the coil. Answer: A Var: 1 20) A bar magnet is close to a solenoid, as shown in the figure. As viewed through the solenoid looking toward the magnet, what is the direction (clockwise or counterclockwise) of the current (if any) induced in the solenoid in each case? (a) The magnet is pushed toward the solenoid. (b) The magnet and solenoid both move to the right at 25 cm/s.

Answer: (a) counterclockwise Var: 1

(b) no induced current

21) A bar magnet is oriented above a copper ring, as shown in the figure. If the magnet is pulled upward, what is the direction of the current induced in the ring, as viewed from above?

22) A bar magnet is oriented above a copper ring, as shown in the figure. If the magnet is kept fixed while the ring is dropped, what is the direction of the current induced in the ring, as viewed from below the ring?

A) There is no current in the ring. B) counterclockwise C) clockwise Answer: C Var: 1 23) A bar magnet is oriented above a copper ring, as shown in the figure. The magnet is dropped and passes completely through the ring. As viewed from above, what is the direction of the current induced in the ring after the magnet has completely passed through the ring and is somewhat below it?

A) There is no current in the ring. B) counterclockwise C) clockwise Answer: B Var: 1

24) The three loops of wire shown in the figure are all hanging in the same uniform magnetic field that is perpendicular to the page and does not vary with time. Loop 1 swings back and forth like the bob in a pendulum, Loop 2 rotates about a vertical axis, and Loop 3 oscillates up and down at the end of a spring. Which loop (or loops) will have an emf induced in them?

A) Loop 1 B) Loop 2 C) Loop 3 D) Loops 1 and 3 E) Loops 2 and 3 Answer: B Var: 1 25) The wire in the figure carries a current I that is increasing with time at a constant rate. The wire and the three loops are all in the same plane. What is true about the currents induced in each of the three loops shown?

26) The wire in the figure carries a current I that is decreasing with time at a constant rate. The wire and the three loops are all in the same plane. What is true about the currents induced in each of the three loops shown?

A) No current is induced in any loop. B) The currents are counterclockwise in all three loops. C) The currents are clockwise in all three loops. D) Loop A has clockwise current, loop B has no induced current, and loop C has counterclockwise current. E) Loop A has counterclockwise current, loop B has no induced current, and loop C has clockwise current. Answer: E Var: 1 27) The wire in the figure carries a steady current I. What is true about the currents induced in each of the three loops shown? The wire and the three loops are all in the same plane.

28) As shown in the figure, a coil of wire is placed in the xy-plane, centered on the z-axis. A solenoid is centered on the z-axis and is carrying a steady dc current. Which one of the following actions will not result induce an emf in the coil?

A) Rotate the coil about the x-axis. B) Rotate the coil about the y-axis. C) Rotate the coil about the z-axis. D) Move the coil toward point P. E) Change the current in the solenoid. Answer: C Var: 1 29) In the figure, a bar magnet moves away from the solenoid. The direction of the induced current through the resistor R is

A) from a to b. B) from b to a. C) No current is induced. Answer: A Var: 1 30) As shown in the figure, two parallel wires carry a current I in opposite directions, and this current is decreasing. A rectangular loop is centered between the wires. The direction of the induced current through the resistor R is

A) from a to b. B) from b to a. C) No current is induced. Answer: B Var: 1

31) As shown in the figure, two solenoids are side by side. The switch S is initially open. When S is suddenly closed, the direction of the induced current through the resistor R is

A) from a to b. B) from b to a. C) No current is induced. Answer: B Var: 1 32) As shown in the figure, a battery supplies a steady current to the solenoid on the left. The two solenoids are moving toward each other with speeds v. The direction of the induced current through the resistor R is

A) from a to b. B) from b to a. C) No current is induced. Answer: A Var: 1 33) As shown in the figure, a straight wire carries a current I into the page. The wire passes through the center of a toroidal coil. If the current I is quickly reduced to zero, the direction of the induced current through the resistor R is

A) from a to b. B) from b to a. C) No current is induced. Answer: B Var: 1

34) As shown in the figure, a C-shaped conductor is in a uniform magnetic field B out of the page, and this field is increasing. What is the polarity of the induced emf in terminals X and Y?

A) X and Y are at the same potential. B) X is positive and Y is negative. C) Y is positive and X is negative. Answer: C Var: 1 35) As shown in the figure, a metal bar is in contact with a pair of parallel rails. A steady, uniform, magnetic field B is present directed to the right. The bar is moving upward with velocity of magnitude ν. What is the polarity of the induced emf in terminals X and Y?

A) X and Y are at the same potential. B) X is positive and Y is negative. C) Y is positive and X is negative. Answer: A Var: 1 36) As shown in the figure, two solenoids are in line. The switch S, initially closed, is suddenly opened. Just after opening S, what is the polarity of the induced emf in terminals X and Y?

A) X and Y are at the same potential. B) X is positive and Y is negative. C) Y is positive and X is negative. Answer: B Var: 1

37) A circular wire ring is situated above a long straight wire, as shown in the figure. The straight wire has a current I flowing to the right, and this current is increasing at a constant rate. Which of the following statements is true?

A) There is an induced current in the wire ring, directed in clockwise orientation. B) There is an induced current in the wire ring, directed in a counterclockwise orientation. C) There is no induced current in the wire ring. Answer: A Var: 1 38) As shown in the figure, a metal bar is in contact with a pair of parallel rails and is in motion with an upward velocity of magnitude ν. A uniform magnetic field is present, directed downward as shown. The direction of the induced current through the resistor R is

A) from a to b. B) from b to a. C) No current is induced. Answer: C Var: 1 39) As shown in the figure, one end of a metal bar is in contact with a circular rail and the other end is pivoted at P. A steady uniform, magnetic field B into the page is present. As the bar rotates about point P in a clockwise direction, the direction of the induced current through the resistor R is

A) from a to b. B) from b to a. C) No current is induced. Answer: B Var: 1

40) As shown in the figure, a metal bar is in contact with a pair of metal parallel rails. A steady uniform magnetic field B, perpendicular to the plane of the rails and pointing outward from the page, is present. The bar is in downward motion with velocity of magnitude ν. The direction of the induced current through the resistor R is

A) from a to b. B) from b to a. C) No current is induced. Answer: A Var: 1 41) As shown in the figure, a straight wire carries a steady current I. A metal bar is in contact with a pair of rails and is in upward motion with velocity of magnitude ν. The polarity of the induced emf in terminals X and Y is

A) X and Y are at the same potential. B) X is positive and Y is negative. C) Y is positive and X is negative. Answer: C Var: 1 42) Which one of the following is not an electromagnetic wave? A) ultraviolet B) infrared C) radio waves D) sound waves E) gamma rays Answer: D Var: 1 43) Which one of the following lists gives the correct order of the electromagnetic spectrum from low to high frequencies? A) radio waves, infrared, microwaves, ultraviolet, visible, x-rays, gamma rays B) radio waves, ultraviolet, x-rays, microwaves, infrared, visible, gamma rays C) radio waves, microwaves, infrared, visible, ultraviolet, x-rays, gamma rays D) radio waves, microwaves, visible, x-rays, infrared, ultraviolet, gamma rays E) radio waves, infrared, x-rays, microwaves, ultraviolet, visible, gamma rays Answer: C Var: 1 13 Copyright © 2019 Pearson Education, Inc.

44) Which one of the following lists gives the correct order of the electromagnetic waves from longer wavelength to shorter wavelength? A) radio waves, infrared, microwaves, ultraviolet, visible, x-rays, gamma rays B) radio waves, ultraviolet, x-rays, microwaves, infrared, visible, gamma rays C) radio waves, microwaves, visible, x-rays, infrared, ultraviolet, gamma rays D) radio waves, microwaves, infrared, visible, ultraviolet, x-rays, gamma rays E) radio waves, infrared, x-rays, microwaves, ultraviolet, visible, gamma rays Answer: D Var: 1 45) In an electromagnetic wave in free space, the electric and magnetic fields are A) parallel to one another and perpendicular to the direction of wave propagation. B) parallel to one another and parallel to the direction of wave propagation. C) perpendicular to one another and perpendicular to the direction of wave propagation. D) perpendicular to one another and parallel to the direction of wave propagation. Answer: C Var: 1 46) Which of the following statements about electromagnetic waves in free space are true? (There could be more than one correct choice.) A) The higher-frequency travel faster than the lower-frequency waves. B) The higher-frequency waves have shorter wavelengths than the lower-frequency waves. C) The wavelengths of the visible waves are some of the longest electromagnetic waves. D) The wavelengths of the visible waves are some of the shortest electromagnetic waves. E) The electric field vector is always at right angles to the magnetic field vector. Answer: B, E Var: 1 47) Which one of the following types of electromagnetic wave travels through space the fastest? A) radio waves B) infrared C) ultraviolet D) microwaves E) They all travel through space at the same speed. Answer: E Var: 1

48) At a certain instant in time, the electric field of an electromagnetic wave in free space points in the -z direction, and the magnetic field points in the +y direction. In what direction is this wave traveling? A) +x direction B) -x direction C) +y direction D) -z direction E) +z direction Answer: A Var: 1 49) An electromagnetic wave travels in free space in the +y direction, as shown in the figure. If the electric field at the origin is along the +z direction, what is the direction of the magnetic field?

A) +z B) -z C) +y D) +x E) -x Answer: D Var: 1

50) For a certain electromagnetic wave in free space, at one instant the electric field vector points in the +z direction while the magnetic field vector points in the +x direction, as shown in the figure. In what direction is this wave traveling?

A) +x B) -x C) +y D) -y E) +z Answer: C Var: 1 51) An electromagnetic wave is propagating towards the west in free space. At a certain moment the direction of the magnetic field vector associated with this wave points vertically upward. What is the direction of the electric field vector? A) horizontal and pointing south B) vertical and pointing down C) horizontal and pointing north D) vertical and pointing upward E) horizontal and pointing east Answer: A Var: 1 52) For an electromagnetic wave in free space having an electric field of amplitude E and a magnetic field of amplitude B, the ratio of B/E is equal to A) c B) c2 C) 1/c D) 1/c2 E) Answer: C Var: 1

53) Which one of the following expressions is the correct representation for the speed of light in vacuum? A) B) C) D) 1 / E) 1 / ε0μ0 Answer: D Var: 1 54) Which of the following statements about electromagnetic waves in free space are true? (There could be more than one correct choice.) A) The electric field carries more energy than the magnetic field. B) The electric and magnetic fields have equal amplitudes. C) The electric field carries the same mount of energy as the magnetic field. D) The frequency of the magnetic field is the same as the frequency of the electric field. E) The frequency of the electric field is higher than the frequency of the magnetic field. Answer: C, D Var: 1 55) If unpolarized light of intensity I0 passes through an ideal polarizer, what is the intensity of the emerging light? A) I0 B) I0/2 C) I0/4 D) I0/ E) I0/16 Answer: B Var: 1 56) For a beam of light, the direction of polarization is defined as A) the beam's direction of travel. B) the direction of the electric field's vibration. C) the direction of the magnetic field's vibration. D) the direction that is perpendicular to both the electric and magnetic field vectors. Answer: B Var: 1 57) As the temperature of a blackbody increases, what happens to the peak wavelength of the light it radiates? A) It gets longer. B) It gets shorter. C) The wavelength is not affected by the temperature of the object. Answer: B Var: 1 17 Copyright © 2019 Pearson Education, Inc.

58) Two identical metal bars are heated up until they are both glowing. One of them is "red hot" and the other is "blue hot." Which one is hotter, the one that glows red or the one that glows blue? A) the red one B) the blue one C) We cannot tell without knowing more about the two bars. Answer: B Var: 1 59) A photon of blue light and a photon of red light are traveling in vacuum. The photon of blue light A) has a smaller wavelength than a photon of red light and travels with the same speed. B) has a smaller wavelength than a photon of red light and travels with a greater speed. C) has a longer wavelength than a photon of red light and travels with the same speed. D) has a longer wavelength than a photon of red light and travels with a greater speed. Answer: A Var: 1 60) Increasing the brightness of a beam of light without changing its color will increase A) the number of photons per second traveling in the beam. B) the energy of each photon. C) the speed of the photons. D) the frequency of the light. E) the wavelength of the photons. Answer: A Var: 1 61) If the wavelength of a photon is doubled, what happens to its energy? A) It is reduced to one-half of its original value. B) It stays the same. C) It is doubled. D) It is increased to four times its original value. E) It is reduced to one-fourth of its original value. Answer: A Var: 1 62) If you double the frequency of the light in a laser beam, but keep the number of photons per second in the beam fixed, which of the following statements are correct? (There could be more than one correct choice.) A) The power in the beam does not change. B) The intensity of the beam doubles. C) The energy of individual photons does not change. D) The energy of individual photons doubles. E) The wavelength of the individual photons doubles. Answer: B, D Var: 1 18 Copyright © 2019 Pearson Education, Inc.

63) Which of the following actions will increase the energy of a photon? (There could be more than one correct choice.) A) Increase its wavelength. B) Increase its frequency. C) Decrease its wavelength. D) Decrease its frequency. E) Increase its speed. Answer: B, C Var: 1 25.2 Problems 1) A sphere of surface area 1.25 m2 and emissivity 1.0 is at a temperature of 100°C. At what rate does it radiate heat into empty space? (σ = 5.67 × 10-8 W/m2 ∙ K4) A) 7.1 W B) 0.71 mW C) 1.4 kW D) 9.9 mW E) 3.7 W Answer: C Var: 1 2) The cylindrical filament in a light bulb has a diameter of 0.050 mm, an emissivity of 1.0, and a temperature of 3000°C. How long should the filament be in order to radiate 60 W of power? (σ = 5.67 × 10-8 W/m2 ∙ K4) A) 11 cm B) 9.4 cm C) 8.6 cm D) 7.2 cm E) 5.9 cm Answer: E Var: 1 3) How much power does a sphere with a radius of 10 cm radiate into empty space if is has an emissivity of 1.0 and is kept at a temperature of 400 K? (σ = 5.67 × 10-8 W/m2 ∙ K4) A) 60 W B) 70 W C) 180 W D) 210 W E) 360 W Answer: C Var: 1

4) A blacksmith is flattening a steel plate having dimensions 10 cm × 15 cm × 1 mm. He has heated the plate to 900 K. If the emissivity of the plate is 0.75, at what rate does it lose energy by radiation? Ignore any heat exchange with the surroundings. (σ = 5.67 × 10-8 W/m2 ∙ K4) A) 360 W B) 760 W C) 790 W D) 850 W E) 880 W Answer: D Var: 1 5) The radius of a star is 6.95 × 108 m, and its rate of radiation has been measured to be 5.32 × 1026 W. Assuming that it is a perfect emitter, what is the temperature of the surface of this star? (σ = 5.67 × 10-8 W/m2 ∙ K4) A) 6.27 × 103 K B) 8.25 × 103 K C) 8.87 × 103 K D) 3.93 × 107 K E) 5.78 × 107 K Answer: A Var: 1 6) A giant star radiates energy at the rate of 3.0 × 1030 W, and its surface temperature has been measured to be 3000 K. Assuming that it is a perfect emitter, what is the radius of this star?(σ = 5.67 × 10-8 W/m2 ∙ K4) A) 7.8 × 1010 m B) 8.7 × 1010 m C) 1.4 × 1010 m D) 1.9 × 1011 m E) 2.3 × 1011 m Answer: E Var: 1 7) In an electric furnace used for refining steel, the temperature is monitored by measuring the radiant power emitted through a small hole in the wall of the furnace, of area 0.5 cm2. This hole acts like a perfect blackbody radiator having the same temperature as the interior of the furnace. If the temperature of the furnace (and therefore of the hole) is to be maintained at 1650°C, how much power will the hole radiate? A) 20 W B) 30 W C) 40 W D) 50 W Answer: C Var: 1 20 Copyright © 2019 Pearson Education, Inc.

8) A flat circular loop of radius 0.10 m is rotating in a uniform magnetic field of 0.20 T. Find the magnetic flux through the loop when the plane of the loop and the magnetic field vector are parallel. A) 0 T ∙ m2 B) 3.1 × 10-3 T ∙ m2 C) 5.5 × 10-3 T ∙ m2 D) 6.3 × 10-3 T ∙ m2 Answer: A Var: 1 9) A flat circular loop of radius 0.10 m is rotating in a uniform magnetic field of 0.20 T. Find the magnetic flux through the loop when the plane of the loop and the magnetic field vector are perpendicular. A) 0 T ∙ m2 B) 3.1 × 10-3 T ∙ m2 C) 5.5 × 10-3 T ∙ m2 D) 6.3 × 10-3 T ∙ m2 Answer: D Var: 1 10) A flat circular loop of radius 0.10 m is rotating in a uniform magnetic field of 0.20 T. Find the magnetic flux through the loop when the plane of the loop and the magnetic field vector are at an angle of 30°. A) 0 T ∙ m2 B) 3.1 × 10-3 T ∙ m2 C) 5.5 × 10-3 T ∙ m2 D) 6.3 × 10-3 T ∙ m2 Answer: B Var: 1 11) A 2.00-m long metal wire is formed into a square and placed in the horizontal xy-plane. A uniform magnetic field is oriented at 30° above the horizontal with a strength of 0.344 T. What is the magnetic flux through the square due to this field? A) 0.0745 T ∙ m2 B) 0.172 T ∙ m2 C) 0.0430 T ∙ m2 D) 0.298 T ∙ m2 Answer: C Var: 1

12) A rectangular loop of wire that can rotate about an axis through its center is placed between the poles of a magnet in a magnetic field with a strength of 0.40 T, as shown in the figure. The length of the loop L is 0.16 m and its width w is 0.040 m. What is the magnetic flux through the loop when the plane of the loop is perpendicular to the magnetic field?

A) 13 × 10-3 T ∙ m2 B) 2.6 × 103 T ∙ m2 C) 0.80 T ∙ m2 D) 2.6 × 10-3 T ∙ m2 E) 0 T ∙ m2 Answer: D Var: 1 13) A rectangular loop of wire that can rotate about an axis through its center is placed between the poles of a magnet in a magnetic field with a strength of 0.40 T, as shown in the figure. The length of the loop L is 0.16 m and its width w is 0.040 m. What is the magnetic flux through the loop when the plane of the loop is parallel to the magnetic field?

A) 13 × 10-3 T ∙ m2 B) 2.6 × 103 T ∙ m2 C) 0.80 T ∙ m2 D) 2.6 × 10-3 T ∙ m2 E) 0 T ∙ m2 Answer: E Var: 1

14) A rectangular loop of wire that can rotate about an axis through its center is placed between the poles of a magnet in a magnetic field with a strength of 0.40 T, as shown in the figure. The length of the loop L is 0.16 m and its width w is 0.040 m. What is the magnetic flux through the loop when the plane of the loop makes an angle of 60° with the magnetic field?

A) 2.6 × 10-3 T ∙ m2 B) 1.3 × 10-3 T ∙ m2 C) 0 T ∙ m2 D) 2.2 × 10-3 T ∙ m2 E) 0.80 T ∙ m2 Answer: D Var: 1 15) As shown in the figure, a large round loop of 269 turns and radius 67.0 cm carries a current of I = A small square loop of 31.0 turns and 1.00 cm on a side is placed at the center of the large loop. If the current in the large loop drops to 0.00 A in 0.0470 s, find the induced emf in the small loop. The square loop is small enough that you can assume that the magnetic field in its region is uniform and equal to the magnetic field at the center of the round loop. (μ0 = 4π × 10-7 T ∙ m/A) Answer: 1.30 × 10-3 V Var: 50+ 16) A flat circular loop having one turn and radius 5.0 cm is positioned with its plane perpendicular to a uniform 0.60-T magnetic field. The area of the loop is suddenly reduced to essentially zero in 0.50 ms. What emf is induced in the loop? Answer: 9.4 V Var: 1 17) A flat coil having 40 turns, each one of cross-sectional area 12.0 cm2, is oriented with its plane perpendicular to a uniform magnetic field. The field varies steadily from 0.00 T to 1.20 T in 20.0 ms. What emf is induced in the coil during this time? Answer: 2.88 V Var: 1

18) A flat circular coil having 16 turns, each of diameter 20 cm, is in a uniform and steady 0.13T magnetic field. (a) Find the total magnetic flux through the coil when the field is perpendicular to the plane of the coil. (b) If the coil is rotated in 10 ms so its plane is parallel to the field, find the average induced emf in the coil. Answer: (a) 0.065 T ∙ m2 (b) 6.5 V Var: 1 19) As shown in the figure, a uniform magnetic field B is confined to a cylindrical volume of radius 0.050 m. This field is directed into the plane of the page and is increasing at a constant rate of Calculate the magnitude and direction (clockwise or counterclockwise) of the current induced in a circular wire ring of radius 0.16 m and resistance that encircles the magnetic field region.

Answer: 1.0 × 10-3 A, counterclockwise Var: 50+ 20) A flux of 4.0 × 10-5 T ∙ m2 is maintained through a coil of area 7.5 cm2 for 0.50 s. What emf is induced in this coil during this time by this flux? A) 8.0 × 10-5 V B) 4.0 × 10-5 V C) 3.0 × 10-5 V D) 2.0 × 10-5 V E) No emf is induced in this coil. Answer: E Var: 1

21) A bar magnet is pushed through a coil of wire of cross-sectional area 0.020 m2 as shown in the figure. The coil has seven turns, and the rate of change of the strength of the magnetic field in it due to the motion of the bar magnet is 0.040 T/s. What is the magnitude of the induced emf in that coil of wire?

A) 5.6 × 10-3 V B) 5.6 × 10-2 V C) 5.6 × 10-1 V D) 5.6 × 10-4 V E) 5.6 × 10-5 V Answer: A Var: 1 22) A circular conducting loop with a radius of and a small gap filled with a resistor is oriented in the If a uniform magnetic field of making an angle of with the increases to in what is the magnitude of the current that will be caused to flow in the loop if it has negligible resistance? A) 0.01530393 A B) 0.08835729 A C) 0.15303932 A D) 0 A Answer: C Var: 50+ 23) A closed flat loop conductor with radius is located in a changing uniform magnetic field. If the emf induced in the loop is what is the rate at which the magnetic field strength is changing if the magnetic field is oriented perpendicular to the plane in which the loop lies? A) 0.16 T/s B) 1.0 T/s C) 0.080 T/s D) 2.0 T/s Answer: A Var: 9

24) A conductor is formed into a flat loop that encloses an area of The plane of the loop is oriented at a 30.0° angle with the xy-plane. A uniform time-varying magnetic field is oriented parallel to the z-axis. If the emf induced in the loop is what is the rate at which the magnetic field strength is changing? A) 29 T/s B) 22 T/s C) 50 T/s D) 13 T/s Answer: A Var: 50+ 25) A circular coil of 20 turns and radius 5.0 cm is placed with its plane oriented at 90° to a uniform magnetic field of The field is now increased at a steady rate, reaching a value of after 4.0 seconds. What emf is induced in the coil? A) 0.016 V B) 0.021 V C) 0.026 V D) 0.031 V E) 0.036 V Answer: A Var: 50+ 26) The magnetic flux through a coil changes steadily from 4.0 × 10-5 T ∙ m2 to 5.0 × 10-5 T ∙ m2 in 0.10 s. What emf is induced in this coil? A) 5.0 × 10-4 V B) 4.0 × 10-4 V C) 1.0 × 10-4 V D) None of the given answers are correct. Answer: C Var: 3 27) A flat coil is wrapped with 200 turns of very thin wire on a square frame with sides 18 cm long. A uniform magnetic field is applied perpendicular to the plane of the coil. If the field changes uniformly from 0.50 T to 0.00 T in 8.0 s, find the emf induced in the coil. A) 2.1 mV B) 4.1 mV C) 0.21 V D) 0.41 V Answer: D Var: 1

28) A flat square coil of wire with 15 turns and an area of 0.40 m2 is placed with the plane of its area parallel to a magnetic field of 0.75 T. The coil is flipped so its plane is perpendicular to the magnetic field in a time of 0.050 s. What is the magnitude of the average induced emf in the coil? A) 6.0 V B) 36 V C) 45 V D) 90 V Answer: D Var: 1 29) A flat coil having 160 turns, each with an area of 0.20 m2, is placed with the plane of its area perpendicular to a magnetic field of 0.40 T. The magnetic field changes uniformly from 0.40 T in the +x direction to 0.40 T in the -x direction in 2.0 s. If the resistance of the coil is 16 Ω, at what rate is power generated in the coil during this change? A) 5.0 W B) 10 W C) 15 W D) 20 W Answer: B Var: 1 30) As shown in the figure, a wire and a 10-Ω resistor are used to form a circuit in the shape of a square with dimensions 20 cm by 20 cm. A uniform but non-steady magnetic field is directed into the plane of the circuit. The magnitude of the magnetic field is steadily decreased from 2.70 T to 0.90 T in a time interval of 96 ms. What is the induced current in the circuit, and what is its direction through the resistor?

A) 75 mA, from b to a B) 45 mA, from b to a C) 75 mA, from a to b D) 45 mA, from a to b E) 110 mA, from a to b Answer: A Var: 50+

31) A round flat conducting loop is placed perpendicular to a uniform 0.50 T magnetic field. If the area of the loop increases at a rate of 3.0 × /s, what is the induced emf in the loop? A) 4.3 mV B) 0 mV C) 1.5 mV D) 1.7 mV E) 5.5 mV Answer: C Var: 5 32) The area of a rectangular loop of wire is 3.6 × . The loop is placed in a uniform magnetic field that changes steadily from 0.20 T to 1.4 T in 1.6 s. The plane of the loop is perpendicular to the direction of the magnetic field. What is the magnitude of the induced emf in that loop? A) 2.8 × V B) 2.7 × V C) 0 V D) 1.8 × V E) 3.0 × V Answer: B Var: 5 33) A constant uniform magnetic field of 0.50 T is applied at right angles to the plane of a flat rectangular loop of area 3.0 × . If the area of this loop changes steadily from its original -3 2 value to a new value of 1.6 × 10 m in 1.6 s, what is the emf induced in the loop? A) 1.6 × V B) 0 V C) 7.5 × V D) 4.4 × V E) 9.0 × V Answer: D Var: 5 34) A flat rectangular coil with dimensions of 8.0 cm × 10 cm is dropped from a zero magnetic field position into a 1.4-T magnetic field in 0.10 s. The coil has 60 turns and is perpendicular to the magnetic field. What is the average induced emf in the coil as a result of this action? A) 8.6 V B) 2.4 V C) 6.7 V D) 3.6 V E) 0 V Answer: C Var: 5

35) A single-turn loop of wire, having a resistance of 8.00 Ω and a cross-sectional area 200 cm2, is perpendicular to a uniform magnetic field that increases steadily from 0.200 T to 2.800 T in 2.20 seconds. What is the magnitude of the induced current in the loop? A) 2.95 A B) 3.18 A C) 0 A D) 3.18 mA E) 2.95 mA Answer: E Var: 1 36) A round flat metal coil has 180 turns and negligible resistance. It is connected in a series circuit with a resistor, with nothing else in the circuit. You measure that a current flows through the resistor when a magnetic field through the coil, perpendicular to its area, is changing at What is the radius of the coil? A) 0.25 m B) 0.014 m C) 0.54 m D) 0.043 m Answer: A Var: 50+ 37) As shown in the figure, a region of space contains a uniform magnetic field. The magnitude of this field is 2.8 T, and it is directed straight into the plane of the page in the region shown. Outside this region the magnetic field is zero. A rectangular loop measuring 0.20 m by 0.60 m and having a resistance of 2 Ω is being pulled into the magnetic field by an external force, as shown. (a) What is the direction (clockwise or counterclockwise) of the current induced in the loop? (b) Calculate the magnitude of the external force Fext that is required to move the loop at a constant speed of 3.9 m/s.

Answer: (a) counterclockwise Var: 50+

(b) 6 × 10-1 N

38) A airplane having a metal surface and a wingspan of 25.0 m flies horizontally at 200. m/s where the earth's magnetic field is vertical with magnitude 45.0 μT. (a) What emf is induced across the wings? (b) What wingspan would the plane need to produce 1.00-V emf across its wings? (c) The plane now reverses direction. Does the polarity of the wingtip emf change? That is, if the left wing was positive before, does it now become negative? Answer: (a) 0.225 V (b) 111. m (c) no polarity change Var: 5 39) An eagle, with a wingspread of 2.0 m, flies toward the north at 8.0 m/s in a region where the vertical component of the earth's magnetic field is 0.20 × 10-4 T. What emf would be developed between the eagle's wing tips? (It has been speculated that this phenomenon could play a role in the navigation of birds, but the effect is too small, in all likelihood.) Answer: 0.32 mV Var: 1 40) A long vertical wire carries a steady 70 A current. As shown in the figure, a pair of horizontal rails are 0.20 m apart. A 20-Ω resistor connects points a and b, at the end of the rails. A bar is in contact with the rails, and is moved by an external force with a constant horizontal velocity of 0.90 m/s to the right, as shown. The bar and the rails have negligible resistance. At the instant that the bar is 0.20 m from the wire, what are the induced current in the resistor and its direction through the resistor? (μ0 = 4π × 10-7 T ∙ m/A)

A) 0.63 μA, from a to b B) 0.63 μA, from b to a C) 0.32 μA, from a to b D) 0.32 μA, from b to a E) 1.9 μA, from b to a Answer: A Var: 1

41) An electromagnetic flowmeter is useful when it is desirable not to interrupt the system in which the fluid is flowing (such as the blood in an artery during heart surgery). Such a device is illustrated in the figure. The conducting fluid moves with speed v in a tube of diameter d. Perpendicular to this tube is a magnetic field B. A voltage V is induced between opposite sides of the tube due to the motion of the conducting fluid in the magnetic field. For a certain case, B = 0.120 T, d = 1.2 cm, and the measured voltage is Determine the speed of the fluid.

