TEST BANK for College Physics, 11th Edition. Hugh Young, Philip Adams, Raymond Joseph Chastain by digitaldownload87

College Physics, 11e Hugh Young, Philip Adams, Raymond Joseph Chastain (Test Bank All Chapters, 100% Original Verified, A+ Grade) College Physics, 11e (Young) Chapter 1 Models, Measurements and Vectors 1.1 Multiple Choice Questions 1) The following conversion equivalents are given: 1 gal = 231 1 ft = 12 in 1 min = 60 s A pipe delivers water at the rate of 95 gal/min. The rate in A) 0.21 B) 0.19 C) 0.17 D) 0.15 E) 0.14 Answer: A Var: 50+ 2) The following conversion equivalents are given: 1 m = 100 cm 1 in = 2.54 cm 1 ft = 12 in A bin has a volume of 1.5 . The volume of the bin, in A) 35 B) 41 C) 47 D) 53 E) 59 Answer: D Var: 1

/s, is closest to:

, is closest to:

3) The following conversion equivalents are given: 1 mile = 5280 ft 1 ft = 12 in 1 m = 39.37 in 1 hour = 60 min 1 min = 60 s A particle has a velocity of 4.7 miles per hour. The velocity, in m/s, is closest to: A) 2.1 B) 1.7 C) 1.9 D) 2.3 E) 2.5 Answer: A Var: 50+

4) A speed of 65 miles per hour is the same as A) 24 m/s B) 29 m/s C) 32 m/s D) 37 m/s E) 42 m/s Answer: B Var: 1 5) The following conversion equivalents are given: 1 kg = 1000g 1 l = 1000 1 l = 0.0353 The density of a liquid is 0.83 g/ A) 24 B) 19 C) 21 D) 26 E) 28 Answer: A Var: 50+ 6) A weight lifter can bench press A) 2.7 × 108 mg B) 2.7 × 109 mg C) 2.7 × 107 mg D) 2.7 × 106 mg Answer: A Var: 50+ 7) Your car gets 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+

. The density of the liquid, in kg/

, is closest to:

How many milligrams (mg) is this?

on a trip. How many

did it get? (3.79 = 1 gal; 1 mi =

8) The wavelength of a certain laser is

where

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+ 9) Add

and

and express your answer in milligrams (mg).

A) 4.64 × 107 mg B) 4.64 × 104 mg C) 4.64 × 105 mg D) 4.64 × 106 mg Answer: A Var: 50+ 10) 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 11) What is

to the proper number of significant figures?

A) 0.53 B) 0.533 C) 0.5329 D) 0.5 Answer: A Var: 50+ 12) What is 0.3272/3, to the proper number of significant figures? A) 0.475 B) 0.47 C) 0.5 D) 0.4746 Answer: A Var: 50+ 13) Which of the following is a reasonable estimate of the number of characters (typed letters or

numbers) in a 609 page book? Assume an average of number of A) 5 × 105 char B) 5 × 107 char C) 5 × 106 char D) 5 × 104 char Answer: A Var: 50+

and a reasonable average

14) A marathon is and long. Estimate how many strides would be required to run a marathon. Assume a reasonable value for the average number of A) 4.5 × 104 strides B) 4.5 × 103 strides C) 4.5 × 105 strides D) 4.5 × 106 strides Answer: A Var: 1 15) 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 A) 3 × 109 beats B) 3 × 108 beats C) 3 × 1010 beats D) 3 × 107 beats Answer: A Var: 50+ 16) The components of vector

are given as follows:

= +7.6 = -6.4 The magnitude of A) 9.9 B) 7.9 C) 8.9 D) 11 E) 12 Answer: A Var: 50+

is closest to:

17) The components of vector

are given as follows:

= +6.1 = -8.6 The angle measured counterclockwise from the x-axis to vector A) 305 B) 125 C) 215 D) 145 E) 55 Answer: A Var: 50+ 18) The components of vectors = +7.6

= -5.1

= -9.2

= -6.8

and

are given as follows:

The magnitude of the vector difference A) 13 B) 3.5 C) 16 D) 170 E) 3.4 Answer: A Var: 50+

19) The components of vectors

are given as follows:

= -9.2

= -4.5

= -6.1

= +4.3

and

, is closest to:

The angle (less than 180 degrees) between vectors A) 77 B) 103 C) 10 D) 170 E) 84 Answer: A Var: 50+ 20) The magnitude of

is 5.5. Vector

, in degrees, is closest to:

and

, in degrees, is closest to:

lies in the second quadrant and forms an angle of

with the y-axis. The components, A)

= -3.1,

= +4.6

= +3.1,

= -4.6

= +4.6,

= -3.1

= -4.6,

= +3.1

= -4.6,

= -3.1

and

, are closest to:

Answer: A Var: 50+ 21) Vector

has length 2 units and directed to the north. Vector

has length

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 Figure 1.1 Vectors

and

are shown. Vector

22) In Figure 1.1, the magnitude of A) 3.2 B) 5.3 C) 6.6 D) 8.0 E) 9.2 Answer: C Var: 1

is given by

is closest to:

23) In Figure 1.1, the angle, measured counterclockwise from the x-axis to vector is closest to:

, in degrees,

A) 12 B) 102 C) 168 D) 192 E) 258 Answer: C Var: 1 24) You walk to the north, then turn 60° to your right and walk another you from where you originally started? A) 69 m B) 40 m C) 76 m D) 36 m Answer: A Var: 31

How far are

25) A rabbit trying to escape a fox runs north for 4.0 m, darts northwest for 8.0 m, then drops 1.0 m down a hole into its burrow. What is the magnitude of the net displacement of the rabbit? A) 11 m B) 8.9 m C) 81 m D) 13 m Answer: A Var: 50+ 26) Which of the following is an accurate statement about vectors? A) The magnitude of a vector can be zero even though one of its components is not zero. B) It is possible to add a scalar quantity to a vector. C) Even though two vectors have unequal magnitudes, it is possible that their vector sum is zero. D) Rotating a vector about an axis passing through the tip of the vector does not change the vector. E) The magnitude of a vector is positive even if all of its components are negative. Answer: E Var: 1

Figure 1.2 Three vectors are given as shown.

27) In Figure 1.2, the magnitude of the resultant of the three vectors is closest to: A) 19 B) 16 C) 13 D) 10 E) 7 Answer: C Var: 1 28) An airplane undergoes the following displacements: First, it flies in a direction 30° east of north. Next, it flies due south. Finally, it flies 30° north of west. Using analytical methods, determine how far the airplane ends up from its starting point. A) 71.5 km B) 73 km C) 74.4 km D) 70.1 km E) 68.7 km Answer: A Var: 50+

1.2 Short Answer Questions 1) Albert defines his own unit of length, the albert, to be the distance Albert can throw a small rock. One albert is How many square alberts is one acre? (1 acre = 43,560

= 4050

)

Answer: 5.55555556 Var: 50+ Figure 1.3

2) Find the magnitude and direction of the resultant of the three vectors shown in Figure 1.3. The vectors have the following magnitudes: A = 5.0, B = 7.9, and C = 8.0. Express the direction of the vector sum by specifying the angle it makes with the positive x-axis, with the counterclockwise angles taken to be positive. Answer: magnitude: R = 1.6, direction: Θ = Var: 1 3) 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° Var: 1 4) A vector in the x-yplane 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: +6.61 units and –6.61 units Var: 1

5) Three ropes are tied in a knot as indicated in Figure 1.4. One student pulls on rope A with 1 pound of force, and another student pulls on rope B with 7 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 of the pull with the direction of rope A and its direction (clockwise or counterclockwise). Figure 1.4

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

College Physics, 11e (Young) Chapter 2 Motion Along a Straight Line 2.1 Multiple Choice Questions 1) If the fastest you can safely drive is you must travel in total? A) 2.3 h B) 2.5 h C) 1.8 h D) You can't stop at all. Answer: A Var: 50+ 2) A car accelerates from accelerating? A) 69 m B) 207 m C) 41 m D) 117 m Answer: A Var: 50+

what is the longest time you can stop for dinner if

at a rate of

How far does it travel while

3) An airplane needs to reach a velocity of to take off. On a the minimum acceleration necessary for the plane to take flight? A) 0.79 m/s2 B) 0.87 m/s2 C) 0.95 m/s2 D) 1.0 m/s2 Answer: A Var: 50+

runway, what is

4) Assuming equal rates of 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+

5) Acceleration is sometimes expressed in multiples of g, where due to the earth's gravity. In a car crash, the car's velocity may go from 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

is the acceleration to in

6) 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 what is the ratio of the acceleration to the original velocity? A) -6.7 s-1 B) -4.4 s-1 C) -2.2 s-1 D) -0.15 s-1 Answer: A Var: 50+

Use Figure 2.1 to answer the following question(s). Figure 2.1

7) The graph in Figure 2.1 shows the position of an object as a function of time. The letters H-L represent particular moments of time. At which moment in time is the speed of the object the highest? A) J B) H C) I D) K E) L Answer: A Var: 1 8) The graph in Figure 2.1 shows the position of an object as a function of time. The letters H-L represent particular moments of time. At which moment in time is the speed of the object equal to zero? A) I B) H C) J D) K E) L Answer: A Var: 1

9) A train starts from rest and accelerates uniformly, until it has traveled 5.6 km and acquired a velocity of The train then moves at a constant velocity of for 420 s. The train then slows down uniformly at 5.6 km of travel is closest to: A) 0.16 m/

until it is brought to a halt. The acceleration during the first

B) 0.14 m/ C) 0.17 m/ D) 0.19 m/ E) 0.20 m/ Answer: A Var: 50+ 10) A train starts from rest and accelerates uniformly, until it has traveled 2.1 km and acquired a 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, in km, is closest to: A) 4.4 B) 4.2 C) 4.0 D) 3.8 E) 3.6 Answer: A Var: 50+ 11) A car moving at a velocity of 20 m/s is behind a truck moving at a constant velocity of When the car is 50 m behind the front of the truck, the car accelerates uniformly at The car continues at the same acceleration until it reaches a velocity of which is the legal speed limit. The car then continues at a constant velocity of until it passes the front of the truck. The distance the car travels while accelerating, in meters, is closest to: A) 50 B) 54 C) 58 D) 62 E) 66 Answer: D Var: 1

12) 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 13) A racquetball strikes a wall with a speed of 30 m/s and rebounds with a speed of collision takes What is the average acceleration of the ball during the collision? A) zero B) 200 m/ C) 2800 m/ D) 1500 m/ E) 1300 m/ Answer: C Var: 1 14) 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

The

15) 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 Figure 2.2. The car reaches a speed of 140 km/h as it passes marker 2. Figure 2.2

Whereabouts on the track was the car when it was travelling at half this speed, i.e. at 70 km/h? A) Before marker 1 B) At marker 1 C) Between marker 1 and marker 2 Answer: A Var: 1 16) A stone is thrown vertically upwards, reaches a highest point, and returns to the ground. When the stone is at the top of its path, its acceleration A) is zero. B) is directed upwards. C) is directed downwards. D) changes direction from upwards to downwards. Answer: C Var: 1

17) The motions of a car and a truck along a straight road are represented by the velocity-time graphs in Figure 2.3. The two vehicles are initially alongside each other at time t = 0. Figure 2.3

At time T, what is true of the distances travelled by the vehicles since time t = 0? A) They will have travelled 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 18) Two identical objects A and B fall from rest from different heights to the ground. If object B takes twice as long as A to reach the ground, what is the ratio of the heights from which A and B fell? Neglect air resistance. A) 1 : B) 1 : 2 C) 1 : 4 D) 1 : 8 Answer: C Var: 1

19) A ball is projected upward at time t = 0.0 s, from a point on a roof 60 m above the ground. The ball rises, then falls and strikes the ground. The initial velocity of the ball is Consider all quantities as positive in the upward direction. At time the acceleration of the ball is closest to: A) zero B) +5 m/ C) +10 m/ D) -5 m/ E) -10 m/ Answer: E Var: 50+ 20) A ball is projected upward at time t = 0.0 s, from a point on a roof 10 m above the ground. The ball rises, then falls and strikes the ground. The initial velocity of the ball is Consider all quantities as positive in the upward direction. At time the velocity of the ball is closest to: A) zero B) +175 m/s C) +12 m/s D) -175 m/s E) -12 m/s Answer: A Var: 50+ 21) A ball is projected upward at time t = 0.0 s, from a point on a roof 90 m above the ground. The ball rises, then falls and strikes the ground. The initial velocity of the ball is Consider all quantities as positive in the upward direction. The 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+

22) A test rocket is fired straight up from rest with a net acceleration of 20 m/ . After 4 seconds the motor turns off, but the rocket continues to coast upward. What maximum elevation does the rocket reach? A) 487 m B) 327 m C) 320 m D) 408 m E) 160 m Answer: A Var: 1

23) A child standing on a bridge throws a rock straight down. The rock leaves the child's hand at Which of the graphs shown here best represents the velocity of the stone as a function of time? A)

Answer: C Var: 1

24) A toy rocket is launched vertically from ground level (y = 0 m), at time t = 0.0 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 a velocity of The rocket continues to rise in unpowered flight, reaches maximum height, and falls back to the ground. The time interval, during which the rocket engine provides 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+ 25) A toy rocket is launched vertically from ground level (y = 0 m), at time t = 0.0 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 a velocity of The rocket continues to rise 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+ 26) A toy rocket is launched vertically from ground level (y = 0 m), at time t = 0.0 s. The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to 49 m and acquired a velocity of The rocket continues to rise 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+

Situation 2.1 A rock is projected upward from the surface of the moon, at time t = 0.0 s, with a velocity of The acceleration due to gravity at the surface of the moon is 27) In Situation 2.1, the time when the rock is ascending and at a height of 180 m is closest to: A) 8 s B) 12 s C) 17 s D) 23 s E) 30 s Answer: A Var: 1 28) In Situation 2.1, the height of the rock when it is descending with a velocity of 20 m/s is closest to: A) 115 m B) 125 m C) 135 m D) 145 m E) 155 m Answer: E Var: 1 29) A ball is thrown straight upward with a velocity of ball strikes the ground? 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 passes before the

30) An object is dropped from rest into a pit, and accelerates due to gravity at roughly 10 m/s2. It hits the ground in 5 seconds. A rock is then dropped from rest into a second pit, and hits the ground in 10 seconds. How much deeper is the second pit, compared to the first pit? Neglect air resistance. A) four times deeper B) two times deeper C) three times deeper D) five times deeper Answer: A Var: 1

2.2 Short Answer Questions 1) A soccer ball is released from rest at the top of a grassy incline. After 6.4 seconds, the ball travels 91 meters. One second later, the ball reaches the bottom of the incline. a) What was the ball's acceleration? (Assume that the acceleration was constant.) b) How long was the incline? Answer: a) 4.4 m/ b) 120 m Var: 50+ 2) A rock is thrown directly upward from the edge of the 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+ 3) A package is dropped from a helicopter 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: 1300 m Var: 25 4) At the same moment, one rock is dropped and one is thrown downward with an initial velocity of from the top of a building. How much earlier does the thrown rock strike the ground? Neglect air resistance. Answer: 2.4 s Var: 21 5) 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 mph 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. Answer: 49 ft Var: 1

College Physics, 11e (Young) Chapter 3 Motion in a Plane 3.1 Multiple Choice Questions 1) Shown here 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? A)

E) Answer: B Var: 1

2) Shown here 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? A)

E) None of these cases. Answer: D Var: 1 3) Which of the following ideas is true about projectile motion with no air drag? A)

= constant.

B) The acceleration is +g when the object is rising and -g when falling. C) The velocity of the object is zero at the point of maximum elevation. D) The trajectory will depend on the object's mass as well as its initial velocity and launch angle. E) The horizontal motion is independent of the vertical motion. Answer: E Var: 1

Figure 3.1

4) A projectile is fired from the origin (at y = 0 m) as shown in Figure 3.1. The initial velocity components are and The projectile reaches maximum height at point P, then it falls and strikes the ground at point Q. In Figure 3.1, the y-coordinate of point P is closest to: A) 470 m B) 45,550 m C) 45,080 m D) 940 m E) 90,160 m Answer: A Var: 1 5) A projectile is fired from the origin (at y = 0 m) as shown in Figure 3.1. The initial velocity components are and The projectile reaches maximum height at point P, then it falls and strikes the ground at point Q. In Figure 3.1, the y-component of the velocity of the shell of point P is closest to: A) zero B) +40 m/s C) +70 m/s D) -40 m/s E) -70 m/s Answer: A Var: 50+ 6) A projectile is fired from the origin (at y = 0 m) as shown in Figure 3.1. The initial velocity components are and The projectile reaches maximum height at point P, then it falls and strikes the ground at point Q. In Figure 3.1, the y-component of the acceleration of the shell at point P is closest to: A) zero B) +5 m/s2 C) +10 m/s2 D) -5 m/s2 E) -10 m/s2 Answer: E Var: 50+ 7) A projectile is fired from the origin (at y = 0 m) as shown in Figure 3.1. The initial velocity

components are

and

The projectile reaches maximum height at

point P, then it falls and strikes the ground at point Q. In Figure 3.1, the x-component of the velocity of the shell at point P is closest to: A) 140 m/s B) 35 m/s C) 70 m/s D) 105 m/s E) zero Answer: A Var: 1 8) Two bullets are fired simultaneously parallel to a horizontal plane. The bullets have different masses and different initial velocities. Which one will strike the plane first? A) The fastest one. B) The slowest one. C) The heaviest one. D) The lightest one. E) They strike the plane at the same time. Answer: E Var: 1

9) A projectile is fired at time t = 0.0s, from point 0 at the edge of a cliff, with initial velocity components of and The projectile rises, then falls into the sea at point P. The time of flight of the projectile is Figure 3.2a

In Figure 3.2a, the magnitude of the velocity at time t = 15.0 is closest to: A) 56 m/s B) 47 m/s C) 49 m/s D) 249 m/s E) 247 m/s Answer: A Var: 50+

10) A projectile is fired at time t = 0.0s, from point 0 at the edge of a cliff, with initial velocity components of and The projectile rises, then falls into the sea at point P. The time of flight of the projectile is Figure 3.2b

In Figure 3.2b, the x-coordinate of the projectile when its y-component of velocity equals upward is closest to: A) 330 m B) 310 m C) 290 m D) 280 m E) 340 m Answer: A Var: 50+

11) A projectile is fired at time t = 0.0s, from point 0 at the edge of a cliff, with initial velocity components of and The projectile rises, then falls into the sea at point P. The time of flight of the projectile is Figure 3.2c

In Figure 3.2c, the height H of the cliff is closest to: A) 36,000 m B) 32,130 m C) 39,810 m D) 43,650 m E) 47,490 m Answer: A Var: 50+

12) A projectile is fired at time t = 0.0s, from point 0 at the edge of a cliff, with initial velocity components of and The projectile rises, then falls into the sea at point P. The time of flight of the projectile is Figure 3.2d

In Figure 3.2d, the horizontal distance D is closest to: A) 2,250 m B) 2,520 m C) 2,790 m D) 3,060 m E) 3,330 m Answer: A Var: 50+

13) A projectile is fired at time t = 0.0s, from point 0 at the edge of a cliff, with initial velocity components of and The projectile rises, then falls into the sea at point P. The time of flight of the projectile is Figure 3.2e

In Figure 3.2e, the y-coordinate of the projectile when its x-coordinate is 1,000 m is closest to: A) +2,040 m B) 150 m C) -150 m D) +1,240 m E) +600 m Answer: A Var: 50+ 14) A rescue plane spots a survivor

directly below and releases an emergency kit with a

parachute. If the package descends at a constant vertical acceleration of and the initial plane horizontal speed was how far away from the survivor will it hit the waves? A) 426 m B) 2.64 km C) 301 m D) 446 m Answer: A Var: 50+ 15) 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? A) 0.160 s B) 0.282 s C) 0.313 s D) 0.441 s Answer: A Var: 50+

16) What is the maximum distance we can shoot a dart, provided our toy dart gun gives a maximum initial velocity of A) 6.14 m B) 12.28 m C) 3.88 m D) More information needed. Answer: A Var: 50+ 17) A cat leaps to catch a bird. If the cat's jump was at 60.0° off the ground and its initial velocity was what is the highest point of its trajectory? A) 0.29 m B) 0.58 m C) 10.96 m D) 0.19 m Answer: A Var: 50+ 18) A fisherman casts his bait toward the river at an angle of 25°. 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. A) 18 m/s B) 7.9 m/s C) 7.6 m/s D) 6.3 m/s Answer: A Var: 30 19) 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? A) 21.5 m/s B) 19.7 m/s C) 2.2 m/s D) 39 m/s Answer: A Var: 50+

20) You throw a rock horizontally off a cliff with a speed of 20 m/s. After two seconds, 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 21) A child is sitting on the outer edge of a merry-go-round that is in diameter. If the merry-go-round makes what is the velocity of the child in A) 7.8 m/s B) 15.6 m/s C) 1.2 m/s D) 5.5 m/s Answer: A Var: 50+ Figure 3.3

A wind farm generator uses a two-bladed propeller mounted on a pylon at a height of 20 m. The length of each propeller blade is 12 m. A tip of the propeller breaks off when the propeller is vertical. The fragment flies off horizontally, falls, and strikes the ground at P. Just before the fragment broke off, the propeller was turning uniformly, taking 1.2 s for each rotation. 22) In Figure 3.3, the distance from the base of the pylon to the point where the fragment strikes the ground is closest to: A) 120 m B) 130 m C) 140 m D) 150 m E) 160 m Answer: E Var: 1

23) In Figure 3.3, the angle with respect to the vertical at which the fragment strikes the ground is closest to: A) 58° B) 63° C) 68° D) 73° E) 78° Answer: C Var: 1 24) Two particles, A and B, are in uniform circular motion about a common center. The acceleration of particle A is 4.7 times that of particle B. Particle B takes 2.4 times as long for a rotation as particle A. The ratio of the radius of the motion of particle A to that of particle B is closest to: A) 0.82 B) 2.0 C) 3.8 D) 0.51 E) 11 Answer: A Var: 50+ 25) You are taking a turn at 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 ramp of radius

What is your acceleration?

26) An aircraft performs a maneuver called an aileron roll. During this maneuver, the plane turns like a screw as it maintains a straight flight path, by using its ailerons to set the wings in circular motion. If it takes the plane to complete the circle and each wing length is what is the acceleration of the wing tip? A) 0.15 m/s2 B) 0.69 m/s2 C) 6.7 m/s2 D) 1.4 m/s2 Answer: A Var: 50+

27) An aircraft performs a maneuver called an aileron roll. During this maneuver, the plane turns like a screw as it maintains a straight flight path, by using its ailerons to set the wings in circular motion. Due to structural strength, the airplane can only withstand an acceleration of on its wing tips. If the wing span is what is the shortest time it can make a full turn when it performs an aileron roll? A) 6.6 s B) 6.0 s C) 1.1 s D) 9.4 s Answer: A Var: 50+ 3.2 Short Answer Questions 1) 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? (Use g = 9.80 m/ ) Answer: 27.4 m/s Var: 1 2) A rock is thrown from the roof of a building, with an initial velocity of 10.0 m/s at an angle of 30.0° above the horizontal. The rock is observed to strike the ground 43.0 m from the base of the building. What is the height of the building assuming no air drag? Answer: 96.0 meters Var: 1 3) 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 How long does it take for the merry-go-round to make one revolution? Answer: 5.1 seconds Var: 1 4) 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? Answer: 15.9 s Var: 1 5) A 5.00 kg stone is thrown upward at 7.50 m/s at an angle of 51.0° above the horizontal from the upper edge of a cliff, and it hits the ground 1.50 s later with no air drag. Find the magnitude of its velocity vector just as it reaches the ground. Answer: 10.0 m/s Var: 1 6) A projectile is thrown upward at 24.0° 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) 67.0 m/s, (b) 341 m, (c) 191 m Var: 1

College Physics, 11e (Young) Chapter 4 Newton's Laws of Motion 4.1 Multiple Choice Questions 1) A force of 1 Newton will cause a mass of 1 kg to have an acceleration of 1 m/ . Thus it follows that a force of 9 Newtons applied to a mass of 9 kg will cause it to acquire an acceleration of A) 1 m/ B) 0.11 m/ C) 10 m/ D) 9 m/ E) 81 m/ Answer: A Var: 8 2) A plastic ball in a liquid is acted upon by its weight and by a buoyant force. The weight of the ball is NaN N. The buoyant force has a magnitude of NaN N and acts vertically upward. An external force acting on the ball maintains it in a state of rest. The external force, including direction, is closest to: A) NaN N, downward B) NaN N, upward C) NaN N, upward D) NaN N, upward E) NaN N, downward Answer: A Var: 50+ 3) A plastic ball in a liquid is acted upon by its weight and by a buoyant force. The weight of the ball is 3.6 N. The buoyant force has a magnitude of 4.3 N and acts vertically upward. At a given instant, the ball is released from rest. The acceleration of the ball at that instant, including direction, is closest to: A) 1.9 m/ , upward B) 0.95 m/ , upward C) zero D) 0.95 m/ , downward E) 1.9 m/ , downward Answer: A Var: 50+

4) A plastic ball in a liquid is acted upon by its weight and by a buoyant force. The weight of the ball is 2.6 N. The buoyant force has a magnitude of 4.4 N and acts vertically upward. At a given instant, the ball has zero velocity. At that instant, an external force acting on the ball imparts an acceleration of 3.0 m/ in the downward direction of the ball. The external force, including direction, is closest to: A) 2.6 N, downward B) 1.8 N, upward C) 1.8 N, downward D) 9.6 N, upward E) 9.6 N, downward Answer: A Var: 50+ 5) Consider what happens when you jump up in the air. Which of the following is the most accurate statement? A) It is the upward force exerted by the ground that pushes you up, but this force can never exceed your weight. B) You are able to spring up because the earth exerts a force upward on you which is stronger than the downward force you exert on the earth. C) Since the ground is stationary, it cannot exert the upward force necessary to propel you into the air. Instead, it is the internal forces of your muscles acting on your body itself which propels the body into the air. D) When you push down on the earth with a force greater than your weight, the earth will push back with the same magnitude force and thus propel you into the air. Answer: D Var: 1

Figure 4.1

6) In Figure 4.1, a 10-lb weight is suspended from two spring scales, each of which has negligible weight. Thus 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 7) If you were to move into outer space far from any stars or planets, A) your mass would change, but your weight would not change. B) your weight would change, but your mass would not change. C) both your weight and mass would change. D) neither your weight nor your mass would change. E) None of these is true. Answer: B Var: 1

8) 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. The acceleration due to gravity at the surface of the moon 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+ 9) 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. The acceleration due to gravity at the surface of the moon is 1.62 m/ . A horizontal force of 5 N is applied to the block when it is on the moon. The acceleration imparted to the block 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+ 10) A block is on a frictionless table, on earth. The block accelerates at 8.5 m/ when a horizontal force is applied to it. The block and table are set up on the moon. The acceleration due to gravity at the surface of the moon is 1.62 m/ . A horizontal force, equal in magnitude to the weight of the block on earth, is applied to the block when it is on the moon. The acceleration imparted to the block is closest to: A) 10 m/ B) 4 m/ C) 6 m/ D) 8 m/ E) 2 m/ Answer: A Var: 50+

Figure 4.2

A 5.0 kg block and a 4.0 kg block are connected by a 0.6 kg rod. The links between the blocks and the rod are denoted by A and B. A force F is applied to the upper block. 11) In Figure 4.2, the blocks and rod assembly move downward at constant velocity. The applied force F is closest to: A) 88 N B) 90 N C) 92 N D) 94 N E) 96 N Answer: D Var: 1 12) In Figure 4.2, the blocks and rod assembly move upward at constant velocity. The force in link A is closest to: A) 39 N B) 41 N C) 43 N D) 45 N E) 47 N Answer: D Var: 1 13) In Figure 4.2, the applied force F equals 150 N. The force in link B is closest to: A) 54 N B) 56 N C) 58 N D) 60 N E) 62 N Answer: E Var: 1

14) In Figure 4.2, the force in link B is 40 N. The acceleration of the blocks and rod assembly, including direction, is closest to: A) zero B) 1.2 m/ , upward C) 2.4 m/ , upward D) 1.2 m/ , downward E) 2.4 m/ , downward Answer: A Var: 1 15) A man pushes against a rigid, immovable wall. Which of the following is the most accurate statement concerning this situation? A) The man can never exert a force on the wall which exceeds his weight. B) If the man pushes on the wall with a force of 200 N, we can be sure that the wall is pushing back with a force of exactly 200 N on him. C) Since the wall cannot move, it cannot exert any force on the man. D) The man cannot be in equilibrium since he is exerting a net force on the wall. E) The friction force on the man's feet is directed to the left. Answer: B Var: 1 16) Bumpers on cars are not of much use in a collision. To see why, calculate the average force a bumper would have to exert if it brought a 1200 kg car (a so-called "compact" model) to a rest in 15 cm when the car had an initial speed of 2 m/s (about 4.5 mph). Bumpers are built with springs which compress to provide a stopping force without (hopefully) denting the metal. A) 1.8 × N B) 1.6 ×

C) 5.4 ×

D) 6.5 ×

E) 3.2 × N Answer: B Var: 1 17) What is the mass of an object that experiences a gravitational force of 685 N near Earth's surface? A) 69.9 kg B) 68.5 kg C) 71.3 kg D) 72.7 kg Answer: A Var: 50+

18) If I weigh 741 N on Earth and 5320 N on the surface of a nearby 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+ 19) As shown in Figure 4.3, a woman is straining to lift a large crate, without success. It is too heavy. We denote the forces on the crate as follows: P is the upward force being exerted on the crate by the person, C is the contact force on the crate by the floor, and W is the weight of the crate. Figure 4.3

How are the magnitudes of these forces related, while the person is trying unsuccessfully to lift the crate? Explain your reasoning. A) P + C = W B) P + C < W C) P + C > W D) P = C Answer: A Var: 1 20) Joe and Bill are playing tug-o-war. Joe is pulling with a force of 200 N. Bill is simply hanging on to the rope. Neither person is moving. What is the tension of the rope? A) 200 N B) 400 N C) 0 N D) 300 N Answer: A Var: 1

21) Joe and Bill are playing tug-o-war. Joe is pulling with a force of 200 N. Bill is simply hanging on, but skidding towards Joe at a constant velocity. What is the force of friction between Bill's feet and the ground? A) 200 N B) 400 N C) Less than 200 N D) Greater than 200 N, but less than 400 N Answer: A Var: 1 22) A person who normally weighs 200 pounds is standing on a scale inside an elevator. The elevator is moving upwards with a speed of 7 m/s, and then begins to slow down at a rate of 5 m/ . Before the elevator begins to slow down, the reading of the scale is _________, and while the elevator is slowing down, the reading of the scale is ________. A) 200 pounds, 100 pounds B) greater than 200 pounds, 100 pounds C) greater than 200 pounds, 0 pounds D) less than 200 pounds, 100 pounds E) none of the above Answer: A Var: 1 23) A small car and an SUV are at a stoplight. The car has a mass equal to half that of the SUV, and the SUV's engine can produce a maximum force equal to twice that of the car. When the light turns green, both drivers floor it at the same time. Which vehicle pulls ahead of the other vehicle after a few seconds? A) It is a tie. B) The car C) The SUV Answer: A Var: 1 24) An object is moving to the right in a straight line. The net force acting on the object is also directed to the right, but the magnitude of the force is decreasing with time. The object will A) continue to move to the right, with its speed increasing with time. B) continue to move to the right, with its speed decreasing with time. C) continue to move to the right with a constant speed. D) stop and then begin moving to the left. Answer: A Var: 1

25) A person gives a shopping cart an initial push along a horizontal floor to get it moving, and then lets go. The cart travels forward along the floor, gradually slowing as it moves. Consider the horizontal force(s) on the cart while it is moving forward and slowing. Which of the following statements is correct? A) Both a forward and a backward force are acting on the cart, but the forward force is larger. B) Both a forward and a backward force are acting on the cart, but the backward force is larger. C) Only a forward force is acting which diminishes with time. D) Only a backward force is acting, no forward force. Answer: D Var: 1 26) Two bodies P and Q on a perfectly smooth horizontal surface are connected by a light cord. The mass of P is greater than that of Q. A horizontal force 4.4, accelerating the bodies to the right.

is applied to Q as shown in Figure

Figure 4.4

The magnitude of the force exerted by the connecting cord on body P will be A) zero. B) less than F but not zero. C) equal to F. D) greater than F. Answer: B Var: 1 27) Two blocks, A and B, are being pulled to the right along a horizontal surface by a horizontal 100 N pull, as shown in Figure 4.5. 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 freebody diagram of the horizontal forces acting on upper block, A?

Figure 4.5

A) B) C) D) E) Answer: E Var: 1 28) Two blocks, A and B, are being pulled to the right along a horizontal surface by a horizontal 100 N pull, as shown in Figure 4.5. 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 freebody diagram of the horizontal forces acting on lower block, B? A)

B) C) D) E) None of these diagrams is correct. Answer: B Var: 1

29) An object that weighs 75.0 N is pulled on a horizontal surface by a horizontal pull of 50.0 N to the right. The friction force on this object is 30.0 N to the left. The acceleration of the object is closest to A) 0.267 m/s2 B) 1.07 m/s2 C) 2.61 m/s2 D) 10.5 m/s2 Answer: C Var: 1 30) In addition to gravity, a falling object is subject to a constant air drag equal to 1/10 of its weight. Its acceleration is A) 0.10 g B) 0.90 g C) g D) 1.1 g Answer: B Var: 1 4.2 Short Answer Questions Figure 4.6

1) In Figure 4.6, the three forces shown on the diagram act on an object at the origin. Find the magnitude and direction of the resultant of these forces. Express the direction by giving the angle that the resultant force makes with the positive x-axis, and take counterclockwise angles to be positive. Answer: magnitude: R = 720 N direction: Φ = Var: 1

2) A box of mass 72 kg is at rest on a horizontal frictionless surface. A constant horizontal force F then acts on the box, and accelerates it to the right. It is observed that it takes the box 3.4 seconds to travel 13 meters. What is the magnitude of the force? Answer: 160 N Var: 50+ 3) A locomotive is pulling 9 freight cars, each of which is loaded with roughly the same weight. The mass of each can be taken to be If the train is accelerating 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. Answer: 210,000 N Var: 50+ Figure 4.7

4) In Figure 4.7, two blocks are connected by a string, as shown, and the upper block is pulled upward by a different string. The masses of the upper and lower blocks are 300 grams and 240 grams respectively. The string between the blocks will break if its tension exceeds 3.6 newtons, and the string which pulls the combination upward will break if its tension exceeds 7.8 newtons. a) What is the largest upward acceleration that the blocks can be given without either string breaking? (Take g = 9.8 m/ .) b) If the upward acceleration is slightly higher than this, which string breaks? Answer: a) 4.6m/ b) upper string. Var: 1 5) A 10.0 kg object is hanging by a massless rope in an elevator that is traveling upward. The tension in the rope is measured to be 75.0 N. What are the magnitude and direction of the acceleration of the elevator? Answer: 2.30 m/s2, downward Var: 1

College Physics, 11e (Young) Chapter 5 Applications of Newton's Laws 5.1 Multiple Choice Questions 1) Figure 5.1 shows two forces acting on an object. They have magnitudes 3.2 N. What third force will cause the object to be in equilibrium? Figure 5.1

A) 10 N at 162° counterclockwise from B) 10 N at 108° counterclockwise from C) 6.4 N at 162° counterclockwise from D) 6.4 N at 108° counterclockwise from Answer: A Var: 24

= 9.6 N and

2) Figure 5.2 shows two forces of equal magnitude acting on an object. If the common magnitude of the forces is 2.3 N and the angle between them is 40°, what third force will cause the object to be in equilibrium? Figure 5.2

A) 4.3 N pointing to the right B) 3.5 N pointing to the right C) 2.2 N pointing to the right D) 1.8 N pointing to the right Answer: A Var: 50+

3) A piano mover raises a 100 kg piano at a constant rate using a frictionless pulley system, as shown in Figure 5.3. With roughly what force is the mover pulling down on the rope? Figure 5.3

A) 2000 N B) 1000 N C) 500 N D) 250 N E) Depends on the velocity! Answer: C Var: 1

Figure 5.4

4) Dick and Jane stand on a platform of negligible weight, as shown in Figure 5.4. Dick weighs 500 N and Jane weighs 400 N. Jane is supporting some of her weight on the end of the rope she is holding. What is the downward force she is exerting on the platform? A) 0 B) 50 N C) 100 N D) 240 N E) 300 N Answer: C Var: 1

Figure 5.5

Three forces A, B, and C act on a body as shown. A fourth force F is required to keep the body in equilibrium. 5) In Figure 5.5, the x-component of force F is closest to: A) +19 N B) +28 N C) +32 N D) -28 N E) -32 N Answer: C Var: 1 6) In Figure 5.5, the y-component of force F is closest to: A) +24 N B) +28 N C) +32 N D) -28 N E) -32 N Answer: A Var: 1

Figure 5.6

7) A 6.0 kg box is held at rest by two ropes that form 30° angles with the vertical. An external force F acts vertically downward on the box. The force exerted by each of the two ropes is denoted by T. A force diagram, showing the four forces that act on the box in equilibrium, is shown in Figure 5.6. The magnitude of force F is 410 N. The magnitude of force T is closest to: A) 271 N B) 235 N C) 188 N D) 376 N E) 470 N Answer: A Var: 50+ 8) A 3.6 kg box is held at rest by two ropes that form 30° angles with the vertical. An external force F acts vertically downward on the box. The force exerted by each of the two ropes is denoted by T. A force diagram, showing the four forces that act on the box in equilibrium, is shown in Figure 5.6. The force F is adjusted so that the magnitude of force T is equal to the weight w. The magnitude of force F, for which this occurs, is closest to: A) 26 N B) 27 N C) 28 N D) 29 N E) 30 N Answer: A Var: 50+

Figure 5.7

9) A box with weight 74 N is on a rough horizontal surface. An external force F is applied horizontally to the box. A normal force and a friction force are also present, denoted by n and f. A force diagram, showing the four forces that act on the box, is shown in Figure 5.7. When force F equals 4.8 N, the box is in motion at constant velocity. When force F equals 6.24 N, the acceleration of the box is closest to: A) 0.19 m/ B) 0.23 m/ C) 0.26 m/ D) 0.29 m/ E) 0.32 m/ Answer: A Var: 50+ 10) A box with weight 40 N is on a rough horizontal surface. An external force F is applied horizontally to the box. A normal force and a friction force are also present, denoted by n and f. A force diagram, showing the four forces that act on the box, is shown in Figure 5.7. When force F equals 8.8 N, the box is in motion at constant velocity. The box decelerates when force F is removed. The magnitude of the acceleration of the box is closest to: A) 2.2 m/ B) 1.7 m/ C) 1.1 m/ D) 0.55 m/ E) zero Answer: A Var: 50+

Figure 5.8

11) In Figure 5.8, a block of mass M hangs in equilibrium. The rope which is fastened to the wall is horizontal and has a tension of 38 N. The rope which is fastened to the ceiling has a tension of and makes an angle Θ with the ceiling. The angle Θ is A) 50° B) 40° C) 33° D) 65° E) 45° Answer: A Var: 50+

Figure 5.9

12) In Figure 5.9, a certain type of string will break if the tension in the string exceeds 300 N. A number of weights are hung one below the other from a hook in the ceiling using this string. The number of weights which causes the string to break and the string segment which will break are as follows: A) When the 4th weight is added, the top string segment will break. B) Each segment has a tension of 78.4 N, and there is no limit to the number of weights which can be suspended. C) When the 4th weight is added, the bottom string segment will break. D) When the 4th weight is added, all string segments will break. E) When the 38th weight is added, all string segments will break. Answer: A Var: 23 13) Figure 5.10 shows a 4,800 kg cable car descending a high hill. A counterweight of mass 4,600 kg on the other side of the hill aids the breaks in controlling the cable car's speed. The rolling friction of both the cable car and the counterweight are negligible. How much braking force does the cable car need to descend at constant speed? Figure 5.10

A) 8,100 N B) 5,800 N C) 3,500 N D) 980 N Answer: A Var: 50+

14) A device has a 100 g wooden shuttle that is pulled horizontally along a square frictionless wooden rail by an elastic band. The shuttle is released when the elastic band has 6.4 N tension at a angle. What is the magnitude of the initial acceleration of the shuttle? (See Figure 5.11.) Figure 5.11

A) 52 m/ B) 37 m/ C) 64 m/ D) 62 m/ Answer: A Var: 50+ 15) A 10.0 kg block on a table is connected by a string to a 63 kg mass, which is hanging over the edge of the table. Assuming that frictional forces may be neglected, what is the magnitude of acceleration of the block when the other block is released? (See Figure 5.12.) Figure 5.12

A) 8.5 m/s2 B) 8.1 m/s2 C) 7.5 m/s2 D) 9.0 m/s2 Answer: A Var: 1

16) A 15 kg block is on a ramp which is inclined at 20° above the horizontal. It is connected by a string to a 19 kg mass which hangs over the top edge of the ramp. Assuming that frictional forces may be neglected, what is the magnitude of the acceleration of the 19 kg block? (See Figure 5.13.) Figure 5.13

A) 4.0 m/s2 B) 3.8 m/s2 C) 4.2 m/s2 D) 4.5 m/s2 Answer: A Var: 1 17) A tightrope walker walks across a wire tied between two poles. The center of the wire is displaced vertically downward by 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+

Figure 5.14

Three blocks, connecting ropes, and a light frictionless pulley comprise a system, as shown. An external force P is applied downward on block A. The system accelerates at the rate of 2.5 m/s2. The tension in the rope connecting block B and block C equals 60 N.