A) 2.0 m/s B) 11 m/s C) 0.075 m/s D) 1.1 m/s E) 750 m/s Answer: A Var: 50+ 42) It is known that birds can detect the earth's magnetic field, but the mechanism of how they do this is not known. It has been suggested that perhaps they detect a motional emf as they fly north to south, but it turns out that the induced voltages are small compared to the voltages normally encountered in cells, so this is probably not the mechanism involved. To check this out, calculate the induced voltage across the wingtips of a wild goose with a wingspan of if it is flying directly south at at a point where the earth's magnetic field is 5.0 ×10-5 T directed downward from the horizontal by A) 0.50 mV B) 0.60 mV C) 0.78 mV D) 0.060 mV E) 0.25 mV Answer: A Var: 50+

43) A conducting rod of length ℓ= 25 cm is placed on a U-shaped metal wire that is connected to a lightbulb having a resistance of 8.0 Ω, as shown in the figure. The wire and the rod are in the plane of the page. A constant uniform magnetic field of strength 0.40 T is applied perpendicular to and into the paper. An applied external force pulls the rod to the right with a constant speed of 6.0 m/s. What is the magnitude of the emf induced in the rod?

A) 0.20 V B) 0.30 V C) 0.40 V D) 0.50 V E) 0.60 V Answer: E Var: 1 44) A conducting rod with a length ℓ = 25 cm is placed on a U-shaped metal wire that is connected to a lightbulb having a resistance of 8.0 Ω as shown in the figure. The wire and the rod are in the plane of the page. A constant uniform magnetic field of strength 0.40 T is applied perpendicular to and into the paper. An external applied force moves the rod to the right with a constant speed of 6.0 m/s. What are the magnitude and direction of the induced current in the circuit?

A) 17 mA clockwise B) 17 mA counterclockwise C) 75 mA counterclockwise D) 75 mA clockwise E) 52 mA clockwise Answer: C Var: 1

45) A conducting rod whose length is ℓ = 25 cm is placed on a U-shaped metal wire that is connected to a lightbulb having a resistance of 8.0 Ω as shown in the figure. The wire and the rod are in the plane of the page. A constant uniform magnetic field of strength 0.40 T is applied perpendicular to and out of the paper. An external applied force moves the rod to the left with a constant speed of 12 m/s. What are the magnitude and direction of the induced current in the

circuit? A) 150 mA clockwise B) 150 mA counterclockwise C) 34 mA counterclockwise D) 34 mA clockwise E) 100 mA clockwise Answer: B Var: 1 46) A conducting rod whose length is ℓ = 1.60 m is placed on frictionless U-shaped metal rails that is connected to a lightbulb having a resistance of 4.00 Ω as shown in the figure. The rails and the rod are in the plane of the page. A constant uniform magnetic field of strength 2.20 T is applied perpendicular to and out of the paper. What is the magnitude of the external applied force needed to move the rod to the right with a constant speed of 6.00 m/s?

A) 8.60 N B) 9.30 N C) 10.6 N D) 12.6 N E) 18.6 N Answer: E Var: 1

47) A conducting rod whose length is ℓ = 1.60 m is placed on frictionless U-shaped metal rails that is connected to a lightbulb having a resistance of 4.00 Ω as shown in the figure. The rails and the rod are in the plane of the page. A constant uniform magnetic field of strength 2.20 T is applied perpendicular to and out of the paper. An external applied force moves the rod to the right with a constant speed of 6.00 m/s. At what rate is energy dissipated in the lightbulb?

A) 60.0 W B) 121 W C) 21.2 W D) 112 W E) 11.5 W Answer: D Var: 1 48) A conducting rod whose length is ℓ = 27.0 cm is placed on frictionless U-shaped metal rails that is connected to a lightbulb having a resistance of 5.00 Ω as shown in the figure. The rails and the rod are in the plane of the page. A constant uniform magnetic field of strength 1.20 T is applied perpendicular to and out of the paper. An external applied force moves the rod to the right with a constant speed. At what speed should the rod be pulled so that the lightbulb will consume energy at a rate of 1.10 W?

A) 2.00 m/s B) 3.50 m/s C) 4.26 m/s D) 6.00 m/s E) 7.24 m/s Answer: E Var: 1

49) A cordless phone operates at 900 MHz. What is the wavelength of the electromagnetic wave used by this phone? (c = 3.0 × 108 m/s) Answer: 0.33 m Var: 1 50) An FM radio station broadcasts at 96.7 MHz. What is the wavelength of the radio wave used for this broadcast? (c = 3.0 × 108 m/s) Answer: 3.1 m Var: 1 51) What is the wavelength used by a radio station that broadcasts at a frequency of 920 kHz? (c = 3.00 × 108 m/s) A) 22.6 m B) 226 m C) 326 m D) 175 m E) 276 m Answer: C Var: 1 52) The frequency of a microwave signal is 9.76 GHz. What is its wavelength? (c = 3.00 × 108 m/s) A) 3.07 cm B) 2.07 cm C) 1.07 cm D) 5.07 cm E) 4.07 cm Answer: A Var: 1 53) What is the frequency of 20-mm microwaves? (c = 3.0 × 108 m/s) A) 100 MHz B) 400 MHz C) 15 GHz D) 73 GHz Answer: C Var: 1

54) The wavelength of an electromagnetic wave is 600 nm. What is its frequency? (c = 3.0 × 108 m/s) A) 200 × 1012 Hz B) 300 × 1012 Hz C) 400 × 1012 Hz D) 500 × 1012 Hz E) 600 × 1012 Hz Answer: D Var: 1 55) A certain part of the electromagnetic spectrum ranges from 200 nm to 400 nm. What is the highest frequency associated with this portion of the spectrum? (c = 3.00 × 108 m/s) A) 1.50 × 1014 Hz B) 7.50 × 1013 Hz C) 7.50 × 1014 Hz D) 7.50 × 1015 Hz E) 1.50 × 1015 Hz Answer: E Var: 1 56) A certain part of the electromagnetic spectrum ranges from 200 nm to 400 nm. What is the lowest frequency associated with this portion of the spectrum? (c = 3.00 × 108 m/s) A) 1.50 × 1014 Hz B) 7.50 × 1013 Hz C) 7.50 × 1014 Hz D) 7.50 × 1015 Hz E) 1.50 × 1015 Hz Answer: C Var: 1 57) A 7.55 × Hz electromagnetic wave travels in carbon tetrachloride with a speed of 2.05 ×108 m/s. What is the wavelength of the wave in this material? A) 272 nm B) 301 nm C) 338 nm D) 361 nm E) 397 nm Answer: A Var: 50+

58) The distance between two asteroids is 1600 km. How much time does it take for a light signal to go from one asteroid to the other? (c = 3.0 × 108 m/s) A) 19 ms B) 4.5 ms C) 5.3 ms D) 13 ms E) 19 µs Answer: C Var: 1 59) How far does a beam of light travel in 2.0 ms? (c = 3.0 × 108 m/s) A) 6.0 × 105 m B) 0.66 × 105 m C) 90 m D) 70 m E) 60 m Answer: A Var: 1 60) How far does light travel in 1.0 μs? (c = 3.0 × 108 m/s) A) 3.0 × 1014 m B) 0.30 km C) 3.0 m D) 30 cm Answer: B Var: 1 61) How long does it take light to travel 1.0 m? (c = 3.0 × 108 m/s) A) 3.3 ns B) 3.3 μs C) 3.3 ms D) 3.3 s Answer: A Var: 1 62) How much time does it take a beam of light to travel 2.9 km through space. (c = 3.0 × 108 m/s) A) 9.7 s B) 9.7 ms C) 9.7 μs D) 9.7 ns E) 9.7 ps Answer: C Var: 1

63) A radio station broadcasts at 80 MHz. How long does it take for this radio signal to travel a distance of through space? (c = 3.0 × 108 m/s) A) 0.15 × 10-2 s B) 15 ms C) 6.7 × 10-2 s D) 20 ms E) 25 ms Answer: C Var: 1 64) How far does a beam of light travel through space in one 365-day year? (c = 3.0 × 108 m/s) A) 80 × 1012 m B) 95 × 1014 m C) 30 × 108 m D) 20 × 1015 m E) 36 × 1016 m Answer: B Var: 1 65) A radio station broadcasts at a frequency of 80 MHz. How far from the transmitter will this signal travel in 67 ms? (c = 3.0 × 108 m/s) A) 60 × 106 m B) 67 m C) 40 km D) 80 km E) 20 × 106 m Answer: E Var: 1 66) A laser beam takes 24 ms to travel from a rocket to the reflective surface of a planet and back to the rocket. How far is the rocket from this planet's surface? (c = 3.0 × 108 m/s) A) 2400 km B) 1200 km C) 1800 km D) 3600 km E) 4800 km Answer: D Var: 1

67) A radar receiver indicates that a pulse return as an echo in 20 μs after it was sent. How far away is the reflecting object? (c = 3.0 × 108 m/s) A) 1.5 km B) 3.0 km C) 6.0 km D) 9.0 km Answer: B Var: 1 68) A sinusoidal electromagnetic wave is propagating in vacuum. At a given point and at a particular time the electric field is in the +x direction and the magnetic field is in the -y direction, and at that point the intensity of the wave is (a) What is the direction of propagation of the wave? (b) What is the electric field amplitude at the given point? Answer: (a) -z direction (b) 18 V/m Var: 50+ 69) A sinusoidal electromagnetic wave has a peak electric field of of the wave? A) 170 kW/m2 B) 85 kW/m2 C) 21 kW/m2 D) 11 kW/m2 Answer: B Var: 8

What is the intensity

70) If the magnetic field in a traveling electromagnetic wave has a maximum value of 16.5 nT, what is the maximum value of the electric field associated with this wave? (c = 3.00 × 108 m/s) A) 5.5 × 10-17 V/m B) 4.95 V/m C) 0.495 V/m D) 55.0 × 10-16 V/m E) 55.0 × 10-15 V/m Answer: B Var: 1

71) A certain electromagnetic field traveling in vacuum has a maximum electric field of 1200 V/m. What is the maximum magnetic field of this wave? (c = 3.0 × 108 m/s) A) 3.4 × 10-4 T B) 4.0 × 10-6 T C) 2.2 × 10-5 T D) 9.6 × 10-6 T E) 8.7 × 10-6 T Answer: B Var: 1 72) The amplitude of the electric field for a certain type of electromagnetic wave is 570 N/C. What is the amplitude of the magnetic field for that wave? (c = 3.00 × 108 m/s) A) 2.91 µT B) 1.90 µT C) 1.10 µT D) 1.41 µT E) 2.41 µT Answer: B Var: 5 73) The maximum value of the electric field in an electromagnetic wave is 2.0 V/m. What is the maximum value of the magnetic field in that wave? (c = 3.0 × 108 m/s) A) 6.7 pT B) 6.7 mT C) 6.7 nT D) 6.7 μT E) 6.7 T Answer: C Var: 1 74) About 1350 W/m2 of electromagnetic energy reaches the upper atmosphere of the earth from the sun, which is 1.5 × 1011 m away. Use this information to estimate the average power output of the sun. A) 1 × 1026 W B) 2 × 1026 W C) 3 × 1026 W D) 4 × 1026 W Answer: D Var: 1

75) A radio transmitter is operating at an average power of all directions. What is the average intensity of the signal A) 4.97 μW/m2 B) 2.49 μW/m2 C) 0.00497 W/m2 D) 0.00249 W/m2 Answer: A Var: 25

and is radiating uniformly in from the transmitter?

76) Radiation of a single frequency reaches the upper atmosphere of the earth with an intensity of 1350 W/m2. What is the maximum value of the electric field associated with this radiation? (c = 3.00 × 108 m/s, μ0 = 4π × 10-7 T ∙ m/A, ε0 = 8.85 × 10-12 C2/N ∙ m2) A) 675.0 V/m B) 1604 V/m C) 1400 V/m D) 1350 V/m E) 1010 V/m Answer: E Var: 1 77) A radiometer has two square vanes (1.0 cm by 1.0 cm), attached to a light horizontal cross arm, and pivoted about a vertical axis through the center, as shown in the figure. The center of each vane is 6.0 cm from the axis. One vane is silvered and it reflects all radiant energy that falls upon it. The other vane is blackened and it absorbs all incident radiant energy. Radiant energy, having an intensity of 300 W/m2, is incident normally upon the front surfaces of both vanes. What is the radiant power absorbed by the blackened vane?

A) 0.030 W B) 0.040 W C) 0.050 W D) 0.060 W E) 0.090 W Answer: A Var: 1

78) The rate of energy flow per unit area of a sinusoidal electromagnetic wave has an average value of 0.601 W/m2. What is the maximum value of the magnetic field in the wave? (c = 3.00 × 108 m/s, μ0 = 4π × 10-7 T ∙ m/A, ε0 = 8.85 × 10-12 C2/N ∙ m2) A) 7.09 × 10-8 T B) 5.02 × 10-8 T C) 3.55 × 10-8 T D) 9.81 × 10-8 T E) 1.42 × 10-7 T Answer: A Var: 1 79) The rate of energy flow per unit area of an electromagnetic wave has an average value of 0.695 W/m2. The wave is incident at right angles upon a rectangular area measuring 1.5 m by 2.0 m. How much total energy falls upon this rectangle each minute? (ε0 = 8.85 × 10-12 C2/N ∙ m2, μ0 = 4π × 10-7 T ∙ m/A, c = 3.0 × 108 m/s) A) 130 J B) 160 J C) 190 J D) 220 J E) 250 J Answer: A Var: 1 80) An 800-kHz sinusoidal radio signal is detected at a point 6.6 km from the transmitter tower. The electric field amplitude of the signal at that point is 0.780 V/m. Assume that the signal power is radiated uniformly in all directions and that radio waves incident upon the ground are completely absorbed. What is the amplitude of the magnetic field of the signal at that point? (ε0 = 8.85 × 10-12 C2/N ∙ m2, c = 3.0 × 108 m/s, μ0 = 4π × 10-7 T ∙ m/A) A) 2.6 nT B) 2.1 nT C) 1.6 nT D) 3.1 nT E) 3.6 nT Answer: A Var: 1

81) An 800-kHz sinusoidal radio signal is detected at a point 2.1 km distant from a transmitter tower. The electric field amplitude of the signal at that point is 0.80 V/m. Assume that the signal power is radiated uniformly in all directions and that radio waves incident upon the ground are completely absorbed. What is the intensity of the radio signal at that point? (ε0 = 8.85 × 10-12 C2/N ∙ m2, μ0 = 4π × 10-7 T ∙ m/A, c = 3.0 × 108 m/s) A) 8.5 × 10-4 W/m2 B) 1.2 × 10-3 W/m2 C) 1.7 × 10-3 W/m2 D) 6.0 × 10-4 W/m2 E) 4.2 × 10-4 W/m2 Answer: A Var: 1 82) What is the maximum value of the magnetic field at a distance of 2.5 m from a light bulb that radiates 100 W of single-frequency sinusoidal electromagnetic waves uniformly in all directions? (ε0 = 8.85 × 10-12 C2/N ∙ m2, μ0 = 4π × 10-7 T ∙ m/A, c = 3.0 × 108 m/s) A) 0.10 μT B) 0.40 μT C) 0.50 μT D) 0.60 μT E) 0.80 μT Answer: A Var: 1 83) A light source radiates 60.0 W of single-wavelength sinusoidal light uniformly in all directions. What is the average intensity of the light from this bulb at a distance of 0.400 m from the bulb? A) 14.9 W/m2 B) 37.2 W/m2 C) 27.4 W/m2 D) 11.9 W/m2 E) 29.8 W/m2 Answer: E Var: 1 84) A light source radiates 60.0 W of single-wavelength sinusoidal light uniformly in all directions. What is the amplitude of the electric field of this light at a distance of 0.400 m from the bulb? (ε0 = 8.85 × 10-12 C2/N ∙ m2, μ0 = 4π × 10-7 T ∙ m/A, c = 3.00 × 108 m/s) A) 162 N/C B) 212 N/C C) 82.1 N/C D) 150 N/C E) 52.9 N/C Answer: D Var: 1 43 Copyright © 2019 Pearson Education, Inc.

85) A light source radiates 60.0 W of single-wavelength sinusoidal light uniformly in all directions. What is the amplitude of the magnetic field of this light at a distance of 0.700 m from the bulb?(ε0 = 8.85 × 10-12 C2/N ∙ m2, μ0 = 4π × 10-7 T ∙ m/A, c = 3.0 × 108 m/s) A) 1.76 × 10-7 T B) 2.02 × 10-7 T C) 2.22 × 10-7 T D) 2.86 × 10-7 T Answer: D Var: 1 86) An 8.0-mW laser beam emits a cylindrical beam of single-wavelength sinusoidal light 0.90 mm in diameter. What is the rms value of the electric field in this laser beam? (ε0 = 8.85 × 10-12 C2/N ∙ m2, μ0 = 4π × 10-7 T ∙ m/A, c = 3.0 × 108 m/s) A) 2200 N/C B) 1000 N/C C) 1100 N/C D) 4100 N/C E) 2000 N/C Answer: A Var: 1 87) An 8.00-mW laser beam emits a cylindrical beam of single-wavelength sinusoidal light 0.600 mm in diameter. What is the maximum value of the magnetic field in the laser beam? (ε0 = 8.85 × 10-12 C2/N ∙ m2, μ0 = 4π × 10-7 T ∙ m/A, c = 3.0 × 108 m/s) A) 9.24 µT B) 17.2 µT C) 12.4 µT D) 20.5 µT E) 15.4 µT Answer: E Var: 1 88) How much energy is transported across a 1.00-cm2 area per hour by a sinusoidal electromagnetic wave whose electric field has a maximum strength of 30.4 V/m? (ε0 = 8.85 × 10-12 C2/N ∙ m2, μ0 = 4π × 10-7 T ∙ m/A, c = 3.0 × 108 m/s) A) 0.44 nJ B) 0.44 μJ C) 0.44 mJ D) 0.44 J Answer: D Var: 1

89) Unpolarized light of intensity I0 passed through an ideal polarizing sheet with its polarizing axis at the 12 o'clock position and then through a second ideal sheet with its polarizing axis at the 1 o'clock position. What is the intensity of the emerging light in terms of I0? Answer:

Var: 1 90) Three ideal polarizers are oriented as follows: The axis of the second polarizer is at an angle of 59.0° relative to the first one. The axis of the third polarizer is at an angle of 31.0° relative to the second one, so the axis of the axis of the third polarizer is perpendicular to the axis of the first one. Unpolarized light of intensity is incident on the first polarizer. (a) What is the intensity of the light after it passes through all three polarizers? (b) What is the intensity of the transmitted light if the second polarizer is removed? Answer: (a) 1.81 W/ (b) 0 W/ Var: 50+ 91) Light passes through three ideal polarizing sheets. Unpolarized light enters the first sheet and the resultant vertically polarized beam continues through the second sheet and third sheet. The second sheet has its transmission axis at 50° with respect to the first sheet, and the third sheet is at 70° with respect to the first sheet. (a) What percent of the original intensity emerges from filter #1? (b) What percent of the original intensity emerges from filter #2? (c) What percent of the original intensity emerges from filter #3? Answer: (a) 50% (b) 21% (c) 18% Var: 1 92) Unpolarized light of intensity I0 passes through four ideal polarizing sheets. The polarizing angle of each sheet is rotated 30° from the one before it, so that the last sheet is aligned at 90° to the first sheet. What is the intensity of the light emerging from the fourth sheet in terms of I0? Answer: 0.21 I0 Var: 1 93) An ideal polarizer with its transmission axis rotated 30° to the vertical is placed in a beam of unpolarized light of intensity 10 W/m2. After passing through the polarizer, what is intensity of the beam? A) 2.5 W/m2 B) 5.0 W/m2 C) 8.7 W/m2 D) 7.5 W/m2 E) 10 W/m2 Answer: B Var: 1

94) As shown in the figure, the orientation of the transmission axis for each of three ideal polarizing sheets is labeled relative to the vertical direction. A beam of light, polarized in the vertical direction, is incident on the first polarizer with an intensity of 1.00 kW/m2. What is the intensity of the beam after it has passed through the three polarizing sheets when θ1 = 30°, θ2 = 30°, and θ3= 60°?

A) 141 W/m2 B) 316 W/m2 C) 433 W/m2 D) 563 W/m2 E) 188 W/m2 Answer: D Var: 1 95) The following items are positioned in sequence: A source of a beam of natural light of intensity I0, three ideal polarizers A, B, and C; and an observer. Polarizer axis angles are measured clockwise from the vertical, as viewed by the observer. The axis angle of polarizer A is set at 0° (vertical), and the axis angle of polarizer C is set at 50°. Polarizer B is set so that the beam intensity is zero at the observer. What are the two possible axis angle settings (less than 180°) of polarizer B? A) 40° and 90° B) 40° and 130° C) 40° and 140° D) 90° and 130° E) 90° and 140° Answer: E Var: 1 96) The following items are positioned in sequence: A source of a beam of natural light of intensity I0, three ideal polarizers A, B, and C; and an observer. Polarizer axis angles are measured clockwise from the vertical, as viewed by the observer. The axis angle of polarizer A is set at 0° (vertical), and the axis angle of polarizer C is set at 50°. Polarizer B is set so that the beam intensity at the observer is a maximum. What is the axis angle settings of polarizer B? A) 0° B) 25° C) 50° D) 75° E) 100° Answer: B Var: 1 46 Copyright © 2019 Pearson Education, Inc.

97) The following items are positioned in sequence: A source of a beam of natural light of intensity I0, three ideal polarizers A, B, and C; and an observer. Polarizer axis angles are measured clockwise from the vertical, as viewed by the observer. The axis angle of polarizer A is set at 0° (vertical), and the axis angle of polarizer C is set at 50°. The axis angle of polarizer B is set at 120°. What is ratio of the intensity of the beam at the observer to the intensity I0 of the source? A) 0.015 B) 0.020 C) 0.025 D) 0.030 E) 0.035 Answer: A Var: 1 98) A beam of light is polarized in a vertical plane and has an intensity I0. The beam passes through an ideal polarizer and then through an ideal analyzer whose axis is set horizontally. If the axis of the polarizer is set at 60° with the vertical, what is the ratio of the intensity of the final beam to I0? A) 0.19 B) 0.25 C) 0.31 D) 0.37 E) 0.43 Answer: A Var: 1 99) Light of intensity S0 that is polarized horizontally passes through three ideal polarizers. The first and third are horizontal, but the second one is oriented at to the horizontal. In terms of S0, the intensity of the light that passes through the set of polarizers is closest to which one of the following choices? A) 0.729 S0 B) 0.125 S0 C) 0.427 S0 D) 0.854 S0 Answer: A Var: 6

100) Polarized light of intensity S0 passes through an ideal polarizer. If the electric vector of the polarized light is horizontal what, in terms of the initial intensity S0, is the intensity of the light that passes through a polarizer if that polarizer is tilted from the horizontal? A) 0.812 S0 B) 0.188 S0 C) 0.217 S0 D) 0.284 S0 Answer: A Var: 5 101) Unpolarized light is incident upon two ideal polarizing filters that do not have their transmission axes aligned. If of the light passes through this combination, what is the angle between the transmission axes of the two filters? A) 52° B) 72° C) 0° D) 0° Answer: A Var: 31 102) Unpolarized light passes through a combination of two ideal polarizers. The transmission axes of the first polarizer and the second polarizer are at 30.0° to each other. What percentage of the original light gets through the combination? A) 37.5% B) 50% C) 75% D) 100% Answer: A Var: 1 103) Unpolarized light passes through three ideal polarizing filters. The first filter is oriented with a horizontal transmission axis, the second one has its transmission axis at 30° from the horizontal, and the third filter has a vertical transmission axis. What percent of the light gets through this combination? A) 9.4% B) 91% C) 50% D) 0% E) 33% Answer: A Var: 1

104) A vertically polarized beam of light of intensity 100 W/m2 passes through two ideal polarizers. The transmission axis of the first polarizer makes an angle of 20.0° with the vertical, and the transmission axis of the second one makes an angle of 40.0° with the vertical. What is the intensity of the light after it has passes through both polarizers? A) 22.2 W/m2 B) 44.4 W/m2 C) 66.6 W/m2 D) 78.0 W/m2 E) 11.7 W/m2 Answer: D Var: 1 105) If the surface of our bodies is at 37°C, at what wavelength does the radiation that we emit peak if we behave like a blackbody? The constant in Wien's law is 0.0029 m ∙ K. Answer: 9.4 μm Var: 1 106) The cosmic background radiation permeating the universe has the spectrum of a 2.7-K blackbody radiator. What is the peak wavelength of this radiation? The constant in Wien's law is 0.0029 m ∙ K. Answer: 1.1 mm (microwave region) Var: 1 107) What are the wavelength and the corresponding photon energy (in electron-volts) of the primary light emitted by an ideal blackbody at each of the following temperatures? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J, and the constant in Wein's law is 0.00290 m ∙ K) (a) 400°C? (b) 800°C? (c) 1200°C? Answer: (a) 4.31 μm, 0.288 eV (b) 2.70 μm, 0.459 eV (c) 1.97 μm, 0.631 eV Var: 6 108) What is the surface temperature of a star, if its radiation peak occurs at a frequency of 1.06 × 1015 Hz? (c = 3.00 × 108 m/s, and the constant in Wien's law is 0.00290 m ∙ K) A) 17,000 K B) 14,500 K C) 19,000 K D) 20,400 K E) 10,200 K Answer: E Var: 1

109) If the sunlight from a star peaks at a wavelength of 0.55 µm, what temperature does this imply for the surface of that star? The constant in Wien's law is 0.00290 m ∙ K. A) 9500 K B) 5300 K C) 2500 K D) 25,000 K E) 15,000 K Answer: B Var: 1 110) The surface temperature of the star is 6000 K. At what wavelength is its light output a maximum? The constant in Wien's law is 0.00290 m ∙ K. A) 850 nm B) 907 nm C) 311 nm D) 483 nm E) 502 nm Answer: D Var: 1 111) What is the wavelength of the most intense light emitted by a giant star of surface temperature 5000 K? The constant in Wien's law is 0.00290 m ∙ K. A) 576 nm B) 578 nm C) 580 nm D) 582 nm Answer: C Var: 3 112) What is the frequency of the most intense radiation from an object with temperature 100°C? The constant in Wien's law is 0.0029 m ∙ K. (c = 3.0 × 108 m/s) A) 2.9 × 10-5 Hz B) 3.9 × 1013 Hz C) 1.0 × 1013 Hz D) 1.0 × 1011 Hz Answer: B Var: 1 113) An x-ray tube accelerates electrons through a potential difference of 50.0 kV. If an electron in the beam suddenly give up its energy in a collision, what is the shortest wavelength x-ray it could produce? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, e = 1.60 × 10-19 C) Answer: 2.48 × 10-11 m Var: 1

114) At what rate are photons emitted by a 50.0-W sodium vapor lamp if it is producing monochromatic light of wavelength 589 nm? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s) Answer: 1.48 × 1020 photons per second Var: 1 115) The human eye can just detect green light of wavelength 500 nm if it arrives at the retina at the rate of 2 × 10-18 W. How many photons arrive each second? (c = 3.0 × 108 m/s, h = 6.626 × 10-34 J ∙ s) Answer: 5 Var: 1 116) What is the wavelength of a photon having energy 2.00 eV? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) Answer: 621 nm Var: 1 117) A small gas laser of the type used in classrooms may radiate light at a power level of 2.0 mW. If the wavelength of the laser light is 642 nm, how many photons does it emit per second? (c = 3.0 × 108 m/s, h = 6.626 × 10-34 J ∙ s) Answer: 6.5 × 1015 Var: 1 118) How much energy is carried by a photon of light having frequency 110 GHz? (h = 6.626 × 10-34 J ∙ s) A) 1.1 × 10-20 J B) 1.4 × 10-22 J C) 7.3 × 10-23 J D) 1.3 × 10-25 J Answer: C Var: 3 119) What frequency of electromagnetic radiation has photons of energy 4.7 × 10-25 J? (h = 6.626 × 10-34 J ∙ s) A) 710 kHz B) 4.7 MHz C) 710 MHz D) 1.4 GHz Answer: C Var: 1