18) In Figure 5.14, the external force P is closest to: A) 170 N B) 190 N C) 210 N D) 230 N E) 250 N Answer: B Var: 1 19) In Figure 5.14, the tension in the rope connecting block A and block B is closest to: A) 240 N B) 260 N C) 280 N D) 300 N E) 320 N Answer: C Var: 1

20) In Figure 5.14, the mass of block C is closest to: A) 5 kg B) 7 kg C) 9 kg D) 11 kg E) 13 kg Answer: A Var: 1 Figure 5.15

A system comprising blocks, a light frictionless pulley, a frictionless incline, and connecting ropes is shown. The 9 kg block accelerates downward when the system is released from rest. 21) In Figure 5.15, the acceleration of the system is closest to: A) 1.5 m/ B) 1.7 m/ C) 1.9 m/ D) 2.1 m/ E) 2.3 m/ Answer: D Var: 1 22) In Figure 5.15, the tension in the rope connecting the 6 kg block and the 4 kg block is closest to: A) 30 N B) 33 N C) 36 N D) 39 N E) 42 N Answer: E Var: 1

23) A 22 kg box must be slid across the floor. If the coefficient of static friction between the box and floor is 0.37, what is the minimum force needed to start the box moving from rest? A) 80 N B) 216 N C) 56 N D) 112 N Answer: A Var: 18 24) A 53 N force is needed to slide a box across a flat surface at a constant velocity. 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+ 25) In a shuffleboard game, the puck slides a total of 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 26) 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 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 27) 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+

28) You push downward on a trunk at an angle 25° below the horizontal with a force of If the trunk is on a flat surface and the coefficient of static friction 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 29) Jason takes off across level water on his jet-powered skis. The combined mass of Jason and skis is 75 kg (the mass of the fuel is negligible). The skis have a thrust of 200 N and a coefficient of kinetic friction on water of 0.1. 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+ 30) Jason takes off across level water on his jet-powered skis. The combined mass of Jason and skis is 75 kg (the mass of the fuel is negligible). The skis have a thrust of 200 N and a coefficient of kinetic friction on water of 0.1. Unfortunately, the skis run out of fuel after only 41 s. How far has Jason traveled when he finally coasts to a stop? A) 3,900 m B) 2,900 m C) 2,000 m D) 1,400 m Answer: A Var: 50+ 31) A 200 g hockey puck is launched 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 and respectively. The puck's initial speed is 16 m/s. 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+

32) Figure 5.16 shows a 100 kg block being released from rest from a height of 1.0 m. It then takes 0.53 s to reach the floor. What is the mass of the block on the left? There is no friction or mass in the pulley. Figure 5.16

A) 16 kg B) 14 kg C) 13 kg D) 11 kg Answer: A Var: 50 33) Figure 5.17 shows a block of mass m resting on a 20° slope. The block has coefficients of friction and with the surface. It is connected via a massless string over a massless, frictionless pulley to a hanging block of mass 2.0 kg. What is the minimum mass m that will stick and not slip? Figure 5.17

A) 2.1 kg B) 3.3 kg C) 1.3 kg D) 3.6 kg Answer: A Var: 50+

Figure 5.18

A system comprising blocks, a light frictionless pulley, and connecting ropes is shown. The 9 kg block is on a smooth horizontal table The surfaces of the 12 kg block are rough, with μk = 0.30. 34) In Figure 5.18, the mass M is set so that it descends at constant velocity when released. The mass M is closest to: A) 2.4 kg B) 2.7 kg C) 3.0 kg D) 3.3 kg E) 3.6 kg Answer: E Var: 1 35) In Figure 5.18, mass M is set at 5.0 kg. It accelerates downward when it is released. The acceleration of mass M is closest to: A) 1.0 m/ B) 1.2 m/ C) 1.4 m/ D) 1.6 m/ E) 1.8 m/ Answer: A Var: 1

Figure 5.19

36) Block A of mass 7 kg and block X are attached to a rope which passes over a pulley. A 60 N force is applied horizontally to block A, keeping it in contact with a rough vertical face. The coefficients of static and kinetic friction are and The pulley is light and frictionless. In Figure 5.19, the mass of block X is set so that block A is on the verge of slipping upward. The mass of block X is closest to: A) 9.4 kg B) 9.9 kg C) 9.0 kg D) 8.5 kg E) 8.0 kg Answer: A Var: 50+ 37) Block A of mass 4 kg and block X are attached to a rope which passes over a pulley. A 40 N force is applied horizontally to block A, keeping it in contact with a rough vertical face. The coefficients of static and kinetic friction are and The pulley is light and frictionless. In Figure 5.19, the mass of block X is set at 9.5 kg. The system is at rest. The friction force, including direction, on the 5 kg block is closest to: A) 54 N, downward B) 54 N, upward C) 27 N, downward D) 27 N, upward E) zero Answer: A Var: 50+

38) Block A of mass 3 kg and block X are attached to a rope which passes over a pulley. A 20 N force is applied horizontally to block A, keeping it in contact with a rough vertical face. The coefficients of static and kinetic friction are and The pulley is light and frictionless. In Figure 5.19, the mass of block X is set so that block A descends at constant velocity when it is set into motion. The mass of block X is closest to: A) 2.4 kg B) 2.7 kg C) 3.0 kg D) 3.3 kg E) 3.6 kg Answer: A Var: 50+ 39) Block A of mass 3 kg and block X are attached to a rope which passes over a pulley. A 100 N force is applied horizontally to block A, keeping it in contact with a rough vertical face. The coefficients of static and kinetic friction are and The pulley is light and frictionless. In Figure 5.19, the mass of block X is set so that block A moves upward with an acceleration of The mass of block X is closest to: A) 7.8 kg B) 7.3 kg C) 6.9 kg D) 6.4 kg E) 5.9 kg Answer: A Var: 50+

Figure 5.20

40) Blocks A and B of masses 10 kg and 7 kg, respectively, are connected by a rope, which passes over a light frictionless pulley, as shown. The horizontal surface is rough. The coefficients of static and kinetic friction are 0.40 and 0.20, respectively. External forces P and Q act on block B, as shown. In Figure 5.20, force P equals 28 N. The maximum value of force Q, for which the system remains at rest is closest to: A) 140 N B) 120 N C) 98 N D) 110 N E) 130 N Answer: A Var: 50+ 41) Blocks A and B of masses 18 kg and 19 kg, respectively, are connected by a rope, which passes over a light frictionless pulley, as shown. The horizontal surface is rough. The coefficients of static and kinetic friction are 0.40 and 0.20, respectively. External forces P and Q act on block B, as shown. In Figure 5.20, force P equals 76 N. The force Q for which the block descends at constant speed is closest to: A) 120 N B) 130 N C) 140 N D) 160 N E) 72 N Answer: A Var: 50+

42) Blocks A and B of masses 14 kg and 15 kg, respectively, are connected by a rope, which passes over a light frictionless pulley, as shown. The horizontal surface is rough. The coefficients of static and kinetic friction are 0.40 and 0.20, respectively. External forces P and Q act on block B, as shown. In Figure 5.20, force Q equals zero. The force P, for which block B is on the verge of moving, is closest to: A) 200 N B) 540 N C) 310 N D) 1,200 N E) 400 N Answer: A Var: 50+ 43) An object of weight W falls from rest subject to a frictional drag force ("terminal") velocity will it approach if W = 4 N and b = 3 N∙ A) 1.78 m/s B) 3.42 m/s C) 1.15 m/s D) 2.25 m/s E) 0.75 m/s Answer: C Var: 1 44) A force of constant? A) 41 N/m B) 22 N/m C) 34 N/m D) 46 N/m Answer: A Var: 50+

stretches a spring

45) A spring stretches by that would stretch the spring by A) 289 N B) 63 N C) 176 N D) 405 N Answer: A Var: 50+

when a

. What maximum

/m?

from equilibrium. What is the value of the spring

object is attached. What is the weight of a fish

46) An object attached to a spring is pulled across a frictionless surface. If the spring constant is and the spring is stretched by 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 5.2 Short Answer Questions 1) Jack is pulling a sled to haul firewood up a snowy hill to his cabin. The slope of the hill is 22° from the horizontal, the sled has a mass of 16 kg, the coefficient of kinetic friction between the sled runners and the snow is 0.13, and Jack can exert a force of 1400 newtons parallel to the surface of the hill. What is the largest load of wood (in kilograms) that Jack can take in one trip? (Use g = 9.8 m/ .) Answer: 270 kg Var: 1 Figure 5.21

2) In Figure 5.21, a block of mass 7.0 kg on a tabletop is attached by strings to vertically hanging masses, 12 kg and 10 kg, as shown. The strings and pulleys are massless, the pulleys are frictionless, but the coefficient of kinetic friction between the block and the tabletop is 0.10. Describe the motion of the block, including the magnitude and direction of the acceleration. Answer: acceleration = 0.44 m/ ; the block accelerates to the left. Var: 1 3) A 200 g hockey puck is launched up a metal ramp that is inclined at a 30° angle. The coefficients of static and kinetic friction between the puck and the ramp are µs = 0.40 and µk = 0.30, 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 4) Three objects are connected by weightless flexible strings as shown in Figure 5.22. 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 µs = 0.660 and µk = 0.325. You observe that this system remains at rest. Find (a) the mass of A and (b) the friction force on the block on the bench. Figure 5.22

Answer: (a) 22.0 kg, (b) 267 N Var: 1 5) A weightless spring of force constant 2.50 N/cm is 15.0 cm long when nothing is attached to it. It is now used to pull horizontally on a 12.5 kg box on a smooth horizontal floor. You observe that the box starts from rest and moves 96.0 cm during the first 1.60 s of its motion. How long is the spring during this motion? Answer: 18.8 cm Var: 1

College Physics, 11e (Young) Chapter 6 Circular Motion and Gravitation 6.1 Multiple Choice Questions 1) A person ties a rock to a string and whirls it around in a vertical circle such that sometimes the rock is going straight upward and sometimes the rock is going straight down. She whirls the rock at the minimum speed (constant in time) such that the string is always taut (no sag). If she were to use a longer string, she would have to whirl the rock at a A) higher velocity. B) lower velocity. C) the same velocity. Answer: A Var: 1 2) A person ties a rock to a string and whirls it around in a vertical circle such that sometimes the rock is going straight upward and sometimes the rock is going straight down. She whirls the rock at the minimum speed (constant in time) such that the string is always taut (no sag). When is the tension the highest? A) It is highest when the rock is at the lowest elevation. B) It is highest when the rock is at the highest elevation. C) The tension is constant as the rock moves around in a circle. Answer: A Var: 1 3) A 76 kg mass is connected to a nail on a frictionless table by a (massless) string of length If the tension in the string is while the mass moves in a uniform circle on the table, how long does it take for the mass to make one complete revolution? A) 8.7 s B) 7.0 s C) 8.1 s D) 9.5 s Answer: A Var: 50+ 4) A new 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) 13.2 m/s B) 14.5 m/s C) 10.1 m/s D) 14.9 m/s Answer: A Var: 50+

5) A tetherball is on a string which makes an angle of 56° with the vertical as it moves around the pole in a horizontal plane. If the mass of the ball is what is the ball's speed? A) 5.0 m/s B) 4.0 m/s C) 4.6 m/s D) 5.7 m/s Answer: A Var: 50+ 6) A merry-go-round is spinning at a fixed rate. As a person is walking toward the edge, A) the force of static friction must increase in order for the person not to slide off. B) the force of static friction must decrease in order for the person not to slide off. C) the force of static friction such that the person does not slide off remains the same. Answer: A Var: 1 7) You need to make a sharp turn on a flat road, making a radius of curvature of 15 meters. How does the required force of static friction between your tires compare if you make the turn at 30 mph vs. 60 mph? A) The force of friction needs to be four times as large. B) The force of friction needs to be twice as large. C) the force of friction is the same for both speeds since the radius of curvature is the same. D) None of the above Answer: A Var: 1 8) A roadway is designed for traffic moving at a speed of 66 m/s. A curved section of the roadway is a circular arc of 290 m radius. The roadway is banked—so that a vehicle can go around the curve—with the lateral friction forces equal to zero. The angle at which the roadway is banked is closest to: A) 57° B) 59° C) 55° D) 53° E) 51° Answer: A Var: 50+

9) A roadway is designed for traffic moving at a speed of 94 m/s. A curved section of the roadway is a circular arc of 740 m radius. The curved section is temporarily replaced with an unbanked roadway of the same radius. The coefficient of friction of this roadway is 0.40. The maximum safe driving speed for this unbanked, curved section is closest to: A) 54 m/s B) 52 m/s C) 50 m/s D) 48 m/s E) 46 m/s Answer: A Var: 50+ Figure 6.1

10) A ball of mass 8.0 kg is suspended by two wires from a horizontal arm, which is attached to a vertical shaft, as shown in Figure 6.1. The shaft is in uniform rotation about its axis such that the linear speed of the ball equals 2.3 m/s. The tension in wire 1 is closest to: A) 39 N B) 49 N C) 29 N D) 20 N E) 9.8 N Answer: A Var: 50+

11) A ball of mass 6.0 kg is suspended by two wires from a horizontal arm, which is attached to a vertical shaft, as shown in Figure 6.1. The shaft is in uniform rotation about its axis such that the linear speed of the ball equals 1.5 m/s. The tension in wire 2 is closest to: A) 21 N B) 17 N C) 25 N D) 28 N E) 32 N Answer: A Var: 50+ 12) A ball of mass 7.0 kg is suspended by two wires from a horizontal arm, which is attached to a vertical shaft, as shown in Figure 6.1. The shaft is in uniform rotation about its axis such that the linear speed of the ball equals 2.2 m/s. The rate of rotation is adjusted so that the tensions in the two wires are equal. The radial acceleration of the ball is closest to: A) 5 m/ B) 6 m/ C) 7 m/ D) 8 m/ E) 10 m/ Answer: A Var: 50+ 13) In an amusement park ride passengers stand inside an 8 m radius cylinder. Initially the cylinder rotates with its axis oriented along the vertical. After the cylinder has acquired sufficient speed, it tilts into a vertical plane, that is, the axis tilts into the horizontal, as shown in Figure 6.2. Suppose that, once the axis has tilted into the horizontal, the ring rotates once every . If a rider's mass is 40 kg, with how much force does the ring push on her at the top of the ride?

Figure 6.2

A) 230 N B) 620 N C) 1,000 N D) 390 N Answer: A Var: 50+ 14) Future space stations will create an artificial gravity by rotating. Consider a cylindrical space station of 380 m diameter rotating about its axis. Astronauts walk on the inside surface of the space station. What rotation period will provide "normal" gravity? A) 28 s B) 39 s C) 6.2 s D) 4.4 s Answer: A Var: 50+ 15) A 90 g bead on a 60 cm long string is swung in a vertical circle about a point 200 cm above the floor. The tension in the string when the bead is at the very bottom of the circle is 2.2 N. A very sharp knife is suddenly inserted, as shown in Figure 6.3, to cut the string directly below the point of support. How far to the right of the center of the circle does the ball hit the floor?

Figure 6.3

A) 160 cm B) 200 cm C) 240 cm D) 190 cm Answer: A Var: 40 16) Figure 6.4 shows a 3.0 kg ball tied to the end of a 50 cm long string being swung in a circle in a vertical plane at constant speed. The center of the circle is above the floor. The ball is swung at the minimum speed necessary to make it over the top without the string going slack. If the string is released at the instant the ball is at the top of the loop, how far to the right of the center of the circle does the ball hit the ground?

Figure 6.4

A) 240 cm B) 230 cm C) 210 cm D) 0.0 cm Answer: A Var: 50+

17) Figure 6.5 shows two wires that are tied to a 150 g mass which revolves in a horizontal circle at a constant speed of 7.5 m/s. What is the tension in the upper wire?

A) 7.1 N B) 4.2 N C) 5.7 N D) 8.6 N Answer: A Var: 50+

18) Figure 6.6 shows two wires tied to a 8.8 kg sphere which revolves in a horizontal circle at constant speed. At this particular speed the tension is the same in both wires. What is the tension?

A) 63 N B) 86 N C) 120 N D) 59 N Answer: A Var: 50+ 19) The gravitational acceleration at the surface of planet X is 11.6 m/ , and the radius of the planet is 66,500 km. The altitude above the surface of planet X at which the weight of a body is equal to that on the surface of the earth, in km, is closest to: A) 5,800 B) 7,000 C) 8,200 D) 9,400 E) 11,000 Answer: A Var: 50+ 20) At a given point above the surface of the earth, the gravitational acceleration is equal to The altitude of this point, above the surface of the earth, in km, is closest to: A) 770 B) 970 C) 1,500 D) 2,000 E) 2,400 Answer: A Var: 39

21) What is the gravitational force acting on a person due to another person standing 2 meters away? Assume each individual has 59 kg mass. 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+ Table 6.1 gravitational acceleration at the surface

orbital period

Moon I

orbital radius 5× m

Moon II

9×

3×

2×

radius

Moon III

2×

0.20 m/

An Earth station receives data transmitted back in time from a future intergalactic expedition. Table 6.1 summarizes the data for the moons of a planet that will be discovered in a distant galaxy. 22) In Table 6.1, the mass of the planet is closest to: A) 1.2 × kg B) 1.7 ×

C) 2.4 ×

D) 3.4 ×

E) 4.8 × Answer: E Var: 1

23) In Table 6.1, the mass of Moon III is closest to: A) 2.4 × kg B) 4.8 ×

C) 1.2 ×

D) 2.4 ×

E) 4.8 × Answer: C Var: 1

24) In Table 6.1, the centripetal acceleration of Moon II due to orbital motion is closest to: A) 0.02 m/ B) 0.04 m/ C) 0.06 m/ D) 0.08 m/ E) 0.10 m/ Answer: B Var: 1 Table 6.2

Ekapluto is an unknown planet that has two moons in circular orbits. Table 6.2 summarizes the hypothetical data about the moons. 25) In Table 6.2, the mass of Ekapluto is closest to: A) 1 × kg B) 3 ×

C) 1 ×

D) 3 ×

E) 1 × kg Answer: D Var: 1

26) In Table 6.2, the maximum gravitational force between the two moons is closest to: A) 1.6 × N B) 4.4 ×

C) 1.0 ×

D) 2.0 ×

E) 4.0 × Answer: E Var: 1

27) In Table 6.2, a meteoroidal fragment is in circular orbit around Moon B, at a small altitude above the surface. The speed of this body is closest to: A) 220 m/s B) 320 m/s C) 440 m/s D) 640 m/s E) 880 m/s Answer: A Var: 1 28) In Table 6.2, the gravitational acceleration at the surface of Moon B is closest to: A) 0.10 m/ B) 0.15 m/ C) 0.20 m/ D) 0.25 m/ E) 0.30 m/ Answer: D Var: 1 29) 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

30) From what height off the surface of the Earth should an object be dropped to initially experience an acceleration of A) 2,298 km B) 1,689 km C) 5,426 km D) 2,930 km Answer: A Var: 46 31) An astronaut is in equilibrium when he is positioned from planet X and from planet Y, along the straight line joining the planets' centers. What is the ratio of the masses X/Y? A) 0.382 B) 2.62 C) 0.618 D) 1.62 Answer: A Var: 50+ 32) If we assume that an electron is orbiting a proton just like the moon orbits the Earth, find the electron's orbital speed due to the gravitational attraction between itself and the proton. Take the orbital radius as (This is a very wrong assumption to make.) A) 3.33 × 10-14 m/s B) 1.11 × 10-13 m/s C) 1.11 × 10-27 m/s D) 1.06 × 10-27 m/s Answer: A Var: 1 33) Suppose we want a satellite to revolve around the Earth 5 times a day. What should the radius of its orbit be? (Neglect the presence of the moon.) A) 1.44 × 107 m B) 0.69 × 107 m C) 7.22 × 107 m D) 2.11 × 107 m Answer: A Var: 9

34) Spaceman Speff orbits planet X with his spaceship. To remain in orbit at from the planet's center, he should maintain a speed of What is the mass of planet X? A) 2.8 × 1019 kg B) 4.2 × 1017 kg C) 2.8 × 1016 kg D) 4.2 × 1014 kg Answer: A Var: 50+ 35) A proton moving at 0.999 of the speed of light orbits a black hole of the attractor. What is the mass of the black hole? A) 6.71 × 1033 kg B) 6.71 × 1030 kg C) 6.71 × 1036 kg D) 6.71 × 1025 kg Answer: A Var: 50+

from the center

36) Find the orbital speed of an ice cube in the rings of Saturn, if the mass of Saturn is and the rings have an average radius of A) 19.5 km/s B) 27.5 km/s C) 13.8 km/s D) 1.95 km/s Answer: A Var: 1 37) 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? A) (a) 2.4 kg × kg, (b) 1.2 kg × kg B) (a) 4.3 kg ×

kg, (b) 1.2 kg ×

C) (a) 2.4 kg ×

kg, (b) 7.1 kg ×

D) (a) 4.3 kg × Answer: A Var: 50+

kg, (b) 7.1 kg ×

38) If you stood on a planet having a mass four times higher than Earth's mass, and a radius two times longer than 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 39) 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 would be A) V B) 2V C) V D) V/ E) V/2 Answer: D Var: 1 40) 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 would be A) 4T B) 2T C) T D) T/2 E) T/4 Answer: C Var: 1 6.2 Short Answer Questions 1) A tobogganer coasts down a hill and then goes over a slight rise with speed 2.7 m/s. The top of this rise can be taken to be a circle of radius 4.1 m. The toboggan and occupant have a combined mass of 110 kg. If the coefficient of kinetic friction between the snow and the toboggan is 0.10, what frictional force is exerted on the toboggan by the snow as the toboggan goes over the top of the rise? Start with a free-body diagram of the toboggan with the person inside, at the top of the rise. Answer: 88 N Var: 1

2) A Ferris wheel has radius 5.0 m and makes one revolution in 8.0 seconds. A person weighing 670 N is sitting on one of the benches attached at the rim of the wheel. What is the apparent weight (the 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 3) What is the difference in the weight of a 117 kg person as measured at sea level and at the top of the Vinson Massif, the highest peak in Antarctica? The product the radius of the Earth is and the height above sea level of the Vinson Massif is poles. Answer: 1.85 N Var: 50+

Neglect the flattening of the Earth at the

4) A man-made satellite of mass 8,410 kg is in orbit around the earth, making one revolution in 927 minutes. What is the magnitude of the gravitational force exerted on the satellite by the earth? (The mass of the earth is Answer: 3.4 × 103 N Var: 50+ 5) A 1500 kg point mass (A) and a 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 masses 20.0 cm from B along the line connecting A and B and then released. Find the magnitude and direction (toward A or toward B) of the acceleration of the third mass just after it is released. Answer: 1.84 × 10-6 m/s2, toward B Var: 1

College Physics, 11e (Young) Chapter 7 Work and Energy 7.1 Multiple Choice Questions 1) In the absence of friction, how much work would a child do while pulling a distance of with a force? A) 95 J B) 52 J C) 67 J D) 109 J Answer: A Var: 33

wagon a

2) A child does 350 J of work while pulling a box from the ground up to his tree house with a 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 velocity across a room. How much work do you do on the bag in the process? A) 0.0 J B) 82 J C) 185 J D) 157 J Answer: A Var: 50+ 4) 300 J of work are required 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

steel beam vertically upward a distance of

the crane do on the beam if the beam accelerates upward at A) 4.7 × 105 J B) 2.7 × 105J C) 3.2 × 105 J D) 4.0 × 105 J Answer: A Var: 50+

How much work does Neglect frictional forces.

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 spring with a spring constant of 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 equilibrium to

8) 87 J of work are needed to stretch a spring from value of the spring constant? A) 27 N/m B) 77 N/m C) 52 N/m D) 39 N/m Answer: A Var: 50+

How much

from equilibrium. What is the

9) A car drives 5.0 km north, then

east, then

northeast, all at a constant velocity. If

the car had to perform of work during this trip, what was the magnitude of the average frictional force on the car? A) 1.4 × 102 N B) 2.0 × 102 N C) 2.6 × 102 N D) 3.0 × 102 N Answer: A Var: 50+ 10) You do 116 J of work while pulling your sister back on a swing, whose chain is 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+ 11) How much work must be done by frictional forces in slowing a to 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+ 12) 4.00 × 105 J of work are done on a final velocity. Find this final velocity. A) 28.0 m/s B) 22.4 m/s C) 25.2 m/s D) 30.8 m/s Answer: A Var: 50+

car while it accelerates from

long,

car from

to some

13) A 1000.0 kg car experiences a net force of while decelerating from How far does it travel while slowing down? A) 34 m B) 31 m C) 37 m D) 41 m Answer: A Var: 50+ 14) A child pulls on a wagon with a force of If the wagon moves a total of what is the average power generated by the child, in watts? A) 17 W B) 21 W C) 22 W D) 26 W Answer: A Var: 29 15) If electricity costs 7.06 cents/kWh, how much would it cost you to run a system per day for A) $0.95 B) $0.14 C) $1.62 D) $2.66 Answer: A Var: 50+

stereo

16) A 1,321 kg car climbs a 5.0° slope at a constant velocity of Assuming that air resistance may be neglected, at what rate must the engine deliver energy to the drive wheels of the car? Express your answer in kW. A) 25 kW B) 287 kW C) 38 kW D) 48 kW Answer: A Var: 50+

17) Find the net work done by friction between the ground and the body of a snake slithering in a complete circle of radius. The coefficient of friction between the ground and the snake is 0.25, and the snake's weight is A) 190 J B) 0 J C) 1,800 J D) 370 J Answer: A Var: 50+ 18) A tennis ball bounces on the floor three times. If each time it loses 23.0% of its energy due to heating, how high does it bounce after the third time, provided we released it from the floor? A) 180 cm B) 18 cm C) 180 mm D) 240 cm Answer: A Var: 50+ 19) A 28 g bullet pierces a sand bag thick. If the initial bullet velocity was and it emerged from the sandbag with what is the magnitude of the friction force (assuming it to be constant) 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+ 20) Three cars (car F, car G, and car H) are moving with the same velocity, and slam on the brakes. The most massive car is car F, and the least massive is car H. Assuming all three cars have identical tires, 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

21) Three cars (car L, car M, and car N) are moving with the same velocity, and slam on the brakes. The most massive car is car L, and the least massive is car N. Assuming all three cars have identical tires, for which car is the amount of work done by friction in stopping it the highest? 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 22) Three cars with identical engines and tires start from rest, and accelerate at their maximum rate. Car X is the most massive, and car Z is the least massive. Which car needs to travel the furthest distance before reaching a speed of 60 mi/h? A) Car X B) Car Y C) Car Z D) All cars need to travel the same distance, although some cars will take longer than other cars. Answer: A Var: 1 23) 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. Which statement is true? A) Ignoring friction and wind resistance, 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) Ignoring friction and wind resistance, 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) Ignoring friction and wind resistance, Bob and Joe exerted the same amount of work, and the average power of each cyclist was also the same. D) Ignoring friction and wind resistance, the average power exerted by Bob and Joe was the same, but Joe exerted more work in getting there. Answer: A Var: 1 24) A 1000.0 kg car is moving at 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+

If a

truck has 23 times the kinetic energy of

25) A prankster drops a water balloon from the top of a building on an unsuspecting person on the sidewalk below. If the balloon is traveling at when it strikes a person's head ( above the ground), how tall is the building? Neglect air resistance. A) 44 m B) 43 m C) 46 m D) 47 m Answer: A Var: 50+ 26) If a ball is released from a window ledge, how fast will it be travelling when it reaches the ground, below? A) 37 m/s B) 74 m/s C) 304 m/s D) 1.38 km/s Answer: A Var: 50+ 27) A horizontal spring-mass system oscillates on a frictionless table. If the ratio of the mass to the spring constant is and the maximum speed of the mass was measured to be find the maximum extension of the spring. A) 3.8 m B) 3.8 cm C) 0.57 m D) 57 cm Answer: A Var: 50+ 28) A block slides down a frictionless inclined ramp. If the ramp angle is 17.0° and the length of it is find the speed of the block as it reaches the end 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+

29) 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. Assuming the elevation loss of the three rocks is the same (the base of the cliff is flat), which rock hits the ground with the highest speed? A) They all hit the ground with the same speed. B) Rock X C) Rock Y D) Rock Z Answer: A Var: 1 30) Sue and Betti both ski straight down a hill, both starting from rest. Sue weighs more than Betti. Neglecting friction and wind resistance, which skier will be moving the fastest at the bottom of the hill? A) They will be moving with the same speed. B) Sue C) Betti Answer: A Var: 1 31) Joe and Bill throw identical balls vertically upward. Joe throws his ball with an initial speed twice as high as Bill. 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 1.3 times that of Bill's ball. Answer: A Var: 1

32) A ball can be rolled down one of four different ramps, as shown in Figure 7.1. The final elevation loss of each of the ramps is the same. Neglecting friction, for which ramp will the speed of the ball be the highest at the bottom? Figure 7.1

A) The speed of the ball will be the same for all ramps. B) Ramp X C) Ramp Y D) Ramp Z Answer: A Var: 1 33) 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 friction and assume the spring obeys Hooke's law)? A) 6 meters B) 12 meters C) 3 meters D) 48 meters Answer: A Var: 1 34) 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? 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 35) A certain car traveling 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 stop had it been going 105.4 mph? A) 279 meters B) 158 meters C) 90 meters D) 51 meters E) 29 meters Answer: A Var: 50+ 36) A sand mover at a quarry lifts 2,000 kg of sand per minute a vertical distance of 12 meters. The sand is initially at rest and is discharged at the top of the sand mover with speed 5 m/s into a loading chute. At what minimum rate must power be supplied to this machine? A) 524 w B) 3.92 kw C) 6.65 kw D) 4.34 kw E) 1.13 kw Answer: D Var: 1

37)

Figure 7.2a

A 5.7 m massless rod is loosely pinned to a frictionless pivot at 0. A 4.0 kg ball is attached to the other end of the rod. The ball is held at A, where the rod makes a 30° angle above the horizontal, and is released. The ball-rod assembly then swings freely in a vertical circle between A and B. In Figure 7.2a, the ball passes through C, where the rod makes an angle of 30° below the horizontal. The speed of the ball as it passes through C is closest to: A) 10.6 m/s B) 9.5 m/s C) 8.4 m/s D) 11.9 m/s E) 13.9 m/s Answer: A Var: 1

38)

Figure 7.2b

A 4.6 m massless rod is loosely pinned to a frictionless pivot at 0. A 8.7 kg ball is attached to the other end of the rod. The ball is held at A, where the rod makes a 30° angle above the horizontal, and is released. The ball-rod assembly then swings freely in a vertical circle between A and B. In Figure 7.2b, the tension in the rod when the ball passes through the lowest point at D is closest to: A) 348 N B) 435 N C) 261 N D) 171 N E) 87 N Answer: A Var: 1

Figure 7.3

39) In Figure 7.3, a 4.0 kg ball is on the end of a 1.6 m rope which is fixed at 0. The ball is held at A, with the rope horizontal, and is given an initial downward velocity. The ball moves through three quarters of a circle and arrives at B, with the rope barely under tension. The initial velocity of the ball, at A, is closest to: A) 4.0 m/s B) 5.6 m/s C) 6.3 m/s D) 6.9 m/s E) 7.9 m/s Answer: D Var: 1 40) Two objects, one of mass m and the other of mass 2 m, are dropped from the top of a building. 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 41) A 2.0 kg ball is attached to one end of a light rod that is 1.2 m long. The other end of the rod is loosely pinned at a frictionless pivot. The rod is raised until it is vertical, with the ball above the pivot. The rod is released and the ball moves in a vertical circle. The tension in the rod as the ball moves through the bottom of the circle is closest to: A) 20 N B) 40 N C) 60 N D) 80 N E) 100 N Answer: E Var: 1

42)

Figure 7.4

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 upon separation 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 track is frictionless between points A and B. The block enters a rough section at B, extending to E. The coefficient of kinetic friction is 0.26. The velocity of the block is at C. The block moves on to D, where it stops. In Figure 7.4, the initial compression of the spring, in cm, is closest to: A) 0.49 B) 0.26 C) 0.18 D) 0.99 E) 0.67 Answer: A Var: 50+ 43) 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 upon separation 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 is 0.29. The velocity of the block is at C. The block moves on to D, where it stops. In Figure 7.4, the work done by friction between points B and C is closest to: A) -1.8 J B) -3.6 J C) -14 J D) -6.4 J E) -7.0 J Answer: A Var: 50+

44) 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. The block descends a ramp and has a velocity

at the bottom. The

track is frictionless between points A and B. 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 is 0.38. The velocity of the block is at C. The block moves on to D, where it stops. In Figure 7.4, the distance s that the block travels between points B and D is closest to: A) 0.30 m B) 0.039 m C) 0.26 m D) 0.40 m E) 0.60 m Answer: A Var: 50+ 7.2 Short Answer Questions 1) A roller coaster descends 35 meters in its initial drop and then rises 23 meters before going over the first hill. If a passenger at the top of the hill feels an apparent weight which is one half of her normal weight, what is the radius of curvature of the first hill? Assume no frictional losses, and neglect the initial speed of the roller coaster. Answer: 48 m Var: 1 Figure 7.5

2) In Figure 7.5, a block of mass m is moving along the horizontal frictionless surface with a speed of 5.70 m/s. If the slope is 11.0° and the coefficient of kinetic friction between the block and the incline is 0.260, how far does the block travel up the incline? Answer: 3.72 m Var: 1

Figure 7.6

3) In Figure 7.6, two masses, each 24 kg, are at rest and connected as shown. The coefficient of kinetic friction between the inclined surface and the mass is 0.31. Find the speed of the masses after they have moved 1.6 m. Answer: 1.9 m/s Var: 1 Figure 7.7

4) In Figure 7.7, a 5.00-kg block is moving at 5.00 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 5) An engine is being used to raise a 89 kg crate vertically upward. 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 seconds Var: 1

College Physics, 11e (Young) Chapter 8 Momentum 8.1 Multiple Choice Questions 1) Three objects are moving along a straight line as shown in Figure 8.1. Taking the positive direction to be to the right, what is the total momentum of this system? Figure 8.1

A) +106 kg m/s B) -106 kg m/s C) +14 kg m/s D) -14 kg m/s E) 0 kg m/s Answer: D Var: 1 2) A 328 kg car moving at 19.1 m/s hits from behind another car moving at direction. If the second car has a mass of and a new speed of velocity of the first car after the 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+

in the same what is the

3) Two vehicles approach a right angle intersection and then collide. After the collision, they become entangled. If their mass ratios were 1:4 and their respective speeds as they approached were both , find the magnitude and direction of the final velocity of the wreck. A) 13.1 m/s at 79° B) 16.3 m/s at 79° C) 12.5 m/s at 79° D) 15.7 m/s at 79° Answer: A Var: 50+

4) A 0.140 kg baseball is thrown with a velocity of It is struck with an average force of which results in a velocity of in the opposite direction. How long were the bat and ball in contact? A) 1.85 × 10-3 s B) 1.32 × 10-2 s C) 3.17 × 10-2 s D) 4.44 × 10-3 s Answer: A Var: 50+ 5) A golf ball of mass 0.050 kg is at rest on the tee and has a velocity of immediately after being struck. If the club and ball were in contact for what is the average force exerted on the ball? A) 6.3 kN B) 7.1 kN C) 5.5 kN D) 4.9 kN Answer: A Var: 44 6) A 0.24 kg blob of clay is thrown at a wall with an initial velocity of to a stop in what is the average force experienced by the clay? A) 42 N B) 26 N C) 35 N D) 51 N Answer: A Var: 14

If the clay comes

7) A 1200 kg car moving at 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+

8) A 1200 kg ore cart is rolling at across a flat surface. A crane dumps of ore (vertically) into the cart. How fast does the cart move after being loaded with ore? Assume that frictional forces with the flat surface may be neglected. A) 6.3 m/s B) 3.8 m/s C) 4.2 m/s D) 5.7 m/s Answer: A Var: 50+ 9) A 1200 kg cannon fires a cannonball at What is the recoil velocity 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+ 10) A car heading north collides at an intersection with a truck 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? Assume that the two vehicles have the same mass. A) 14 m/s B) 7 m/s C) 28 m/s D) 11 m/s Answer: A Var: 41 11) 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 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

12) A 5 kg ball collides head-on with a 10 kg ball, which is initially stationary. The collision is inelastic. Which statement is true? 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 10 kg 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) Two of the above statements are true. Answer: A Var: 1 13) Two friends are standing on opposite ends of a canoe. The canoe is initially at rest with respect to the lake. The person on the right throws a very massive ball to the left, and the person on the left catches it. After the ball is caught, the canoe is (ignore friction between the canoe and the water) A) stationary B) moving to the right. C) moving to the left. Answer: A Var: 1 14) You are standing on a skateboard, initially at rest. A friend throws a very heavy ball towards you. You can either catch the object or deflect the object back toward your friend (such that it moves away from you with the same speed as it was originally thrown). What should you do 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 15) A steady horizontal force lasting for 2.10 s gives a 1.25 kg object an acceleration of 3.20 m/s2 on a frictionless table. What impulse does this force give to the object? A) 25.7 kg m/s B) 10.9 kg m/s C) 8.40 kg m/s D) 4.00 kg m/s E) 2.63 kg m/s Answer: C Var: 1

16) 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 Figure 8.2

17) A block of mass m = 2.6 kg, moving on frictionless surface with a speed

makes

a perfectly elastic collision with a block of mass M at rest. After the collision, the 2.6 kg block recoils with a speed of In Figure 8.2, the mass M is closest to: A) 4.0 kg B) 1.7 kg C) 3.2 kg D) 15 kg E) 2.6 kg Answer: A Var: 50+ 18) A block of mass m = 3.6 kg, moving on a frictionless surface with a speed makes a perfectly elastic collision with a block of mass M at rest. After the collision, the 3.6 kg block recoils with a speed of In Figure 8.2, the speed of the block of mass M after the collision is closest to: 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+

19) A block of mass m = 3.5 kg, moving on a frictionless surface with a speed makes a perfectly elastic collision with a block of mass M at rest. After the collision, the 3.5 kg block recoils with a speed of In Figure 8.2, the blocks are in contact for 0.20 s. The average force on the 3.5 kg block, while the two blocks are in contact, is closest to: A) 102 N B) 98 N C) 95 N D) 91 N E) 88 N Answer: A Var: 50+ Figure 8.3

20) A block of mass m = 9 kg has a speed V and is behind a block of mass M = 27 kg that has a speed of The surface is frictionless. The blocks collide and couple. After the collision, the blocks have a common speed of 0.9 m/s. In Figure 8.3, the loss of kinetic energy of the blocks due to the collision is closest to: A) 8.6 J B) 2.0 J C) 4.6 J D) 11 J E) 31 J Answer: A Var: 50+ 21) A block of mass m = 34 kg has a speed V and is behind a block of mass M = 81 kg that has a speed of The surface is frictionless. The blocks collide and couple. After the collision, the blocks have a common speed of In Figure 8.3, the impulse on the 12 kg block due to the collision is closest to: A) 32 N ∙ s B) 14 N ∙ s C) 41 N ∙ s D) 57 N ∙ s E) 73 N ∙ s Answer: A Var: 50+

22) A 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 0.5 ms. The ball rebounds elastically, and returns to its original height. The time interval for a round trip is 3.00 s. In this situation, the average force exerted on the ball during contact with the plate is closest to: A) 3,000 N B) 1,500 N C) 2,490 N D) 2,000 N E) 3,500 N Answer: A Var: 50+ 23) A 83 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 0.5 ms. The ball rebounds elastically, and returns to its original height. The time interval for a round trip is 4.00 s. In this situation, assume the plate does not deform during contact. The maximum elastic energy stored by the ball is closest to: A) 16 J B) 24 J C) 32 J D) 48 J E) 64 J Answer: A Var: 50+

Figure 8.4

24) In Figure 8.4, a bullet of mass 0.01 kg moving horizontally strikes a block of wood of mass 1.5 kg which is suspended as a pendulum. The bullet lodges in the wood, and together they swing upward a distance of 0.40 m. What was the velocity of the bullet just before it struck the wooden block? The length of the string is 2 meters. A) 66.7 m/s B) 250 m/s C) 366 m/s D) 423 m/s E) 646 m/s Answer: A Var: 1 25) Consider two less-than-desirable options. In the first you are driving 30 mph and crash 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 off the thing it hits, and the collision time is the same in both cases. Which of these two situations would result in the greatest impact force? A) Hitting the other car. B) Hitting the brick wall. C) The force would be the same in both cases. D) We cannot answer this question without more information. E) None of these is true. Answer: C Var: 1

Figure 8.5

26) An 8 g bullet is shot into a 4.0 kg block, at rest on a frictionless horizontal surface. The bullet remains lodged in the block. The block moves into a spring and compresses it by 3.7 cm. The force constant of the spring is In Figure 8.5, the initial velocity of the bullet is closest to: A) 460 m/s B) 440 m/s C) 480 m/s D) 500 m/s E) 520 m/s Answer: A Var: 50+ 27) An 8 g bullet is shot into a 4.0 kg block, at rest on a frictionless horizontal surface. The bullet remains lodged in the block. The block moves into a spring and compresses it by 8.9 cm. The force constant of the spring is In Figure 8.5, the impulse of the block (including the bullet), due to the spring, during the entire time interval in which block and spring are in contact is closest to: 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+ 28) A girl of mass 55 kg throws a ball of mass 0.8 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 0.05 s. What is 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+

29) During World War I, Germany used a "Big Bertha" cannon to hurl shells into Paris 30 miles away. This gun also had a long barrel. What is the reason for using a long barrel in these guns? A) To provide a larger ratio of kinetic energy to potential energy. 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 Figure 8.6

30) Ball A, of mass 3.0 kg, is attached to a 0.4 m light rod, freely pivoted at P. Ball B is suspended from Q by a 0.6 m rope and is at rest. Ball A is raised to a certain level and is released. Ball A descends, and has a speed at the bottom, prior to striking ball B. The speed of balls A and B after the collision are Figure 8.6, the mass of ball B is closest to: A) 7.8 kg B) 6.8 kg C) 5.9 kg D) 4.9 kg E) 3.9 kg Answer: A Var: 50+

and

as shown. In

31) Ball A, of mass 3.0 kg, is attached to a 0.4 m light rod, freely pivoted at P. Ball B is suspended from Q by a 0.6 m rope and is at rest. Ball A is raised to a certain level and is released. Ball A descends, and has a speed at the bottom, prior to striking ball B. The speed of balls A and B after the collision are

and

as shown. In

Figure 8.6, the magnitude of the impulse on ball A is closest to: A) 14.1 N ∙ s B) 7.5 N ∙ s C) 9.7 N ∙ s D) 8.6 N ∙ s E) 15.2 N ∙ s Answer: A Var: 50+ Figure 8.7

32) In Figure 8.7, four point masses are placed as shown. The x- and y-coordinates of the center of mass are closest to: A) (2.2, 2.6) B) (2.2, 2.7) C) (2.3, 2.6) D) (2.3, 2.7) E) (2.3, 2.8) Answer: E Var: 1

Figure 8.8

33) In Figure 8.8, a 60 cm length of uniform wire, of 60 g mass, is bent into a right triangle. The x- and y-coordinates of the center of mass, in cm, are closest to: A) (8, 3) B) (8, 5) C) (9, 4) D) (10, 3) E) (10, 5) Answer: D Var: 1 Figure 8.9

34) In Figure 8.9, an L-shaped piece is cut from a uniform sheet of metal. Which of the points indicated is closest to the center of mass of the object? A) A B) B C) C D) D E) E Answer: C Var: 1

Figure 8.10

35) In Figure 8.10, determine the character of the collision. The masses of the blocks, and the velocities before and after are given. 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 Figure 8.11

36) In Figure 8.11, determine the character of the collision. The masses of the blocks, and the velocities before and after are given. 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

Figure 8.12

37) In Figure 8.12, determine the character of the collision. The masses of the blocks, and the velocities before and after are given. 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 38) An object initially at rest explodes in two fragments of masses diametrically opposite directions. If the speed of the first fragment is energy of the explosion. A) 30J B) 30kJ C) 38J D) 38kJ Answer: A Var: 50+

and

that move in find the internal

39) Two pendulums of equal length l = 0.45 m are suspended from the same point. The pendulum bobs are steel spheres. The first bob is drawn back to make a 35° angle with the vertical. If the first bob has mass and the second has mass 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+

40) A car of mass 1,411 kg collides head-on with a parked truck of mass Spring mounted bumpers ensure that the collision is essentially elastic. If the velocity of the truck is (in the same direction as the car's initial velocity) after the collision, what is the initial speed of the car? A) 21 km/h B) 42 km/h C) 32 km/h D) 11 km/h Answer: A Var: 50+ 8.2 Short Answer Questions 1) Find the magnitude and direction of the net momentum of the system shown in Figure 8.13. Express the direction by giving the angle the net momentum makes with the +x-axis. Figure 8.13

Answer: 123 kg m/s, 212° Var: 1 2) 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 ms) was it in contact with the ball? Answer: 7.64 ms Var: 1

3) On a frictionless horizontal surface, a 1.50 kg mass traveling at 3.50 m/s collides with and sticks to a 3.00 kg mass that is initially at rest, as shown in Figure 8.14. This system then runs into an ideal spring of force constant 50.0 N/cm. (a) What will be the maximum compression 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? Figure 8.14

Answer: (a) 3.50 cm, (b) 6.13 J during the inelastic collision Var: 1 4) Three balls are moving along a straight line having the instantaneous positions shown in Figure 8.15. At that instant, find the location and velocity of the center of mass of this system. Figure 8.15

Answer: 7.00 m to the right of the 2.00 kg ball, 1.11 m/s to the right Var: 1 5) A 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 at the clay, the ball becomes embedded in the clay and the two swing up to a maximum height of 0.08 m. If the mass of the baseball is 0.21 kg, find the speed of the pitch. Answer: 21 m/s Var: 50+ 6) 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 x kg, and each 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 × per second Var: 1

College Physics, 11e (Young) Chapter 9 Rotational Motion 9.1 Multiple Choice Questions 1) Calculate the angular speed, in A) 85.12 rad/s B) 13.53 rad/s C) 63.84 rad/s D) 95.33 rad/s Answer: A Var: 50+

of a flywheel turning at

2) A child is sitting on the outer edge of a merry-go-round that is go-round makes what is the velocity of the child in A) 4.6 m/s B) 9.2 m/s C) 0.7 m/s D) 3.2 m/s Answer: A Var: 50+ 3) Through what angle in degrees does a A) 63° B) 35° C) 46° D) 74° Answer: A Var: 26 4) An electrical motor spins at a constant the acceleration of the edge of the rotor? A) 5,707 m/s2 B) 281.6 m/s2 C) 572,400 m/s2 D) 28.20 m/s2 Answer: A Var: 50+

in diameter. If the merry-

record turn in

If the armature radius is

what is

5) A wheel accelerates from rest to at a 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