120) What is the energy (in eV) of an optical photon of frequency 34 J ∙ s, 1 eV = 1.60 × 10-19 J) A) 2.66 eV B) 1.62 eV C) 1.94 eV D) 3.27 eV Answer: A Var: 50+

(h = 6.626 × 10-

121) What is the photon energy of red light having a wavelength of 6.40 × 102 nm? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s) A) 1.13 × 10-19 J B) 1.31 × 10-19 J C) 3.11 × 10-19 J D) 1.94 × 10-19 J Answer: C Var: 1 122) Each photon in a beam of light has an energy of 4.20 eV. What is the wavelength of this light? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) A) 321 nm B) 103 nm C) 296 nm D) 412 nm E) 420 nm Answer: C Var: 1

College Physics: A Strategic Approach, 4e (Knight) Chapter 26 AC Electricity 26.1 Conceptual Questions 1) A transformer is a device used to A) transform an alternating current into a direct current. B) transform a direct current into an alternating current. C) increase or decrease an ac voltage. D) increase or decrease a dc voltage. Answer: C Var: 1 2) A transformer is a device that normally A) operates on either dc or ac. B) operates only on ac. C) operates only on dc. Answer: B Var: 1 3) If the secondary coil of a transformer contains more loops than the primary coil, then it is a A) step-up transformer. B) step-down transformer. Answer: A Var: 1 4) If the primary coil of a transformer contains more loops than the secondary coil then it is a A) step-up transformer. B) step-down transformer. Answer: B Var: 1 5) An ideal solenoid has a self-inductance L. If you now double its radius and its length, but do not change the number of coils, what will its self-inductance be? A) 4L B) 2L C) L D) L/2 E) L/4 Answer: D Var: 1

6) A resistor and an inductor are connected in series to an ideal battery of constant terminal voltage. At the moment contact is made with the battery, the voltage across the resistor is A) greater than the battery's terminal voltage. B) equal to the battery's terminal voltage. C) less than the battery's terminal voltage, but not zero. D) zero. E) equal to the voltage across the inductor. Answer: D Var: 1 7) A resistor and an inductor are connected in series to an ideal battery of constant terminal voltage. At the moment contact is made with the battery, the voltage across the inductor is A) greater than the battery's terminal voltage. B) equal to the battery's terminal voltage. C) less than the battery's terminal voltage, but not zero. D) zero. E) equal to the voltage across the resistor. Answer: B Var: 1 8) A resistor and an inductor are connected in series to a battery. The time constant for the circuit represents the time required for the current to reach A) 25% of the maximum current. B) 37% of the maximum current. C) 63% of the maximum current. D) 75% of the maximum current. E) 100% of the maximum current. Answer: C Var: 1 9) A resistor and an inductor are connected in series to a battery. The battery is suddenly removed from the circuit and replaced by a wire to complete the circuit. The time constant for of the new circuit represents the time required for the current to decrease to A) 25% of the original value. B) 37% of the original value. C) 63% of the original value. D) 75% of the original value. E) zero. Answer: B Var: 1

10) A simple ac circuit is composed of a capacitor connected across the terminals of an ac power source. If the frequency of the source is doubled, what happens to the reactance of the capacitor? A) It increases by a factor of 4. B) It increases by a factor of 2. C) It increases by a factor of D) It decreases by a factor of 2. E) It decreases by a factor of 4. Answer: D Var: 1 11) Consider a capacitor connected across the ac source. As the capacitance is increased, the current through the capacitor will A) increase. B) remain constant. C) decrease. Answer: A Var: 1 12) A pure capacitor is connected to an ac power supply. In this circuit, the current A) leads the voltage by 90°. B) lags the voltage by 90°. C) lags the voltage by 180°. D) is in phase with the voltage. E) None of the given answers are correct. Answer: A Var: 1 13) A pure inductor is connected to an ac power supply. In this circuit, the current A) leads the voltage by 90°. B) is in phase with the voltage. C) lags the voltage by 45°. D) lags the voltage by 90°. E) leads the voltage by 45°. Answer: D Var: 1 14) A simple ac circuit consists of an inductor connected across the terminals of an ac power source. If the frequency of the ac source is decreased by a factor of four, what happens to the reactance of the inductor? A) It decreases by a factor of four. B) It decreases by a factor of eight. C) It increases by a factor of two. D) It increases by a factor of four. E) It increases by a factor of eight. Answer: A Var: 1 3 Copyright © 2019 Pearson Education, Inc.

15) As the frequency of the ac voltage across an inductor approaches zero, the inductive reactance of that coil A) approaches zero. B) approaches one. C) approaches infinity. D) becomes negative. Answer: A Var: 1 16) What is the phase angle between the voltages of the inductor and capacitor in a RLC series circuit? A) 0° B) 45° C) 90° D) 180° E) 270° Answer: D Var: 1 17) Which of the following statements is true for a series RLC ac circuit in resonance? (There could be more than one correct choice). A) The inductive reactance and the capacitive reactance are both equal to zero. B) The inductive reactance is equal to the capacitive reactance. C) The current in the circuit is a minimum. D) The current in the circuit is a maximum. E) The rms current is equal to the peak current. Answer: B, D Var: 1 18) In the figure, which of the phasor diagrams represents a series RLC circuit driven at resonance?

A) 1 B) 2 C) 3 D) 4 E) 5 Answer: C Var: 1

19) In an RLC ac circuit, the values of the inductance and capacitance are both doubled. As a result of this change, the resonance frequency of the circuit is A) the same as before. B) reduced to one-half the original value. C) reduced to one-fourth the original value. D) twice the original value. E) four times the original value. Answer: B Var: 1 20) In a RLC circuit, the values of the inductance and capacitance are both halved. As a result of this change, the resonance frequency of the circuit is A) the same as before. B) reduced to one-half the original value. C) reduced to one-fourth the original value. D) twice the original value. E) four times the original value. Answer: D Var: 1 26.2 Problems 1) The primary coil of an ideal transformer has 100 turns and its secondary coil has 400 turns. If the ac voltage applied to the primary coil is 120 V, what voltage is present in its secondary coil? A) 100 V B) 30 V C) 70 V D) 480 V E) 400 V Answer: D Var: 1 2) An ideal transformer has 60 turns on its primary coil and 300 turns on its secondary coil. If 120 V at 2.0 A is applied to the primary, (a) what voltage is present in the secondary? (b) what current is present in the secondary? Answer: (a) 240 V (b) 0.40 A Var: 1

3) An ideal step-up transformer doubles a primary voltage of 110 V. What is the ratio of the number of turns in its primary coil to the number of turns in the secondary coil? A) 1:4 B) 4:1 C) 2:1 D) 1:2 E) 1:8 Answer: D Var: 1 4) When 5.0 A at 110 V flows in the primary of an ideal transformer, how many amps at 24 V can flow in the secondary? A) 1.1 A B) 4.6 A C) 5.0 A D) 23 A Answer: D Var: 1 5) The secondary coil of an ideal neon sign transformer provides 7500 V at 10.0 mA. The primary coil operates on 120 V. What current does the primary draw? A) 0.625 A B) 0.625 mA C) 0.160 A D) 1.66 A Answer: A Var: 1 6) The primary coil of an ideal transformer has 100 turns and its secondary coil has 400 turns. If the ac current in the secondary coil is 2 A, what is the current in its primary coil? A) 2 A B) 8 A C) 1/2 A D) 1/4 A E) 4 A Answer: B Var: 1 7) The primary coil of an ideal transformer has 600 turns and its secondary coil has 150 turns. If the current in the primary coil is 2 A, what is the current in its secondary coil? A) 8 A B) 1/2 A C) 1/4 A D) 2 A E) 4 A Answer: A Var: 1 6 Copyright © 2019 Pearson Education, Inc.

8) A current of 2.0 A in the 100-turn primary of an ideal transformer causes 14 A to flow in the secondary. How many turns are in the secondary? A) 700 B) 114 C) 14 D) 4 Answer: C Var: 1 9) In an ideal transformer, how many turns are necessary in a 110-V primary if the 24-V secondary has 100 turns? A) 458 B) 240 C) 110 D) 22 Answer: A Var: 1 10) An ideal transformer consists of a 500-turn primary coil and a 2000-turn secondary coil. If the current in the secondary is 3.0 A, what is the current in the primary? A) 0.75 A B) 1.3 A C) 12 A D) 48 A Answer: C Var: 1 11) An ideal step-down transformer is needed to reduce a primary voltage of 120 V to 6.0 V. What must be the ratio of the number of turns in the secondary to the number of turns in the primary? Answer: 1 to 20 Var: 1 12) An ideal transformer steps down 120 V to 12. V and the 2630.-turn secondary supplies 12. A. (a) Determine the current in the primary. (b) Determine the turns ratio. (c) What is the ratio of output power to input power? Answer: (a) 1.2 A (b) 1.0:10. (c) 1:1 for ideal transformer Var: 5

13) An ideal transformer with 120 turns in its secondary supplies 12 V at 220 mA to a toy train. The primary is connected across a 120-V wall outlet. (a) How many turns are in the primary? (b) What is the primary current? (c) What power is delivered by the wall outlet? Answer: (a) 1200 (b) 22 Ma (c) 2.6 W Var: 1 14) An ideal transformer has 60 turns on its primary coil and 300 turns on its secondary coil. If 120 V at 2.0 A is applied to the primary, what voltage and current are present in the secondary? Answer: 600 V, 0.40 A Var: 1 15) You need an ideal transformer to reduce a voltage of 150 V in the primary circuit to 25 V in the secondary circuit. The primary circuit has 130 windings and the secondary circuit is completed through a 55-Ω resistor. How many windings should the secondary circuit contain? Answer: 22 Var: 1 16) The primary of an ideal transformer has 100 turns and its secondary has 200 turns. If the input current at the primary is 100 A, we can expect the output current at the secondary to be A) 50 A. B) 100 A. C) 200 A. D) none of the given answers. Answer: A Var: 1 17) The primary of an ideal transformer has 100 turns and its secondary has 200 turns. If the input voltage to the primary is 100 V, we can expect the output voltage of the secondary to be A) 50 V. B) 100 V. C) 200 V. D) none of the given answers. Answer: C Var: 1 18) The primary of an ideal transformer has 100 turns and its secondary has 200 turns. Neglecting frictional losses, if the power input to the primary is 100 W, we can expect the power output of the secondary to be A) 50 W. B) 100 W. C) 200 W. D) none of the given answers. Answer: B Var: 1 8 Copyright © 2019 Pearson Education, Inc.

19) A generator produces 60 A of current at 120 V. The voltage is usually stepped up to 4500 V by an ideal transformer and transmitted through a power line of total resistance 1.0 Ω. Find the number of turns in the secondary if the primary has 200 turns. A) 5 B) 200 C) 4500 D) 7500 Answer: D Var: 1 20) What is the self-inductance of an ideal solenoid that is 300 cm long with a cross-sectional area of 1.00 × 10-4 m2 and has 1000 turns of wire? (μ0 = 4π × 10-7 T ∙ m/A) A) 4.19 nH B) 4.19 pH C) 4.19 μH D) 41.9 nH E) 41.9 µH Answer: E Var: 1 21) A coil with a self-inductance of 6.0 H has a constant current of 2.0 A flowing through it for 2.0 s. What is the emf induced in this coil? A) 6.0 V B) 12 V C) 0.0 V D) 4.0 V E) 8.0 V Answer: C Var: 1 22) A coil with a self-inductance of 6.0 H is connected to a dc battery through a switch. As soon as the switch is closed, the rate of change of current is 2.0 A/s. What is the emf induced in this coil at this instant? A) 6.0 V B) 3.0 V C) 12 V D) 0.33 V E) 0.0 V Answer: C Var: 1

23) The inductance of a solenoid that is 16.0 cm long and has a cross-sectional area of 1.00 × is How many turns of wire does this solenoid have? (μ0 = 4π × 10-7 T ∙ m/A) A) 318,000 B) 159,000 C) 1130 D) 282 E) 150 Answer: C Var: 5 24) The figure shows a solenoid having no appreciable resistance. When the current in this solenoid is decreasing at a rate of 5.5 A/s, the self-induced emf in the solenoid is measured to be 9.5 V. ((a) What is the self-inductance of this solenoid? (b) If the current is in the direction from b to a in the figure, which point, a or b, is at higher potential?

Answer: (a) 1.7 H Var: 50+

(b) point b

25) The current flowing through a circuit is changing at a rate of 6.0 A/s. If the circuit contains a 190-H inductor, what is the emf across the inductor? A) 1100 V B) 11 mV C) 32 mV D) 32 V Answer: A Var: 1 26) An ideal solenoid with 3000 turns is 70.0 cm long. If its self-inductance is 25.0 mH, what is its radius? (μ0 = 4π × 10-7 T ∙ m/A) A) 0.0222 m B) 0.00199 m C) 327 m D) 52.0 m Answer: A Var: 1 27) A simple series circuit consists of just a 3.4-µF capacitor and an 80-mH inductor, with no appreciable resistance. At t = 0 the capacitor has charge 5.4 µC and the current in the inductor is zero. (a) How long after t = 0 will the current in the circuit be maximum? (b) What will be this maximum current? Answer: (a) 0.82 ms (b) 10 mA Var: 1 10 Copyright © 2019 Pearson Education, Inc.

28) A simple circuit consists only of of a 1.0-μF capacitor and a 15-mH coil in series. At what frequency will this circuit oscillate? A) 15 kHz B) 1.3 kHz C) 0.77 kHz D) 67 Hz Answer: B Var: 2 29) What inductance is needed in series with a 4.7-μF capacitor so the circuit will oscillate at a frequency of 10 kHz? A) 21 μH B) 54 μH C) 4.7 mH D) 5.4 mH Answer: B Var: 1 30) What capacitance is needed in series with a 3.7-mH inductor so the circuit will oscillate at a frequency of 1000 Hz? A) 0.15 mF B) 15 μF C) 6.8 μF D) 0.015 μF Answer: C Var: 1 31) What size capacitor must be placed in series with a 40-mH coil so the circuit will oscillate with a frequency of 1000 Hz? A) 0.63 μF B) 0.50 μF C) 0.22 μF D) 0.17 μF Answer: A Var: 1 32) A series circuit contains an 80-μF capacitor, a 0.020-H inductor, and a switch. The resistance of the circuit is negligible. Initially, the switch is open, the capacitor voltage is 50 V, and the current in the inductor is zero. At time t = 0 s, the switch is closed. How long after closing the switch does the magnetic energy in the inductor first reach its maximum value? A) 2.0 ms B) 4.0 ms C) 6.0 ms D) 8.0 ms E) 10 ms Answer: A Var: 1 11 Copyright © 2019 Pearson Education, Inc.

33) A series circuit contains an 80-μF capacitor, a 0.020-H inductor, and a switch. The resistance of the circuit is negligible. Initially, the switch is open, the capacitor voltage is 50 V, and the current in the inductor is zero. At time t = 0 s, the switch is closed. What is the maximum current in the circuit? A) 2.2 A B) 2.4 A C) 2.8 A D) 3.0 A E) 3.2 A Answer: E Var: 1 34) A series circuit contains an 80-μF capacitor, a 0.020-H inductor, and a switch. The resistance of the circuit is negligible. Initially, the switch is open, the capacitor voltage is 50 V, and the current in the inductor is zero. At time t = 0 s, the switch is closed. When the current in the circuit is 1.5 A, what is the charge on the capacitor? A) 2000 µC B) 2500 µC C) 3000 µC D) 3500 µC E) 4000 µC Answer: D Var: 1 35) A series circuit contains an 80-μF capacitor, a 0.020-H inductor, and a switch. The resistance of the circuit is negligible. Initially, the switch is open, the capacitor voltage is 50 V, and the current in the inductor is zero. At time t = 0 s, the switch is closed. When the potential across the capacitor is 30 V, what is the rate of change of the current? A) 1000 A/s B) 1500 A/s C) 2000 A/s D) 2500 A/s E) 3000 A/s Answer: B Var: 1 36) American power plants usually supply 120 V ac. (a) At what frequency is this voltage supplied? (b) What is the maximum voltage? Answer: (a) 60 Hz (b) 170 V (120 V is the rms voltage) Var: 1 37) A 100-W light bulb is powered by 120 V ac 60.0-Hz household connection. Determine the rms current and the current amplitude. Answer: 0.833 A rms, 1.18 A amplitude Var: 1 12 Copyright © 2019 Pearson Education, Inc.

38) The peak current and voltage outputs of a generator are 20 A and 240 V, respectively. What average power is provided by the generator? Answer: 2.4 kW Var: 1 39) The potential applied to a 20-Ω resistor is v = (60 V) cos(33t). What is the rms current through this resistor? Answer: 2.1 A Var: 1 40) The current through a 50-Ω resistor is I = (0.80 A) sin(240t). What are (a) the current amplitude and (b) the rms current? Answer: (a) 0.80 A (b) 0.57 A Var: 1 41) A 0.150-kW lamp is plugged into a 120-V ac wall outlet. What are (a) the peak current through the lamp, (b) the rms current through the lamp, and (c) the resistance of the lamp? Answer: (a) 1.77 A (b) 1.25 A (c) 96.0 Ω Var: 1 42) The potential applied to a 20-Ω resistor is (60 V) cos(33t). What is the average power consumed in the resistor? Answer: 90 W Var: 1 43) If the maximum voltage of an ac signal is 8.0 V, what is the rms value of this voltage? A) 2.8 V B) 5.7 V C) 6.2 V D) 4.0 V E) 16.0 V Answer: B Var: 1 44) A 120-V rms voltage at 60.0 Hz is applied across an inductor, capacitor and a 100-Ω resistor in series. If the maximum value of the current in this circuit is 1.60 A, what is the rms value of the current in this circuit? A) 1.13 A B) 2.26 A C) 1.82 A D) 1.60 A E) 2.66 A Answer: A Var: 1

45) An alternating current is supplied to an electronic component with a rating that the voltage across it can never, even for an instant, exceed What is the highest rms voltage that can be supplied to this component while staying below the voltage limit? A) 8 V B) 16 V C) 256 V D) 8 V Answer: A Var: 11 46) What is the peak voltage in an ac circuit where the rms voltage is 120 V? A) 84.8 V B) 120 V C) 170 V D) 240 V Answer: C Var: 1 47) A 150-W lamp is placed into a 120-V ac outlet. What is the peak current? A) 0.80 A B) 0.88 A C) 1.2 A D) 1.8 A Answer: D Var: 1 48) A 10-Ω resistor is connected to a 120-V ac power supply. What is the peak current through the resistor? A) 12 A B) 17 A C) 0.083 A D) 0.12 A Answer: B Var: 1 49) The current through a 50-Ω resistor is I = (0.80 A) sin(240t), where t is measured in seconds. What is the rms current? A) 0.57 A B) 0.80 A C) 1.1 A D) 1.6 A Answer: A Var: 1

50) The current through a 50-Ω resistor is I = (0.80 A) sin(240t), where t is measured in seconds. How much power on average is dissipated in the resistor? A) 16 W B) 32 W C) 45 W D) 64 W Answer: A Var: 1 51) At what frequency does a 10-μF capacitor have a reactance of 0.12 kΩ? Answer: 0.13 kHz Var: 1 52) At what frequency will the inductive reactance of a 44-mH inductor be equal to the capacitive reactance of a 27-pF capacitor? Answer: 0.15 MHz Var: 1 53) A 0.10-μF capacitor is connected to a 120-V rms 60-Hz source. (a) What is its capacitive reactance? (b) What is the rms current to the capacitor? (c) If both the capacitance and the frequency were doubled, what would be the rms current? Answer: (a) 27 kΩ (b) 4.5 mA (c) 18 mA Var: 1 54) A 0.200-H inductor is connected to a 60.0-Hz 120-V rms source. (a) What is the inductive reactance? (b) What is the rms current to the inductor? (c) If both the inductance and the frequency were doubled, what would be the rms current? Answer: (a) 75.4 Ω (b) 1.59 A (c) 0.398 A Var: 1 55) What capacitance will have the same reactance as a 100-mH inductance of both of them are in a 120-V 60-Hz circuit? Answer: 70 µF Var: 1

56) In the circuit shown in the figure, the 60-Hz ac source has a voltage amplitude of 120 V, the capacitive reactance is the inductive reactance is and the resistance is What is the capacitance C of the capacitor?

A) 3.2 µF B) 6.3 µF C) 9.4 µF D) 13 µF E) 20 µF Answer: A Var: 50+ 57) The reactance of a capacitor is A) 0.066 μF B) 0.42 μF C) 2.6 μF D) 0.093 μF Answer: A Var: 50+

at a frequency of

What is the capacitance?

58) A 6.0-μF capacitor is connected to an ac signal with a frequency of 60 Hz. If the maximum voltage applied to the capacitor is 8.0 V, what is its capacitive reactance? A) 6.0 Ω B) 440 Ω C) 7.5 × Ω D) 740 Ω E) 160 Ω Answer: B Var: 5 59) The capacitive reactance of a 44-μF capacitor in an ac circuit is 6.0 × frequency of the applied signal? A) 80 Hz B) 17 Hz C) 800 Hz D) 6.0 Hz E) 2.2 Hz Answer: D Var: 5

Ω. What is the

60) A 120-V rms voltage is applied across a 6.0-μF capacitor. If the frequency of the generator is 60 Hz, what is the rms value of the current in the circuit? A) 0.47 A B) 0.37 A C) 0.071 A D) 0.17 A E) 0.27 A Answer: E Var: 1 61) At what frequency does a 10-μF capacitor have a reactance of 1200 Ω? A) 13 Hz B) 42 Hz C) 60 Hz D) 83 Hz Answer: A Var: 1 62) At what frequency will the capacitive reactance of a 0.010-μF capacitor be 100 Ω? A) 1.0 kHz B) 16 kHz C) 0.16 MHz D) 0.31 MHz Answer: C Var: 1 63) What is the rms current through a 0.0010-μF capacitor at 1000 Hz and 5.0 V? A) 5.4 μA B) 31 μA C) 3.1 mA D) 10 mA Answer: B Var: 1 64) What is the reactance of a 20-mH inductor at a frequency of 60 Hz? A) 7.5 Ω B) 0.13 Ω C) 1.2 Ω D) 1.2 mΩ E) 7.5 mΩ Answer: A Var: 1

65) At what frequency is the reactance of a 20.0-mH inductor equal to 120 Ω? A) 318 Hz B) 637 Hz C) 796 Hz D) 955 Hz E) 1110 Hz Answer: D Var: 1 66) In the circuit shown in the figure, the 60-Hz ac source has a voltage amplitude of 120 V, the capacitive reactance is the inductive reactance is and the resistance is What is the inductance L of the inductor?

A) 770 mH B) 1700 mH C) 2900 mH D) 3700 mH E) 4800 mH Answer: A Var: 50+ 67) What is the reactance of a 1.0-mH inductor at 60 Hz? A) 0.19 Ω B) 0.38 Ω C) 2.7 Ω D) 5.3 Ω Answer: B Var: 1 68) What is the inductive reactance of a 2.50-mH coil at 1000 Hz? A) 2500 Ω B) 796 Ω C) 15.7 Ω D) 2.50 Ω Answer: C Var: 1

69) At what frequency will a 14.0-mH coil have 14.0 Ω of inductive reactance? A) 1000 Hz B) 505 Hz C) 257 Hz D) 159 Hz Answer: D Var: 1 70) The inductor in a radio receiver carries a current of amplitude 0.200 A when an ac voltage of amplitude 2.40 V is across it at a frequency of 1400 Hz. What is the value of the inductance? A) 1.43 mH B) 1.36 mH C) 9.20 mH D) 4.42 mH E) 1.97 mH Answer: B Var: 1 71) At what frequency will a 20.0-mH inductor have an inductive reactance of 100 Ω? A) 225 Hz B) 655 Hz C) 796 Hz D) 457 Hz E) None of the other answers is correct. Answer: C Var: 1 72) What rms current flows in a 60-mH inductor when 120-V rms ac at a frequency of 20 kHz is applied to it? A) 8.0 mA B) 16 mA C) 24 mA D) 32 mA Answer: B Var: 1 73) What is the rms current through a 2.50-mH coil due to a 110-V rms, 60-Hz source? A) 0.94 A B) 2.5 A C) 104 A D) 117 A Answer: D Var: 1

74) A 120-V rms signal at 60.0 Hz is applied across a series combination of a 30.0-mH inductor and a resistor. If the rms value of the current in this circuit is 0.600 A, what is the resistance of the resistor? A) 80.0 Ω B) 268 Ω C) 143 Ω D) 200 Ω E) 30.0 Ω Answer: D Var: 5 75) A 120-V rms signal at 60 Hz is applied across a series combination of a 30-mH inductor and a 100-Ω resistor. What is the rms value of the current in this circuit? A) 0.80 A B) 1.2 A C) 1.4 A D) 1.6 A E) 1.8 A Answer: B Var: 1 76) A 120-V rms signal at 60 Hz is applied across a series combination of a 30-mH inductor and a 100-Ω resistor. What is the rms value of the voltage across the resistor? A) 120 V B) 60 V C) 100 V D) 150 V E) 0.70 V Answer: A Var: 1 77) A 120-V rms voltage is applied across a 6.0-μF capacitor and a series combination of a 100Ω resistor. If the frequency of the power source is 60 Hz, what is the rms value of the current in the circuit? A) 0.26 A B) 0.36 A C) 0.46 A D) 0.56 A E) 0.76 A Answer: A Var: 1

78) A 120-V rms voltage at 60 Hz is applied across a series combination of a 20-μF capacitor and an unknown resistor. If the rms value of the current in the circuit is 0.60 A, what is the resistance of the resistor? A) 60 Ω B) 120 Ω C) 180 Ω D) 150 Ω E) 200 Ω Answer: D Var: 1 79) A 120-V rms signal at 60.0 Hz is applied across a series combination of a 30.0-mH inductor and a 100-Ω resistor. What is the rms value of the voltage across the inductor? A) 0.700 V B) 119 V C) 100 V D) 13.5 V E) 120 V Answer: D Var: 5 80) As shown in the figure, an ac source whose rms voltage is 80 V is in series with a 100-Ω resistor and a capacitor whose reactance is 200 Ω at the frequency of the source. What is the rms voltage across the capacitor?

A) 66 V B) 68 V C) 70 V D) 72 V E) 74 V Answer: D Var: 1 81) A 120-V rms voltage at 2000 Hz is applied to a 6.0-mH inductor, a 2.0-μF capacitor, and a 200-Ω resistor. What is the rms value of the current in this circuit? A) 1.5 A B) 0.48 A C) 2.5 A D) 3.5 A E) 0.59 A Answer: E Var: 5

82) A 120-V rms voltage at 1000 Hz is applied to an inductor, a 2.00-μF capacitor and a 100-Ω resistor. If the rms value of the current in this circuit is 0.680 A, what is the inductance of the inductor? A) 34.2 mH B) 35.8 mH C) 11.4 mH D) 17.9 mH E) 22.8 mH Answer: B Var: 1 83) A 120-V rms voltage at 1.0 kHz is applied to a 2.0-mH inductor, a 4.0-μF capacitor and a resistor. If the rms value of the current in this circuit is 0.40 A, what is the value of the resistor? A) 300 Ω B) 95 Ω C) 420 Ω D) 120 Ω E) 240 Ω Answer: A Var: 1 84) A series circuit has a sinusoidal voltage supplied to it at It also contains a resistance, a capacitance, and a current for this circuit? A) 6.3 μA B) 11 μA C) 26 μA D) 30 μA Answer: A Var: 50+

with a peak voltage of inductance. What is the peak

85) In the circuit shown in the figure, the 60-Hz ac source has a voltage amplitude of 120 V, the capacitive reactance is the inductive reactance is and the resistance is What is the rms current in the circuit?

86) The figure shows a series ac circuit. The inductor has a reactance of 60 Ω and an inductance of 150 mH. A 50-Ω R and a capacitor C whose reactance is 90 Ω are also in the circuit, and the rms current in the circuit is 1.5 A. What is the rms voltage of the source?

A) 87 V B) 84 V C) 81 V D) 78 V E) 75 V Answer: A Var: 50+ 87) The figure shows a series ac circuit. The inductor has a reactance of 80 Ω and an inductance of 220 mH. A 30-Ω resistor and a capacitor whose reactance is 80 Ω are also in the circuit, and the rms current in the circuit is 2.0 A. What is the capacitance of the capacitor?

A) 34 μF B) 37 μF C) 32 μF D) 30 μF E) 27 μF Answer: A Var: 50+ 88) The figure shows a series ac circuit. The inductor has a reactance of 50 Ω and an inductance of 220 mH. An 80-Ω resistor and a capacitor whose reactance is 160 Ω are also in the circuit, and the rms current in the circuit is 2.2 A. What is the voltage amplitude across the capacitor?

89) A series circuit has a 50-Hz ac source, a 40-Ω resistor, a 0.70-H inductor, and a 60-μF capacitor, as shown in the figure. The rms current in the circuit is 1.6 A. What is the voltage amplitude of the source?