6) At time t = 0 s, a wheel has an angular displacement of zero radians and an angular velocity of The wheel has a constant acceleration of In this situation, the time t, at which the wheel comes to a mandatory halt, is closest to: A) 130 s B) 120 s C) 96 s D) 78 s E) 55 s Answer: A Var: 50+ 7) At time t = 0 s, a wheel has an angular displacement of zero radians and an angular velocity of The wheel has a constant acceleration of In this situation, the time t (after at which the kinetic energy of the wheel is twice the initial value, is closest to: A) 150 s B) 130 s C) 110 s D) 85 s E) 60 s Answer: A Var: 1 8) At time t = 0 s, a wheel has an angular displacement of zero radians and an angular velocity of The wheel has a constant acceleration of In this situation, the maximum value of the angular displacement, in rad, is closest to: A) +809 B) +1,011 C) +1,213 D) +1,415 E) +1,617 Answer: A Var: 50+

9) At time t = 0 s, a wheel has an angular displacement of zero radians and an angular velocity of The wheel has a constant acceleration of In this situation, the time at which the angular displacement is +88 rad and decreasing is closest to: A) 61 s B) 34 s C) 7 s D) 6 s E) 74 s Answer: A Var: 50+ 10) At time t = 0 s, a wheel has an angular displacement of zero radians and an angular velocity of The wheel has a constant acceleration of In this situation, the average angular velocity in the interval from to is closest to: A) 25 rad/s B) 15 rad/s C) 20 rad/s D) 28 rad/s E) 16 rad/s Answer: A Var: 50+ 11) A machinist turns the power on to a grinding wheel, at rest, at time t = 0 s. The wheel accelerates uniformly for 10 s and reaches the operating angular velocity 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. In this situation, the angular acceleration of the wheel between and is closest to: A) 3.8 rad/ B) 4.6 rad/ C) 5.3 rad/ D) 6.1 rad/ E) 6.8 rad/ Answer: A Var: 50+

12) A machinist turns the power on to a grinding wheel, at rest, at time t = 0 s. The wheel accelerates uniformly for 10 s and reaches the operating angular velocity 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. In this situation, the total number of revolutions made by the wheel is closest to: A) 510 B) 280 C) 320 D) 470 E) 750 Answer: A Var: 50+ 13) A machinist turns the power on to a grinding wheel, at rest, at time t = 0 s. The wheel accelerates uniformly for 10 s and reaches the operating angular velocity 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. In this situation, the time interval of deceleration is closest to: A) 64 s B) 62 s C) 66 s D) 68 s E) 70 s Answer: A Var: 50+ 14) A machinist turns the power on to a grinding wheel, at rest, at time t = 0 s. The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of The wheel is run at that angular velocity for 27 s and then power is shut off. The wheel slows down uniformly at until the wheel stops. In this situation, the average angular velocity in the time interval from to is closest to: A) 17 rad/s B) 15 rad/s C) 13 rad/s D) 11 rad/s E) 8.7 rad/s Answer: A Var: 50+

15) A machinist turns the power on to a grinding wheel, at rest, at time t = 0 s. The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of The wheel is run at that angular velocity for 36 s and then power is shut off. The wheel slows down uniformly at until the wheel stops. In this situation, the average angular acceleration in the time interval from to s is closest to: A) 1.0 rad/ B) 0.75 rad/ C) 1.3 rad/ D) 1.5 rad/ E) 1.8 rad/ Answer: A Var: 50+ 16) A small mass is placed on a record turntable that is rotating at 45 rpm. The linear acceleration of the mass is A) directed perpendicular to the line joining the mass and the center of rotation. B) independent (in magnitude) of the position of the mass on the turntable. C) greater the closer the mass is to the center. D) greater the farther the mass is from the center. E) zero. Answer: D Var: 1

Figure 9.1

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 The wheel undergoes a uniform angular acceleration of about the center O. 17) In Figure 9.1, the tangential acceleration of P at time t = 0 s is closest to: A) zero B) 0.005 m/ C) 0.010 m/ D) 0.015 m/ E) 0.020 m/ Answer: E Var: 1 18) In Figure 9.1, the linear speed of P, when it reaches the y-axis, is closest to: A) 0.18 m/s B) 0.24 m/s C) 0.35 m/s D) 0.49 m/s E) 0.71 m/s Answer: C Var: 1 19) In Figure 9.1, the magnitude of the linear acceleration of P, when it reaches the y-axis, is closest to: A) 0.063 m/ B) 0.066 m/ C) 0.069 m/ D) 0.072 m/ E) 0.075 m/ Answer: B Var: 1

20) In Figure 9.1, the time t, when P returns to the original position on the x-axis, is closest to: A) 13 s B) 18 s C) 25 s D) 35 s E) 50 s Answer: D Var: 1 21) A tire is rolling along a road, without slipping, with a velocity v. A piece of tape is attached to the tire. When the tape is opposite the road (at the top of the tire), its velocity with respect to the road is A) 2v B) v C) 1.5 v D) The velocity depends on the radius of the tire. Answer: A Var: 1 Table 9.1

22) Table 9.1 shows the masses and the coordinates x and y of a set of three point masses in the x-y plane. The masses are interconnected by light struts, forming a rigid body. The moment of inertia of the rigid body, through the center of mass and perpendicular to the x-y plane, is closest to: A) 3000 B) 3200 C) 3400 D) 3600 E) 3800 Answer: E Var: 1

23) A potter's wheel (a solid, uniform disk) of mass and radius central axis. A lump of clay is dropped onto the wheel at a distance Calculate the rotational inertia of the system. A) 1.8 kg ∙ m2 B) 1.5 kg ∙ m2 C) 0.40 kg ∙ m2 D) 2.5 kg ∙ m2 Answer: A Var: 31

spins about its from the axis.

24) To drive a typical car at 40 mph on a level road for one hour requires about 3.2 × J of energy. Suppose one tried to store this much energy in a spinning solid cylindrical flywheel which was then coupled to the wheels of the car. A large flywheel cannot be spun too fast or it will fracture. If one used a flywheel of radius 0.60 m and mass 400 kg, what angular speed would be required to store (Incidentally, 2500 rpm is about the maximum feasible rate of revolution with present materials technology for such a flywheel.) A) 1800 rad/s B) 3620 rad/s C) 943 rad/s D) 530 rad/s E) 5470 rad/s Answer: C Var: 1 Figure 9.2

25) In Figure 9.2, two blocks, of masses 2 kg and 3 kg, are connected by a light string which passes over a pulley of moment of inertia and radius 5 cms. The coefficient of friction for the table top is 0.30. The blocks are released from rest. Using energy methods, one can deduce that after the upper block has moved 0.6 m, its speed is: A) 1.22 m/s B) 5.44 m/s C) 3.19 m/s D) 1.95 m/s E) 1.40 m/s Answer: E Var: 1

Figure 9.3

26) A uniform disk is attached at the rim to a vertical shaft and is used as a cam. Two views of the disk and shaft are shown. The disk has a diameter of 80 cm. The moment of inertia of the disk about the axis of the shaft is The shaft rotates uniformly about its axis at 96 rpm. In Figure 9.3, the kinetic energy of the disk, in mJ, is closest to: A) 300 B) 180 C) 91 D) 520 E) 880 Answer: A Var: 50+ 27) A uniform disk is attached at the rim to a vertical shaft and is used as a cam. Two views of the disk and shaft are shown. The disk has a diameter of 82 cm. The moment of inertia of the disk about the axis of the shaft is The shaft rotates uniformly about its axis at 89 rpm. In Figure 9.3, the linear velocity of point P is closest to: A) 5.4 m/s B) 3.6 m/s C) 4.3 m/s D) 6.1 m/s E) 7.2 m/s Answer: A Var: 50+

28) A uniform disk is attached at the rim to a vertical shaft and is used as a cam. Two views of the disk and shaft are shown. The disk has a diameter of 30 cm. The moment of inertia of the disk about the axis of the shaft is The shaft rotates uniformly about its axis at 19 rpm. In Figure 9.3, the magnitude of the acceleration of point Q is closest to: A) 1.2 m/ B) 0.87 m/ C) 0.54 m/ D) 11,000 m/ E) 5,400 m/ Answer: A Var: 50+ 29) While spinning down from 500.0 rpm to rest, a solid uniform flywheel does If the radius of the disk is what is its mass? A) 4.0 kg B) 3.4 kg C) 4.6 kg D) 5.2 kg Answer: A Var: 50+

of work.

30) A solid, uniform sphere of mass 2.0 kg and radius rolls without slipping down an inclined plane of height What is the angular velocity 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: 50+ 31) A solid disk of radius 1.60 m and mass rolls without slipping to the bottom of an inclined plane. If the angular velocity of the disk is at the bottom, what is the height of the inclined plane? A) 3.57 m B) 2.68 m C) 3.14 m D) 4.28 m Answer: A Var: 50+

Figure 9.4

32) In Figure 9.4 are scale drawings of four objects, each of the same mass and uniform thickness. Which has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing? In each case the axis passes through 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 9.2 Short Answer Questions 1) A bicycle wheel has an initial angular velocity of 7.2 rad/s. After turning through of a revolution, the angular velocity is reduced to 2.2 rad/s. If the angular acceleration of the wheel is constant during the motion, how long will it take the wheel to make the revolution? Answer: 0.67 seconds Var: 50+ Figure 9.5

2) In Figure 9.5, a rope is wrapped around a wheel of radius R = 2.0 meters. The wheel is mounted with frictionless bearings on an axle through its center. A block of mass 14 kg is suspended from the end of the rope. When the system is released from rest it is observed that the block descends 10 meters in 2.0 seconds. What is the moment of inertia of the wheel? Answer: 54 Var: 1

3) A futuristic design for a car is to have a large disk-like flywheel within the car storing kinetic energy. The flywheel has mass 370 kg with a radius of 0.50 m and can rotate up to Assuming all of this stored kinetic energy could be transferred to the linear velocity of the car, find the maximum attainable speed of the car. Answer: 221 m/s Var: 50+ Figure 9.6

4) In Figure 9.6, a weightlifter's barbell consists of two identical small but dense spherical weights each of mass 50 kg. The weights are connected by a 0.96 m steel rod with mass of Find the moment of inertia of the barbell through the axis at the center, assuming the two weights are small enough to be treated as point masses. Answer: 24.9 Var: 1 5) A marble that is rolling without slipping approaches a hill traveling at 8.50 m/s. How high vertically will the marble go (a) if the hill is rough enough to prevent any slipping, and (b) if the hill is perfectly smooth? (c) Why does the marble rise to different heights when it had the same initial kinetic energy in both cases? Answer: (a) 5.16 m, (b) 3.69 m, (c) With friction, all the kinetic energy is converted to gravitational potential energy. Without friction, only the translational kinetic energy is converted to potential energy. Var: 1 6) A solid uniform 3.33 kg disk has string of negligible mass wrapped around its rim, with one end of the string tied to the ceiling, as shown in Figure 9.7. The disk is released from rest and turns as it falls as the string unwraps. At the instant its center has fallen 2.25 m, (a) how fast is it moving, and (b) how much rotational kinetic energy does it have? Figure 9.7

Answer: (a) 5.42 m/s, (b) 24.5 J Var: 1

College Physics, 11e (Young) Chapter 10 Dynamics of Rotational Motion 10.1 Multiple Choice Questions Figure 10.1

1) A light triangular plate OAB is in a horizontal plane. Three forces,

and

act on the plate, which is pivoted about a vertical axis through point O. In Figure 10.1, the torque of force

about the axis through point O is closest to:

A) 0.52 N ∙ m B) 0.30 N ∙ m C) 0.37 N ∙ m D) 0.45 N ∙ m E) 0.60 N ∙ m Answer: A Var: 50+ 2) A light triangular plate OAB is in a horizontal plane. Three forces,

and

act on the plate, which is pivoted about a vertical axis through point O. In Figure 10.1, consider the counterclockwise sense as positive. The sum of the torques about the vertical axis through point O, acting on the plate due to forces , , and , is closest to: A) 2.2 N ∙ m B) 2.6 N ∙ m C) -2.2 N ∙ m D) -2.6 N ∙ m E) zero Answer: A Var: 50+

3) A light triangular plate OAB is in a horizontal plane. Three forces,

and

act on the plate, which is pivoted about a vertical axis through point O. In Figure 10.1, the plate is not moving. The magnitude of the force exerted on the plate by the pivot is closest to: A) 2.3 N B) 3.7 N C) 1.1 N D) 10 N E) 11 N Answer: A Var: 50+ 4) A force of 17 N is applied to the end of a torque wrench at an angle 45° from a line joining the pivot point to the handle. What is the magnitude of the torque generated about the pivot point? A) 7.6 N∙m B) 10.7 N∙m C) 12.0 N∙m D) 9.7 N∙m Answer: A Var: 12 5) A force in the +y direction applied at the point about the origin. Find the magnitude of the force. A) 17 N B) 28 N C) 39 N D) 48 N Answer: A Var: 46

gives rise to a torque of

6) A 95 N force exerted at the end of a torque wrench gives rise to a torque of What is the angle (assumed to be 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+

7) A force of

is applied tangentially to a wheel of radius

angular acceleration of A) 4.78 kg ∙ m2 B) 3.59 kg ∙ m2 C) 5.98 kg ∙ m2 D) 7.17 kg ∙ m2 Answer: A Var: 50+

and gives rise to an

Calculate the rotational inertia of the wheel.

8) A torque of 12 N ∙ m is applied to a solid, uniform disk of radius 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+

If the disk

9) A particular motor can provide a maximum of of torque. Assuming that all of this torque is used to accelerate a solid, uniform flywheel of mass and radius 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+

Figure 10.2

10) A drum (see Figure 10.2) has a radius of 0.40 m and a moment of inertia of 2.3 . The frictional torque of the drum axle is 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 velocity of the drum is The drum then decelerates and comes to a halt. In this situation, the constant force applied to the rope is closest to: A) 51 N B) 40 N C) 29 N D) 18 N E) 7.5 N Answer: A Var: 50+ 11) A drum (see Figure 10.2) has a radius of 0.40 m and a moment of inertia of 7.8 . The frictional torque of the drum axle is A 20 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 velocity of the drum is The drum then decelerates and comes to a halt. In this situation, the angular momentum of the drum at the instant the rope slips off the peg is closest to: A) 195 kg ∙ /s B) 176 kg ∙

C) 146 kg ∙

D) 117 kg ∙

E) 234 kg ∙ Answer: A Var: 50+

Figure 10.3

12) In Figure 10.3, the mass of the block is closest to: A) 1.9 kg B) 2.0 kg C) 2.1 kg D) 2.2 kg E) 2.3 kg Answer: D Var: 1 13) In Figure 10.3 the moment of inertia of the wheel is closest to: A) 3.5 B) 3.7 C) 3.9 D) 4.1 E) 4.3 Answer: E Var: 1

Figure 10.4

14) In Figure 10.4, a given force F is applied to a rod in several different ways. In which case is the torque due to F about the pivot P greatest? A) 1 B) 2 C) 3 D) 4 E) 5 Answer: A Var: 1 Figure 10.5

15) In Figure 10.5, a solid cylinder of 90 cm radius is positioned on a frictionless plane inclined at above horizontal. A force F is exerted by a string wrapped around the spool. When F has a certain critical value the center of mass of the spool does not move. When this is the case, what is the angular acceleration of the spool? A) 11 rad/ B) 19 rad/ C) 14 rad/ D) 22 rad/ E) 5 rad/ Answer: A Var: 50+

Figure 10.6

16) In Figure 10.6, a mass of 35.30 kg is attached to a light string which is wrapped around a cylindrical spool of radius 10 cm and moment of inertia The spool is suspended from the ceiling, and the mass is then released from rest a distance 3.50 m above the floor. How long does it take 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+ Figure 10.7

The radius of a 3.0 kg wheel is 6.0 cm. The wheel is released from rest at point A on a incline. The wheel rolls without slipping and moves 2.4 m to point B in 1.20s. 17) In Figure 10.7, the moment of inertia of the wheel is closest to: A) 0.0048 B) 0.0051 C) 0.0054 D) 0.0057 E) 0.0060 Answer: B Var: 1

18) In Figure 10.7, the angular acceleration of the wheel is closest to: A) 48 rad/ B) 56 rad/ C) 65 rad/ D) 73 rad/ E) 82 rad/ Answer: B Var: 1 19) A hoop is released from rest at the top of a plane inclined at 21° above horizontal. How long does it take the hoop to roll 26.5 m down the plane? A) 5.49 s B) 5.13 s C) 3.40 s D) 3.29 s E) 9.18 s Answer: A Var: 50+ 20) A uniform, solid flywheel of radius 1.4 m and mass 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

rotates at

What is the

21) A 1.4 kg object at x = 2.00 m, y = 3.10 m moves at at an angle 45° north of east. Calculate the magnitude of the object's angular momentum about the origin. A) 6.9 kg∙m2/s B) 4.9 kg∙m2/s C) 8.3 kg∙m2/s D) 9.7 kg∙m2/s Answer: A Var: 50+

22) Three solid, uniform flywheels, each of mass and radius rotate independently around a common axis. Two of the flywheels rotate in one direction at the other rotates in the opposite direction at Calculate the magnitude of the net angular momentum of the system. A) 1,016 kg∙m2/s B) 1,496 kg∙m2/s C) 975 kg∙m2/s D) 940 kg∙m2/s Answer: A Var: 50+ 23) A potter's wheel, with rotational inertia is spinning freely at The potter drops a lump of clay onto the wheel, where it sticks a distance from the rotational axis. If the subsequent angular speed of the wheel and clay is 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 Figure 10.8

24) In Figure 10.8, a carousel has a radius of 3.0 m and a moment of inertia of 8000 . The carousel is rotating unpowered and without friction with an angular velocity of An man runs with a velocity of on a line tangent to the rim of the carousel, overtaking it. The man runs onto the carousel and grabs hold of a pole on the rim. The change in the angular velocity of the carousel is closest to: A) +0.04 rad/s B) +0.06 rad/s C) +0.08 rad/s D) -0.05 rad/s E) -0.07 rad/s Answer: A Var: 1

25) A disk and a sphere are released simultaneously at the top of an inclined plane. They roll down without slipping. Which 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 26) A spinning ice skater is able to control the rate at which she rotates by pulling in her arms. We can best understand this effect by observing that in this process: A) her angular momentum remains constant. B) her moment of inertia remains constant. C) her kinetic energy remains constant. D) her total velocity remains constant. E) she is subject to a constant non-zero torque. Answer: A Var: 1 27) A uniform disk has a mass of 4.9 kg and a radius of 0.53 m. The disk is mounted on frictionless bearings and is used as a turntable. The turntable is initially rotating at 50 rpm. A hollow cylinder has the same mass and radius as the disk. It is released from rest, just above the turntable, and on the same vertical axis. The hollow cylinder slips on the turntable for 0.20 s until it acquires the same final angular velocity as the turntable. The final angular momentum of the system is closest to: A) 3.6 /s B) 4.4

C) 5.2

D) 6.2

E) 7.2 Answer: A Var: 50+

28) When is the angular momentum of a system constant? A) When the total kinetic energy is constant. B) When no net external force acts on the system. C) When the linear momentum and the energy are constant. D) When no net external torque acts on the system. E) When the moment of inertia is constant. Answer: D Var: 1 29) An irregularly shaped object 10 m long is placed with each end on a scale. If the scale on the right reads and the scale on the left reads how far from the left is the center of

gravity. A) 5.7 m B) 7.4 m C) 4.3 m D) 14 m Answer: A Var: 50+ 30) A uniform sign is supported at P as shown in Figure 10.9. If the sign is a square on its side and its mass is what is the magnitude of the horizontal force that P experiences? Figure 10.9

A) 34 N B) 0 N C) 24 N D) 98 N Answer: A Var: 50+ 31) A uniform 1200 N beam that is 3.50 m long is suspended horizontally by two vertical wires at its ends. A small but dense 550 N weight is placed on the beam 2.00 m from one end, as shown in Figure 10.10. The tensions, A and B, in the two wires are Figure 10.10

A) A = 875 N, B = 875 N B) A = 836 N, B = 914 N C) A = 8960 N, B = 8190 N D) A = 914 N, B = 836 N E) A = 8190 N, B = 8960 N Answer: D Var: 1 Figure 10.11

32) A uniform 200 kg beam, 6 m long, is freely pivoted at P. The beam is supported in a horizontal position by a light strut, 5 m long, which is freely pivoted at Q and is loosely pinned to the beam at R. A load of mass is suspended from the end of the beam at S. A maximum compression of in the strut is permitted, due to safety. In Figure 10.11, the maximum mass M of the load is closest to: A) 920 kg B) 665 kg C) 1,175 kg D) 1,120 kg E) 1,375 kg Answer: A Var: 50+ 33) A uniform 600 kg beam, 6 m long, is freely pivoted at P. The beam is supported in a horizontal position by a light strut, 5 m long, which is freely pivoted at Q and is loosely pinned to the beam at R. A load of mass is suspended from the end of the beam at S. A maximum compression of in the strut is permitted, due to safety. In Figure 10.11, under maximum load, the of the force exerted on the beam by the pivot at P is closest to: A) 10,800 N B) 14,400 N C) 12,600 N D) 16,200 N E) 18,000 N Answer: A Var: 50+

34) A uniform 600 kg beam, 6 m long, is freely pivoted at P. The beam is supported in a horizontal position by a light strut, 5 m long, which is freely pivoted at Q and is loosely pinned to the beam at R. A load of mass is suspended from the end of the beam at S. A maximum compression of in the strut is permitted, due to safety. In Figure 10.11, under maximum load the of the force exerted on the beam by the pivot at P is closest to: A) 7,060 N B) 4,560 N C) 9,560 N D) 10,000 N E) zero Answer: A Var: 50+ 35) Suppose that a heavy person and a light person are balanced on a teeter-totter made of a plank of wood. Each person now moves in toward the fulcrum a distance of 25 cm. What effect will this have on the balance of the teeter-totter? A) The teeter-totter will remain in balance. B) The heavy person's end will go down. C) The light person's end will go down. D) One cannot tell whether either end will rise or fall without knowing the relative mass of the plank. E) Only if the plank has significant mass will the light person's end go down. Answer: C Var: 1