A) 390 V B) 330 V C) 270 V D) 220 V E) 190 V Answer: A Var: 50+ 90) A series circuit has a 100-Ω resistor, a 0.100-μF capacitor, and a 2.00-mH inductor connected across a 120 V rms ac source operating at resonant frequency. What is the rms value of the voltage across the inductor? A) 170 V B) 150 V C) 120 V D) 54.0 V E) 533 V Answer: A Var: 1 91) A series circuit has a 100-Ω resistor, a 0.100-μF capacitor, and a 2.00-mH inductor connected across a 120-V rms ac source operating at resonant frequency. What is the rms value of the voltage across the capacitor? A) 54.0 V B) 120 V C) 150 V D) 533 V E) 170 V Answer: E Var: 1

92) A series circuit has a 100-Ω resistor, a 0.100-μF capacitor, and a 2.00-mH inductor connected across a 120-V rms ac source operating at 1000/π Hz. What is the rms voltage across the inductor? A) 120 mV B) 87.1 mV C) 302 mV D) 96.1 mV E) 200 mV Answer: D Var: 1 93) A series circuit consists of a 100-Ω resistor, a 10.0-μF capacitor, and a 0.350-H inductor. The circuit is connected to a 120-V rms, 60-Hz power supply. What is the rms current in the circuit? A) 0.42 A B) 0.52 A C) 0.62 A D) 0.72 A Answer: D Var: 1 94) A resistance of 55 Ω, a capacitor of capacitive reactance 30 Ω, and an inductor of inductive reactance 30 Ω are connected in series to a 110-V rms, 60-Hz power source. What rms current flows in this circuit? A) 2.0 A B) less than 2.0 A C) more than 2.0 A D) none of the given answers Answer: A Var: 1 95) A resistance of 55 Ω, a capacitor of capacitive reactance 30 Ω, and an inductor of inductive reactance 30 Ω are connected in series to a 110-V rms 60-Hz power source. What rms current flows in this circuit? A) more than 4.0 A B) 2.0 A C) more than 2.0 A but less than 4.0 A D) 4.0 A E) less than 2.0 A Answer: B Var: 1 96) A series circuit consists of a 0.440-H inductor, a 380.0-Ω resistor, a 5.70-μF capacitor, and an ac voltage source of amplitude Find the rms voltage across the capacitor when the circuit operates at resonance. Answer: 129 V Var: 50+ 25 Copyright © 2019 Pearson Education, Inc.

97) A 120-mH inductor is in series with a 20-Ω resistor and a variable capacitor that can range from 0.110 μF to 0.400 μF. (a) What is the range of possible resonance frequencies? (b) If the power supply is a 24-V rms source, what rms current flows at resonance? Answer: (a) 0.726 kHz to 1.39 kHz (b) 1.20 A Var: 1 98) What is the resonance frequency of a series ac circuit consisting of a 40.0 μF capacitor, a 55Ω resistor, and a 0.030 H inductor? A) 0.15 kHz B) 0.9 kHz C) 6.9 kHz D) 6 kHz Answer: A Var: 1 99) A series ac circuit has a resonance frequency of 9.0 kHz. If the inductor in the circuit has a value of 2.0 H, and the resistance is 75 Ω, what is the capacitance of the circuit? A) 0.16 pF B) 156 pF C) 6.2 pF D) 17.7 pF Answer: A Var: 1 100) An ac circuit has a 100-Ω resistor in series with a 4.9-μF capacitor and a 700-mH inductor. At what frequency does the circuit act like a pure resistance? A) 0.29 MHz B) 1.9 MHz C) 12 MHz D) 0.54 kHz E) 86 Hz Answer: E Var: 1 101) A series RLC circuit has a 100-Ω resistor, a 0.100-μF capacitor and a 2.00-mH inductor connected across a 120-V rms ac voltage source operating at 1000/π Hz. What is the resonant frequency of this circuit? A) 70.7 kHz B) 17.9 kHz C) 22.5 kHz D) 35.3 kHz E) 11.3 kHz Answer: E Var: 1 26 Copyright © 2019 Pearson Education, Inc.

102) What size capacitor should be placed in series with a 30-Ω resistor and a 40-mH inductive coil if the resonant frequency of the circuit is to be 1.0 kHz? A) 2.0 µF B) 0.63 µF C) 3.3 µF D) 6.0 µF E) 4.5 µF Answer: B Var: 1

College Physics: A Strategic Approach, 4e (Knight) Chapter 27 Relativity 27.1 Conceptual Questions 1) Which of the following are basic postulates of special relativity? (There could be more than one correct choice.) A) Nothing can travel faster than the speed of light. B) No material object can be accelerated to the speed of light. C) The speed of light is the same for all observers. D) The laws of physics are the same in all reference frames. E) The laws of physics are the same in all inertial reference frames. Answer: C, E Var: 1 2) If you were in a spaceship traveling close to the speed of light with respect to Earth, you would notice that A) some of your physical dimensions were smaller than normal. B) your mass was less than normal. C) your mass was greater than normal. D) your pulse rate was greater than normal. E) none of the above effects occur. Answer: E Var: 1 3) You are riding in a spaceship that has no windows, radios, or other means for you to observe or measure what is outside. You wish to determine if the ship is stopped or moving at constant velocity. How can you do this? A) You can determine if the ship is moving by determining the apparent velocity of light in the spaceship. B) You can determine if the ship is moving by checking your precision time piece. If it's running slow, the ship is moving. C) You can determine if the ship is moving by lying down and measuring your height. If you are shorter than usual, the ship is moving. D) You should give up because you have taken on an impossible task! Answer: D Var: 1 4) One of Einstein's postulates in formulating the special theory of relativity was that the laws of physics are the same in reference frames that A) accelerate. B) move at constant velocity with respect to an inertial frame. C) oscillate. D) are stationary, but not in moving frames. Answer: B Var: 1 1 Copyright © 2019 Pearson Education, Inc.

5) You are a passenger on a spaceship. As the speed of the spaceship increases, you will observe A) your watch slowing down. B) your watch speeding up. C) your watch losing time. D) your watch gaining time. E) nothing unusual about the behavior of your watch. Answer: E Var: 1 6) A spaceship traveling at constant velocity passes by Earth and later passes by Mars. In which frame of reference is the amount of time separating these two events the proper time? A) the Earth frame of reference B) the Mars frame of reference C) the spaceship frame of reference D) any inertial frame of reference E) any frame of reference, inertial or not Answer: C Var: 1 7) Observer A sees a pendulum oscillating back and forth in a relativistic rocket and measures its period to be TA. Observer B moves along with the rocket and measures the period of the pendulum to be TB. What is true about these two time measurements? A) TA > TB B) TA = TB C) TA < TB D) TA could be greater or smaller than TB depending on the direction of the motion. Answer: A Var: 1 8) A 30-year-old astronaut goes off on a long-term mission in a spacecraft that travels at speeds close to that of light. The mission lasts exactly 20 years as measured on Earth. Biologically speaking, at the end of the mission, the astronaut's age would be A) more than 50 years. B) exactly 50 years. C) less than 50 years. D) exactly 30 years. E) exactly 25 years. Answer: C Var: 1

9) Suppose one twin takes a ride in a spaceship traveling at a very high speed to a distant star and then back again, while the other twin remains on Earth. Compared to the twin who remained on Earth, the astronaut twin is A) younger than the Earth-twin. B) the same age as the Earth-twin. C) older than the Earth-twin. D) The ages cannot be determined from the information provided. Answer: A Var: 1 10) You are a passenger on a spaceship. As the speed of the spaceship increases, you will observe A) the length of your spaceship getting shorter. B) the length of your spaceship getting longer. C) the length of your spaceship is zero. D) no change in the length of your spaceship. Answer: D Var: 1 11) Observer A sees a ruler moving by in a relativistic rocket and measures its length to be LA. Observer B moves along with the rocket and measures the length of the ruler to be LB. What is true about these two length measurements? A) LA > LB B) LA = LB C) LA < LB D) LA could be greater or smaller than LB depending on the direction of the motion. Answer: C Var: 1 12) An astronaut is resting on a bed inclined at an angle above the floor of a spaceship, as shown in the figure. From the point of view of an observer who sees the spaceship moving near the speed of light parallel to the floor, the angle the bed makes with the floor

A) is greater than the angle observed by the astronaut. B) is the same as the angle observed by the astronaut. C) is smaller than the angle observed by the astronaut. D) could be greater or smaller than the angle observed by the astronaut depending on whether the rocket is moving to the right or to the left. Answer: A Var: 1

13) When an object moves close to the speed of light relative to Earth, what happens to its dimensions compared to what they were before it began moving, as measured by an Earth-based observer? A) Only lengths parallel to the direction of travel are decreased. B) Only lengths perpendicular to the direction of travel are decreased. C) All lengths are decreased. D) No lengths are affected. Answer: A Var: 1 14) A really high-speed train moves in a direction parallel to its length with a speed that approaches the speed of light. The height of the train, as measured by a stationary observer on the ground, A) approaches infinity. B) approaches zero. C) increases slightly. D) decreases slightly. E) does not change due to the motion. Answer: E Var: 1 15) A really high-speed train moves in a direction parallel to its length with a speed that approaches the speed of light. The length of the train, as measured by a stationary observer on the ground, A) approaches infinity. B) increases due to the motion. C) decreases due to the motion. D) is not affected by the motion. Answer: C Var: 1 16) A spaceship is moving in a straight line away from Earth at 0.80c, measured relative to Earth. It launches a missile that moves away from the spaceship in the forward direction at 0.60c, relative to the ship. Relative to Earth, what is the speed of this missile? A) greater than 0.80c but less than c B) 1.4 c C) c D) greater than c but less than 1.4c Answer: A Var: 1

17) You are moving at a speed 2/3 c toward Randy when shines a light toward you. At what speed do you see the light approaching you? A) 1/3 c B) 2/3 c C) 4/3 c D) c Answer: D Var: 1 18) The special theory of relativity predicts that there is an upper limit to the speed of an object. It therefore follows that there is also an upper limit on which of the following properties of the object? (There could be more than one correct choice.) A) The kinetic energy of the object. B) The total energy of the object. C) The linear momentum of the object. D) None of the above. Answer: D Var: 1 19) The relativistic kinetic energy formula is valid A) only for speeds near the speed of light. B) at all speeds. C) only for subatomic particles, such as electrons and protons. Answer: B Var: 1 20) According to the equation E = mc2, an object turns into energy when it reaches the speed of light. A) True B) False Answer: B Var: 1

27.2 Problems 1) An unstable particle is moving at a speed of 1.6 × m/s relative to a laboratory. Its lifetime is measured by a stationary observer in the laboratory to be 6.8 × s. What is the lifetime of the particle as measured in the rest frame of the particle? (c = 3.0 × 108 m/s) Answer: 5.8 × 10-6 seconds Var: 50+ 2) A spaceship visits a star that is 4.5 light-years from Earth, and the spaceship travels at onehalf the speed of light for the entire trip. (a) How long did the trip take according to an observer on Earth? (b) How long did the trip take according to an observer on the spaceship? Answer: (a) 9.0 light-years (b) 7.8 years Var: 1 3) How fast (in terms of the speed of light) should a moving clock travel if it is to be observed by a stationary observer as running at one-half its normal rate? Answer: 0.866c Var: 1 4) A muon at rest decays in 2.2 μs. Moving at 99.00% the speed of light, it would be seen to "live" for how long? Answer: 16 μs Var: 1 5) A spaceship carrying a light clock moves at a speed of 0.960c relative to an observer on Earth. If the clock on the ship advances by 1.00 s as measured by the space travelers aboard the ship, how long did that advance take as measured by the observer on Earth? A) 0.96 s B) 1.2 s C) 2.6 s D) 3.6 s E) 5.8 s Answer: D Var: 1 6) Astronaut Rob leaves Earth in a spaceship at a speed of 0.960c relative to an observer on Earth. Rob's destination is a star system 14.4 light-years away (one light-year is the distance light travels in one year). Relative to a frame of reference that is fixed with respect to Earth, how long does it take Rob to complete the trip? A) 14.4 years B) 15.0 years C) 10.8 years D) 4.20 years E) 22.7 years Answer: B Var: 1 6 Copyright © 2019 Pearson Education, Inc.

7) Astronaut Rachel leaves Earth in a spaceship at a speed of 0.960c relative to an observer on Earth. Rachel's destination is a star system 14.4 light-years away (one light-year is the distance light travels in one year). According to Rachel, how long does the trip take? A) 14 years B) 15 years C) 11 years D) 4.2 years E) 23 years Answer: D Var: 1 8) At age 21, you set out for a star that is 50 light-years from Earth. How fast would your spaceship have to travel in order to reach that star when you are 61 years old? One light-year is the distance light travels in one year. A) 0.58c B) 0.68c C) 0.78c D) 0.88c E) 0.96c Answer: C Var: 1 9) A spaceship approaches Earth with a speed 0.50c. A passenger in the spaceship measures his heartbeat as 70 beats per minute. What is his heartbeat rate according to an observer that is at rest relative to Earth? A) 61 beats per minute B) 65 beats per minute C) 69 beats per minute D) 73 beats per minute E) 75 beats per minute Answer: A Var: 5 10) A spaceship enters the solar system moving toward the Sun at a constant speed relative to the Sun. By its own clock, the time elapsed between the time it crosses the orbit of Jupiter and the time it crosses the orbit of Mars is 50.0 minutes. How fast is the spaceship traveling towards the Sun? The radius of the orbit of Jupiter is 778 × 109 m, and that of the orbit of Mars is 228 × 109 m. A) 0.319c B) 0.438c C) 0.522c D) 0.671c E) 0.982c Answer: C Var: 5 7 Copyright © 2019 Pearson Education, Inc.

11) A spaceship enters the solar system moving toward the sun at a constant speed relative to the sun. By its own clock, the time elapsed between the time it crosses the orbit of Jupiter and the time it crosses the orbit of Mars is 50.0 minutes. As measured in the coordinate system of the sun, how long did it take for the spaceship to travel that distance? The radius of the orbit of Jupiter is 778 × 109 m, and that of the orbit of Mars is 228 × 109 m. A) 30.0 minutes B) 43.6 minutes C) 58.6 minutes D) 69.8 minutes E) 95.8 minutes Answer: C Var: 5 12) A pion is an unstable particle that has a mean lifetime of 2.55 × 10-8 s. This is the time interval between its creation in a nuclear process and its extinction into decay products, as measured in a frame of reference at rest with respect to the pion. An average pion is traveling at 0.230c relative to Earth. How far does it travel in its lifetime, relative to Earth? A) 2.07 m B) 1.81 m C) 2.23 m D) 3.22 m E) 3.50 m Answer: B Var: 5 13) A certain unstable particle has a mean lifetime of 1.52 × 10-6 s. This is the time interval between its creation in a nuclear process and its extinction into decay products, as measured in a frame of reference at rest with respect to the particle. An average such particle is observed by a scientist on Earth to travel 342 m in its lifetime. What is the speed of the particle relative to Earth? (c = 3.00 × 108 m/s) A) 0.821c B) 0.681c C) 0.600c D) 0.551c E) 0.335c Answer: C Var: 1

14) A particle physicist observes cosmic rays creating a new particle high in the atmosphere, and the speed of this particle is measured at 99.7% the speed of light. It is unstable, and is observed to decay in an average 37.0 μs. If this particle were at rest in the laboratory, what would be its average lifetime? A) 2.9 µs B) 18 µs C) 5.3 µs D) 12 µs E) 4.3 µs Answer: A Var: 1 15) You are moving past the Earth at 0.990c and notice your heart beating 88 beats per minute. (a) If a doctor on Earth measures your heart rate as you zip past, what will the measured rate be? (b) If you had been moving 99.99% the speed of light, what rate would you have observed your heart beats? Answer: (a) 12 beats/min (b) 88 beats/min Var: 9 16) As measured in Earth's rest frame, a spaceship traveling at 0.9640c takes to travel between two planets that are not moving relative to each other. How long does the trip take as measured by someone on the spaceship? A) 2.79 y B) 6.83 y C) 39.5 y D) 28.8 y Answer: A Var: 50+ 17) An astronaut on a spaceship moving at 0.927c says that the trip between two stationary stars took How long does this journey appear to take to someone in the rest frame of the two stars? A) 11.4 y B) 1.60 y C) 2.30 y D) 12.6 y Answer: A Var: 50+

18) Someone in Earth's rest frame says that a spaceship's trip between two planets took 10.0 y, while an astronaut on the space ship says that the trip took What is the speed of the spaceship, assuming the planets are at essentially at rest? A) 0.816 c B) 0.735 c C) 0.975 c D) 0.384 c Answer: A Var: 50+ 19) A spaceship with a constant speed of 0.800c relative to Earth travels to a star that is 4.30 light-years from Earth. How much time for this trip would elapse on a clock on board the spaceship? A) 3.23 y B) 4.40 y C) 5.15 y D) 5.38 y Answer: A Var: 1 20) A spaceship with a constant speed of 0.800c relative to Earth travels to a star that is 4.30 light-years from Earth. How much time for this trip would elapse on a clock on Earth? A) 3.23 y B) 4.40 y C) 5.15 y D) 5.38 y Answer: A Var: 1 21) A set of twins, Andrea and Courtney, are initially 10 years old. While Courtney remains on Earth, Andrea rides on a spaceship that travels away from Earth at a speed of 0.60c for 10 years (as measured by Courtney). At the end of the trip, Courtney is 20 years old. How old is Andrea? A) 10 years B) 12 years C) 18 years D) 20 years Answer: C Var: 1

22) One 20-year-old twin brother takes a space trip with a speed of 0.80c for 30 years according to a clock on his spaceship. At the end of this trip, what are (a) his own age and (b) the age of his Earth-based twin brother? A) (a) 20 y (b) 30 y B) (a) 30 y (b) 50 y C) (a) 50 y (b) 70 y D) (a) 70 y (b) 90 y Answer: C Var: 1 23) How fast would a rocket ship have to move past Earth to contract to half of its proper length as observed by an Earth-based physicist? Answer: 0.87c Var: 1 24) A spacecraft is measured by a scientist on the ground to have a length of 81 m as it flies overhead with a speed The spacecraft then lands and its length is again measured by the scientist at rest on the ground. What result does he now get for the length of the spacecraft? (c = 3.0 × 108 m/s) Answer: 1.4 × 102 m Var: 50+ 25) A stretch of land is 12.5 km long on a map. (a) What would be its length to an observer moving by, parallel to the stretch, at (b) Which is the proper length for this stretch of land? (c) How fast relative to Earth would the observer have to move for the land to appear 6.50 km long? Express your answer in terms of the speed of light. Answer: (a) 3.90 km (b) 12.5 km (c) 0.854c Var: 8 26) A starship is constructed to be 100 m long in the factory. It is launched and as it coasts by Earth, it is measured to be shortened to 5.48 m long. (a) How fast, in terms of the speed of light, is it moving past Earth? (b) What length does the ship's crew measure for the ship? Answer: (a) 0.9985c (b) 100 m Var: 1 27) Two stars are at rest relative to each other. In their common rest frame, these stars are 90.0 light-years apart. If they are measured to be apart by the navigator of a spaceship traveling between them, how fast is the spaceship moving relative to these stars? A) 0.646c B) 0.604c C) 0.558c D) 0.505c Answer: A Var: 50+ 11 Copyright © 2019 Pearson Education, Inc.

28) A particle in a 799=m-long linear particle accelerator is moving at particle accelerator appear to the particle? A) 387 m B) 1039 m C) 184 m D) 1651 m Answer: A Var: 50+

How long does the

29) Two stars are at rest relative to each other. A spaceship is moving between these two stars at 0.932c relative to each star. To someone in the ship, the distance between the two stars appears to be What is the distance between the stars in their own rest frame? A) 72.8 light-years B) 9.57 light-years C) 21.1 light-years D) 55.4 light-years Answer: A Var: 50+ 30) Astronaut Jill leaves Earth in a spaceship and is now traveling at a speed of 0.280c relative to an observer on Earth. When Jill left Earth, the spaceship was equipped with all kinds of scientific instruments, including a meter stick. Now that Jill is underway, how long does she measure the meter stick to be? A) 1.00 m B) 0.960 m C) 1.04 m D) 0.280 m E) 1.28 m Answer: A Var: 1 31) How fast must a meter stick move, relative to the frame of the observer making the measurement, so its length will be measured to be 0.60 m? A) 0.40c B) 0.60c C) 0.70c D) 0.80c E) 0.90c Answer: D Var: 1

32) Astronaut Sarah leaves Earth in a spaceship at a speed of 0.280c relative to Earth. Sarah's destination is a star system 12.5 light-years away (one light-year is the distance light travels in one year). According to Sarah, how far did she travel during the trip? A) 13.0 light-years B) 12.5 light-years C) 12.0 light-years D) 11.5 light-years E) 11.0 light-years Answer: C Var: 1 33) Astronaut Hans leaves Earth in a spaceship traveling at a speed of 0.280c relative to the observer Brian at rest on Earth. Hans is holding a pencil at an angle of 30° with the direction of travel, as seen by Hans. What angle does the pencil make with the direction of travel, as seen by Brian on Earth? A) 29° B) 30° C) 31° D) 33° E) 90° Answer: C Var: 1 34) The figure shows a right-angled construction frame ABC. When measured at rest, it has dimensions as follows: AB = 18.9 m, AC = 10.0 m, and BC = 16.0 m. This frame is now given a new velocity of 0.420c, relative to Earth, in a direction parallel to AC. How long is part BC of this frame with the new velocity as measured by Earth-based engineers?

A) 16.0 m B) 14.0 m C) 12.0 m D) 10.0 m E) 18.0 m Answer: A Var: 1

35) The figure shows a right-angled construction frame ABC. When measured at rest, it has dimensions as follows: AB = 26.0 m, AC = 10.0 m, and BC = 24.0 m. This frame is now given a new velocity of 0.760c, relative to Earth, in a direction parallel to AC. How long is part AC of this frame with the new velocity as measured by Earth-based engineers?

A) 6.50 m B) 25.4 m C) 24.3 m D) 23.7 m E) 24.9 m Answer: A Var: 1 36) A spaceship with a constant velocity of 0.800c relative to Earth travels to the star that is 4.30 light-years from Earth. What distance does the space ship travel as measured by a passenger on the ship? A) 2.58 light-years B) 3.52 light-years C) 4.12 light-years D) 4.30 light-years Answer: A Var: 1 37) A person in a rocket ship traveling past the earth at a speed of 0.500c fires a laser gun in the forward direction. With what speed does an observer on Earth measure for the light pulse? Answer: c = 3.00 × 108 m/s Var: 1 38) A rocket is traveling away from Earth at 90% the speed of light. The captain turns on a laser light. What is the speed of the light as measured by an Earth-based astronomer if the captain aims the laser (a) directly forward or (b) directly backward? Answer: (a) c = 3.00 × 108 m/s (b) c = 3.00 × 108 m/s Var: 1 39) Two spaceships are approaching one another, each at a speed of 0.31c relative to a stationary observer on Earth. What speed, in terms of the speed of light, does an observer on one spaceship record for the other approaching spaceship? Answer: 0.57c Var: 50+

40) From the Earth, the Earthlings see the Enterprise approaching from the west at 0.800c and the Klingons approaching from the east at 0.900c. What speed, in terms of the speed of light, does the crew of the Enterprise measure for the Klingon ship? Answer: 0.988c Var: 1 41) Two spaceships are traveling through space at speeds of 0.600c and 0.900c, respectively, with respect to Earth. If they are headed directly toward each other, what is their approach speed (in terms of the speed of light) as measured by the captain of either ship? Answer: 0.974c Var: 1 42) Two spaceships approach each other along a straight line at a constant relative velocity of 0.9880c as measured by the captain of one of the ships. An observer on Earth is able to measure the speed of only one of the ships as 0.9000c. From the point of view of the observer on Earth, what is the speed of the other ship in terms of the speed of light? Answer: 0.794c Var: 1 43) A tracking station on Earth observes a rocket move away at 0.370c. This rocket is designed to launch a projectile at 0.505c relative to the rocket. What speed (in terms of the speed of light) does the tracking station measure for the projectile if it is fired (a) straight ahead of the rocket or (b) backward from the rocket? Answer: (a) 0.737c (b) 0.166c Var: 1 44) A spaceship is moving away from an asteroid with a speed of 0.80c relative to the asteroid. The spaceship then fires a missile with a speed of 0.50c relative to the spaceship. What is the speed of the missile measured by astronauts on the asteroid if the missile is fired away from the asteroid? A) 0.30c B) 0.50c C) 0.93c D) 1.3c E) 0.65c Answer: C Var: 1

45) A spaceship is moving away from an asteroid with a speed of 0.80c relative to the asteroid. The spaceship then fires a missile with a speed of 0.50c relative to the spaceship. What is the speed of the missile measured by astronauts on the asteroid if the missile is fired toward the asteroid? A) 0.30c B) 0.50c C) 0.93c D) 1.3c E) 0.65c Answer: B Var: 1 46) A spaceship leaves Earth at a steady forward speed of 70% the speed of light. How fast relative to the ship must the spaceship launch a shuttlecraft in the forward direction so that it will be moving away from Earth at 98.7% the speed of light? A) 0.91c B) 0.97c C) 0.93c D) 0.99c E) 0.84c Answer: C Var: 1 47) A spaceship traveling at 0.50c away from Earth launches a secondary rocket in the forward direction at 0.50c relative to the spaceship. As measured by Earthlings, how fast is the secondary rocket moving away from Earth? A) 0.90c B) 0.50c C) 0.80c D) 0.70c E) c Answer: C Var: 1 48) A star is moving toward Earth at 90% the speed of light. The star emits light, which moves away from the star at the speed of light. What do Earth-based astronomers measure for the speed of this light? A) c B) 1.9c C) 1.2c D) 0.98c E) 0.95c Answer: A Var: 1

49) A spaceship, traveling at 0.560c towards a stationary space platform, launches a secondary towards the station with a speed of 0.100c relative to the spaceship. What is the speed of the secondary rocket relative to the space platform? A) 0.460c B) 0.575c C) 0.600c D) 0.625c E) 0.660c Answer: D Var: 1 50) A spaceship, traveling at 0.100c away from a stationary space platform, launches a secondary rocket towards the station, with a speed of 0.560c relative to the spaceship. What is the speed of the secondary rocket relative to the space platform? A) 0.460c B) 0.487c C) 0.492c D) 0.660c Answer: B Var: 1 51) Two spaceships approach Earth from the same direction. One has a speed of 0.21c and the other a speed of 0.34c, both relative to Earth. What is the speed of one spaceship relative to the other? A) 0.13c B) 0.14c C) 0.15c D) 0.16c E) 0.18c Answer: B Var: 1 52) Two spaceships approach Earth from opposite directions. One has a speed of 0.21c and the other a speed of 0.34c, both relative to Earth. What is the speed of one spaceship relative to the other? A) 0.51c B) 0.55c C) 0.58c D) 0.61c E) 0.64c Answer: A Var: 1

53) Two spaceships, each 100 m long in its own rest frame, approach Earth from opposite directions, each with a speed 0.50c relative to Earth. As measured by a passenger in one of the spaceships, how long is the other spaceship? A) 50 m B) 60 m C) 70 m D) 80 m E) 90 m Answer: B Var: 1 54) Two spaceships, each 100 m long in its own rest frame, approach Earth from opposite directions, with equal speeds relative to Earth. As measured by a passenger in one of the spaceships, the other spaceship is 96 m long. What is the speed of the spaceships relative to Earth? A) c/7 B) c/6 C) c/5 D) c/4 E) c/3 Answer: A Var: 1 55) A spaceship approaching an asteroid at a speed of 0.60c launches a scout rocket with speed 0.40c relative to the spaceship. At what speed is the scout rocket approaching the asteroid? A) 0.81c B) 1.0c C) 0.76c D) 0.64c E) 0.96c Answer: A Var: 1 56) In an "atom smasher," two particles collide head on at relativistic speeds. If the velocity of the first particle is 0.741c to the left, and the velocity of the second particle is to the right (both as measured in the lab rest frame), how fast are the particles moving with respect to each other? A) 0.916c B) 1.284c C) 0.934c D) 0.834c Answer: A Var: 50+

57) As shown in the figure, the captain of spaceship A observes spaceship E escaping with a relative velocity of 0.35c. A missile M is fired from ship A directly toward ship E, with a velocity of 0.76c relative to ship A. What does the captain of ship E measure for the velocity of the missile M?

A) 0.56c B) 0.41c C) 0.52c D) 0.48c E) 0.45c Answer: A Var: 1 58) Three spaceships A, B, and C are in motion as shown in the figure. The commander on ship B observes ship C approaching with a relative velocity of 0.82c. The commander also observes ship A, advancing in the rear, with a relative velocity of 0.50c. What is the speed of ship C as measured by the captain of ship A?

A) 0.94c B) 0.23c C) 2.2c D) 0.54c E) 1.3c Answer: A Var: 1 59) Consider three galaxies, Alpha, Beta and Gamma. An astronomer in Beta sees each of the other two galaxies moving away from her in opposite directions at 0.70c. At what speed would an observer in Alpha see the galaxy Beta moving? A) 0.82c B) 0.70c C) 0.94c D) 0.35c E) 0.57c Answer: B Var: 1

60) Consider three galaxies, Alpha, Beta and Gamma. An astronomer in Beta sees each of the other two galaxies moving away from him in opposite directions at 0.70c. At what speed would an observer in Alpha see the galaxy Gamma moving? A) 0.70c B) 1.4c C) 0.82c D) 0.94c E) 0.98c Answer: D Var: 1 61) As an electron slows down from 0.9980c to 0.5000c, how much momentum does it lose? (c = 3.0 × 108 m/s, melectron = 9.11 × 10-31 kg) Answer: 4.2 × 10-21 kg ∙ m.s Var: 1 62) Calculate the speed at which a 0.723-kg object has the same momentum as a 1.30-kg object that is moving 0.515c. A) 0.734c B) 0.712c C) 0.981c D) 0.592c Answer: A Var: 50+ 63) What is the momentum of a proton when it is moving with a speed of 0.60c? (mproton = 1.67 × 10-27 kg) A) 1.2 × 10-19 kg∙ m/s B) 1.5 × 10-19 kg ∙ m/s C) 3.0 × 10-19 kg ∙ m/s D) 3.8 × 10-19 kg ∙ m/s Answer: D Var: 1 64) A particle is moving at 0.86c. By what magnitude percentage is the Newtonian expression for momentum in error? (The percentage error is the difference between the erroneous and correct expressions, relative the correct one). A) 49% B) 40% C) 55% D) 62% Answer: A Var: 46

65) An object with a rest mass of 0.456-kg is moving at 1.20 × 108 m/s. What is the magnitude of its momentum? (c = 3.00 × 108 m/s) A) 5.47 × 107 kg ∙ m/s B) 5.57 × 107 kg ∙ m/s C) 5.67 × 107 kg ∙ m/s D) 5.87 × 107 kg ∙ m/s E) 5.97 × 107 kg ∙ m/s Answer: E Var: 1 66) A satellite, initially at rest in deep space, separates into two pieces, which move away from each other. One piece has a rest mass of 190 kg and moves away with a speed 0.280c, and the second piece moves in the opposite direction with a speed 0.600c. What is the rest mass of the second piece? A) 88.7 kg B) 79.6 kg C) 73.9 kg D) 68.8 kg E) 52.7 kg Answer: C Var: 1 67) A satellite, initially at rest in deep space, separates into two pieces, which move away from each other. One piece has a rest mass of 190 kg and moves away with a speed 0.500c, and the second piece has a rest mass of 250 kg and moves in the opposite direction. What is the speed of the second piece? A) 0.212c B) 0.380c C) 0.402c D) 0.473c E) 0.500c Answer: C Var: 1 68) Two satellites with equal rest masses of 100 kg are traveling toward each other in deep space. They have identical speeds of 0.600c. The satellites collide and somehow manage to stick together. What is the rest mass of the combined object after the collision? A) 200 kg B) 225 kg C) 250 kg D) 275 kg E) 300 kg Answer: C Var: 1

69) A satellite with a rest mass of 200 kg and a speed of 0.800c and a second satellite with a rest mass of 100 kg and a speed of 0.600c are traveling toward each other in deep space. The satellites collide and somehow manage to stick together. What is the rest mass of the combined object after the collision? A) 300 kg B) 389 kg C) 416 kg D) 457 kg E) 587 kg Answer: C Var: 1 70) A satellite with a rest mass of 200 kg and a speed of 0.800c and a second satellite with a rest mass of 100 kg and a speed of 0.600c are traveling toward each other in deep space. The satellites collide and somehow manage to stick together. What is the speed of the combined object after the collision? A) 0.333c B) 0.374c C) 0.397c D) 0.418c E) 0.432c Answer: D Var: 1 71) Two satellites with equal rest masses are traveling toward each other in deep space. One is traveling at 0.550c and the other at 0.750c. The satellites collide and somehow manage to stick together. What is the speed of the combined object after the collision? A) 0.100c B) 0.113c C) 0.150c D) 0.175c E) 0.311c Answer: D Var: 5 72) Two satellites with equal rest masses of 100 kg are traveling toward each other in deep space. One is traveling at 0.650c and the other at 0.850c. The satellites collide and somehow manage to stick together. What is the rest mass of the combined object after the collision? A) 100 kg B) 200 kg C) 277 kg D) 378 kg E) 312 kg Answer: E Var: 5

73) A proton, which has a mass of 1.67 × 10-27, is moving at 0.80c relative to the laboratory. What does a physicist in that lab measure for its momentum? (c = 3.0 × 108 m/s) A) 4.0 × 10-19 kg ∙ m/s B) 4.4 × 10-19 kg ∙ m/s C) 5.0 × 10-19 kg ∙ m/s D) 5.8 × 10-19 kg ∙ m/s E) 6.7 × 10-19 kg ∙ m/s Answer: E Var: 1 74) How much work must be done to accelerate a particle of mass to a speed of (c = 3.0 × 108 m/s) Answer: 630 J Var: 50+

from a speed of

75) An electron has a relativistic momentum of 1.1 × 10-21 kg ∙ m/s. What percent of its total energy is its kinetic energy? (melectron = 9.11 ×10-31 kg, c = 3.0 × 108 m/s) Answer: 76% Var: 1 76) When a proton is traveling at 0.80c, what is the ratio of its kinetic energy to its rest energy? A) 0.60 B) 0.67 C) 0.80 D) 1.2 E) 1.7 Answer: B Var: 1 77) If an electron in the lab has a kinetic energy equal to twice its rest energy, what is its speed in the lab? A) 0.84c B) 0.87c C) 0.89c D) 0.91c E) 0.94c Answer: E Var: 1

78) Calculate the amount of energy needed to accelerate an electron from to Express your answer in The rest mass energy of an electron is 0.511 MeV. A) 2.71 MeV B) 1.90 MeV C) 4.61 MeV D) 5.69 MeV Answer: A Var: 50+ 79) If the kinetic energy of a proton is 80% of its total energy, what is the speed of the proton? A) 0.02c B) 0.87c C) 0.98c D) 1.0c Answer: C Var: 1 80) What is the total energy of an electron moving with a speed of 0.950c? (c = 3.0 × 108 m/s, mel = 9.11 × 10-31 kg) A) 2.6 × 10-13 J B) 8.2 × 10-14 J C) 1.1 × 10-13 J D) 1.2 × 10-14 J Answer: A Var: 1 81) How many joules of energy are required to accelerate a 1.0-kg rock from rest to a speed of 0.866c? (c = 3.0 × 108 m/s) A) 1.8 × 1017 J B) 9.0 × 1016 J C) 3.0 × 103 J D) 3.3 × 1016 J Answer: B Var: 1 82) If, instead of the correct formula for kinetic energy, we carelessly use the classical expression for kinetic energy for a particle moving at half the speed of light, by what magnitude percent will our calculation be in error? (c = 3.0 × 108 m/s) A) 24% B) 19% C) 27% D) 7% E) 1% Answer: B Var: 1 24 Copyright © 2019 Pearson Education, Inc.

83) How much energy would be required to accelerate a 77-kg professor from rest to 90% the speed of light? (c = 3.0 × 108 m/s) A) 1.6 × 1019 J B) 2.1 × 1019 J C) 9.0 × 1019 J D) 2.8 × 1019 J E) 3.5 × 1019 J Answer: C Var: 1 84) If the kinetic energy of a particle is 3.00 times its rest energy, the speed of the particle is closest to which of the following values? A) 0.950c B) 0.968c C) 0.976c D) 0.984c E) 0.990c Answer: B Var: 1 85) A space barge pushes on a spaceship with a rest mass of 15,000 kg and accelerates it from a speed of 0.600c to a speed of 0.700c. How much work does the barge have to do to accomplish this? (c = 3.00 × 108 m/s) A) 1.35 × 1020 J B) 2.03 × 1020 J C) 2.70 × 1020 J D) 5.42 × 1020 J E) 8.78 × 1019 J Answer: B Var: 1 86) An electron has a speed of 0.783c. Through what potential difference would the electron need to be accelerated from rest in order to reach this speed? The rest mass energy of an electron is 0.511 MeV. A) 310 kV B) 260 kV C) 360 kV D) 400 kV Answer: A Var: 50+

87) Consider a student whose mass is 70 kg. If all his mass were converted to electrical energy, for how many years could he keep a 100-W light bulb burning? (c = 3.0 × 108 m/s) Answer: 6.3 × 1016 s = 2.0 billion years! Var: 1 88) An electron-volt is the energy gained by an electron if it is accelerated through a potential difference of one volt. What is the equivalent to an electron-volt in kilograms? (c = 3.00 × 108 m/s, e = 1.60 × 10-19 C) Answer: 1.78 × 10-36 kg Var: 1 89) One of the first atomic bombs released energy equivalent to that of 20,000 tons of TNT explosive. How much mass was converted to energy by this explosion, given that 1000 tons of TNT produce 4.3 × 1012 J of energy. Incidentally, modern H-bombs have energy yields 1000 times as much! (c = 3.0 × 108 m/s) Answer: 0.96 g Var: 1 90) An alpha particle has a mass of 6.64 × 10-27 kg and a charge of 3.20 × 10-19 C, and it is traveling at 0.9650c. (c = 3.00 × 108 m/s), 1 eV = 1.60 × 10-19 J) (a) What is its rest energy (in GeV)? (b) What is its total energy (in GeV)? (c) What is its kinetic energy (in GeV)? Answer: (a) 3.74 GeV (b) 14.2 GeV (c) 10.5 GeV Var: 1 91) A person with an initial mass of 70 kg climbs a stairway and thereby rises 6.0 m in elevation. By how much does his mass increase by virtue of his increased potential energy? (c = 3.0 × 108 m/s) Answer: 4.6 × 10-14 kg Var: 1 92) If the mass of a 1.0-kg book could be entirely converted into electrical energy, how many kW ∙ h of energy would that generate? (c = 3.0 × 108 m/s) Answer: 2.5 × 1010 kW ∙ h Var: 1

93) If a typical city consumes electrical energy at a rate of how many kilograms of matter would have to be converted entirely into electrical energy in order to keep this city running for A) 0.19 kg B) 0.21 kg C) 0.27 kg D) 0.32 kg Answer: A Var: 17 94) In a nuclear plant, 1017 J of energy is available from mass conversion. How much mass of fuel was lost to produce this energy? (c = 3.0 × 108 m/s) A) 0.1 kg B) 1 kg C) 10 kg D) 100 kg Answer: B Var: 1 95) In a certain chemical reaction, 8.1 × 10-19 J of energy is released per molecule formed. What is the difference in mass per molecule between the sum of the masses of the molecules of the reagents before the reaction and the mass of the molecules produced by the reaction? (c = 3.0 × 108 m/s) A) 8.1 × 10-28 kg B) 2.7 × 10-27 kg C) 3.2 × 10-27 kg D) 5.4 × 10-32 kg E) 9.0 × 10-36 kg Answer: E Var: 1 96) During a reaction, a reactant loses 4.8 × 10-28 kg of mass. How many joules of energy are released? (c = 3.0 × 108 m/s) A) 4.3 × 10-11 J B) 1.4 × 10-19 J C) 1.6 × 10-36 J D) 5.3 × 10-45 J Answer: A Var: 1

97) During a reaction, 170 µJ of energy is released. What change of mass would accompany this release? (c = 3.0 × 108 m/s) A) 5.1 × 10-4 kg B) 1.5 × 10-13 kg C) 4.8 × 10-18 kg D) 1.9 × 10-21 kg Answer: D Var: 1 98) How many MeV of energy is released during a reaction in which 1.67 × 10-25 kg of material is converted to energy? (c = 3.0 × 108 m/s, 1 eV = 1.67 × 10-19 J) A) 5.0 × 10-14 MeV B) 4.1 × 10-7 MeV C) 3.1 × 10-4 MeV D) 9.4 × 104 MeV Answer: D Var: 1 99) How much mass is lost during a reaction in which 1.7 × 108 MeV of energy is released? (c = 3.0 × 108 m/s, 1 eV = 1.6 × 10-19 J) A) 1.8 × 10-8 kg B) 5.7 × 10-9 kg C) 1.9 × 10-17 kg D) 3.0 × 10-22 kg Answer: D Var: 1 100) How much energy would be released if 2.0 kg of material was lost during a reaction? (c = 3.0 × 108 m/s) A) 1.8 × 1017 J B) 1.5 × 1016 J C) 6.0 × 108 J D) 4.7 × 10-8 J Answer: A Var: 1 101) The energy released by a certain reaction is enough to totally evaporate 125 kg of water at its boiling point. How much mass was lost during this reaction? (LF = 334,000 J/kg for water, c = 3.00 × 108 m/s) Answer: 4.64 × 10-10 kg Var: 1

102) One of the first atomic explosion released approximately 1.0 × 1014 J of energy. How much matter had to be changed into energy to produce this yield? (c = 3.0 × 108 m/s) A) 1.1 g B) 23 g C) 13 g D) 0.45 kg E) 1.1 kg Answer: A Var: 1 103) A 1.00-kg gold ingot is carried from the bottom of the Eiffel tower to the top, 300 m above ground level. By what amount does its mass change? (c = 3.00 × 108 m/s) A) Its mass does not change. B) Its mass increases by 3.27 × 10-14 kg C) Its mass decreases by 3.27 × 10-14 kg D) Its mass increases by 1.64 × 10-14 kg E) Its mass decreases by 1.64 × 10-14 kg Answer: B Var: 1 104) A 1.0-kg aluminum ingot is heated from 0°C to 100°C. By what amount does its mass change? The specific heat of aluminum is 900 J/kg ∙ K. (c = 3.0 × 108 m/s) A) Its mass does not change. B) Its mass increases by 0.50 × 10-12 kg C) Its mass decreases by 0.50 × 10-12 kg D) Its mass increases by 1.0 × 10-12 kg E) Its mass decreases by 1.0 × 10-12 kg Answer: D Var: 1 105) If a particle has a total energy that is 5.00 times its rest energy, the speed of the particle is closest to which one of the following values? A) 0.980c B) 0.985c C) 0.950c D) 0.990c E) 0.998c Answer: A Var: 1

106) The total energy of a moving electron is What is the speed of the electron in terms of c? The rest mass energy of an electron is 0.511 MeV. A) 0.739 c B) 0.794 c C) 0.306 c D) 0.933 c Answer: A Var: 50+

College Physics: A Strategic Approach, 4e (Knight) Chapter 28 Quantum Physics 28.1 Conceptual Questions 1) Two sources emit beams of microwaves. The microwaves from source A have a frequency of 10 GHz, and the ones from source B have a frequency of 20 GHz. This is all we know about the two beams. Which of the following statements about these beams are correct? (There could be more than one correct choice.) A) Beam B carries twice as many photons per second as beam A. B) A photon in beam B has twice the energy of a photon in beam A. C) The intensity of beam B is twice as great as the intensity of beam A. D) A photon in beam B has the same energy as a photon in beam A. E) None of the above statements are true. Answer: B Var: 1 2) Two sources emit beams of light of wavelength 550 nm. The light from source A has an intensity of 10 µW/m 2, and the light from source B has an intensity of 20 µW/m 2. This is all we know about the two beams. Which of the following statements about these beams are correct? (There could be more than one correct choice.) A) Beam B carries twice as many photons per second as beam A. B) A photon in beam B has twice the energy of a photon in beam A. C) The frequency of the light in beam B is twice as great as the frequency of the light in beam A. D) A photon in beam B has the same energy as a photon in beam A. E) None of the above statements are true. Answer: A Var: 1 3) A beam of light falling on a metal surface is causing electrons to be ejected from the surface. If we now double the frequency of the light, which of the following statements are correct? (There could be more than one correct choice.) A) The kinetic energy of the ejected electrons doubles. B) The speed of the ejected electrons doubles. C) The number of electrons ejected per second doubles. D) Twice as many photons hit the metal surface as before. E) None of the above things occur. Answer: E Var: 1

4) Light of a given wavelength is used to illuminate the surface of a metal, however, no photoelectrons are emitted. In order to cause electrons to be ejected from the surface of this metal you should A) use light of a longer wavelength. B) use light of a shorter wavelength. C) use light of the same wavelength but increase its intensity. D) use light of the same wavelength but decrease its intensity. Answer: B Var: 1 5) A blue laser beam is incident on a metallic surface, causing electrons to be ejected from the metal. If the frequency of the laser beam is increased while the intensity of the beam is held fixed, A) the rate of ejected electrons will decrease and their maximum kinetic energy will increase. B) the rate of ejected electrons will remain the same but their maximum kinetic energy will increase. C) the rate of ejected electrons will increase and their maximum kinetic energy will increase. D) the rate of ejected electrons will remain the same but their maximum kinetic energy will decrease. Answer: A Var: 1 6) Monochromatic light falls on a metal surface and electrons are ejected. If the intensity of the light is increased, what will happen to the ejection rate and maximum energy of the electrons? A) greater rate; same maximum energy. B) same rate; greater maximum energy. C) greater rate; greater maximum energy. D) same rate; same maximum energy. Answer: A Var: 1 7) When the surface of a metal is exposed to blue light, electrons are emitted. If the intensity of the blue light is increased, which of the following things will also increase? A) the number of electrons ejected per second B) the maximum kinetic energy of the ejected electrons C) the time lag between the onset of the absorption of light and the ejection of electrons D) the work function of the metal E) all of the above Answer: A Var: 1

8) Monochromatic light is incident on a metal surface, and the ejected electrons give rise to a current in the circuit shown in the figure. The maximum kinetic energy of the ejected electrons is determined by applying a reverse ('stopping') potential, sufficient to reduce the current in the ammeter to zero. If the intensity of the incident light is increased, how will the required stopping potential change?

A) It will remain unchanged. B) It will increase. C) It will decrease. Answer: A Var: 1 9) If the wavelength of a photon in vacuum is the same as the de Broglie wavelength of an electron, which one is traveling faster through space? A) The electron because it has more mass. B) The photon because photons always travel through space faster than electrons. C) They both have the same speed. Answer: B Var: 1 10) If a proton and an electron have the same de Broglie wavelengths, which one is moving faster? A) the electron B) the proton C) They both have the same speed. Answer: A Var: 1 11) If a proton and an electron have the same speed, which one has the longer de Broglie wavelength? A) the electron B) the proton C) It is the same for both of them. Answer: A Var: 1

12) Which of the following actions will increase the de Broglie wavelength of a speck of dust? (There could be more than one correct choice.) A) Increase its mass. B) Increase its speed. C) Decrease its mass. D) Decrease its speed. E) Decrease its momentum. Answer: C, D, E Var: 1 13) Protons are being accelerated in a particle accelerator. When the energy of the protons is doubled, their de Broglie wavelength will A) increase by a factor of 4. B) increase by a factor of 2. C) decrease by a factor of 2. D) increase by a factor of . E) decrease by a factor of . Answer: E Var: 1 14) Protons are being accelerated in a particle accelerator. When the speed of the protons is doubled, their de Broglie wavelength will A) increase by a factor of 4. B) increase by a factor of 2. C) decrease by a factor of 2. D) increase by a factor of . E) decrease by a factor of . Answer: C Var: 1 15) A proton and an electron are both accelerated to the same final speed. If λp is the de Broglie wavelength of the proton and λe is the de Broglie wavelength of the electron, then A) λp > λe. B) λp = λe. C) λp < λe. Answer: C Var: 1 16) A proton and an electron are both accelerated to the same final kinetic energy. If λp is the de Broglie wavelength of the proton and λe is the de Broglie wavelength of the electron, then A) λp > λe. B) λp = λe. C) λp < λe. Answer: C Var: 1 4 Copyright © 2019 Pearson Education, Inc.

17) If the maximum possible accuracy in measuring the position of a particle increases, the maximum possible accuracy in measuring its velocity will A) increase. B) decrease. C) not be affected. Answer: B Var: 1 18) If the maximum possible accuracy in measuring the velocity of a particle increases, the maximum possible accuracy in measuring its position will A) increase. B) decrease. C) not be affected. Answer: B Var: 1 28.2 Problems 1) A researcher is using x-rays to investigating a cubic crystal. He is looking at Bragg reflection from the planes parallel to the cube faces. He finds that when using x-rays with a wavelength of 0.165 nm, a strong first maximum occurs when the beam makes an angle of 23.5° with the planes. What is the spacing of adjacent atoms in this crystal? Answer: 0.207 nm Var: 1 2) Certain planes of a crystal of halite have a spacing of 0.399 nm. The crystal is irradiated by a beam of x-rays. First order constructive interference occurs when the beam makes an angle of 20° with the planes of the crystal surface. What is the wavelength of the x-rays? A) 0.14 nm B) 0.17 nm C) 0.21 nm D) 0.24 nm E) 0.27 nm Answer: E Var: 1 3) Certain planes of a crystal of halite have a spacing of 0.399 nm. The crystal is irradiated by a beam of x-rays. First order constructive interference occurs when the beam makes an angle of 20° with the planes of the crystal surface. What angle does the beam make with the crystal planes for second order constructive? A) 37° B) 40° C) 43° D) 46° E) 49° Answer: C Var: 1 5 Copyright © 2019 Pearson Education, Inc.

4) A crystal is irradiated with x-rays with a wavelength of 0.120 nm. The atomic planes in the crystal are separated by 0.21 nm. At what angles of incidence with respect to the normal will the x-rays reflect from the crystal? A) 73°, 55°, 31° B) only 55° C) only 73° and 31° D) only 73° Answer: A Var: 1 5) The lattice spacing of the principal Bragg planes in sodium chloride is 0.282 nm. For what wavelength of x-rays will the first order reflected beam diffract at 55° with respect to the normal to the crystal planes? A) 0.323 nm B) 0.530 nm C) 0.662 nm D) 0.150 nm E) 0.462 nm Answer: A Var: 1 6) What is the wavelength of a 6.32-eV photon? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) A) 197 nm B) 167 nm C) 216 nm D) 234 nm Answer: A Var: 1 7) Gamma rays are photons with very high energy. What is the wavelength of a gamma-ray photon with energy 7.7 × 10-13 J? (c = 3.0 × 108 m/s, h = 6.626 × 10-34 J ∙ s) A) 2.6 × 10-13 m B) 3.9 × 10-13 m C) 3.1 × 10-13 m D) 3.5 × 10-13 m Answer: A Var: 50+

8) Gamma rays are photons with very high energy. How many visible-light photons with a wavelength of 500 nm would you need to equal the energy of a gamma-ray photon with energy A) 1.0 × 106 B) 1.4 × 108 C) 6.2 × 109 D) 3.9 × 103 Answer: A Var: 50+ 9) An 84-kW AM radio station broadcasts at 1000 kHz. How many photons are emitted each second by the transmitting antenna? (h = 6.626 × 10-34 J ∙ s) A) 1.3 × B) 2.9 × C) 6.3 × D) 1.4 × Answer: A Var: 50+ 10) A laser pulse of duration 25 ms has a total energy of 1.4 J. If the wavelength of this radiation is 567 nm, how many photons are emitted in one pulse? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s) A) 4.0 × 1018 B) 9.9 × 1019 C) 4.8 × 1019 D) 1.6 × 1017 E) 3.2 × 1017 Answer: A Var: 50+ 11) A laser emits a pulse of light that lasts 10 ns. The light has a wavelength of 690 nm, and each pulse has an energy of 480 mJ. How many photons are emitted in each pulse? (c = 3.0 × 108 m/s, h = 6.626 × 10-34 J ∙ s) A) 1.7 × 1018 B) 2.1 × C) 2.6 × D) 3.1 × Answer: A Var: 50+

12) For what wavelength does a 100-mW laser beam deliver 1.6 × 1017 photons in one second? (c = 3.0 × 108 m/s, h = 6.626 × 10-34 J ∙ s) A) 320 nm B) 330 nm C) 340 nm D) 350 nm Answer: A Var: 25 13) A helium-neon laser emits light at 632.8 nm. If the laser emits photons/second, what is its power output in mW? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s) A) 57.2 mW B) 28.6 mW C) 37.2 mW D) 45.7 mW Answer: A Var: 50+ 14) A photoelectric surface has a work function of 2.10 eV. Calculate the maximum kinetic energy, in eV, of electrons ejected from this surface by electromagnetic radiation of wavelength 356 nm. (1 eV = 1.60 × 10-19 J, c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s) Answer: 1.39 eV Var: 50+ 15) If the longest wavelength of light that is able to dislodge electrons from a metal is 373 nm, what is the work function of that metal, in electron-volts? (1 eV = 1.60 × 10-19 J, c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s) Answer: 3.33 eV Var: 1 16) A metallic surface is illuminated with light of wavelength 400 nm. If the work function for this metal is 2.40 eV, what is the maximum kinetic energy of the ejected electrons, in electronvolts? (1 eV = 1.60 × 10-19 J, c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s) Answer: 0.71 eV Var: 1 17) A metal surface has a work function of 2.50 eV. What is the longest wavelength of light that will eject electrons from the surface of this metal? (1 eV = 1.60 × 10-19 J, c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s) Answer: 497 nm Var: 1

18) The work function of a particular metal is What is the photoelectric cutoff (threshold) wavelength for this metal? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s) A) 473 nm B) 308 nm C) 393 nm D) 554 nm Answer: A Var: 50+ 19) What is the cutoff (threshold) frequency for a metal surface that has a work function of 5.42 eV? (1 eV = 1.60 × 10-19 J, h = 6.626 × 10-34 J ∙ s) A) 1.31 × Hz B) 2.01 × Hz C) 3.01 × Hz D) 5.02 × Hz E) 6.04 × Hz Answer: A Var: 5 20) The work function of a certain metal is 1.90 eV. What is the longest wavelength of light that can cause photoelectron emission from this metal? (1 eV = 1.60 × 10-19 J, c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s) A) 231 nm B) 14.0 nm C) 62.4 nm D) 344 nm E) 654 nm Answer: E Var: 1 21) A metal has a work function of 4.50 eV. Find the maximum kinetic energy of the photoelectrons if light of wavelength 250 nm shines on the metal. (1 eV = 1.60 × 10-19 J, c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s) A) 0.00 eV B) 0.37 eV C) 0.47 eV D) 0.53 eV Answer: C Var: 1

22) What is the longest wavelength of light that can cause photoelectron emission from a metal that has a work function of 2.20 eV? (1 eV = 1.60 × 10-19 J, c = 3.00 × 108 m/s, h = 6.626 × 1034 J ∙ s) A) 417 nm B) 257 nm C) 344 nm D) 565 nm E) 610 nm Answer: D Var: 1 23) Light with a wavelength of 310 nm is incident on a metal that has a work function of 3.80 eV. What is the maximum kinetic energy that a photoelectron ejected in this process can have? (1 eV = 1.60 × 10-19 J, c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s) A) 0.62 × 10-19 J B) 0.21 × 10-19 J C) 0.36 × 10-19 J D) 0.48 × 10-19 J E) 0.33 × 10-19 J Answer: E Var: 1 24) Light with a frequency of 8.70 × 1014 Hz is incident on a metal that has a work function of 2.80 eV. What is the maximum kinetic energy that a photoelectron ejected in this process can have? (1 eV = 1.60 × 10-19 J, h = 6.626 × 10-34 J ∙ s) A) 8.7 × 10-19 J B) 3.1 × 10-19 J C) 1.3 × 10-19 J D) 2.4 × 10-19 J E) 4.5 × 10-19 J Answer: C Var: 1 25) If the work function of a metal surface is 2.20 eV, what frequency of incident light would give a maximum kinetic energy of 0.25 eV to the photoelectrons ejected from this surface? (1 eV = 1.60 × 10-19 J, h = 6.626 × 10-34 J ∙ s) A) 2.05 × 1014 Hz B) 1.02 × 1014 Hz C) 2.50 × 1014 Hz D) 3.53 × 1014 Hz E) 5.92 × 1014 Hz Answer: E Var: 1 10 Copyright © 2019 Pearson Education, Inc.