Figure 10.12

36) A 40 kg uniform ladder, 5.0 m long, is placed against a smooth wall at a height of h = 4.0 m. The base of the ladder rests on a rough horizontal surface whose coefficient of static friction is 0.40. An 80 kg block is suspended from the top rung of the ladder, just at the wall. In Figure 10.12, the force exerted on the wall by the ladder is closest to: A) 740 N B) 1,300 N C) 980 N D) 900 N E) 1,100 N Answer: A Var: 50+ 37) A 50 kg uniform ladder, 5.0 m long, is placed against a smooth wall at a height of h = 3.7 m. The base of the ladder rests on a rough horizontal surface whose coefficient of static friction is 0.40. An 80 kg block is suspended from the top rung of the ladder, just at the wall. In Figure 10.12, the magnitude of the force exerted on the base of the ladder, due to contact with the rough horizontal surface is closest to: A) 1,580 B) 1,560 C) 1,550 D) 1,600 E) 1,610 Answer: A Var: 50+

Figure 10.13

38) In Figure 10.13, 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 Figure 10.14

39) A 100 kg nonuniform boom, 6.0 m long, is loosely pinned at the pivot at P. A 600 kg block is suspended from the end of the boom at A. The boom forms a 30° angle with the horizontal, and is supported by a cable, 4.0 m long, 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. In Figure 10.14, the tension in the cable is closest to: A) 9,300 N B) 8,400 N C) 8,100 N D) 7,500 N E) 6,900 N Answer: A Var: 7

40) A 500 kg nonuniform boom, 6.0 m long, is loosely pinned at the pivot at P. A 800 kg block is suspended from the end of the boom at A. The boom forms a 30° angle with the horizontal, and is supported by a cable, 4.0 m long, 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. In Figure 10.14, the of the pivot force on the boom at P is closest to: A) 12,000 N B) 5,500 N C) 19,000 N D) 7,100 N E) 3,200 N Answer: A Var: 35 41) A 100 kg nonuniform boom, 6.0 m long, is loosely pinned at the pivot at P. A 700 kg block is suspended from the end of the boom at A. The boom forms a 30° angle with the horizontal, and is supported by a cable, 4.0 m long, 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. In Figure 10.14, the of the pivot force on the boom at P is closest to: A) 2,500 N B) 4,200 N C) 6,100 N D) 7,800 N E) 8,100 N Answer: A Var: 34

Figure 10.15

42) In Figure 10.15, a ladder of weight 200 N and length 10 meters leans against a smooth wall (no friction on wall). A firefighter of weight 600 N climbs a distance x up the ladder. The coefficient of friction between the ladder and the floor is 0.5. What is the maximum value of x if the ladder is not to slip? A) 3.93 m B) 5.00 m C) 6.04 m D) 6.28 m E) 8.44 m Answer: D Var: 1

Figure 10.16

A 20 kg uniform door has a width of 1.2 m and a height of 2.5 m. The door is mounted on a post by a pair of hinges, marked 1 and 2, at the top and bottom of the door. An external force of 60 N, at an angle of 30° above the horizontal, is applied to the doorknob, as shown. The doorknob is 1.0 m above the bottom of the door. 43) In Figure 10.16, the x-component of the force, exerted on the door at the top by hinge 1, is closest to: A) zero B) +55 N C) +80 N D) -55 N E) -80 N Answer: D Var: 1 44) In Figure 10.16, the x-component of the force, exerted on the door at the bottom by hinge 2, is closest to: A) zero B) +29 N C) +65 N D) -29 N E) -65 N Answer: A Var: 1 45) In Figure 10.16, the sum of the y-components of the forces, exerted on the door by hinges 1 and 2, is closest to: A) 145 N B) 165 N C) 195 N D) 225 N E) 250 N Answer: B Var: 1

Figure 10.17

46) In Figure 10.17, the Achilles tendon exerts a force F = 720 N. What is the torque it exerts about the ankle joint? A) 12.2 N ∙ m B) 16.2 N ∙ m C) 21.2 N ∙ m D) 25.9 N ∙ m E) 36.0 N ∙ m Answer: B Var: 1 10.2 Short Answer Questions Figure 10.18

1) A lawn roller in the form of a solid uniform cylinder is being pulled horizontally by a horizontal force B applied to an axle through the center of the roller, as shown in Figure 10.18. The roller has radius 0.59 meters and mass 48 kg. What magnitude B of the force is required to produce an acceleration of the center of mass of the roller if the lawn roller rolls without slipping? Answer: 300 N Var: 50+

2) A 24.5-kg child is standing on the outer edge of a merry-go-round which has moment of inertia and radius 2.40 m. The entire system is initially rotating at Find the angular velocity if the child moves to a final position 1.10 m from the center of the Answer: 0.200 rev/s Var: 50+ Figure 10.19

3) Figure 10.19 represents an Atwood's machine. There is no slipping between the cord and the surface of the wheel. The blocks have mass of 3.0 kg and 5.7 kg and the wheel has a radius of 0.12 m and mass of 10.3 kg. If the 5.7 kg mass falls 1.5 m, find the speed of each block. (Assume the wheel is in the shape of a disk.) Answer: 2.4 m/s Var: 1 Figure 10.20

4) In Figure 10.20, a 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 F is applied at a distance h above the floor. If what minimum value of F is required to make the crate start to tip over? (Assume that μ is large enough that the crate does not start to slide.) Answer: 133 N Var: 50+

Figure 10.21

5) In Figure 10.21, a 10.0 m long bar is attached by a frictionless hinge to a wall and held horizontal by a rope that makes an angle θ of 49° with the bar. The bar is uniform and weighs How far from the hinge should a 10.0 kg mass be suspended for the tension T in the rope to be Answer: 10 meters from the hinge Var: 50+ Figure 10.22

6) In Figure 10.22, a uniform ladder 12 meters long rests against a vertical frictionless wall. The ladder weighs 400.0 N and makes an angle θ of 51° with the floor. A man weighing 874 N climbs slowly up the ladder, the ladder starts to slip. What is , the coefficient of static friction between the floor and the ladder? Answer: 0.49 Var: 50+

College Physics, 11e (Young) Chapter 11 Elasticity and Periodic Motion 11.1 Multiple Choice Questions 1) 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 . 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 Situation 11.1 The base of an aluminum block, which is fixed in place, measures 90 cm by 90 cm. The height of the block is 60 cm. A force, applied to the upper force and parallel to it, produces a shear strain of 0.0060. The shear modulus of aluminum is 2) In Situation 11.1, the displacement of the upper force, in the direction of the applied force is closest to: A) 3.0 mm B) 3.6 mm C) 4.2 mm D) 4.8 mm E) 5.4 mm Answer: B Var: 1 3) In Situation 11.1, the shear stress on the block, in MPa, is closest to: A) 180 B) 360 C) 600 D) 720 E) 900 Answer: A Var: 1

4) Which of the following is an accurate statement? A) The ratio stress/strain is called the elastic 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 Situation 11.2 A 12 liter volume of oil is subjected to pressure which produces a volume strain of -3.0 × The bulk modulus of the oil is 6.0 ×

Pa and is independent of the pressure.

5) In Situation 11.2, the reduction in the volume of the oil, in ml, is closest to: A) 2.0 B) 2.4 C) 2.8 D) 3.2 E) 3.6 Answer: E Var: 1 6) In Situation 11.2, the change in the pressure of the oil, in atm, is closest to: A) 12 B) 14 C) 16 D) 18 E) 20 Answer: D Var: 1 7) 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?

8) A 88.6 kg bungee jumper jumps off a bridge and undergoes simple harmonic motion. If the period of oscillation is what is the spring constant of the bungee cord? A) 27.9 N/m B) 33.5 N/m C) 44.6 N/m Answer: A Var: 50+ 9) 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+ 10) An object undergoing simple harmonic motion has an amplitude of velocity of the object is what is the object's angular frequency? A) 6.5 rad/s B) 7.2 rad/s C) 5.2 rad/s D) 5.9 rad/s Answer: A Var: 11

If the maximum

11) A mass m = 9.0 kg is attached to a spring and allowed to hang in the Earth's gravitational field. The spring stretches before it reaches its equilibrium position. If allowed to oscillate, what would be its frequency? A) 2.9 Hz B) 0.33 x 10-3 Hz C) 0.58 Hz D) 1.8 Hz Answer: A Var: 50+

12) A 3.42 kg mass hanging vertically from a spring on the Earth (where undergoes simple oscillatory motion. If the spring constant is find the period of oscillation of this setup on the moon, where A) 3.35 s B) 2.51 s C) 4.36 s D) 5.70 s Answer: A Var: 31 13) A child on a swing-set swings back and forth. If the length of the supporting cables for the swing is what is the period of oscillation? A) 3.5 s B) 3.9 s C) 4.2 s D) 4.6 s Answer: A Var: 30 14) The period of a simple pendulum in a grandfather clock on another planet is the acceleration due to gravity on this planet if the length of the pendulum is A) 12.2 m/s2 B) 11.3 m/s2 C) 13.4 m/s2 D) 14.6 m/s2 Answer: A Var: 50+

What is

15) A mass on a spring has an angular oscillation frequency of The mass has a maximum displacement (when of If the spring constant is what is the potential energy stored in the mass-spring system when A) 0.350 J B) 0.256 J C) 0.329 J D) 0.399 J Answer: A Var: 50+

16) A 0.25 kg harmonic oscillator has a total oscillation energy of amplitude is what is the oscillation frequency? A) 7.1 Hz B) 2.1 Hz C) 3.6 Hz D) 5.0 Hz Answer: A Var: 50+

If the oscillation

17) A 2.0 kg block on a frictionless table is connected to two springs with spring constants and

whose opposite ends are fixed to walls, as show in Figure 11.1. What is the oscillation

angular frequency if

and Figure 11.1

A) 2.6 rad/s B) 3.7 rad/s C) 0.42 rad/s D) 0.59 rad/s Answer: A Var: 50+ 18) If the frequency of a harmonic oscillator doubles, by what factor does the maximum value of acceleration change? A) 4 B) 2 C) D) 2/π Answer: A Var: 1

19) If the total energy of a harmonic oscillator is reduced by amplitude of the oscillations? A) B) C) 1/3 D) 3 Answer: A Var: 1

what is the change in the

20) A simple pendulum has a period T on the earth. If it were used on Planet X, where the acceleration due to gravity is 3 times what it is on earth, its period would be A) 3T B) T C) T D) T/ E) T/3 Answer: D Var: 1 21) A simple pendulum having a bob of mass M has a period T. If you double M but change nothing else, the period would be A) 2T B) T C) T D) T/ E) T/2 Answer: C Var: 1 22) A mass attached to a very light spring executes simple harmonic motion. If you want to double its total energy, you should A) double the amplitude of vibration while changing nothing else. B) double the force constant of the spring while changing nothing else. C) double both the amplitude and force constant. D) double the mass while changing nothing else. E) double both the mass and amplitude of vibration. Answer: B Var: 1

23) A 4.8 kg block attached to a spring executes simple harmonic motion on a frictionless horizontal surface. At time t = 0 s, the block has a displacement of a velocity of and an acceleration of A) 15 N/m B) 14 N/m C) 13 N/m D) 12 N/m E) 11 N/m Answer: A Var: 50+

The force constant of the spring is closest to:

24) A 5.7 kg block attached to a spring executes simple harmonic motion on a frictionless horizontal surface. At time t = 0 s, the block has a displacement of a velocity of and an acceleration of

The amplitude of the motion is closest to:

A) 0.81 m B) 2.7 m C) 1.0 m D) 1.1 m E) 1.2 m Answer: A Var: 50+ 25) A 0.12 kg block on a horizontal frictionless surface is attached to a spring whose force constant is The block is pulled from its equilibrium position at to a displacement and is released from rest. The block then executes simple harmonic motion along the (horizontal). The displacement of the block at time is closest to: A) 0.01 m B) -0.01 m C) 0.08 m D) -0.08 m E) 0.1 m Answer: A Var: 50+

26) A 2.0 kg block on a horizontal frictionless surface is attached to a spring whose force constant is The block is pulled from its equilibrium position at to a displacement and is released from rest. The block then executes simple harmonic motion along the (horizontal). The velocity of the block at time is closest to: A) -1 m/s B) 1 m/s C) 0.2 m/s D) -0.2 m/s E) zero Answer: A Var: 50+ 27) A 0.39 kg block on a horizontal frictionless surface is attached to a spring whose force constant is The block is pulled from its equilibrium position at to a displacement and is released from rest. The block then executes simple harmonic motion along the (horizontal). When the displacement is the kinetic energy of the block 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+ 28) A 0.16 kg block on a horizontal frictionless surface is attached to a spring whose force constant is The block is pulled from its equilibrium position at to a displacement and is released from rest. The block then executes simple harmonic motion along the (horizontal). When the displacement is the acceleration of the block is closest to: A) 85 B) 43 C) 64 D) 270 E) 370 Answer: A Var: 50+

29) A 3.7 kg block on a horizontal frictionless surface is attached to a spring whose force constant is The block is pulled from its equilibrium position at to a displacement and is released from rest. The block then executes simple harmonic motion along the (horizontal). 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+ 30) For an object undergoing simple harmonic motion, A) the acceleration is greatest when the speed is greatest. B) the displacement is greatest when the speed is greatest. C) the acceleration is greatest when the displacement is greatest. D) the maximum potential energy is larger than the maximum kinetic energy. E) the total energy oscillates at frequency f = Answer: C Var: 1 31) 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 1.4 E) increase by a factor of 0.71. Answer: D Var: 1

11.2 Short Answer Questions 1) An object of mass 6.8 kg is attached to a spring of force constant 1,720 N/m. The object is set into simple harmonic motion, with an initial velocity of and an initial displacement of

Calculate the maximum velocity the object has during its motion.

Answer: 4.5 m/s Var: 50+ Figure 11.2

2) In Figure 11.2, a 0.44 kg ball is suspended from a string 8.33 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 is (Assume that once the pendulum ball hits the spring there is no effect due to the vertical movement of the ball.) Answer: 3.2 s Var: 50+ 3) A 2.0 kg mass is traveling at 5.0 m/s on a smooth horizontal surface when it collides with and sticks to a stationary 6.0 kg mass. The larger mass is attached to a light spring of force constant 150 N/m, as shown in Figure 11.3. Find (a) the amplitude of the resulting oscillations of this system, (b) the frequency and (c) the period of the oscillations. Figure 11.3

Answer: (a) 0.29 m, (b) 0.69 Hz, (c) 1.5 s Var: 1

4) An aluminum wire and a steel wire, each of length 2 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? The Young's modulus for aluminum is and for steel it is Answer: 1.3 mm Var: 1 5) When the pressure applied to an unknown liquid is increased from

the volume of the liquid decreases by 0.70%. Calculate the bulk modulus of the liquid. Answer: 6.4 × Var: 1

College Physics, 11e (Young) Chapter 12 Mechanical Waves and Sound 12.1 Multiple Choice Questions 1) If a wave has a wavelength of 25.4 cm and a frequency of 1.63 kHz, its speed is closest to A) 0.414 m/s B) 41.4 m/s C) 414 m/s D) 41,400 m/s E) 15.6 m/s Answer: C Var: 1 2) If a wave has a speed of 362 m/s and a period of 4.17 ms, its wavelength is closest to A) 1510 m B) 1.51 m C) 86.8 m D) 86,800 m E) 0.0115 m Answer: B Var: 1 3) 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+ 4) Crests of an ocean wave pass a pier every the 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

what is

5) Transverse waves propagate at in a string that is subjected to a tension of the 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+ 6) The density of aluminum is 2700 kg/m3. If transverse waves propagate at aluminum wire, what is the tension on the wire? A) 65 N B) 39 N C) 52 N D) 78 N Answer: A Var: 21

in a

7) A 2.31 kg rope is stretched between supports apart. If one end of the rope is tweaked, how long will it take for the resulting disturbance to reach the other end? Assume that the tension in the rope is A) 0.699 s B) 0.720 s C) 0.664 s D) 0.615 s Answer: A Var: 50+ 8) A uniform bar of metal, 0.40 m long, with a diameter of 2.0 cm, has a mass of A longitudinal wave is propagated along the length of the bar. A wave compression traverses the length of the bar in The wavelength of the longitudinal wave in the metal, in mm, is closest to: A) 2.2 B) 2.6 C) 3.0 D) 3.4 E) 3.8 Answer: A Var: 1

9) A string, 30 cm long and having a mass of 45 g, is attached to a 810 Hz vibrator at one end. The other end of the string is fixed and the string is kept under tension. The vibrator produces a transverse wave in the string, whose amplitude is and which propagates with a velocity of The energy of the wave is absorbed at the fixed end. In this situation, the tension in the string, in SI units, is closest to: A) 870 B) 830 C) 900 D) 940 E) 970 Answer: A Var: 50+ 10) Which of the following is a FALSE statement? A) In a transverse wave the particle motion is perpendicular to the velocity vector of the wave. B) Not all waves are mechanical in nature. C) The speed of a wave and the speed of the vibrating particles that constitute the wave are different entities. D) Waves transport energy and matter from one region to another. E) A wave in which particles move back and forth in the same direction as the wave is moving is called a longitudinal wave. Answer: D Var: 1 11) A wire, 6.0 m long, with a mass of 10 g, is under tension. A transverse wave is propagated on the wire, for which the frequency is 280 Hz, the wavelength is 0.60 m, and the amplitude is 8.4 mm. The time, for a crest of the transverse wave to travel the length of the wire, in ms, is closest to: A) 36 B) 31 C) 40 D) 44 E) 49 Answer: A Var: 50+ 12) A wire, 1.0 m long, with a mass of 90 g, is under tension. A transverse wave is propagated on the wire, for which the frequency is 890 Hz, the wavelength is 0.10 m, and the amplitude is 6.5 mm. The tension in the line, in SI units, is closest to: A) 710 B) 820 C) 930 D) 1,000 E) 1,100 Answer: A Var: 50+

Figure 12.1

13) In Figure 12.1, which of the curves best represents the variation of wave speed 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 14) A crane lifts a 2500 kg mass 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) 225 m/s B) 578 m/s C) 1220 m/s D) 1880 m/s E) 194 m/s Answer: E Var: 1 15) A 4.0 g string, 0.36 m long, is under tension. The string produces a 500 Hz tone when it vibrates in the third harmonic. The speed of sound in air is In this situation, the wavelength of the standing wave in the string, in SI units, is closest to: A) 0.24 B) 0.36 C) 0.54 D) 0.72 E) 0.90 Answer: A Var: 50+

16) A 2.0 g string, 0.67 m long, is under tension. The string produces a 700 Hz tone when it vibrates in the third harmonic. The speed of sound in air is The wavelength of the tone in air, in SI units, is closest to: A) 0.49 B) 0.55 C) 0.61 D) 0.67 E) 0.45 Answer: A Var: 50+ 17) A 4.0 g string, 0.39 m long, is under tension. The string produces a 600 Hz tone when it vibrates in the third harmonic. The speed of sound in air is The tension in the string, in SI units, is closest to: A) 250 B) 200 C) 160 D) 290 E) 340 Answer: A Var: 50+ 18) A string, 0.15 m long, vibrating in the n = 5 harmonic, excites an open pipe, long, into second overtone resonance. The speed of sound in air is The distance between a node and an adjacent antinode, in the string, in mm, is closest to: A) 15 B) 7.5 C) 23 D) 30 E) 150 Answer: A Var: 50+ 19) A string, 0.26 m long, vibrating in the n = 6 harmonic, excites an open pipe, long, into second overtone resonance. The speed of sound in air is The common resonant frequency of the string and the pipe, in SI units, is closest to: A) 590 B) 390 C) 490 D) 690 E) 760 Answer: A Var: 50+ 20) A string, 0.13 m long, vibrating in the n = 4 harmonic, excites an open pipe,

long,

into second overtone resonance. The speed of sound in air is waves in the string, in SI units, is closest to: A) 38 B) 36 C) 34 D) 32 E) 30 Answer: A Var: 50+

The velocity of transverse

21) When a guitar is tuned, 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 22) What is the frequency of the fundamental mode of vibration of a steel piano wire stretched to a tension of The wire is long and has a mass of A) 517 Hz B) 234 Hz C) 295 Hz D) 312 Hz E) 366 Hz Answer: C Var: 1 23) Which of the following is an accurate statement? A) A system like a vibrating string has only one possible frequency. B) In order for a singer to break a wine glass by singing, she must adjust the amplitude of the sound she makes so that it is exactly equal to the amplitude of vibration of the wine glass. C) The fundamental frequency of a system is the name given to the highest possible frequency at which the system will naturally vibrate. D) The sound in an organ pipe can vibrate at an infinite number of frequencies. Answer: D Var: 1

24) An open organ pipe is tuned to a given frequency. A second pipe with both ends open resonates with twice this frequency. What is the ratio of the length of the first pipe to the second pipe? A) 1 B) 2 C) 4 D) .5 Answer: A Var: 1 25) A violin with string length 32 cm and string density resonates with the first overtone of an organ pipe with one end closed. The pipe length is What is the tension in the string? A) 2,200 N B) 250 N C) 990 N D) 8,900 N E) 120 N Answer: A Var: 50+ 26) A 500.0 cm rope under a tension of is set into oscillation. The mass density of the rope is What is the frequency of the first harmonic mode A) 0.48 Hz B) 2.92 Hz C) 0.0048 Hz D) 0.153 Hz Answer: A Var: 50+ 27) A 0.588 m string is clamped at both ends. If the lowest standing wave frequency in the string is what is the wave speed? A) 383 m/s B) 475 m/s C) 582 m/s D) 724 m/s Answer: A Var: 50+

28) A string, 2.0 meters in length, is fixed at both ends and tightened until the wave speed is What is the frequency of the standing wave shown in Figure 12.2? Figure 12.2