26) A beam of light with a frequency range from 3.01 × 1014 Hz to 6.10 × 1014 Hz is incident on a metal surface. If the work function of the metal surface is 2.20 eV, what is the maximum kinetic energy of photoelectrons ejected from this surface? (h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) A) 0.33 eV B) 0.21 eV C) 0.42 eV D) 0.16 eV E) 0.48 eV Answer: A Var: 1 27) When it is struck by 240-nm photons, a metal ejects electrons with a maximum kinetic energy of What is the work function of this material? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 16.0 × 10-19 J) A) 2.60 eV B) 2.18 eV C) 3.02 eV D) 3.43 eV Answer: A Var: 50+ 28) When a metal is illuminated by light, photoelectrons are observed provided that the wavelength of the light is less than 520 nm. What is the metal's work function? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) A) 2.4 eV B) 2.6 eV C) 2.8 eV D) 3.0 eV Answer: A Var: 50+ 29) What is the longest wavelength of electromagnetic radiation that will eject photoelectrons from sodium metal for which the work function is 2.28 eV? (c = 3.00 × 108 m/s, h = 6.626 × 1034 J ∙ s, 1 eV = 1.60 × 10-19 J) A) 580 nm B) 499 nm C) 633 nm D) 668 nm E) 545 nm Answer: E Var: 1

30) A photocathode whose work function is 2.9 eV is illuminated with white light that has a continuous wavelength band from 400 nm to 700 nm. What is the range of the wavelength band in this white light illumination for which photoelectrons are not produced?(c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) A) 430 nm to 700 nm B) 400 nm to 480 nm C) 430 nm to 480 nm D) 400 nm to 430 nm E) 480 nm to 700 nm Answer: A Var: 1 31) A photocathode that has a work function of 2.4 eV is illuminated with monochromatic light having photon energy 3.5 eV. What is the wavelength of this light? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) A) 350 nm B) 330 nm C) 300 nm D) 380 nm E) 410 nm Answer: A Var: 50+ 32) A photocathode having a work function of 2.4 eV is illuminated with monochromatic light whose photon energy is 3.4 eV. What is maximum kinetic energy of the photoelectrons produced?(c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) A) 1.6 × 10-19 J B) 3.8 × 10-19 J C) 4.4 × 10-19 J D) 4.9 × 10-19 J E) 5.4 × 10-19 J Answer: A Var: 50+

33) A photocathode having a work function of 2.8 eV is illuminated with monochromatic electromagnetic radiation whose photon energy is 4.0 eV. What is the threshold (cutoff) frequency for photoelectron production? (1 eV = 1.60 × 10-19 J, h = 6.626 × 10-34 J ∙ s) A) 6.8 × 1014 Hz B) 2.9 × 1014 Hz C) 7.7 × 1014 Hz D) 8.6 × 1014 Hz E) 9.7 × 1014 Hz Answer: A Var: 50+ 34) When it is struck by 240-nm photons, a material having a work function of 2.60 eV emits electrons. What is the maximum kinetic energy of the emitted electrons? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) A) 2.58 eV B) 5.18 eV C) 2.00 eV D) 4.21 eV Answer: A Var: 1 35) When a photoelectric surface is illuminated with light of wavelength 437 nm, the stopping potential is measured to be 1.67 V. (1 eV = 1.60 × 10-19 J, e = 1.60 × 10-19 C, melectron = 9.11 × 10-31 kg, h = 6.626 × 10-34 J ∙ s) (a) What is the work function of the metal, in eV? (b) What is the maximum speed of the ejected electrons? Answer: (a) 1.17 eV (b) 7.66 × 105 m/s Var: 1 36) In her physics laboratory, Mathilda shines electromagnetic radiation on a material and collects photoelectric data to determine Planck's constant. She measures a stopping potential of 5.82 V for radiation of wavelength 100 nm, and 17.99 V for radiation of wavelength 50.0 nm. (1 eV = 1.60 × 10-19 J, c = 3.00 × 108 m/s) (a) Using Mathilda's data, what value does she determine for Planck's constant? (b) What is the work function of the material Mathilda is using, in electron-volts? Answer: (a) 6.49 × 10-34 J ∙ s (b) 6.35 eV Var: 1

37) For a certain metal, light of frequency 7.24 × 10-14 Hz is just barely able to dislodge photoelectrons from the metal. (h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J, e = 1.60 × 10-19 C) (a) What will be the stopping potential if light of frequency 8.75 × 10-14 Hz is shone on the metal? (b) What is the work function (in electron-volts) of this metal? Answer: (a) 0.625 V (b) 3.00 eV Var: 1 38) When light of wavelength 350 nm is incident on a metal surface, the stopping potential of the photoelectrons is measured to be 0.500 V. What is the work function of this metal? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) A) 0.500 eV B) 3.05 eV C) 3.54 eV D) 4.12 eV Answer: B Var: 1 39) When light of wavelength 350 nm is incident on a metal surface, the stopping potential of the photoelectrons is 0.500 V. What is the threshold (cutoff) frequency of this metal? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) A) 3.47 × 1014 Hz B) 3.74 × 1014 Hz C) 4.73 × 1014 Hz D) 7.36 × 1014 Hz Answer: D Var: 1 40) When light of wavelength 350 nm is incident on a metal surface, the stopping potential of the photoelectrons is 0.500 V. What is the maximum kinetic energy of these electrons? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) A) 0.500 eV B) 3.04 eV C) 3.54 eV D) 4.12 eV Answer: A Var: 1

41) A monochromatic light beam is incident on the surface of a metal having a work function of 2.50 eV. If a 1.0-V stopping potential is required to make the electron current zero, what is the wavelength of light? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) A) 355 nm B) 423 nm C) 497 nm D) 744 nm Answer: A Var: 1 42) Calculate the kinetic energy, in electron-volts, of a neutron that has a de Broglie wavelength of (mneutron = 1.675 × 10-27 kg, 1 eV = 1.6 × 10-19 J, h = 6.626 × 10-34 J ∙ s) Answer: 16 eV Var: 50+ 43) How "slow" must a 200-g ball move to have a de Broglie wavelength of 1.0 mm? (h = 6.626 × 10-34 J ∙ s) Answer: 3.3 × 10-30 m/s Var: 1 44) What would be the de Broglie wavelength for 1-g object moving at the earth's escape speed 25,000 mph (about 11 km/s)? (h = 6.626 × 10-34 J ∙ s) Answer: 6 × 10-35 m Var: 1 45) Atoms in crystals are typically separated by distances of 0.10 nm. What kinetic energy must a nonrelativistic electron have, in electron-volts, in order to have a wavelength of 0.10 nm? (melectron = 9.11 × 10-31 kg, 1 eV = 1.60 × 10-19 J, h = 6.626 × 10-34 J ∙ s) Answer: 150 eV Var: 1 46) The electrons in a beam are moving at 18 m/s. (melectron = 9.11 × 10-31 kg, h = 6.626 × 10-34 J ∙ s) (a) What is its de Broglie wavelength these electrons? (b) If the electron beam falls normally on a diffraction grating, what would have to be the spacing between slits in the grating to give a first-order maximum at an angle of 30° with the normal to the grating? Answer: (a) 40 μm (b) 81 μm Var: 5

47) A proton that is moving freely has a wavelength of 0.600 pm. (mproton = 1.67 × 10-27 kg, e = 1.60 × 10-19 C, h = 6.626 × 10-34 J ∙ s) (a) What is its momentum? (b) What is its speed? (c) What potential difference would it have been accelerated through, starting from rest, to reach this speed? Answer: (a) 1.10 × 10-21 kg ∙ m/s (b) 6.61 × 105 m/s (c) 2.28 kV Var: 1 48) A crystal diffracts a beam of electrons, like a diffraction grating, as they hit it perpendicular to its surface. The crystal spacing is 0.18 nm, and the first maximum scattering occurs at 80° relative to the normal to the surface. (e = 1.60 × 10-19 C, melectron = 9.11 × 10-13 kg, h = 6.626 × 10-34 J ∙ s) (a) What is the wavelength of the electrons? (b) What potential difference accelerated the electrons if they started from rest? Answer: (a) 0.18 nm (b) 48 V Var: 5 49) What is the wavelength of the matter wave associated with a 0.50-kg ball moving at 25 m/s? (h = 6.626 × 10-34 J ∙ s) A) 3.5 × 10-35 m B) 5.3 × 10-35 m C) 3.5 × 10-33 m D) 5.3 × 10-33 m Answer: B Var: 1 50) What is the de Broglie wavelength of a ball of mass 200 g moving at 30 m/s? (h = 6.626 × 10-34 J ∙ s) A) 1.1 × 10-34 m B) 2.2 × 10-34 m C) 4.5 × 10-28 m D) 6.7 × 10-27 m Answer: A Var: 1

51) A person of mass 50 kg has a de Broglie wavelength of 4.4 × 10-36 m while jogging. How fast is she running? (h = 6.626 × 10-34 J ∙ s) A) 2.0 m/s B) 3.0 m/s C) 4.0 m/s D) 5.0 m/s Answer: B Var: 1 52) Find the de Broglie wavelength of a 1.30-kg missile moving at ∙ s) A) 1.81 × 10-35 m B) 2.05 × 10-35 m C) 2.28 × 10-35 m D) 2.57 × 10-35 m Answer: A Var: 50+

(h = 6.626 × 10-34 J

53) If an electron has a wavelength of 0.123 nm, what is its kinetic energy, in electron-volts? This energy is not in the relativistic region. (melectron = 9.11 × 10-31 kg, 1 eV = 1.60 × 10-19 J, h = 6.626 × 10-34 J ∙ s) A) 19.8 eV B) 60.2 eV C) 80.4 eV D) 99.5 eV E) 124 eV Answer: D Var: 1 54) What is the wavelength of the matter wave associated with an electron moving with a speed of 2.5 × 107 m/s? (melectron = 9.11 × 10-31 kg, h = 6.626 × 10-34 J ∙ s) A) 29 pm B) 35 pm C) 47 pm D) 53 pm Answer: A Var: 1

55) After an electron has been accelerated through a potential difference of 0.15 kV, what is its de Broglie wavelength? (e = 1.60 × 10-19 C, melectron = 9.11 × 10-31 kg, h = 6.626 × 10-34 J ∙ s) A) 0.10 nm B) 1.0 nm C) 1.0 mm D) 1.0 cm Answer: A Var: 1 56) If the momentum of an electron is 1.95 × 10-27 kg ∙ m/s, what is its de Broglie wavelength? (h = 6.626 × 10-34 J ∙ s) A) 340 nm B) 210 nm C) 170 nm D) 420 nm E) 520 nm Answer: A Var: 1 57) If the de Broglie wavelength of an electron is 380 nm, what is the speed of this electron? (melectron = 9.11 × 10-31 kg, h = 6.626 × 10-34 J ∙ s) A) 2.0 km/s B) 3.8 km/s C) 1.9 km/s D) 4.1 km/s E) 5.2 km/s Answer: C Var: 1 58) An electron is moving with the speed of 1780 m/s. What is its de Broglie wavelength? (melectron = 9.11 × 10-31 kg, h = 6.626 × 10-34 J ∙ s) A) 409 nm B) 302 nm C) 205 nm D) 420 nm E) 502 nm Answer: A Var: 1

59) If the de Broglie wavelength of an electron is 2.4 μm, what is the speed of the electron? A) 3.0 × 102 m/s B) 2.5 × 105 m/s C) 1.7 × 103 m/s D) 8.3 × 106 m/s Answer: A Var: 50+ 60) If an electron has the same de Broglie wavelength as the wavelength of a 390-nm photon in vacuum, what is the speed of the electron? (melectron = 9.11 × 10-31 kg, c = 3.0 × 108 m/s, h = 6.626 × 10-34 J ∙ s) A) 1900 m/s B) 2100 m/s C) 1700m/s D) 1500 m/s E) 540 m/s Answer: A Var: 50+ 61) A proton has a speed of 7.2 x m/s. What is the energy of a photon that has the same wavelength as the de Broglie wavelength of this proton? (melectron = 9.11 × 10-31 kg, c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s) A) 230 keV B) 150 keV C) 300 keV D) 370 keV E) 440 keV Answer: A Var: 50+ 62) An electron has the same de Broglie wavelength as the wavelength of a 1.8 eV photon. What is the speed of the electron? (melectron = 9.11 × 10-31 kg, c = 3.00 × 108 m/s, 1 eV = 1.60 × 10-19 J) A) 1100 m/s B) 980 m/s C) 910 m/s D) 840 m/s E) 770 m/s Answer: A Var: 50+

63) An electron is accelerated from rest through a potential difference. After acceleration the electron has a wavelength of 880 nm. What is the potential difference responsible for the acceleration of the electron? (h = 6.626 × 10-34 J ∙ s, melectron = 9.11 × 10-31 kg, e = 1.6 10-19 C) A) 1.9 × 10-6 V B) 1.7 × 10-6 V C) 2.2 × 10-6 V D) 2.5 × 10-6 V Answer: A Var: 50+ 64) Electrons emerge from an electron gun with a speed of 2.0 × 106 m/s and then pass through a double-slit apparatus. Interference fringes with spacing of 2.7 mm are detected on a screen far from the double slit. What would the fringe spacing be if the electrons were replaced by neutrons with the same speed? (h = 6.626 × 10-34 J ∙ s, melectron = 9.11 × 10-31 kg, mneutron = 1.675 × 10-27 kg) A) 1.5 μm B) 4.9 m C) 0.93 nm D) 1.2 km Answer: A Var: 50+ 65) Electrons are accelerated to a speed of 4.0 × m/s and are then aimed at a double-slit apparatus, where interference fringes are detected. If the electrons were replaced by neutrons, what speed must neutrons have to produce interference fringes with the same fringe spacing as that observed with the electrons? (h = 6.626 × 10-34 J ∙ s, melectron = 9.11 × 10-31 kg, mneutron = 1.675 × 10-27 kg) A) 2.2 × 101 m/s B) 7.3 × 107 m/s C) 1.7 × 106 m/s D) 9.3 × 102 m/s Answer: A Var: 50+ 66) Electrons with a speed of 2.1 × 106 m/s are directed towards a 1.0-μm wide slit. An electron detector is placed 1.0 m behind the slit. How wide is the central maximum of the electron diffraction pattern on the detector? (h = 6.626 × 10-34 J ∙ s, melectron = 9.11 × 10-31 kg) A) 690 μm B) 350 μm C) 1000 μm D) 1400 μm Answer: A Var: 50+ 20 Copyright © 2019 Pearson Education, Inc.

67) A certain crystal has a spacing of 0.442 nm between atoms. A beam of neutrons moving with a speed of 1640 m/s perpendicular to the surface is diffracted as it passes through the crystal. What is the angle from the central maximum to the next interference maximum? (mneutron = 1.675 × 10-27 kg, h = 6.626 × 10-34 J ∙ s) A) 17.0° B) 21.0° C) 33.1° D) 60.0° E) 90.0° Answer: C Var: 1 68) The spacing of the atoms of a crystal is 159 pm. A monoenergetic beam of neutrons directed normally at the surface of the crystal undergoes first order diffraction at an angle of 58° from the normal. What is the energy of each of the neutrons? (mneutron = 1.675 × 10-27 kg, 1 eV = 1.6 × 10-19 J, h = 6.626 × 10-34 J ∙ s) A) 0.045 eV B) 0.039 eV C) 0.050 eV D) 0.056 eV E) 0.061 eV Answer: A Var: 50+

College Physics: A Strategic Approach, 4e (Knight) Chapter 29 Atoms and Molecules 29.1 Conceptual Questions 1) To which of the following values of n does the longest wavelength in the Balmer series correspond? A) 3 B) 5 C) 1 D) 7 E) ∞ (very large) Answer: A Var: 1 2) To which of the following values of n does the shortest wavelength in the Balmer series correspond? A) 3 B) 5 C) 7 D) 1 E) ∞ (very large) Answer: E Var: 1 3) The Balmer series is formed by electron transitions in hydrogen that A) end on the n = 1 shell. B) begin on the n = 1 shell. C) end on the n = 2 shell. D) begin on the n = 2 shell. E) are between the n = 1 and n = 3 shells. Answer: C Var: 1 4) The Lyman series is formed by electron transitions in hydrogen that A) end on the n = 1 shell. B) begin on the n = 1 shell. C) end on the n = 2 shell. D) begin on the n = 2 shell. E) are between the n = 1 and n = 3 shells. Answer: A Var: 1

5) The Paschen series is formed by electron transitions that A) end on the n = 1 shell. B) begin on the n = 1 shell. C) end on the n = 2 shell. D) begin on the n = 3 shell. E) end on the n = 3 shell. Answer: E Var: 1 6) Hydrogen atoms can emit four spectral lines with visible colors from red to violet. These four visible lines emitted by hydrogen atoms are produced by electrons A) that start in the n = 2 level. B) that end up in the n = 2 level. C) that end up in the n = 3 level. D) that end up in the ground state. E) that start in the ground state. Answer: B Var: 1 7) When an electron jumps from an orbit where n = 4 to one where n = 2 A) a photon is emitted. B) a photon is absorbed. C) two photons are emitted. D) two photons are absorbed. E) None of the given answers are correct. Answer: A Var: 1 8) The energy difference between adjacent orbit radii in a hydrogen atom A) increases with increasing values of n. B) decreases with increasing values of n. C) remains constant for all values of n. D) varies randomly with increasing values of n. Answer: B Var: 1

9) The figure shows part of the energy level diagram of a certain atom. The energy spacing between levels 1 and 2 is twice that between 2 and 3. If an electron makes a transition from level 3 to level 2, the radiation of wavelength λ is emitted. What possible radiation wavelengths might be produced by other transitions between the three energy levels?

A) both λ/2 and λ/3 B) only λ/2 C) both 2λ and 3λ D) only 2λ Answer: A Var: 1 10) The distance between adjacent orbits in a hydrogen atom A) increases with increasing values of n. B) decreases with increasing values of n. C) remains constant for all values of n. D) varies randomly with increasing values of n. Answer: A Var: 1 11) If a hydrogen atom originally in a state with principal quantum number n is excited to state n' = 2n, then A) its radius and binding energy will double. B) its radius will quadruple and the binding energy will double. C) its radius will double and the binding energy will quadruple. D) its radius will quadruple and the binding energy will be reduced by a factor of four. E) its radius and binding energy will quadruple. Answer: D Var: 1 12) Which of the following statements are true for the Bohr model of the atom? (There could be more than one correct choice.) A) The spacing between all the electron shells is the same. B) The energy difference between all the electron shells is the same. C) As we look at higher and higher electron shells, they get closer and closer together, but the difference in energy between them gets greater and greater. D) As we look at higher and higher electron shells, they get farther and farther apart, but the difference in energy between them gets smaller and smaller. E) There is no general pattern in the spacing of the shells or their energy differences. Answer: D Var: 1 3 Copyright © 2019 Pearson Education, Inc.

13) A hydrogen atom is in the 6h state. What is the principal quantum number. A) 0 B) 3 C) 5 D) 6 E) 7 Answer: D Var: 1 14) The orbital angular momentum quantum number can take which of the following values for any given value of the principal quantum number, n? A) ℓ = 0, 1, 2, . . . B) ℓ = 0, 1, 2, . . . , n C) ℓ = 0, 1, 2, . . . , (n - 1) D) ℓ = 1, 2, 3, 4, . . . E) ℓ = 1, 2, 3, 4, . . ., (n + 1) Answer: C Var: 1 15) Which of the following values can be taken by the electron spin quantum number, ms? A) ±1/2 B) 0 C) ±1 D) ±2 E) ±3 Answer: A Var: 1 16) According to the quantum mechanical model of the hydrogen atom, if the orbital angular momentum quantum number is ℓ, there will be how many permitted magnetic quantum numbers? A) ℓ/2 B) 2ℓ C) 2ℓ + 1 D) 2ℓ - 1 E) 3ℓ Answer: C Var: 1

17) According to the quantum mechanical model of the hydrogen atom, if the principal quantum number is n, how many different orbital angular momentum quantum numbers are permitted? A) n/2 B) n C) 2n D) 3n E) 4n Answer: B Var: 1 18) According to Pauli's exclusion principle, how many electrons in an atom may have a particular set of quantum numbers? A) 1 B) 3 C) 2 D) 4 E) 5 Answer: A Var: 1 19) The principal quantum number n can have any integer value ranging from A) -∞ to +∞. B) 0 to ∞. C) 1 to ∞. D) 1 to 100. Answer: C Var: 1 20) The orbital angular momentum quantum number ℓ can have any integer value ranging from A) 0 to n. B) 0 to (n-1). C) 1 to n. D) 1 to (n+1). E) -n to n. Answer: B Var: 1 21) The magnetic quantum number m1 can have any integer value ranging from A) -n to +n. B) -ℓ to +ℓ. C) 0 to n. D) 0 to ℓ. E) 0 to (n-1) Answer: B Var: 1

22) The electron spin quantum number can have values of A) -1/2, -1, 0, +1, +1/2. B) -1/2, -1, +1, +1/2. C) -1/2, 0, +1/2. D) -1/2, +1/2. E) only +1/2. Answer: D Var: 1 23) What is the atomic number of a neutral atom that has an electron configuration of 1s2 2s2 2p6 3s2 3p2? A) 5 B) 11 C) 14 D) 20 Answer: C Var: 1 24) If ℓ = 4, which one of the following is a possible quantum number for n? A) 0 B) 2 C) 3 D) 4 E) 8 Answer: E Var: 1 25) If n = 5, which one of the following is not an allowed magnetic quantum number m1? A) 0 B) 2 C) 4 D) 5 Answer: D Var: 1 26) In its ground state, the quantum numbers (n, ℓ, m1, ms) for hydrogen are, respectively, A) 1, 1, 1, 1. B) 1, 0, 0, 0. C) 1, 0, 0, ±1/2. D) 1, 1, 1, ±1/2. Answer: C Var: 1

27) Consider ground-state helium having two electrons in orbit. If one of the electrons has quantum numbers (n, ℓl, m1, ms) of 1, 0, 0, -1/2 respectively, the quantum numbers for the other electron will be A) 1, 1, 0, -1/2. B) 1, 0, 0, +1/2. C) 1, 1, 1, +1/2. D) none of the given answers. Answer: B Var: 1 28) The elements in the periodic table that have completely filled shells or subshells are referred to as A) noble gases. B) halogens. C) alkali metals. D) transition elements. Answer: A Var: 1 29.2 Problems 1) One of the emission lines described by the original version of Balmer's formula has wavelength What is the value of n in Balmer's formula that gives this emission line? A) 11 B) 12 C) 13 D) 14 Answer: A Var: 17 2) What is the value of n in the Balmer series for which the wavelength is 410.2 nm. A) 4 B) 5 C) 6 D) 7 E) 9 Answer: C Var: 1 3) What is the wavelength in the Balmer series for n = 15? A) 277.1 nm B) 371.1 nm C) 188.6 nm D) 656 nm E) 754.2 nm Answer: B Var: 5 7 Copyright © 2019 Pearson Education, Inc.

4) The value of a wavelength in the Balmer series is 372.1 nm. What is the corresponding value of n? A) 6 B) 3 C) 9 D) 10 E) 14 Answer: E Var: 5 5) What is the longest wavelength in the Balmer series? A) 240 nm B) 328 nm C) 365 nm D) 656 nm E) 820 nm Answer: D Var: 1 6) What is the shortest wavelength in the Balmer series? A) 328 nm B) 365 nm C) 456 nm D) 656 nm E) 820 nm Answer: B Var: 1 7) What value of n corresponds to a wavelength of 922.7 nm in the Paschen series? A) 3 B) 5 C) 7 D) 9 E) 15 Answer: D Var: 5 8) What value of n corresponds to a wavelength of 91.7 nm in the Lyman series? A) 1 B) 3 C) 5 D) 9 E) 13 Answer: E Var: 5 8 Copyright © 2019 Pearson Education, Inc.

9) What is the longest wavelength in the Paschen series? A) 2.01 nm B) 2.01 μm C) 365 nm D) 1.88 nm E) 1.88 μm Answer: E Var: 1 10) What is the shortest wavelength in the Paschen series? A) 410.2 nm B) 410.2 μm C) 365 nm D) 820.4 nm E) 820.4 μm Answer: D Var: 1 11) What is the shortest wavelength of the Lyman series? A) 91.16 nm B) 45.60 nm C) 121.5 nm D) 204.1 nm E) 365 nm Answer: A Var: 1 12) What is the longest wavelength in the Lyman Series? A) 45.60 nm B) 91.20 nm C) 121.5 nm D) 240.1 nm E) 365 nm Answer: C Var: 1 13) The wavelength of a ruby laser is 694.3 nm. What is the energy difference between the two energy states for the transition that produces this light? (c = 3.00 × 108 m/s, 1 eV = 1.60 × 10-19 J, h = 6.626 × 10-34 J ∙ s) A) 1.54 eV B) 1.65 eV C) 1.79 eV D) 1.81 eV Answer: C Var: 1

14) What is the energy (in electron-volts) of the n = 3 state of atomic hydrogen? Answer: -1.51 eV Var: 1 15) Given that the energy levels of the hydrogen atom are given by En =

, where R = 1.097 ×

107 m-1, what wavelength photon is emitted when the atom undergoes a transition from the n = 4 to the n = 6 level? Answer: 2.625 × 10-6 m Var: 1 16) Consider the Bohr model for the hydrogen atom. (c = 3.00 × 108 m/s, 1 eV = 1.60 × 10-19 J, h = 6.626 × 10-34 J ∙ s) (a) How much energy (in eV) is needed to cause a transition of an electron from the second excited state to the third excited state? (b) What wavelength photon just has enough energy to initiate the transition in (a)? Answer: (a) 0.661 eV (b) 1.88 μm Var: 7 17) Given that the binding energy of the hydrogen atom in its ground state is -13.6 eV, what is the energy when it is in the n = 5 state? A) 2.72 eV B) -2.72 eV C) 0.544 eV D) -0.544 eV Answer: D Var: 1 18) If a hydrogen atom in the ground state absorbs a photon of energy 12.09 eV, to which state will the electron make a transition? A) n = 2 B) n = 3 C) n = 4 D) n = 5 Answer: B Var: 1 19) What is the ionization energy of the neutral hydrogen atom? A) 27.2 eV B) 13.6 eV C) 6.8 eV D) none of the given answers Answer: B Var: 1

20) What is the energy of the photon emitted when an electron drops from the state in a hydrogen atom? A) 0.244 eV B) 0.264 eV C) 0.283 eV D) 0.303 eV Answer: A Var: 17

state to the

21) In a hydrogen atom, the electron makes a transition from the n = 8 to the n = 3 state. The wavelength of the emitted photon is closest to which one of the following values? (c = 3.00 × 108 m/s, 1 eV = 1.60 × 10-19 J, h = 6.626 × 10-34 J ∙ s) A) 9.57 × 10-7 m B) 1.13 × 10-6 m C) 3.12 × 10-7 m D) 4.52 × 10-6 m E) 6.34 × 10-7 m Answer: A Var: 1 22) A hydrogen atom is excited to the n = 11 level. Its decay to the n = 7 level is detected in a photographic plate. What is the wavelength of the light photographed? (c = 3.00 × 108 m/s, 1 eV = 1.60 × 10-19 J, h = 6.626 × 10-34 J ∙ s) A) 7510 nm B) 4670 nm C) 12,400 nm D) 4380 nm Answer: A Var: 44 23) A hydrogen atom is excited to the n = 9 level. Its decay to the n = 6 level detected in a photographic plate. What is the frequency of the light photographed? (1 eV = 1.60 × 10-19 J, h = 6.626 × 10-34 J ∙ s) A) 5.08 × 1013 Hz B) 5910 Hz C) 5910 nm D) 3.28 × 10-9 km Answer: A Var: 44

24) A hydrogen atom is in its n = 2 excited state when its electron absorbs with a photon. What is the energy of the resulting free electron? A) 6.1 eV B) 7.9 eV C) 8.2 eV D) 9.2 eV Answer: A Var: 50

in an interaction

25) A hydrogen atom makes a downward transition from the state to the state. Find 8 -19 the wavelength of the emitted photon. (c = 3.00 × 10 m/s, 1 eV = 1.60 × 10 J, h = 6.626 × -34 10 J ∙ s) A) 2.56 μm B) 1.54 μm C) 2.05 μm D) 3.07 μm Answer: A Var: 15 26) The longest wavelength photon that can be emitted by a hydrogen atom, for which the final state is is closest to which one of the following values? (c = 3.0 × 108 m/s, A) 39,000 nm B) 22,000 nm C) 7400 nm D) 16,000 nm E) 28,000 nm Answer: A Var: 9 27) The shortest wavelength of a photon that can be emitted by a hydrogen atom, for which the initial state is is closest to which one of the following values? A) 92 nm B) 82 nm C) 72 nm D) 62 nm E) 52 nm Answer: A Var: 10

28) The longest wavelength of a photon that can be emitted by a hydrogen atom, for which the initial state is n = 3, is closest to which one of the following values? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) A) 550 nm B) 575 nm C) 600 nm D) 625 nm E) 658 nm Answer: E Var: 1 29) What is the shortest wavelength of a photon that can be emitted by a hydrogen atom, for which the initial state is n = 3? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) A) 822 nm B) 850 nm C) 103 nm D) 91.4 nm E) 950 nm Answer: C Var: 1 30) What is the energy required to remove the electron from a hydrogen atom in the n = 11 state? A) 0.112 eV B) 1.24 eV C) 13.5 eV D) 12.4 eV E) 0.141 eV Answer: A Var: 1 31) If light excites atomic hydrogen from its lowest energy level to the n = 12 level, what is the energy of the photons of this light? A) 13.5 eV B) 32.2 eV C) 13.6 eV D) 0.0944 eV E) 1.13 eV Answer: A Var: 1

32) Light shines through atomic hydrogen gas that was initially in its ground state. You observe that after awhile much of the hydrogen gas has been excited to its n = 5 state. What wavelength of light entering the gas caused this excitation? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) A) 110 nm B) 91.4 nm C) 95.2 nm D) 2280 nm Answer: C Var: 1 33) Radio astronomers often study the radiation emitted by a hydrogen atom from a transition between the two hyperfine levels associated with the ground state. This radiation has a wavelength of 21 cm. What is the energy difference between the hyperfine levels? (1 eV = 1.60 × 10-19 J) A) 5.9 × 10-6 eV B) 5.9 × 10-25 J C) 1.7 × 10-24 J D) 4.7 × 10-25 J Answer: A Var: 1 34) In a transition from one vibrational state to another, a molecule emits a photon of wavelength 5.56 µm. What is the energy difference between these two states? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) A) 0.223 eV B) 2.23 MeV C) 13.6 eV D) 13.6 MeV E) 0.223 MeV Answer: A Var: 1 35) What is the wavelength of the photon emitted when an electron in a hydrogen atom which is in the initial state n = 8 jumps to the final state n = 2? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) A) 205 nm B) 104 nm C) 389 nm D) 486 nm E) 610 nm Answer: C Var: 1

36) What is the wavelength of the photon emitted when an electron in a hydrogen atom which is in the initial state n = 4 jumps to the final state n = 2? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) A) 243 nm B) 486 nm C) 556 nm D) 312 nm E) 609 nm Answer: B Var: 1 37) The wavelength of the emitted photon if an electron in the hydrogen atom makes a transition from the n = 2 state to the ground state is closest to which of the following values? (c = 3.0 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) A) 122 nm B) 203 nm C) 243 nm D) 389 nm E) 411 nm Answer: A Var: 1 38) What is the wavelength of the emitted photon if an electron in the hydrogen atom makes a transition from the n = 7 state to the n = 2 state? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) A) 199 nm B) 365 nm C) 4480 nm D) 398 nm E) 796 nm Answer: D Var: 1 39) What frequency must a photon have to raise an electron in a hydrogen atom from the n = 2 to the n = 4 state? (h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J) A) 3.06 × 1014 Hz B) 6.16 × 1014 Hz C) 4.11 × 1014 Hz D) 5.20 × 1014 Hz E) 9.24 × 1014 Hz Answer: B Var: 1

40) In making a transition from state n = 1 to state n = 2, the hydrogen atom must A) absorb a photon of energy 10.2 eV. B) emit a photon of energy 10.2 eV. C) absorb a photon of energy 13.58 eV. D) emit a photon of energy 13.58 eV. Answer: A Var: 1 41) In the n = 1 state, the energy of the hydrogen atom is -13.6 eV. What is its energy in the n = 2 state? A) -6.79 eV B) -4.53 eV C) -3.40 eV D) -1.51 eV Answer: C Var: 1 42) Consider the Bohr model for the hydrogen atom in its second excited state. (a) Determine the binding energy (eV) of the electron. (b) What is the radius of the electron orbit, given that r1 = 0.0529 nm? (c) How far is it from the next higher excited orbit? Answer: (a) 1.51 eV (b) 0.476 nm (c) 0.370 nm Var: 1 43) A hydrogen atom with a barely bound electron may have an average radius as large as a bacterium, which is a radius of What is the nearest principal quantum number of the atom in this state? The radius for ground state hydrogen is 0.0529 nm. A) 514 B) 51 C) 16 D) 264,650 Answer: A Var: 10 44) Calculate the orbital Bohr radius of the A) 0.212 nm B) 0.106 nm C) 0.170 nm D) 0.244 nm Answer: A Var: 3

excited state in a hydrogen atom.

45) Given that the speed of an electron in the ground state of hydrogen is 2190 km/s, what is the speed of an electron in the n = 4 orbit of hydrogen? A) 547 km/s B) 31,000 km/s C) 139 km/s D) 178 km/s E) 2180 km/s Answer: A Var: 1 46) For an electron in the M (n = 3) shell, find (a) the largest possible orbital angular momentum it can have, and (b) the smallest possible orbital angular momentum it can have. Express your answers in SI units, and for each case indicate the subshell (s, p, d, ...) of the electron. (h = 6.626 × 10-34 J ∙ s) Answer: (a) 2.583 × 10-34 kg ∙ m2/s, d subshell, (b) 0 kg ∙ m2/s, s subshell Var: 1 47) An atom has completely filled inner shells and a single valence electron in an excited p state. The filled inner shells have an orbital momentum equal to zero. What is the magnitude of the orbital angular momentum of the atom? A) 1.0 B) 1.2 C) 1.4 D) 1.7 E) 2.0 Answer: C Var: 1 48) What is the greatest magnitude of the orbital angular momentum L that you can find in a state with A) 5.48 B) 5.92 C) 6 D) 6.48 Answer: A Var: 5 17 Copyright © 2019 Pearson Education, Inc.

49) Consider the n = 10 shell. (a) What is the largest value of the angular momentum quantum number, ℓ, in this shell? (b) How many electrons can be placed in this shell? Answer: (a) 9 (b) 200 Var: 9 50) An atom with atomic number 6 is in its ground state. How many electrons are in its outermost shell? Answer: 4 Var: 8 51) Write out the electron configuration for the ground state of the phosphorus atom, which has 15 electrons. Answer: 1s2 2s2 2p6 3s2 3p3 Var: 1 52) The only valid electron state and shell designation among the following is A) 1p, K (n = 1) shell. B) 2s, K (n = 1) shell. C) 1s, L (n = 2) shell. D) 2p, L (n = 2) shell. E) 3f, M (n = 3) shell. Answer: D Var: 1 53) The only invalid electron state and shell designation among the following is A) 1s, K (n = 1) shell. B) 2s, L (n = 2) shell. C) 2d, L (n = 2) shell. D) 3s, M (n = 3) shell. E) 3d, M (n = 3) shell. Answer: C Var: 1 54) What is the electron configuration for Li, which has 3 electrons? A) 1s3 B) 1s1 2s2 C) 1s2 2s1 D) 1s2 1p1 E) 1s1 2s1 3s1 Answer: C Var: 1

55) What is the correct ground state electron configuration of boron, which has 5 electrons? A) 1s2 2s2 2p B) 1s2 2s2 2p3 C) 1s2 1p2 2s D) 1s2 2p2 3s E) 1s2 2p3 Answer: A Var: 1 56) Which one of the following is the correct electronic configuration for carbon, which has 6 electrons? A) 1s2 2s2 2p2 B) 1s1 2p1 C) 1s1 2s2 2p1 D) 1s1 2s1 2p1 E) 1s2 2s2 2p4 Answer: A Var: 1 57) Which one of the following is the correct electronic configuration for the sodium atom, which has 11 electrons? A) 1s1 2s2 3p6 2s2 B) 1s2 2s1 3p6 2s2 C) 1s1 2s2 2p6 2s2 D) 1s2 2s2 2p6 3s2 E) 1s2 2s2 2p6 3s1 Answer: E Var: 1 58) A hydrogen atom is in the 6h state. How many electrons are allowed in this state? A) 22 B) 18 C) 14 D) 10 E) 6 Answer: A Var: 1

59) A hydrogen atom is in the 6h state. Which one of the following numbers could be an orbital angular momentum quantum number ℓ for that state? A) 5 B) 6 C) 7 D) 8 E) 9 Answer: A Var: 1 60) A hydrogen atom is in the 6h state. Which one of the following is not a magnetic quantum number for that state? A) 0 B) 1 C) 2 D) 4 E) 6 Answer: E Var: 1 61) In a hydrogen atom, a given electron has n = 7. How many possible values can ℓ have? A) 6 B) 7 C) 15 D) 98 Answer: B Var: 1 62) In a hydrogen atom, a given electron has ℓ = 7. How many possible values can m1 have? A) 6 B) 7 C) 15 D) 98 Answer: C Var: 1 63) In a hydrogen atom, an electron with n = 7 can exist in how many different quantum states? A) 6 B) 7 C) 15 D) 98 Answer: D Var: 1

64) How many values of the magnetic quantum number, mℓ, are possible if the orbital angular momentum quantum number is ℓ = 2? A) 1 B) 2 C) 3 D) 4 E) 5 Answer: E Var: 1 65) How many values of the magnetic quantum number, mℓ, correspond to a value of ℓ = 4? A) 3 B) 5 C) 8 D) 9 E) 7 Answer: D Var: 1 66) For the ground state of the hydrogen atom, which of the following numbers represents the correct value of the orbital angular momentum quantum number? A) -1 B) 1 C) 0 D) 2 E) -2 Answer: C Var: 1 67) For the ground state of the hydrogen atom, which of the following numbers represents the correct value of the magnetic quantum number? A) -1 B) 0 C) 1 D) 2 E) -2 Answer: B Var: 1

68) How many values can the magnetic quantum number have in a hydrogen atom for which the orbital angular momentum quantum number is equal to 8? A) 9 B) 15 C) 5 D) 8 E) 17 Answer: E Var: 1 69) How many unique quantum states correspond to the lowest possible energy level of an electron in the hydrogen atom? A) 3 B) 0 C) 1 D) 4 E) 2 Answer: E Var: 1 70) How many electrons can be found with principal quantum number atom? A) 18 B) 6 C) 20 D) 9 Answer: A Var: 3 71) How many 2d electron states can an atom have? A) 0 B) 4 C) 6 D) 8 E) 10 Answer: A Var: 1 72) How many 3d electron states can an atom have? A) 0 B) 4 C) 6 D) 8 E) 10 Answer: E Var: 1 22 Copyright © 2019 Pearson Education, Inc.

in a suitably heavy

73) What is the maximum number of electrons that can occupy the g subshell? A) 10 B) 14 C) 18 D) 22 Answer: C Var: 3 74) How many possible sets of electron states (or quantum numbers) are there in the 5f subshell? A) 2 B) 8 C) 10 D) 14 Answer: D Var: 1 75) How many electrons will fit into a 4f subshell? A) 3 B) 4 C) 7 D) 14 Answer: D Var: 1 76) The values of n and ℓ for a 4f subshell are A) n = 4, ℓ = 4. B) n = 4, ℓ = 3. C) n = 3, ℓ = 3. D) n = 4, ℓ = 2. E) n = 3, ℓ = -3. Answer: B Var: 1 77) Neon has 10 electrons. What is the value of Z of the next higher element that has chemical properties very similar to those of neon? A) 11 B) 17 C) 18 D) 19 E) 36 Answer: C Var: 1

College Physics: A Strategic Approach, 4e (Knight) Chapter 30 Nuclear Physics 30.1 Conceptual Questions 1) Write the standard nuclear notation for the following nuclei: hydrogen-2, sulfur-33, and lead207. Answer: H, S, Pb Var: 1 2) Name the first three isotopes of hydrogen, write their symbols in standard notation, and indicate which one is the most common and which one is the most unstable. Answer: H is ordinary hydrogen, H is deuterium, and H is tritium. H is the most common and H is the most unstable. Var: 1 3) The primary reason that very large nuclei are unstable is due to A) the cumulative repulsive force of the protons. B) the cumulative attractive force between the protons and the orbiting electrons. C) the repulsive force between the neutrons and the protons. D) the extreme weakness of the gravitational attraction of the protons. Answer: A Var: 1 4) Atomic nuclei that are all isotopes of an element all have the same A) number of nucleons. B) mass. C) number of protons. D) number of neutrons. Answer: C Var: 1 5) All nuclei of a given element have the same number of A) neutrons. B) protons. C) nucleons. D) protons + neutrons. Answer: B Var: 1

6) An yttrium isotope has 39 protons and 50 neutrons in its nucleus. Which one of the following symbols accurately represents this isotope? A) Y B)

Answer: C Var: 1 7) The atomic number of an atom is equal to the number of what particles in the nucleus? A) protons B) neutrons C) nucleons D) electrons E) positrons. Answer: A Var: 1 8) The mass number of an atom is equal to the number of what particles in the nucleus? A) protons B) neutrons C) nucleons D) electrons E) positrons. Answer: C Var: 1 9) The atomic number and mass number for calcium-39 are 20 and 39, respectively. How many neutrons are in one atom? A) 1 B) 19 C) 20 D) 39 E) 59 Answer: B Var: 1

10) In a

Nb nucleus, how many protons, neutrons, and electrons are found there?

A) 41, 52, 93. B) 41, 52, 41. C) 52, 41, 41. D) 41, 52, 0. E) 93, 41, 93. Answer: D Var: 1 11) The symbol for a certain isotope of polonium is

Po. How many neutrons are there in the

nucleus of this isotope? A) 84 B) 130 C) 214 D) 298 E) 314 Answer: B Var: 1 12) The symbol for a certain isotope of radium is

Ra. How many nucleons are there in the

nucleus of this isotope? A) 88 B) 138 C) 214 D) 226 E) 314 Answer: D Var: 1 13) The symbol for a certain isotope of strontium is

Sr. What is the mass number of this

isotope? A) 38 B) 52 C) 88 D) 90 E) 128 Answer: D Var: 1

14) What is true of an element of atomic number 15 that has an isotope of mass number 32? (There could be more than one correct choice.) A) the number of protons in the nucleus is 15. B) the number of neutrons in the nucleus is 15. C) the number of protons in the nucleus is 32. D) the number of nucleons in the nucleus is 47. E) the number of neutrons in the nucleus is 17. Answer: A, E Var: 1 15) The atomic mass unit is defined as A) the mass of a proton. B) the mass of an electron. C) the mass of a hydrogen-1 atom. D) one twelfth the mass of a carbon-12 atom. E) the mass of a carbon-12 nucleus. Answer: D Var: 1 16) A stable nucleus contains many protons very close to each other, all positively charged. Why do the protons not fly apart due to mutual Coulomb repulsion? A) An attractive nuclear force in the nucleus counteracts the effect of the Coulomb forces. B) There are an equal number of electrons in the nucleus which neutralize the protons. C) The neutrons in the nucleus shield the protons from each other. D) The Coulomb force does not operate within nuclei. E) The gravity of the protons and neutrons overcomes their repulsion at such close distances. Answer: A Var: 1 17) Which of the following statements is not true of the strong nuclear force? A) The nuclear force has a short range, of the order of nuclear dimensions. B) For two protons that are very close together, the nuclear force and the electric force have about the same magnitudes. C) The nuclear force does not depend on charge. D) A nucleon in a large nucleus interacts via the nuclear force only with nearby nucleons, not with ones far away in the nucleus. E) The nuclear force affects both neutrons and protons. Answer: B Var: 1 18) The two strongest forces that act between protons in a nucleus are A) the weak nuclear and electromagnetic forces. B) the weak nuclear and the gravitational forces. C) the electrostatic and the gravitational forces. D) the strong nuclear and the electrostatic forces. Answer: D Var: 1 4 Copyright © 2019 Pearson Education, Inc.

19) The main reason that there is a limit to the size of a stable nucleus is A) the limited range of the gravitational force. B) the short range nature of the strong nuclear force. C) the weakness of the gravitational force. D) the weakness of the electrostatic force. Answer: B Var: 1 20) In massive stars, three helium nuclei fuse together, forming a carbon nucleus, and this reaction heats the core of the star. The net mass of the three helium nuclei must therefore be A) higher than that of the carbon nucleus. B) less than that of the carbon nucleus. C) the same as that of the carbon nucleus because mass is always conserved. D) the same as that of the carbon nucleus because energy is always conserved. Answer: A Var: 1 21) A fusion reaction releases energy because the binding energy of the resulting nucleus A) is greater than the binding energy of the original nuclei. B) is equal to the binding energy of the original nuclei. C) is less than the binding energy of the original nuclei. D) is released in the process. E) is absorbed in the process. Answer: A Var: 1 22) The binding energy per nucleon of a nucleus A) increases steadily as we go to heavier elements. B) decreases steadily as we go to heavier elements. C) is approximately constant throughout the periodic table, except for very light nuclei. D) has a maximum near iron in the periodic table and decreases after that for heavier elements. E) has a minimum near iron in the periodic table and increases after that for heavier elements. Answer: D Var: 1 23) An α particle is also known as A) an electron. B) a positron. C) a helium nucleus. D) a high-energy photon. Answer: C Var: 1

24) A β- particle is also known as A) an electron. B) a positron. C) a helium nucleus. D) a high-energy photon. Answer: A Var: 1 25) A β+ particle is also known as A) an electron. B) a positron. C) a helium nucleus. D) a high-energy photon. Answer: B Var: 1 26) A gamma ray is also known as A) an electron. B) a positron. C) a helium nucleus. D) a high-energy photon. Answer: D Var: 1 27) What is the mass number of alpha particles? A) 1 B) 2 C) 3 D) 4 E) 6 Answer: D Var: 1 28) What are the mass number, the atomic number, and neutron number for each of the following particles? (a) proton (b) neutron (c) alpha particle Answer: (a) 1, 1, 0 (b) 1, 0, 1 (c) 4, 2, 2 Var: 1

29) What are the mass number A and the charge (in units of e) for each of the following particles or rays? (a) beta-plus (b) beta-minus (c) gamma ray Answer: (a) 0, 1 (b) 0, -1 (c) 0, 0 Var: 1 30) The nuclei of He are also known as A) α particles. B) β particles. C) γ rays. D) x-rays. E) positrons. Answer: A Var: 1 31) In beta-minus decay A) a proton is emitted. B) a neutron is emitted. C) an electron is emitted. D) an electron decays into another particle. E) a proton is transformed into a neutron. Answer: C Var: 1 32) During β+ decay A) a neutron is transformed to a proton. B) a proton is transformed to a neutron. C) a neutron is ejected from the nucleus. D) a proton is ejected from the nucleus. E) the number of nucleons decreases. Answer: B Var: 1 33) During β- decay A) a neutron is transformed to a proton. B) a proton is transformed to a neutron. C) a neutron is ejected from the nucleus. D) a proton is ejected from the nucleus. E) the number of nucleons increases. Answer: A Var: 1

34) When a β+ particle is emitted from an unstable nucleus, the atomic number of the nucleus A) increases by 1. B) decreases by 1. C) increases by 2. D) decreases by 2. E) does not change. Answer: B Var: 1 35) When a β- particle is emitted from an unstable nucleus, the atomic number of the nucleus A) increases by 1. B) decreases by 1. C) increases by 2. D) decreases by 2. E) does not change. Answer: A Var: 1 36) When a β- particle is emitted from an unstable nucleus, the atomic mass number of the nucleus A) increases by 1. B) decreases by 1. C) increases by 2. D) does not change. Answer: D Var: 1 37) In β- decay, the number of neutrons in the nucleus is A) decreased by 1. B) decreased by 2. C) increased by 1. D) increased by 2. E) remains unchanged. Answer: A Var: 1 38) In β- decay, the number of protons in the nucleus is A) decreased by 1. B) decreased by 2. C) increased by 1. D) increased by 2. E) remains unchanged. Answer: C Var: 1

39) In positron decay, the number of protons in the nucleus is A) decreased by 1. B) decreased by 2. C) increased by 1. D) increased by 2. E) remains unchanged. Answer: A Var: 1 40) A radioactive isotope of atomic number Z emits an alpha particle, and the daughter nucleus then emits a beta-minus particle. What is the atomic number of the resulting nucleus? A) Z -1 B) Z + 1 C) Z - 2 D) Z - 3 Answer: A Var: 1 41) A radioactive isotope of atomic number Z emits a beta-minus particle, and then the daughter nucleus emits a gamma ray. What is the atomic number of the resulting nucleus after both processes? A) Z - 1 B) Z + 1 C) Z - 2 D) Z - 3 Answer: B Var: 1 42) Polonium-216 decays to lead-212 by emitting what kind of nuclear radiation? A) alpha B) beta-minus C) beta-plus D) gamma E) x-rays. Answer: A Var: 1 43) The atom

Fr decays to

Ra by emitting what kind of nuclear radiation?

44) A β- decay occurs in an unstable nucleus when A) a proton is converted to an electron by the strong force. B) a proton is converted to a neutron by the strong force. C) a neutron is converted to a proton by the weak force. D) a neutron is converted to an alpha particle by the weak force. E) a neutron is converted to a positron by the weak force. Answer: C Var: 1 45) When an unstable nucleus decays by emitting an alpha particle, the atomic number Z of the nucleus A) increases by 4. B) increases by 2. C) decreases by 2. D) decreases by 4. E) remains unchanged. Answer: C Var: 1 46) When an unstable nucleus decays by emitting an alpha particle, the atomic mass number A of the nucleus A) increases by 4. B) increases by 2. C) decreases by 2. D) decreases by 4. E) remains unchanged. Answer: D Var: 1 47) The half-life of cobalt-60 is 5.3 years, while that of strontium-90 is about 29 years. Suppose you have samples of both isotopes, and that they initially contain equal numbers of atoms of these isotopes. How will the activities (number of decays per second) of the samples compare? A) The activity of the cobalt-60 sample will be greater. B) The activities cannot be compared without more information. C) The activities will be equal. D) The activity of the strontium-90 sample will be greater. Answer: A Var: 1

48) The half-life of cobalt-60 is 5.3 years, while that of strontium-90 is about 29 years. Suppose you have samples of both isotopes, and that they initially have the same activity (number of decays per second). What must be true of the numbers of cobalt-60 and strontium-90 nuclei in these samples? A) There are more strontium-90 than cobalt-60 nuclei. B) There are equal numbers of cobalt-60 and strontium-90 nuclei. C) There are more cobalt-60 than strontium-90 nuclei. D) It is not possible to compare numbers of nuclei without knowing the masses of the samples. Answer: A Var: 1 49) If the half-life of a material is 45 years, how much of it will be left after 100 years? A) more than 1/2 B) less than 1/2 but more than 1/4 C) more than 1/4 but less than 1/2 D) less than 1/4 but more than 1/8 E) less than 1/8 Answer: D Var: 1 50) What happens to the half-life of a radioactive substance as it decays? A) It remains constant. B) It increases. C) It decreases at a constant rate. D) It decreases at an exponential rate. Answer: A Var: 1 51) What happens to the half-life of a radioactive substance as we increase its temperature? A) It does not change. B) It increases. C) It decreases at a constant rate. D) It decreases at an exponential rate. Answer: A Var: 1 52) Two radioactive isotopes, X and Y, both decay to stable products. The half-life of X is about a day, while that of Y is about a week. Suppose a radioactive sample consists of a mixture of these two nuclides. If the mixture is such that the activities arising from X and Y are initially equal, then a few days later the activity of the sample will be due A) predominantly to Y. B) predominantly to X. C) entirely to Y. D) to X and Y equally. Answer: A Var: 1 11 Copyright © 2019 Pearson Education, Inc.

53) Suppose the half-life of an isotope is 2 days. You purchase 10 grams of the isotope, but it was produced in a laboratory 4 days before it was delivered to you. How much of this isotope will you have 3 days after it was delivered to you? A) more than 2.5 grams but less than 5 grams B) 2.5 grams C) more than 1.25 grams but less than 2.5 grams D) 1.25 grams E) less than 1.25 grams Answer: E Var: 1 54) How many protons, neutrons, and nucleons are there in a carbon-14 nucleus? Answer: 6 protons, 8 neutrons, 14 nucleons Var: 1 55) Modern in-air nuclear bomb tests have created an extra high level of 14C in our atmosphere. If future archaeologists date samples from this era, without knowing of this testing, will their carbon-14 dates be too young, too old, or correct? If correct, why? A) Too young. B) Too old. C) Correct, since 14C from bomb tests is different from that produced naturally. D) Correct, because modern biological materials do not gather 14C from bomb tests. Answer: A Var: 1 56) Carbon-14 decays by β- emission. What nucleus is left after this decay? A) carbon-13 B) carbon-14 C) carbon-15 D) nitrogen-14 E) nitrogen-15 Answer: D Var: 1 57) A person receives an absorbed dose of protons of 20 millirads. The RBE of protons is 5. What is this person's equivalent dose in rem? A) 4 millirem B) 15 millirem C) 20 millirem D) 25 millirem E) 100 millirem Answer: E Var: 1

58) The chief hazard of radiation damage to living cells is A) due to heating. B) due to ionization. C) due to the creation of chemical impurities. D) the creation of new isotopes within the body. E) the creation of radioactive material within the body. Answer: B Var: 1 59) Inside the nucleus, the weakest of the four fundamental forces is A) the weak nuclear force. B) the electromagnetic force. C) the gravitational force. D) the strong nuclear force. Answer: C Var: 1 60) Inside the nucleus, the strongest of the four fundamental forces is A) the weak nuclear force. B) the electromagnetic force. C) the gravitational force. D) the strong nuclear force. Answer: D Var: 1 61) Leptons can interact by which of the following forces? A) strong nuclear force, weak nuclear force, electromagnetic force, gravitation B) strong nuclear force, weak nuclear force, electromagnetic force C) weak nuclear force, electromagnetic force, gravitation D) strong nuclear force, weak nuclear force E) strong nuclear force, electromagnetic force, gravitation Answer: C Var: 1 62) Which of the following particles are leptons? (There may be more than one correct choice.) A) protons B) neutrons C) electrons D) photons E) quarks Answer: C Var: 1

63) Elementary particles that experience the weak nuclear force but not the strong nuclear force are called A) leptons. B) hadrons. C) mesons. D) bosons. E) baryons. Answer: A Var: 1 64) What combination of quarks produces a proton and what are the electric charges on these quarks, expressed in terms of e? Answer: uud, with charges +2/3 e, +2/3 e, and -1/3 e Var: 1 65) What combination of quarks produces a neutron and what are the electric charges on these quarks, expressed in terms of e? Answer: udd, with charges +2/3 e, -1/3 e, and -1/3 e Var: 1 66) The proton is made up of which one of the following quark combinations (up, down, strange, charm, top, bottom)? A) uud B) ddu C) udd D) ttb E) bst Answer: A Var: 1 67) The neutron is made up of which one of the following quark combinations (up, down, strange, charm, top, bottom)? A) uud B) ddu C) udd D) ttb E) bst Answer: C Var: 1

68) Which of the following particles are not made up of quarks? (There could be more than one correct choice.) A) alpha particle B) electron C) proton D) positron E) neutron Answer: B, D Var: 1 69) Which of the following particles (or groups of particles) are made up of quarks? A) protons, neutrons, and electrons B) electrons and neutrinos C) photons D) protons and neutrons E) All particles except for photons are made up of quarks. Answer: D Var: 1 70) What are the possible charges of a quark (not an antiquark)? A) -e, 0, e B) -2/3 e, -1/3 e, +1/3 e, +2/3 e C) -2/3 e, +1/3 e D) -1/3 e, +2/3 e E) -1/3 e, +1/3 e Answer: D Var: 1 71) How many quarks are in a deuteron, H? A) 2 B) 3 C) 4 D) 6 E) 9 Answer: D Var: 1 72) How many quarks are in a tritium isotope, H? A) 2 B) 3 C) 4 D) 6 E) 9 Answer: E Var: 1 15 Copyright © 2019 Pearson Education, Inc.