A) 27 Hz B) 54 Hz C) 81 Hz D) 110 Hz Answer: A Var: 50+ 29) A standing wave is oscillating at 950 Hz on a string, as shown in Figure 12.3. What is the wave speed? Figure 12.3

A) 380 m/s B) 570 m/s C) 290 m/s D) 190 m/s Answer: A Var: 50+ 30) A guitar-like stringed instrument has a string that is 16 cm long. It sounds the musical note A when played without fingering. How far from the end of the string should you place your finger to play the note C A) 2.5 cm B) 1.7 cm C) 3.4 cm D) 4.2 cm Answer: A Var: 50+

Situation 12.1 A standing wave of the third overtone is induced in a stopped pipe, sound is

The speed of

31) In Situation 12.1, the number of antinodes in the standing wave pattern is: A) 3 B) 4 C) 5 D) 6 E) 7 Answer: B Var: 1 32) In Situation 12.1, the frequency of the sound produced by the pipe, in SI units, is closest to: A) 210 B) 280 C) 350 D) 430 E) 500 Answer: E Var: 1 33) 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? A) 21.3 mW B) 13.2 mW C) 17.9 mW D) 24.7 mW Answer: A Var: 50+ 34) A gamma ray (a pulse of electromagnetic energy) has a frequency of is the ratio of its wavelength to the radius of the nucleus which produced it A) 248 B) 39.4 C) 1.21 × 108 D) 0.015 Answer: A Var: 1

What

35) Calculate the light intensity 1.45 m from a equally in all directions. A) 3.79 W/m2 B) 4.36 W/m2 C) 47.6 W/m2 D) 54.7 W/m2 Answer: A Var: 50+

light bulb. Assume that the light radiates

36) A glass window is installed in the window space and the intensity level of the sound entering through the window is reduced from 72 dB to 47 dB. The factor, by which the acoustic power entering the chamber is reduced by the glass window, is closest to: 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+ 37) Which of the following increases when a sound becomes louder? A) Frequency B) Wavelength C) Amplitude D) Period E) Velocity Answer: C Var: 1 38) What is the intensity level in decibels of a sound whose intensity is A) 20 dB B) 30 dB C) 40 dB D) 50 dB E) 60 dB Answer: D Var: 1

39) An open pipe, 0.95 m long, vibrates in the second overtone with a frequency of In this situation, the distance from the center of the pipe to the nearest antinode, in cm, is closest to: A) 16 B) 7.9 C) 24 D) 32 E) zero Answer: A Var: 50+ 40) An open pipe, 0.92 m long, vibrates in the second overtone with a frequency of this situation, the speed of sound in air, in SI units, is closest to: A) 358 B) 349 C) 353 D) 344 E) 363 Answer: A Var: 50+ 41) An open pipe, 0.29 m long, vibrates in the second overtone with a frequency of this situation, the fundamental frequency of the pipe, in SI units, is closest to: A) 481 B) 633 C) 949 D) 1,270 E) 1,520 Answer: A Var: 50+

42) An open pipe, 0.85 m long, vibrates in the second overtone with a frequency of In this situation, the length of the shortest stopped pipe, that has the same resonant frequency as the open pipe in the second overtone, in cm, is closest to: A) 14 B) 7.1 C) 17 D) 28 E) 43 Answer: A Var: 50+

43) The howler monkey is the loudest land animal and can be heard up to a distance of 2.5 km. Assume the acoustic output of a howler to be uniform in all directions. The acoustic power emitted by the howler, in mW, is closest to: A) 0.079 B) 0.026 C) 0.26 D) 0.79 E) 2.6 Answer: A Var: 50+ 44) The howler monkey is the loudest land animal and can be heard up to a distance of 9.8 km. Assume the acoustic output of a howler to be uniform in all directions. The distance at which the intensity level of a howler's call is 25 dB, in SI units, is closest to: A) 550 B) 660 C) 830 D) 940 E) 1,100 Answer: A Var: 50+ 45) Two loudspeakers placed 6.0 m apart are driven in phase by an audio oscillator, whose frequency range is to A point P is located from one loudspeaker and from the other. The speed of sound is The frequency produced by the oscillator, for which constructive interference of sound occurs at point P, in SI units, is closest to: A) 2,189 B) 2,424 C) 2,111 D) 2,345 E) 2,267 Answer: A Var: 50+ 46) Two loudspeakers placed 6.0 m apart are driven in phase by an audio oscillator, whose frequency range is to A point P is located from one loudspeaker and from the other. The speed of sound is The frequency produced by the oscillator, for which destructive interference occurs at point P, in SI units, is closest to: A) 2,033 B) 2,127 C) 2,095 D) 2,064 E) 2,001 Answer: A Var: 50+

Situation 12.2 A train is approaching a signal tower at a speed of 40 m/s. The train engineer sounds the 1000 Hz whistle and a switchman in the tower responds by sounding the 1200 Hz siren. The air is still and the speed of sound is 47) In Situation 12.2, the frequency of the train whistle tone, heard by the switchman, in SI units, is given by: A) 1000 B) 300/340 × 1000 C) 340/300 × 1000 D) 340/380 × 1000 E) 380/340 × 1000 Answer: C Var: 1 48) In Situation 12.2, the frequency of the tower siren tone, heard by the engineer, in SI units, is closest to: A) 1200 B) 300/340 × 1200 C) 340/300 × 1200 D) 340/380 × 1200 E) 380/340 × 1200 Answer: E Var: 1 49) The tension in each of two strings is adjusted so that both vibrate at exactly 819 Hz. The tension in one of the strings 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+

Figure 12.4

50) In Figure 12.4 some wavefronts are emitted by a source of sound S. This picture can help us to understand A) why the siren on a police car changes its pitch as it races past us. B) why a sound grows quieter as we move away from the source. C) how sonar works. D) the phenomenon of beats. E) why it is that our hearing is best near 3000 Hz. Answer: A Var: 1 12.2 Short Answer Questions 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) A rope with a total mass of 25.0 kg is tied to a tree on one side of a 125 meter wide ravine, and you're pulling on the other end of the rope with a force of 415 N. If you pluck the rope, how long will it take the pulse to travel across the ravine to the tree? Answer: 2.74 seconds Var: 1 3) A plucked guitar string produces a sound wave of frequency 440 Hz. (a) What is the wavelength of the sound wave (assume the speed of sound in air is 340 m/s)? (b) How much time elapses between the impacts of two adjacent compressions on your eardrum? Answer: (a) 0.77 m (b) 2.3 × 10-3 s Var: 1 4) Standing waves of frequency 17 Hz are produced on a string that has mass per unit length With what tension must the string be stretched between two supports if adjacent

nodes in the standing wave are to be 0.87 meters apart? Answer: 14 N Var: 50+ Figure 12.5

5) In Figure 12.5, two identical loudspeakers, A and B, driven by the same amplifier, are separated by and produce sound waves of the same frequency. A small microphone is placed at point C, from speaker A along the line perpendicular to the line connecting the two speakers. At this point destructive interference occurs. If the microphone is now moved along this line to point D, 5.00 m from speaker A, constructive interference occurs. Find the frequency of the sound waves. The speed of sound is Assume that there are no other points between C and D where interference occurs. Answer: 724 Hz Var: 50+ 6) An organ pipe closed at one end has two successive harmonics with frequencies of and What is the fundamental frequency of the pipe? Answer: 310 Hz Var: 1 7) Two police cars have identical sirens that produce a 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 notices 9.0 beats per second. Find the speed of the approaching police car. (The speed of sound is Answer: 5.3 m/s Var: 50+ 8) The planet Pluto's average distance from the sun is 5.9 × 1012 m. Calculate the sun's intensity at the distance of Pluto, assuming the sun radiates a total power of 4.0 × 1026 W. Answer: 0.92 W/m2 Var: 1

9) A certain source of sound waves radiates uniformly in all directions. At a distance of 17 m from the source the intensity level is 49 db. What is the total acoustic power output of the source, in watts? (Note: The reference intensity is Answer: 2.9 × 10-4 watts Var: 50+ 10) Figure 12.6

In Figure 12.6, a man is traveling on a bicycle at 15 m/s along a straight road that runs parallel to some railroad tracks. He hears the whistle of a train that is behind him, as shown in the sketch. The frequency emitted by the train is but the frequency the man hears is Take the velocity of sound to be 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) 504 Hz b) 11 m/s, away from the bicycle Var: 50+ 11) What must be the length of an organ pipe that is open at one end and closed at the other if its fundamental frequency is to be 5 times that of a pipe that is 8.90 meters long and open at both ends? Answer: 0.890 meters Var: 50+

College Physics, 11e (Young) Chapter 13 Fluid Mechanics 13.1 Multiple Choice Questions Figure 13.1

1) A container has a vertical tube, whose inner radius is 24.00 mm, connected to it at its side. An unknown liquid reaches level A in the container and level B in the tube—level A being higher than level B. The liquid supports a 20.0 cm high column of oil, between levels B and C, whose density is In Figure 13.1, the mass of the oil, in grams, is closest to: A) 210 B) 410 C) 620 D) 820 E) 1,000 Answer: A Var: 50+ 2) A container has a vertical tube, whose inner radius is 12.00 mm, connected to it at its side. An unknown liquid reaches level A in the container and level B in the tube—level A being higher than level B. The liquid supports a 20.0 cm high column of oil, between levels B and C, whose density is In Figure 13.1, 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+

3) A container has a vertical tube, whose inner radius is 20.00 mm, connected to it at its side. An unknown liquid reaches level A in the container and level B in the tube—level A being higher than level B. The liquid supports a 20.0 cm high column of oil, between levels B and C, whose density is In Figure 13.1, the density of the unknown liquid is closest to: A) 3,600 kg/ B) 3,900 kg/ C) 2,800 kg/ D) 3,100 kg/ E) 3,300 kg/ Answer: A Var: 50+ 4) A submarine in neutral buoyancy is 100 m below the surface of the water. What air pressure must be supplied to remove water from the ballast tanks in order for the submarine to surface? A) 9.9 × 105 N/m2 B) 9.8 × 105 N/m2 C) 4.9 × 105 N/m2 D) Cross section area of the tank must be known. Answer: A Var: 1 5) A hollow steel ball of diameter ball?

barely floats in water. What is the wall thickness of the

A) 6.6 cm B) 37 cm C) 131 cm D) 79 cm Answer: A Var: 1 6) A pump uses a piston of 15 cm diameter which moves tube in diameter? A) 50 m/s B) 50 cm/s C) 6 cm/s D) 22 cm/s Answer: A Var: 1

What is the fluid velocity of a

7) A water tank is filled to a depth of 10 m and the tank is above ground. The water pressure at ground level in a hose in diameter is closest to A) 3.9 × 105 N/m2 B) 2.0 × 104 N/m2 C) 9.2 N/m2 D) The cross sectional area of the tank is needed. Answer: A Var: 1 8) A compressed gas with a total mass of is stored in a spherical container which has a radius of 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+ 9) The density of material at the center of a neutron star is approximately Calculate the mass of a cube of this material that is on each side. One micron is equal to A) 5.45 kg B) 4.74 kg C) 6.16 kg D) 6.70 kg Answer: A Var: 50+ 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 when a hurricane hits. The hurricane rapidly decreases the external air pressure to What net force (directed outwards) is exerted on a square window on the house? 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 by that the bottom of the person's foot is wide and A) 2.1 × 104 Pa B) 2.2 × 103 Pa C) 4.8 × 104 Pa D) 5.3 × 104 Pa Answer: A Var: 36

person standing on one foot. Assume long.

12) A cap 6.000 cm in diameter plugs an opening in a spherical container in diameter at atmospheric pressure. The container is submerged to a depth of in water. Assume the plug is planar and the pressure over the container is equalized. The force needed to remove the plug is closest to A) 85 N B) 340 N C) 3.381 × 106 N D) 277 N Answer: A Var: 50+ 13) A house is supported equally on 18 pilings each with a area at the base. The soil can withstand What could be the maximum mass of the house? A) 3.2 × 104 kg B) 6.3 × 104 kg C) 8.0 × 104 kg D) 1.6 × 104 kg Answer: A Var: 50+ 14) How much would a lead brick

A) 5.5 kg B) 0.34 kg C) 6 kg D) 0.49 kg Answer: A Var: 20

weigh if placed in oil with density

15) How many logs 3.00 m long and

in diameter are needed to just barely float a

car? A) 118 B) 117 C) 30 D) 29 Answer: A Var: 50+ 16) A 200.0 kg flat-bottomed boat floats in fresh water, which has a density of Assuming that the base of the boat is wide and long, how much of the boat is 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+ 17) A 4.7 kg solid sphere, made of metal whose density is 4,000 kg/ The density of water is cord is closest to: A) 35 N B) 40 N C) 46 N D) 52 N E) 58 N Answer: A Var: 50+

, is suspended by a cord.

When the sphere is immersed in water, the tension in the

18) A 8.6 kg solid sphere, made of metal whose density is 3,400 kg/ , is suspended 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: A) 1,900 kg/ B) 1,700 kg/ C) 1,600 kg/ D) 1,500 kg/ E) 1,400 kg/ Answer: A Var: 50+ 19) A 9.8 kg solid sphere, made of metal whose density is 3,000 kg/

, is suspended by a cord.

The sphere floats when placed in a liquid of density the sphere that is submerged is closest to: A) 0.71 B) 0.73 C) 0.75 D) 0.69 E) 0.67 Answer: A Var: 50+

The fraction of the volume of

20) How many grams of ethanol (specific gravity 0.80) should be added to 5 grams of chloroform (specific gravity 1.50) if the resulting mixture is to have a specific gravity of 1.20? A) 2.0 gms B) 2.4 gms C) 1.8 gms D) 4.4 gms E) 1.6 gms Answer: A Var: 1 21) Consider a brick that is totally immersed in water. The long edge of the brick is 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 22) An air bubble underwater has the same pressure as that of the 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

23) The tires of a car support the weight of a stationary car. If one tire has a slow leak, the air pressure within the tire will _______ with time, the surface area between the tire and the road will ________ in time, and the net force the tire exerts on the road will ___________ in time. A) decrease, increase, remain constant B) decrease, increase, decrease C) decrease, decrease, decrease D) increase, increase, increase E) decrease, increase, increase Answer: A Var: 1 24) A waitress 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 25) 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. E) none of the above Answer: C Var: 1 26) In England in the Middle Ages an extensive system of canals was used for transportation. Some of these canals crossed over canyons by flowing over bridges (viaducts). Suppose that a heavily loaded barge crossed over such a waterway bridge. A) The force downward on the bridge would increase because of the added weight of the barge. B) The force on the bridge would not change when the barge passed over. C) The force on the barge would become less because some water would be squeezed off of the bridge. D) The force on the bridge would become less because of the buoyancy effect of the water on the barge. E) Whether or not the force on the bridge would increase or decrease would depend on whether the water was flowing or stationary. Answer: B Var: 1

27) A barge loaded with lumber and iron ore floats in a lock by a dam (a closed pool of water like a big swimming pool). If some of the cargo is thrown overboard, the level of water in the lock will A) rise. B) drop. C) stay the same. D) rise, provided it is lumber that is thrown overboard. E) rise, provided it is iron ore that is thrown overboard. Answer: C Var: 1 Figure 13.2

28) In Figure 13.2, fluid fills the container shown here. 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 29) 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

30) Consider a very small hole in the bottom of a tank in diameter 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+ 31) A venturi is constructed of a pipe with a throat. Water pressure in the pipe is twice atmospheric pressure and it flows with a velocity of What is the pressure in the throat? A) 1.5 atm B) 0.49 atm C) 2.5 atm D) 2.0 atm Answer: A Var: 24 32) Water flowing through a pipe suddenly comes to a section of pipe where the pipe 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? A) 43 m/s B) 37 m/s C) 28 m/s D) 24 m/s Answer: A Var: 50+ 33) 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 pressure at the bottom of the trench in atmospheres. 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

34) 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? A) 0.825 g/cm3 B) 1.21 g/cm3 C) 1.65 g/cm3 D) 0.606 g/cm3 E) 0.350g/cm3 Answer: A Var: 1 35) What force does the water exert (in addition to that due to atmospheric pressure) on a submarine window of radius 44 cms at a depth of 9,400 meters in sea water (density 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+

Figure 13.3

36) A pressurized cylindrical tank, 5.0 m in diameter, contains water which emerges from the pipe at point C, with a velocity of Point A is 10 m above point B and point C is 3 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 the water is an ideal fluid in laminar flow. The density of water is In Figure 13.3, 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+ 37) A pressurized cylindrical tank, 5.0 m in diameter, contains water which emerges from the pipe at point C, with a velocity of Point A is 10 m above point B and point C is 3 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 the water is an ideal fluid in laminar flow. The density of water is In Figure 13.3, the rate at which the water level is falling in the tank, in mm/s, is closest to: A) 300 B) 340 C) 250 D) 210 E) 160 Answer: A Var: 50+

38) A pressurized cylindrical tank, 5.0 m in diameter, contains water which emerges from the pipe at point C, with a velocity of Point A is 10 m above point B and point C is 3 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 the water is an ideal fluid in laminar flow. The density of water is In Figure 13.3, the gauge pressure in the pipe at point B, in kPa, is closest to: A) 740 B) 710 C) 770 D) 800 E) 820 Answer: A Var: 50+ 39) The Bernoulli effect is described by the equation + 1/2ρ

1 + ρg

+ 1/2ρ

+ ρg

The origin of this relation is that it is a statement of A) the conservation of linear momentum. B) Newton's Third Law, i.e. equal action and reaction. C) the conservation of energy for a moving fluid. D) the continuity principle for fluids. E) F = ma as applied to a fluid. Answer: C Var: 1 40) The Bernoulli effect is responsible for the lift force on an airplane wing. Wings must therefore be designed so as to insure that A) air molecules will be deflected downward when they hit the wing. B) air molecules will be deflected upward when they hit the wing. C) air molecules move more rapidly past the upper surface of the wing than past the lower surface. D) air molecules move more rapidly past the lower surface of the wing than past the upper surface. E) wings are thick enough to create a significant pressure difference between the top and bottom surfaces of the wings because of the different heights of these surfaces. Answer: C Var: 1

13.2 Short Answer Questions 1) Figure 13.4

In Figure 13.4, water (density 1000 kg/ is

) is flowing in a pipeline. At point 1 the water velocity

Point 2 is 1.3 m above point 1. The cross-sectional area of the pipe is 0.04

1 and

at point 2. What is the pressure difference Answer: 5.49 × 104 Pa

at point

between points 1 and 2?

Var: 50+ Figure 13.5

2) In Figure 13.5, an open tank contains a layer of oil floating on top of a layer of water (density 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

(The density of the oil

is 450 kg/ . ) Answer: 13 meters Var: 50+ 3) A wooden raft has a mass of 55 kg. When empty it floats in water (density with 64% of its volume submerged. What mass of sand can be put on the raft without it sinking? Answer: 31 kg Var: 50+

4) A container consists of two vertical cylindrical columns of different diameter connected by a narrow horizontal section, as shown in Figure 13.6. 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 that at B 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 plate at B to balance it? Figure 13.6

Answer: 10.6 kg Var: 1

5) A large cylindrical water tank 11.5 m in diameter and 13.5 m tall is supported 8.75 m above the ground by a stand as shown in Figure 13.7. The water level in the tank is 10.6 m deep. 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. When this water hits the ground, how far has it traveled horizontally from the hole? Figure 13.7

Answer: 19.3 m Var: 1

College Physics, 11e (Young) Chapter 14 Temperature and Heat 14.1 Multiple Choice Questions 1) 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 Both rods have the same diameter. The rods are joined end-to-end to form a rod

long. The coefficients of linear expansion of aluminum and steel are

and respectively. The temperature is raised to of the joined rod, in mm, is closest to: A) 0.90 B) 0.81 C) 0.72 D) 0.63 E) 0.99 Answer: A Var: 50+

The increase in the length

2) Figure 14.1a

A brass rod is 63.0 cm long and an aluminum rod is 56.1 cm long when both rods are at an initial temperature of The rods are placed in line with a gap of between them. The distance between the far ends of the rods is maintained at 120.0 cm throughout. The temperature is raised until the two rods are barely in contact. The coefficients of linear expansion of brass and aluminum are and respectively. In Figure 14.1a, the temperature at which contact of the rods barely occurs, in °C, is closest to: A) 345 B) 328 C) 311 D) 363 E) 380 Answer: A Var: 50+

Figure 14.1b

A brass rod is 37.5 cm long and an aluminum rod is 81.3 cm long when both rods are at an initial temperature of The rods are placed in line with a gap of between them. The distance between the far ends of the rods is maintained at 120.0 cm throughout. The temperature is raised until the two rods are barely in contact. The coefficients of linear expansion of brass and aluminum are and respectively. In Figure 14.1b, the ratio of the increase in the length of the aluminum rod to that of the brass rod, is closest to: A) 2.60 B) 2.82 C) 3.04 D) 3.25 E) 3.47 Answer: A Var: 50+ 4) A glass flask has a volume of 500 ml at a temperature of 20° C. The flask contains of mercury at an equilibrium temperature of The temperature is raised until the mercury reaches the reference mark. The coefficients of volume expansion of mercury and glass are is closest to: A) 122 B) 112 C) 102 D) 110 E) 132 Answer: A Var: 50+

and

respectively. The temperature at which this occurs, in

Figure 14.2

Shown here is a device that can be used to turn a furnace on or off, depending on the temperature sensed by the device. 5) In Figure 14.2, the principle underlying the operation of this device is that A) different metals have different latent heats. B) different metals have different thermal conductivities. C) different metals have different thermal expansion coefficients. D) heat always flows from hot to cold, never from cold to hot. E) different metals have different heat capacities. Answer: C Var: 1 6) 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 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

7) 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. The increase in the length of the pipe, in mm, is closest to: A) 60 B) 57 C) 54 D) 64 E) 67 Answer: A Var: 50+ 8) A solid cylindrical bar conducts heat at a rate of 25 W from a hot to a cold reservoir. 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 9) A 45.0 kg sample of ice is at 0.00° C. How much heat is needed to melt it? (For water and A) 1.50 × 104 kJ B) 4.10 × 106 kJ C) 0.00 kJ D) 1.02 × 105 kJ Answer: A Var: 45 10) Heat is added to a 3.0 kg piece of ice at a rate of at to melt? (For water and A) 1.6 s B) 640,000 s C) 0.0 s D) 1,000 s Answer: A Var: 50+