30.2 Problems 1) In a head-on collision, an alpha particle (Z = 2) of energy bounces straight back from a nucleus of charge How close were the centers of the objects at closest approach? (1 eV = 1.60 × 10-19 J, e = 1.60 × 10-19 C, 1/4πε0 = 8.99 × 109 N ∙ m2/C2) A) 2.81 × 10-14 m B) 3.39 × 10-12 m C) 6.56 × 10-15 m D) 2.17 × 10-14 m Answer: A Var: 50+ 2) In the first nuclear reaction observed, physicists saw an alpha particle (Z = 2) interact with a nitrogen nucleus in air (Z = 7) to produce a proton. The energy of the alpha particle was enough to enable the nuclei to touch in spite of the Coulomb repulsion. What distance (in fm) between the centers of the alpha particle and the nitrogen was reached? This determines a limit on the radius of the nitrogen nucleus. (1 eV = 1.60 × 10-19 J, e = 1.60 × 10-19 C, 1/4πε0 = 8.99 × 109 N ∙ m2/C2) A) 0 fm B) 0 fm C) 0 fm D) 0 fm Answer: A Var: 11 3) The diameter of an atom is 1.4 × 10-10 m and the diameter of its nucleus is 1.0 × 10-14 m. What fraction of the atom's volume is occupied by its nucleus? A) 3.6 × 10-13 B) 7.1 × 10-5 C) 5.1 × 10-9 D) 2.6 × 10-17 Answer: A Var: 19 4) The radius R of a nucleus of mass number A is given by R = R0 A1/3, where R0 = 1.2 × 10-15 m, calculate the density of a nucleus that has contains 57 protons and 82 neutrons. The mass of a nucleon (proton or neutron) is 1.67 × 10-27 kg. Answer: 2.3 × 1017 kg/m3 Var: 1

5) How much energy is released when 0.60 μg of 3H have decayed to 3He? The mass of 3He is 3.0160293 u, the mass of 3H is 3.0160492 u, 1 u = 931.5 MeV/c2, 1 eV = 1.60 × 10-19 J, and NA = 6.022 × 1023 molecules/mol. Answer: 360 J Var: 1 6) A summary of the nuclear reactions that power our sun is 4p → 4He + 2e-, with masses of 938.272 MeV/c2 for a proton, 3727.38 MeV/c2 for the helium nucleus, and 0.511 MeV/c2 for each electron. How much energy is released by each of these reactions? A) 24.69 MeV B) 28.3 MeV C) 2790.13 MeV D) 279.01 MeV Answer: A Var: 1 7) A beryllium-8 nucleus at rest undergoes double alpha decay as follows: Be → He + He The known atomic masses are: He: 4.002603 u Be:

8.005305 u

What is the kinetic energy of each departing alpha particle? (1 u = 931.5 MeV/c2) A) 46 keV B) 65 keV C) 92 keV D) 130 keV E) 180 keV Answer: A Var: 1

8) One of the fusion reactions that occurs in the sun is: He + He → He + H + H The following atomic masses are known: H: 1.007825 u He:

3.016029 u

He:

4.002603 u

What is the reaction energy released in this fusion reaction? (1 u = 931.5 MeV/c2) A) 11 MeV B) 13 MeV C) 15 MeV D) 17 MeV E) 19 MeV Answer: B Var: 1 9) The following masses are known: n 1.008665 u H

1.007825 u

Ra 226.025403 u What is the binding energy of

Ra? (1 u = 931.5 MeV/c2)

A) 1700 MeV B) 1900 MeV C) 2100 MeV D) 2300 MeV E) 2500 MeV Answer: A Var: 12

10) The stability of

C with respect to alpha, beta-plus and beta-minus decay is to be

determined. The following atomic masses are known: He: 4.002603 u Be:

7.016928 u

11.009305 u

11.011433 u

11.026742 u

The

C nucleus is

A) not subject to alpha, beta-plus or beta-minus decay. B) subject to alpha decay only. C) subject to beta-plus decay only. D) subject to beta-minus decay only. E) subject to beta-plus or beta-minus decay, but not to alpha decay. Answer: C Var: 1 11) The stability of

Cl with respect to alpha, beta-plus and beta-minus decay is to be

determined. The following atomic masses are known: He: 4.002603 u P:

31.973907 u

35.967081 u

Cl: 35.968307 u Ar: 35.967546 u The

Cl nucleus is

12) Bismuth

Bi is known to be radioactive. The stability of

Bi with respect to alpha, beta-

plus and beta-minus decay is to be determined. The following atomic masses are known: He: 4.002603 u Tl:

207.981998 u

Pb:

211.991871 u

Bi:

211.991255 u

Po:

211.988842 u

The

Bi nucleus is

A) subject to alpha decay only. B) subject to beta-plus decay only. C) subject to beta-minus decay only. D) subject to alpha or beta-plus decay, but not beta-minus decay. E) subject to alpha or beta-minus decay, but not beta-plus decay. Answer: E Var: 1 13) Uranium-238 decays into thorium-234 plus an alpha particle. The known masses are He: 4.002603 u Th:

234.043583 u

238.050786 u

How much energy is released in this process? (1 u = 931.5 MeV/c2) A) 4.28 MeV B) 3.76 MeV C) 3.18 MeV D) 2.89 MeV E) 5.05 MeV Answer: A Var: 1

14) Radium-226 decays into radon-222 plus an alpha particle. The relevant masses are He: 4.002603 u Rn: 222.017570 u Ra: 226.025402 u How much energy is released in this process? (1 u = 931.5 MeV/c2) A) 4.24 MeV B) 3.76 MeV C) 4.87 MeV D) 5.05 MeV E) 5.39 MeV Answer: C Var: 1 15) When a stationary plutonium-239,

Pu, decays into uranium-235 plus an alpha particle, the

energy released in the process is 5.24 MeV. The following masses are known: He: 4.002603 u U: 235.043924 u What is the mass of the

Pu nucleus, in amu? (1 u = 931.494 MeV/c2)

A) 239.05215 u B) 239.02775 u C) 239.00189 u D) 238.99919 u E) 238.98884 u Answer: A Var: 1 16) When a stationary plutonium-239 nucleus decays into a uranium-235 nucleus plus an alpha particle, the energy released in the process is 5.24 MeV. The following masses are known: He: 4.002603 u U: 235.043924 u What is the kinetic energy of the

U nucleus? (1 u = 931.5 MeV/c2)

17) The neutral helium atom, He, has a mass of 4.002603 u, a neutron has a mass of 1.008665 u, a proton has a mass of 1.007277 u, and a neutral hydrogen atom has a mass of 1.007825 u. What is the binding energy of the He nucleus? (1 u = 931.5 MeV/c2) A) 20.5 MeV B) 22.4 MeV C) 27.3 MeV D) 28.3 MeV E) 23.4 MeV Answer: D Var: 1 18) A carbon-14 nucleus decays to a nitrogen-14 nucleus by beta-minus decay. How much energy (in MeV) is released if carbon-14 has a mass of 14.003242 u and nitrogen-14 has a mass of 14.003074 u? (1 u = 931.5 MeV/c2) A) 0.0156 MeV B) 0.156 MeV C) 1.56 MeV D) 15.6 MeV Answer: B Var: 1 19) The neutral deuterium atom, H, has a mass of 2.014102 u; a neutral ordinary hydrogen atom has a mass of 1.007825 u; a neutron has a mass of 1.008665 u; and a proton has a mass of 1.007277 u. What is the binding energy of the deuterium nucleus? (1 u = 931.5 MeV/c2) A) 1.1 MeV B) 1.7 MeV C) 2.2 MeV D) 2.9 MeV E) 3.4 MeV Answer: C Var: 1 20) The neutral

Al atom has a mass of 26.981539 u; a neutral hydrogen atom has a mass of

1.007825 u; a neutron has a mass of 1.008665 u; and a proton has a mass of 1.007277 u. What is the binding energy per nucleon for Al? (1 u = 931.5 MeV/c2) A) 8.3 MeV B) 6.7 MeV C) 5.4 MeV D) 3.4 MeV E) 2.8 MeV Answer: A Var: 1 22 Copyright © 2019 Pearson Education, Inc.

21) The carbon in our bodies was formed in nuclear reactions in long-dead stars. How much energy was released when the right number of 4He nuclei combined to make 12C? The mass of 4He is 3728.40 MeV/c2 and the mass of 12C is 11,177.93 MeV/c2. A) 7.27 MeV B) 372 MeV C) 8.42 MeV D) 2.11 MeV Answer: A Var: 1 22) Suppose that starting with

, the following sequence of decays occurs: first an alpha decay,

then a beta-minus decay, and finally another alpha decay. What isotope is left after each one of the decays? Answer: Fr, Ra, Rn Var: 1 23) Starting with

U, assume that the following three decays occur in sequence:

(1) alpha decay (2) beta-minus decay (3) alpha decay Determine the correct isotope that is left after each decay. Answer: T, Pa, Ac Var: 1 24) A sodium-22 nucleus,

Na, decays into a neon-22 nucleus,

Ne, and one other particle.

What is the other particle? Answer: β+ (or a positron) Var: 1 25) In the radioactive decay equation Answer:

→

Th + X, what is X?

He (α particle)

Var: 1 26) In the radioactive decay equation

Po* →

Po + X, what is X?

Answer: gamma ray Var: 1

27) A nucleus

X undergoes one alpha decay followed by 3 beta-minus decays.

(a) What is the resulting nucleus in terms of M and N? (b) If there had been 3 beta-plus decays instead of the beta-minus decays, what would have been the resulting nucleus in terms of M and N? Answer: (a) X (b) X Var: 1 28) The isotope

U is radioactive and decays in a series to

Th. In this series, the particles

ejected from the nucleus are A) one alpha particle and three beta-minus particles. B) three alpha particles and one beta-minus particle. C) one alpha particle and four beta-minus particles. D) four alpha particle and one beta-minus particle. E) two alpha particles and two beta-minus particles. Answer: E Var: 1 29) An oxygen-15 nucleus,

O, decays to another atomic nucleus by emitting a β+ ray. What is

the other atomic nucleus? A) N B)

Answer: A Var: 1

30) Rubidium

Rb is a naturally occurring isotope that undergoes β- decay. What isotope is the

product of this decay? A) Kr B)

Answer: E Var: 1 31) Neodymium

Nd is an isotope that undergoes alpha decay. What isotope is the product of

this decay? A) Ba B)

Answer: B Var: 1 32) Scandium A)

Sc decays by emitting a positron. What isotope is the product of this decay?

Answer: C Var: 1

33) A nuclear reaction is shown:

B + He → H + ? . Which one of the following isotopes is

the missing nuclear product? A) F B)

Answer: C Var: 1 34) The unstable isotope 234Th decays by β emission with a half-life of 24.5 days. If the initial decay rate of the sample is 6.2 × Bq, what is the decay rate after 37 days? Answer: 2.2 × 1017 Bq Var: 50+ 35) Polonium-215,

Po, undergoes alpha decay with a half-life of 1.8 ms.

(a) What percent of the original polonium-215 is left after 0.010 s? (b) How many protons and neutrons does the daughter nucleus contain? Answer: (a) 2.1% (b) 82 protons, 129 neutrons Var: 1 36) Given that the half-life for radium-226 is 1600 y, how long is the "quarter-life" (that is, the time for the radiation to decay to one-fourth of its initial level)? Answer: 3200 years Var: 1 37) Suppose that in a certain collection of nuclei there were initially 1024 billion nuclei, and 20.0 minutes later there was only 1.00 billion nuclei left, the others having decayed. On the basis of this information, how many nuclei would you estimate decayed in the first 6.00 minutes? Answer: 896 billion Var: 1 38) The decay rate of a radioactive sample decreases from 175 kBq to 12.4 kBq in 18.3 s. What is the half-life of this sample? Answer: 4.79 s Var: 1

39) A radioactive substance containing 4.0 × 1016 unstable atoms has a half-life of 2.0 days. What is its activity (in curies, Ci) after 1.0 day? (1 Ci = 3.70 × 1010 Bq) Answer: 4.3 Ci Var: 1 40) The activity of a sample reduces from 7.55 × Bq to 5.11 × Bq in 5.50 months. (a) What is its half life? (b) How many months from the start must one wait for the activity to decrease to 10% of its original value? Answer: (a) 9.77 months (b) 32.4 months Var: 5 41) A 1.0-mol sample of an isotope is decaying with a half-life of 28 y. After 61 y, how many moles of this isotope are left and what is its activity in Bq? Answer: 0.22 mol, 1.0 × 1014 Bq Var: 1 42) The atom 40K decays radioactively to the gas 40Ar. An ancient rock is found to contain enough 40Ar gas to indicate that 77.0% of the 40K in the rock has decayed to 40Ar since the rock solidified. (Any previous argon would have boiled out of liquid rock.) How long ago did the rock solidify? The half-life of 40K is 1.25 billion years. A) 2.65 billion years B) 0.471 billion years C) 1.80 billion years D) 0.324 billion years Answer: A Var: 1 43) The half-life of radon-222 is 3.83 d. If a sample of radon initially contains 6.00 × 108 radon atoms, how many of them are left after 10.0 d? A) 9.82 × 107 B) 7.67 × 107 C) 8.34 × 108 D) 7.29 × 108 E) 8.56 × 108 Answer: A Var: 1

44) The number of radioactive nuclei in a particular sample decreases to one-eighth of its original number in 9 days. What is the half-life of these nuclei? A) 9/8 days B) 2 days C) 3 days D) 8 days E) 10 days Answer: C Var: 5 45) A thallium source with a half-life of 3.7 years was certified at 10 kBq ten years ago. What is its activity now? A) 4.7 kBq B) 3.3 kBq C) 1.5 kBq D) 1.0 kBq Answer: C Var: 1 46) A radioactive sample has a half-life of 10 min. What fraction of the sample is left after 40 min? A) 1/2 B) 1/4 C) 1/8 D) 1/16 Answer: D Var: 3 47) A radioactive substance with a half-life of 3.0 days has an initial activity of 2400 Bq. What is its activity after 6.0 days? A) 1200 Bq B) 1800 Bq C) 600 Bq D) 300 Bq E) 150 Bq Answer: C Var: 1 48) A sample containing 4.0 × 1018 atoms of a radioactive isotope decays with a half-life of 2.3 years. How many undecayed atoms are left after 3.7 years? A) 2.5 × 1018 B) 1.7 × 1018 C) 1.3 × 1018 D) 1.1 × 1018 Answer: C Var: 1 28 Copyright © 2019 Pearson Education, Inc.

49) How long would it take 4.00 × 1020 atoms to decay to 1.00 × 1019 atoms if their half-life was 14.7 years? A) 29.4 years B) 58.8 years C) 78.2 years D) 147 years Answer: C Var: 1 50) How long will it take a 4.50-kBq sample of material to reach an activity level of 0.140 kBq if the half-life of the sample is 435 years? A) 14,478 years B) 3245 years C) 2178 years D) 1993 years Answer: C Var: 1 51) Rutherfordium-261 has a half-life of 1.08 min. How long will it take for a sample of rutherfordium to lose one-third of its nuclei? A) 1.02 min B) 1.62 min C) 0.632 min D) 2.70 min E) 3.24 min Answer: C Var: 5 52) Fermium-253 has a half-life of 3.00 days. If a sample of fermium originally has 7.37 × nuclei, how long will it take for there to be only 3.36 × fermium-253 nuclei left in this sample? A) 2.75 days B) 9.80 days C) 13.4 days D) 15.7 days E) 58.6 days Answer: C Var: 5

53) The half-life of a radioactive material is 4.5 days. How many days are required for a sample, with an initial activity of 1.0 × 105 Bq, to decay to an activity of 100 Bq? A) 45 days B) 36 days C) 54 days D) 31 days Answer: A Var: 41 54) A hospital patient has been given a sample of 131I , which has a half-life of 8.04 days. This sample is decaying at 5.9 times the acceptable level for exposure to the general public. How long must the patient wait for the decay rate of the sample to reach the acceptable level? A) 21 days B) 14 days C) 9.9 days D) 8.9 days Answer: A Var: 31 55) Plutonium has a half life of 2.4 × 104 years. How long does it take for 99.0% of the plutonium to decay? A) 1.6 × 102 y B) 1.6 × 103 y C) 1.6 × 104 y D) 1.6 × 105 y E) 1.6 × 106 y Answer: D Var: 1 56) One material used in nuclear bombs is 239Pu, with a half-life of 24,000 years. How long must we wait for a buried stockpile of this substance to decay to 1/1000 of its original activity? A) 1,200,000 years B) 240,000 years C) 150,000 years D) 82,000 years E) 1,500 years Answer: B Var: 1

57) Time (days) Counts per Minute

1000

899

726

556

356

200

In a laboratory accident, a work area is contaminated with radioactive material. Health physicists monitor the area during a 30-day period and obtain the data shown in the table. The accident occurred at time t = 0 days. They determine that it will not be safe for workers to enter the area until the radioactivity level has dropped to 16 counts per minute. Of the choices listed, which one is the earliest time after the accident that workers could safely return? A) 77 days B) 90 days C) 102 days D) 65 days E) 48 days Answer: A Var: 50+ 58) Today, uranium contains (half-life = 0.70 billion years) and = 4.5 billion years). At a time 1.9 billion years ago, what was the fraction of A) 3.53% B) 4.72% C) 4.90% D) 6.76% Answer: A Var: 17

(half-life in uranium?

59) An air sample is contaminated with 15O, which has a half-life of 2.03 minutes. You can pass it through a long pipe to allow it to decay until it can be safely released into the atmosphere. If the speed of the gas in the pipe is 1.1 m/s, how long must the pipeline be for the sample to decay to 3.0% of its original activity? A) 680 m B) 8.0 m C) 72 m D) 250 m Answer: A Var: 1 60) The mean life (time constant) of rubidium-86 is 26.8 d. What is its half-life? Answer: 18.6 d Var: 1 61) The half-life of tritium is 12.3 y. What is its mean life (time constant)? Answer: 17.7 y Var: 1 31 Copyright © 2019 Pearson Education, Inc.

62) The mean life (time constant) of radon-222 is 5.526 d. If a sample of radon initially contains 6.00 × 108 radon atoms, how many of them are left after 10.0 d? A) 9.82 × 107 B) 7.67 × 107 C) 8.34 × 108 D) 7.29 × 108 E) 8.56 × 108 Answer: A Var: 1 63) The decay rate of a radioactive sample decreases from 175 kBq to 12.4 kBq in 18.3 s. What is the mean life (time constant) of this sample? Answer: 6.91 s Var: 1 64) A radioactive source emits 2.4-MeV neutrons at the rate of 7100 neutrons per second. The number of atoms in the source is What is the activity of the source, in curies (Ci)? (1.00 10 Ci = 3.70 × 10 Bq) A) 190 nCi B) 1900 nCi C) 19 nCi D) 71 nCi E) 710 nCi Answer: A Var: 50+ 65) A certain substance has a half-life of 5.0 hours. How many nuclei of the substance are required to give an initial activity of 6.0 μCi? (1 Ci = 3.7 × Bq) A) 5.8 × nuclei B) 8.5 × nuclei C) 6.3 × nuclei D) 3.2 × nuclei E) 2.4 × nuclei Answer: A Var: 5 66) Fermium-253 has a half-life of 3.00 days. A sample of fermium has 3.88 × 106 nuclei. What is the initial activity of this sample? A) 10.4 Bq B) 10.4 kBq C) 12.9 Bq D) 12.9 kBq Answer: A Var: 1 32 Copyright © 2019 Pearson Education, Inc.

67) The half-life of radioactive iodine-137 is 8.0 days. How many iodine nuclei are necessary to produce an activity of 1.0 μCi? (1 Ci = 3.70 × 1010 Bq) A) 2.9 × 109 B) 4.6 × 109 C) 3.7 × 1010 D) 7.6 × 1012 Answer: C Var: 1 68) What mass of 14C, with a half-life of 5730 y, do you need to provide a decay rate of The mass of 14C is 14.00 u, and 1 u = 1.6605 × 10-27 kg. A) 1.70 × 10-12 kg B) 5.38 × 10-19 kg C) 3.84 × 10-20 kg D) 8.68 × 10-13 kg Answer: A Var: 50+ 69) An old bone sample contains 321 g of carbon and has an activity of 947 decays/min due to the carbon-14 in it. The half-life of carbon-14 is 5730 y. Assume that the activity of the atmospheric carbon is, and has remained, 0.255 Bq per gram of carbon. (a) How old is the sample? (b) What will be the activity of the sample 2000 y from now, in decays per minute? Answer: (a) 13,600 y (b) 743 decays/min Var: 1 70) An archaeologist finds the 14C in a sample of of material to be decaying at 107 Bq. A modern sample of the same material decays at 151 Bq,and assume this rate has also held in the past. The half-life of 14C is 5730 years. How old is the sample? A) 8980 years B) 6230 years C) 17,000 years D) 8530 years Answer: A Var: 17

71) A sample of wood has been recovered by an archaeologist. The sample is sent to a laboratory, where it is determined that the activity of the sample is 0.144 Bq/g. By comparing this activity with the activity of living organic matter, which is 0.230 Bq/g, the scientist determines how old the wood sample is, or more precisely, when the tree that the sample came from died. Carbon-14 has a half-life of 5730 years. If the activity of living matter has been constant over time, how old is the sample of wood? A) 3870 years B) 4250 years C) 4590 years D) 2630 years E) 2940 years Answer: A Var: 1 72) The radioactivity due to carbon-14 measured in a piece of a wooden casket from an ancient burial site is found to produce 20 counts per minute from a given sample, whereas the same amount of carbon from a piece of living wood produces 160 counts per minute. The half-life of carbon-14, a beta-minus emitter, is 5730 years. What would we calculate for the age of the artifact, assuming that the activity for living wood has remained constant over time? A) 5,700 years B) 11,500 years C) 14,800 years D) 17,200 years E) 23,000 years Answer: D Var: 1 73) The maximum permissible workday dose for occupational exposure to radiation is 18 mrem. A 54-kg laboratory technician absorbs 2.6 mJ of 0.30-MeV gamma rays in a work day. The relative biological effectiveness (RBE) for gamma rays is 1.00. What is the ratio of the equivalent dosage received by the technician to the maximum permissible equivalent dosage? A) 0.27 B) 0.29 C) 0.32 D) 0.35 E) 0.37 Answer: A Var: 50+

74) The maximum permissible workday dose for occupational exposure to radiation is 11 mrem. A 77-kg laboratory technician absorbs 2.3 mJ of 0.5-MeV gamma rays in a work day. The relative biological effectiveness (RBE) for gamma rays is 1.00. What is the number of gammaray photons absorbed by the technician in a workday? A) 3 × 1010 B) 3 × 109 C) 3 × 108 D) 1 × 109 E) 1 × 108 Answer: A Var: 50+ 75) A 70-kg researcher absorbs 4.5 × neutrons in a work day, each of energy 1.2 MeV. The relative biological effectiveness (RBE) for these neutrons is 10. What is the equivalent dosage of the radiation exposure for this researcher, in millirem? A) 1.2 mrem B) 0.39 mrem C) 0.77 mrem D) 3.7 mrem E) 12 mrem Answer: A Var: 50+ 76) Determine the missing product X in the nuclear reaction Answer:

U + n → X + 2β-.

Var: 1 77) Determine the missing product X in the following nuclear reaction: O + neutron → X + alpha particle Answer: Var: 1

78) Determine the missing product X in the following nuclear reaction: U + neutron → Ba + X + 3 neutrons Answer:

Var: 1

79) Determine the missing product X in the following nuclear reaction: B + neutron → X + alpha particle Answer:

Var: 1 80) Determine the missing product X in the following nuclear reaction: N + neutron → X + alpha particle Answer:

Var: 1 81) The equation shows a fission reaction: U + n → Nb + X + 4 n What is the missing term X in the equation? A) Ag B)

Answer: E Var: 1 82) In the fission reaction 235U + 1n → 141Ba + 92Kr + x 1n, what is the number x of neutrons produced? A) 0 B) 1 C) 2 D) 3 Answer: D Var: 1

83) In the nuclear reaction

O + He → X +

Ne, what is X?

A) proton B) neutron C) 2H D) 3H E) alpha particle Answer: B Var: 1 84) In the nuclear reaction

O + n → X + He, what is X?

A) 12C B) 13C C) 14C D) 15C E) 17O Answer: B Var: 1 85) In the nuclear reaction

K+ H→X+

Ca, what is X?

A) proton B) neutron C) 2H D) 3H E) alpha particle Answer: B Var: 1 86) In the nuclear reaction H + H → X + He, what is X? A) 2 protons B) 2 neutrons C) 2H D) 3H E) alpha particle Answer: B Var: 1

87) A proton strikes an oxygen-18 nucleus, producing fluorine-18 and another particle X. What is the other particle X? A) neutron B) positron C) alpha particle D) electron E) gamma ray Answer: A Var: 1 88) A hypothetical particle has a mass of 510 MeV/c2. If such a particle at rest decays into two gamma-ray photons, what is the wavelength of each photon? (1 eV = 1.60 × 10-19 J, c = 3.00 × 108 m/s, h = 6.626 × 10-34 J∙ s) Answer: 4.87 × 10-15 m Var: 1 89) If a Σ- particle at rest decays into a neutron and a π- , what is the total kinetic energy of the decay products? The masses of Σ-, neutron, and π- are 1197 MeV/c2, 940 MeV/c2, and 140 MeV/c2, respectively. Answer: 117 MeV Var: 1 90) Consider the fusion reaction: H + H + H → He + H + n The know atomic masses are H: 2.01410 u He:

4.00260 u

1.00783 u

1.008665 u

where 1 u = 1.6605 × 10-27 kg. What mass of deuterium fuel, H, is used up in producing of energy by this reaction? Answer: 1.6 × 101 kg Var: 50+

91) Consider the nuclear reaction N:

14.003074 u

He:

4.002603 u

1.007825 u

16.999131 u

N + He →

O + H. The known atomic masses are

What is the Q-value (or reaction energy) of this reaction? (1 u = 931.5 MeV/c2) A) -1.191 MeV B) -2.020 MeV C) -6.725 MeV D) -9.055 MeV Answer: A Var: 1 92) Consider the nuclear reaction: 7Li + 1p → 4He + 4He. The known atomic masses are 7Li: 7.016005 u He:

4.002603 u

1p: 1.007825 u What is the Q-value (or reaction energy) of this reaction? (1 u = 931.5 MeV/c2) A) 13.57 MeV B) 15.37 MeV C) 17.35 MeV D) 17.53 MeV Answer: C Var: 1

93) Consider the nuclear reaction N:

14.003074 u

He:

4.002603 u

1.007825 u

16.999131 u

N + He →

O + H. The known atomic masses are

What is the Q-value (or reaction energy) of this reaction? (1 u = 931.5 MeV/c2) A) 1.191 MeV B) -1.191 MeV C) 1.279 × 10-3 MeV D) -1.279 × 10-3 MeV Answer: B Var: 1 94) Consider the nuclear reaction H + H → He + 2 n. The known atomic masses are He: 4.002603 u H:

3.016049u

1.008665 u

What is the energy released (positive) or absorbed (negative) in this nuclear reaction? (1 u = 931.5 MeV/c2) A) 0.0122 MeV B) -0.0122 MeV C) 11.3 MeV D) -11.3 MeV Answer: C Var: 1 95) A nuclear explosion results in a mass decrease of this explosion? (c = 3.00 × 108 m/s) A) 1.89 × 1014 J B) 6.30 × 105 J C) 1.89 × 1013 J D) 2.25 × 1012 J Answer: A Var: 28

How much energy is released during

96) An electron and a positron, both essentially at rest, annihilate each other, emitting two identical photons in the process. What is the wavelength of these photons? The mass of an electron or positron is 9.11 × 10-31 kg. (h = 6.626 × 10-34 J ∙ s, c = 3.00 × 108 m/s) A) 1.21 × 10-12 pm B) 1.73 pm C) 2.42 pm D) 3.07 pm E) 3.46 pm Answer: C Var: 1 97) An excited U*→

Ba +

U* nucleus undergoes fission into two fragments as follows: Kr

The following atomic masses are known: Kr: 91.926270 u Ba:

143.922845 u

U*:

236.045563 u

What is the reaction energy released during this fission reaction? (1 u = 931.5 MeV/c2) A) 150 MeV B) 160 MeV C) 170 MeV D) 180 MeV E) 190 MeV Answer: D Var: 1

98) When a neutron collides with a uranium-235 nucleus it can induce a variety of fission reactions. One such reaction is U+ n→ Xe + Sr + 2 n The following mass values are known: Xe: 139.921620 u Sr:

93.915367 u

235.043924 u

1.008665 u

How much energy is released in this reaction? (1 u = 931.5 MeV/c2) A) 185 MeV B) 202 MeV C) 32.6 MeV D) 65.7 MeV E) 98.6 MeV Answer: A Var: 1 99) When a neutron collides with a uranium-235 nucleus it can induce a variety of fission reactions. One such reaction is U+ n→ Xe + Sr + 2 n The following mass values are known: Xe: 139.921620 u Sr:

93.915367 u

235.043924 u

1.008665 u

What mass of uranium is needed to produce a 10-kiloton yield? (1 u = 931.5 MeV/c2 = 1.66054 × 10-27 kg, 1-kiloton yield = 5.0 × 1012 J) A) 0.57 kg B) 0.66 kg C) 6.58 kg D) 3.85 kg E) 1.10 kg Answer: B Var: 1

100) Two deuterium nuclei, H, fuse to produce a tritium nucleus, H, plus an ordinary hydrogen nucleus, H. A neutral deuterium atom has a mass of 2.014102 u; a neutral tritium atom has a mass of 3.016050 u; a neutral hydrogen atom has a mass of 1.007825 u; a neutron has a mass of 1.008665 u; and a proton has a mass of 1.007277 u. How much energy is released in this fusion process? (1 u = 931.5 MeV/c2) A) 3.03 MeV B) 3.53 MeV C) 4.03 MeV D) 4.53 MeV E) 6.58 MeV Answer: C Var: 1 101) If a 2.0-MeV neutron released in a fission reaction loses half its kinetic energy in each moderator collision, how many collisions are needed to reduce its kinetic energy to 1/25 eV? A) 6 B) 18 C) 26 D) 30 E) 4 Answer: C Var: 1 102) If a nuclear fission reactor produces an average power of 1.0 GW over the course of a year, what mass of 235U is used up for a 365-day year if 200 MeV are released per fission reaction? (1 eV = 1.60 × 10-19 J, mneutron ≈ mproton = 1.67 × 10-27 kg) A) 0.35 kg B) 1.75 kg C) 390 kg D) 1.1 × 108 kg E) 3.3 × 108 kg Answer: C Var: 1 103) When 235U undergoes fission, the average energy per fission event is 200 MeV. How much energy is released in the total fission of of (1 eV = 1.60 × 10-19 J, mneutron ≈ mproton = 1.67 × 10-27 kg) A) 1.6 × 1011 J B) 3.9 × 1013 J C) 1.6 × 105 J D) 3.9 × 1010 J Answer: A Var: 6 43 Copyright © 2019 Pearson Education, Inc.

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