How long will it take for the ice

11) 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 and A) 130 kJ B) 14,000 kJ C) 81 kJ D) 59 kJ Answer: A Var: 50+ 12) A 2,294 kg sample of water at 0° C is cooled to much heat is liberated? (For water and

and freezes in the process. How The specific heat for ice

is A) 935,000 kJ B) 597,000 kJ C) 1,110,000 kJ D) 334,000 kJ Answer: A Var: 50+ 13) A 771.0 kg copper bar is put into a smelter for melting. The initial temperature of the copper is How much heat must the smelter produce to completely melt the copper bar? (The specific heat for copper is the heat of fusion for copper is and its melting point is A) 4.73 × 105 kJ B) 3.15 × 1011 kJ C) 3.15 × 108 kJ D) 5.62 × 105 kJ Answer: A Var: 50+ 14) A 7 kg sample of mercury is completely solidified and liberates the original temperature of the mercury? (The melting point of mercury is fusion of mercury is and the specific heat of mercury is A) 240 K B) 580 K C) 2.0 K D) 850 K Answer: A Var: 16

of energy. What is the heat of

15) A person consumes a large meal containing it is to be "burned off" due to exercise in 6 hours? A) 2.7 W B) 9,763 W C) 0.6 W D) 0.0027 W Answer: A Var: 9

What is the power this meal produces if

16) 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 Find the specific heat of the object. A) 7.46 J/kg ∙ K B) 1,500 J/kg ∙ K C) 0.00130 J/kg ∙ K D) 3,020,000 J/kg ∙ K Answer: A Var: 50+ 17) 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 A) 33,900 J B) 40,500 J C) 8,110 J D) 40,100 J Answer: A Var: 50+ 18) 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 A) 71 s B) 4.1 s C) 17 s D) 320,000 s Answer: A Var: 50+ 19) A 960.0 g iron meteor impacts the earth at a speed of If its kinetic energy is entirely converted to heat of the meteorite, what will the resultant temperature rise be? (The specific heat for iron is A) 1,700° C B) 1,630,000° C C) 1.80° C D) 7,110° C Answer: A Var: 50+

20) 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 for glass is A) 140 g B) 560 g C) 540 g D) 270,000 g Answer: A Var: 37 21) 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, 1000, and respectively. The quantity of heat required to raise the temperature of of the substance from to in kJ, is closest to: A) 260 B) 190 C) 230 D) 92 E) 320 Answer: A Var: 50+ 22) 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, 1000, and respectively. The quantity of heat surrendered by of the substance when it is cooled from 170°C to 86°C, at a pressure of one atmosphere, in kJ, is closest to: A) 400 B) 200 C) 300 D) 440 E) 640 Answer: A Var: 50+

23) A 360 g metal container, insulated on the outside, holds 180 g of water in thermal equilibrium at A 24 g ice cube, at the melting point, is dropped into the water, and when thermal equilibrium is reached the temperature is Assume there is no heat exchange with the surroundings. For water, the specific heat capacity is and the heat of fusion is The specific heat capacity for the metal is closest to: A) 1,680 J/kg ∙ K B) 969 J/kg ∙ K C) 2,280 J/kg ∙ K D) 2,780 J/kg ∙ K E) 3,280 J/kg ∙ K Answer: A Var: 50+ Figure 14.3

24) In Figure 14.3, heat is added to a pure substance in a closed container at a constant rate. A graph of the temperature of the substance as a function of time is shown here. If heat of fusion and heat of vaporization, what is the value of the ratio LV/LF for this substance? A) 5.0 B) 4.5 C) 7.2 D) 3.5 E) 1.5 Answer: D Var: 1

25) You may have noticed that when you get out of a swimming pool and stand dripping wet in a light breeze, you feel much colder than you feel after you dry off. Why is this? A) The moisture on your skin has good thermal conductivity. B) Water has a relatively large heat capacity. C) This is a purely psychological effect resulting from the way in which sensory nerves in the skin are stimulated. D) The water on your skin is colder than the surrounding air. E) 540 calories of heat are required to evaporate each gram of water from your skin, and most of this heat flows out of your body. Answer: E Var: 1 26) How much heat must be added to a 8 kg block of ice at -8°C to change it to water at A) 780 kcal B) 140 kcal C) 180 kcal D) 810 kcal E) 730 kcal Answer: A Var: 50+ 27) An 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 Assume there is no external heat exchange.The specific heat capacities of aluminum and water are 910 and respectively. The specific heat capacity of the metal is closest to: 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+ 28) A 100 g aluminum calorimeter contains 500 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 Assume there is no external heat exchange.The specific heat capacities of aluminum and water are 910 and respectively. The ratio of the quantity of heat gained by the aluminum to that of the water, is closest to: A) 0.04 B) 0.08 C) 0.12 D) 0.16 E) 0.20 Answer: A Var: 50+

Situation 14.1 Two experimental runs are performed to determine the calorimetric properties of an alcohol which has a melting point of In the first run, a cube of frozen alcohol, at the melting point, is added to of water at in a styrofoam container. When thermal equilibrium is reached, the alcohol-water solution is at a temperature of In the second run, an identical cube of alcohol is added to of water at and the temperature at thermal equilibrium is The specific heat capacity of water is Assume the styrofoam container and the surroundings do not partake in the heat exchange. 29) In Situation 14.1, the heat of fusion of the alcohol is closest to: A) 5.5 × J/kg B) 6.3 ×

J/kg

C) 7.1 ×

J/kg

D) 7.9 ×

J/kg

E) 8.7 × J/kg Answer: B Var: 1 30) In Situation 14.1, the specific heat capacity of the alcohol is closest to: 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 31) A heat conducting rod, 0.90 m long, is made of an aluminum section, 0.20 m long, and a copper section, long. Both sections have a cross-sectional 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 and 385 W/m ∙ K, respectively. The temperature of the aluminum-copper junction in the rod, in is closest to: A) 100 B) 93 C) 86 D) 80 E) 74 Answer: A Var: 50+

32) A heat conducting rod, 1.60 m long, is made of an aluminum section, 0.90 m long, and a copper section, long. Both sections have a cross-sectional 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 and 385 W/m ∙ K, respectively. The rate at which heat is conducted in the rod is closest to: A) 9.0 W B) 7.9 W C) 10 W D) 11 W E) 12 W Answer: A Var: 50+ Figure 14.4

33) A solid sample of a pure compound is contained in a closed, well-insulated container. Heat is added at a constant rate and the sample temperature is recorded. The resulting data is graphed in Figure 14.4. Which of the following conclusions is justified from the graph shown? A) The sample never boiled. B) The heat of fusion is greater than the heat of vaporization. C) After 5 minutes the sample was a mixture of solid and liquid. D) The heat capacity of the solid phase was greater than that of the liquid phase. E) After 20 minutes the solid was all liquid. Answer: C Var: 1

34) Some properties of glass are listed here.

A glass window pane is 2.7 m high, 2.4 m wide and 9 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+ Situation 14.2 A heat-conducting rod is constructed with a 0.15 m length of alloy A and a

length of

alloy B, joined end-to-end. Both pieces have cross-section areas of 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 and the other end of the rod is maintained at an unknown temperature. The temperature at the junction of the alloys is The rate of heat flow in the rod is 35) In Situation 14.2, the temperature of the end of the rod in alloy B, in °C, is closest to: A) 80 B) 84 C) 88 D) 92 E) 96 Answer: B Var: 1 36) In Situation 14.2, the thermal conductivity of alloy A is closest to: 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

Situation 14.3 A concrete wall of a cold storage room measures 3.0 m high, 5.0 m wide, and thick. The room temperature is maintained at and the outside temperature is 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 thermal conductivities of concrete and wood are 0.8 and respectively. 37) In Situation 14.3, the temperature difference across the layer of wood, in °C, is closest to: A) 24 B) 25 C) 26 D) 27 E) 28 Answer: D Var: 1 38) In Situation 14.3, the thickness of the layer of wood required, in mm, is closest to: A) 60 B) 70 C) 80 D) 90 E) 100 Answer: D Var: 1 39) Which of the following is a true statement? A) Several days after a snowstorm, the roof on Jones's house is uniformly covered with snow, whereas on Smith's house next door the snow has completely melted off. A likely reason for this is that Smith's house has better roof insulation than does Jones's. B) When you get out of a swimming pool and stand dripping wet in a breeze you feel colder than you would if your skin were dry. This is a purely psychological effect, since measurement of your skin temperature would yield the same value in both cases, wet or dry. C) In some regions the following sign is frequently seen as one approaches a bridge: "CAUTION: BRIDGE MAY BE ICY". One reason you might expect a bridge to be icier than the road leading up to it is that the bridge has both its top and bottom exposed to cold air, whereas only the top surface of the road is in contact with cold air. D) When the metal cooling coils in a freezer become coated with ice this helps the freezer more effectively remove heat from warm foods placed in the freezer. E) Thermos bottles have a vacuum between the inner and outer layers of glass in order to reduce heat transfer due to radiation, since radiation cannot travel through a vacuum. Answer: C Var: 1

Figure 14.5

40) In Figure 14.5, an architect is interested in estimating the heat loss (in kcal/sec) 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, which of the graphs best represents the 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 41) A sphere of surface area 1.25 m2 and emissivity 1.0 is at a temperature of 100.0°C. The rate at which it radiates heat into empty space is closest to A) 7.1 W B) 0.71 mW C) 1.4 kW D) 9.9 mW E) 3.7 W Answer: C Var: 1 42) An object having an emissivity 0.725 radiates heat at a rate of 10 W when it is at a temperature T. If its temperature is doubled, it will radiate at a rate of A) 160 W B) 80 W C) 40 W D) 20 W Answer: A Var: 1

43) A sphere, 0.30 m in radius, has a surface emissivity of 0.48 and is at a temperature of The sphere is surrounded by a concentric spherical shell whose inner surface has a radius of and an emissivity of 1.00. The temperature of the shell is 400 K. The rate at which heat is radiated, including direction, in the space between the sphere and the shell, in kW, is closest to: A) 4.0, outward B) 8.3, outward C) 18.8, outward D) 6.5, inward E) 10.8, inward Answer: E Var: 1 44) In years of heavy snow pack in the mountains it is sometimes desirable to induce early melting of the snow, rather than wait until it all melts suddenly and causes floods. It has been suggested that a way to accomplish this might be to have planes fly over the snow fields and sprinkle them with black soot. What do you think of this idea? Would it work? A) Yes, it would probably work because the black surface would be a better absorber of sunlight than would the white snow. B) Yes, it would work because the soot would raise the melting point of the snow. C) Yes, it would work because the soot would decrease the specific heat capacity of the snow. D) No, it would not work because it is infrared radiation and not visible radiation which melts the snow. E) No, it would not work because sunlight has very little effect on how fast the snow melts. Answer: A Var: 1 14.2 Short Answer Questions 1) A rod, with sides insulated to prevent heat loss, has one end immersed in boiling water and the other end in a water-ice mixture. The rod has uniform cross-sectional area and length The heat conducted by the rod melts the ice at a rate of 1 gram every 11 seconds. What is the thermal conductivity of the rod? (Recall that the heat of fusion of water is Answer: 370 W/m ∙ °C Var: 50+ 2) 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 and of ice is For water the normal melting point is and the heat of fusion is is Answer: 430 g Var: 50+

The normal boiling point is

and the heat of vaporization

3) A radiating body has a Kelvin temperature

, and its surroundings are at

If the Kelvin temperature of the radiating body is increased to

, the net rate at which the body

radiates increases by a factor of 39. What was the original temperature

Answer: 567 K Var: 50+ 4) A piece of iron of mass 0.12 kg is taken from an oven where its temperature is and quickly placed in an insulated copper can that contains of water. The copper can has mass and it and the water in it are originally at a temperature of Calculate the final temperature of the system, assuming no heat is lost to the surroundings. Use the following specific heats: water, iron, and copper, Answer: 36°C Var: 1 5) 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

College Physics, 11e (Young) Chapter 15 Thermal Properties of Matter 15.1 Multiple Choice Questions 1) A sealed 62 temperature of oxygen is A) 4.6 B) 2.3 C) 3.5 D) 5.8 E) 9.3 Answer: A Var: 50+

tank is filled with 9,000 moles of ideal oxygen gas (diatomic) at an initial The gas is heated to a final temperature of 390 K. The atomic mass of The mass density of the oxygen gas, in SI units, is closest to:

2) A sealed 29 temperature of oxygen is A) 0.70 B) 0.79 C) 0.88 D) 0.61 E) 0.51 Answer: A Var: 50+

tank is filled with 9,000 moles of ideal oxygen gas (diatomic) at an initial The gas is heated to a final temperature of 330 K. The atomic mass of The initial pressure of the gas, in MPa, is closest to:

3) A sealed 19 temperature of oxygen is A) 1.9 B) 2.0 C) 2.2 D) 2.3 E) 2.4 Answer: A Var: 50+

tank is filled with 9,000 moles of ideal oxygen gas (diatomic) at an initial The gas is heated to a final temperature of 490 K. The atomic mass of The final pressure of the gas, in MPa, is closest to:

4) A sealed 87 temperature of oxygen is A) 24 B) 28 C) 19 D) 14 E) 9.1 Answer: A Var: 50+

tank is filled with 6,000 moles of ideal oxygen gas (diatomic) at an initial The gas is heated to a final temperature of 460 K. The atomic mass of The heat transferred to the gas, in MJ, is closest to:

5) A 5.3 L volume of ideal neon gas (monatomic) is at a pressure of 6.0 atmospheres and a temperature of The atomic mass of neon is The mass of the neon gas, in SI units, is closest to: 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+ 6) A 4.2 L volume of ideal neon gas (monatomic) is at a pressure of 3.3 atmospheres and a temperature of The atomic mass of neon is The number of neon atoms in the gas is closest to: A) 2.2 × B) 2.2 × C) 6.9 × D) 2.2 × E) 6.9 × Answer: A Var: 50+

7) A 3.9 L volume of ideal neon gas (monatomic) is at a pressure of 5.6 atmospheres and a temperature of The atomic mass of neon is In this situation, the temperature of the gas is increased to 430 and the volume is increased to The final pressure of the gas, in atmospheres, is closest to: A) 4.8 B) 4.3 C) 5.3 D) 5.8 E) 6.3 Answer: A Var: 50+ 8) In the equation pV = nRT, A) T is measured in degrees Celsius. B) R has different values for different gases. C) V is the velocity of the flowing gas. D) n is the number of moles of gas. Answer: D Var: 1 9) A 0.90

gas tank holds 9.0 moles of ideal nitrogen gas (diatomic), at a temperature of

The atomic mass of nitrogen is and the molecular radius is mass density of the gas, in SI units, is closest to: A) 0.28 B) 0.14 C) 0.19 D) 0.33 E) 0.38 Answer: A Var: 50+ 10) A 0.40

The

gas tank holds 7.0 moles of ideal nitrogen gas (diatomic), at a temperature of

The atomic mass of nitrogen is pressure of the gas, in kPa, is closest to: A) 42 B) 37 C) 32 D) 27 E) 22 Answer: A Var: 50+

and the molecular radius is

The

11) A 0.50

gas tank holds 3.0 moles of ideal nitrogen gas (diatomic), at a temperature of

The atomic mass of nitrogen is and the molecular radius is rms speed of the molecules, in SI units, is closest to: A) 560 B) 790 C) 390 D) 21 E) 97 Answer: A Var: 50+

The

12) A 24 liter tank contains ideal helium gas at 27°C and a pressure of 22.0 Atm. How many moles of gas are in the tank? A) 238 moles B) 138 moles C) 17.5 moles D) 21.5 moles E) 76.0 moles Answer: D Var: 1 13) A cylinder fitted with a movable piston contains ideal gas at 27°C, pressure and volume the pressure rises to A) 41.8°C B) 67.7°C C) 125°C D) 246°C E) 154°C Answer: A Var: 1

What will be the final temperature if the gas is compressed to

and

Situation 15.1 A sealed container holds 0.020 moles of ideal nitrogen ( and a temperature of

) gas, at a pressure of 1.5 atmospheres

The atomic mass of nitrogen is

14) In Situation 15.1, the number of molecules in the gas, is closest to: A) 1.5 × B) 3.0 × C) 6.0 × D) 1.2 × E) 2.4 × Answer: D Var: 1 15) In Situation 15.1, the mass density of the gas, in SI units, is closest to: A) 0.9 B) 1.3 C) 1.8 D) 2.2 E) 2.6 Answer: C Var: 1 16) In Situation 15.1, the average translational kinetic energy of a nitrogen molecule, in SI units, is closest to: A) 4 x B) 6 x C) 8 x D) 10 x E) 12 x Answer: B Var: 1

17) In Situation 15.1, the quantity of heat, transferred at constant volume, that raises the temperature of the gas to in SI units, is closest to: A) 1.8 B) 2.5 C) 3.3 D) 4.2 E) 5.0 Answer: D Var: 1 18) What is the average translational kinetic energy of an ideal gas at

(The value of

Boltzmann's constant is 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+ 19) At what temperature would the root mean square speed of oxygen molecules be Oxygen is assumed to approximate an ideal gas. The mass of one molecule is A) 0.251 K B) 2,090 K C) 6,270 K D) 1.52 × 1023 K Answer: A Var: 6 20) The temperature 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

21) An oxygen molecule falls in a vacuum. From what height must it fall so that its kinetic energy at the bottom equals the average energy of an oxygen molecule at 920 K? A) 36,500 meters B) 12,100 meters C) 24,300 meters D) 48,700 meters Answer: A Var: 50+ 22) The oxygen molecules and the nitrogen molecules at any one place in our atmosphere are at the same temperature. How do the root-mean-square speeds of the two molecules compare? A) same B) N2 > O2 C) O2 > N2 Answer: B Var: 1 23) Figure 15.1 shows 2.6 g of ideal helium gas that undergoes the process value of . Figure 15.1

A) 25 liters B) 99 liters C) 50 liters D) 12 liters Answer: A Var: 50+

Find the

24) Figure 15.2 shows a PV diagram for 8.3 g of ideal nitrogen gas in a sealed container. The temperature of state 1 is 59° C. What are (a) pressure p1 and (b) temperature T2? Figure 15.2

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+ 25) Figure 15.2 shows a PV diagram for 2.9 g of ideal oxygen gas in a sealed container. The temperature of state 1 is 76° C. 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+ 26) Figure 15.3 shows 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?

Figure 15.3

A) -160°C B) 12°C C) 380°C D) 110°C Answer: A Var: 50+ 27) Figure 15.4 shows 0.0061 mol of ideal gas that undergoes the process 1 → 2 → 3. What is the pressure p2? Figure 15.4

A) 4.9 atm B) 4.9 × 105 atm C) 15 atm D) 1.5 × 106 atm Answer: A Var: 30

28) Figure 15.4 shows 0.0081 mol of ideal gas that undergoes the process 1 → 2 → 3. What is the volume V3? A) 810 B) 670 C) 540 D) 400 Answer: A Var: 47 29) Figure 15.5 shows a 50 kg lead cylindrical piston which floats on 0.37 mol of compressed ideal air at 30°C. How far does the piston move if the temperature is increased to 300°C? Figure 15.5

A) 65 cm B) 140 cm C) 73 cm D) 730 cm Answer: A Var: 50+ 30) An ideal gas in a balloon is kept in thermal equilibrium with its constant-temperature surroundings. How much work is done by the gas if the pressure is slowly reduced and the balloon expands to 7.0 times its original size? The balloon initially has a pressure of and has a volume of A) 94 J B) 340 J C) 81 J D) 5.8 J Answer: A Var: 50+

31) A container with rigid walls is filled with 4 mol of air with internal energy change if the temperature rises from A) 28,000 J B) 337 J C) 2,800 J D) 7,000 J Answer: A Var: 50+

How much does the

32) Dust particles in a grain elevator frequently have masses of the order of rms speed of such a particle in air at A) 3.5 ×

m/s

B) 5.6 ×

m/s

C) 7.8 ×

m/s

D) 5.2 ×

m/s

E) 4.9 × Answer: A Var: 1

m/s

kg. What is the

33) A 500 g cube of copper is heated from 0°C at constant volume. The atomic mass of copper is Assume the rule of Dulong and Petit is applicable. The heat required for the temperature change, in kJ, is closest to: A) 10 B) 13 C) 17 D) 20 E) 23 Answer: D Var: 1 34) The temperature of an ideal gas in a sealed 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 The heat absorbed by the gas, in kJ, is closest to: A) -130 B) -170 C) 130 D) 170 E) zero Answer: A Var: 50+ 35) The temperature of an ideal gas in a sealed 0.20

container is reduced from 360 K to

The final pressure of the gas is The molar heat capacity at constant volume of the gas is The work done by the gas, in kJ, is closest to: A) zero B) -9.0 C) -12 D) 9.0 E) 12 Answer: A Var: 50+ 36) A compression, at a constant pressure of 140 kPa, is performed on 4.0 moles of an ideal monatomic gas The compression reduces the volume of the gas from to The change in the internal energy of the gas, in kJ, is closest to: A) -29 B) -49 C) 29 D) 49 E) zero Answer: A Var: 50+ 37) A compression, at a constant pressure of 200 kPa, is performed on 8.0 moles of an ideal monatomic gas The compression reduces the volume of the gas from to The work done by the gas, in kJ, is closest to: A) -16 B) 16 C) -40 D) 40 E) zero Answer: A Var: 50+

38) A monatomic ideal gas (

= 3/2 R) undergoes an isothermal expansion at 300 K, as the

volume increased from to The final pressure is internal energy of the gas, in kJ, is closest to: A) zero B) 3.6 C) 7.2 D) -3.6 E) -7.2 Answer: A Var: 50+

The change in the

39) A monatomic ideal gas (

= 3/2 R) undergoes an isothermal expansion at 300 K, as the

volume increased from the gas, in kJ, is closest to: A) 21 B) 11 C) -21 D) -11 E) zero Answer: A Var: 50+

The final pressure is

40) An expansion process on a diatomic ideal gas (

The heat transfer to

= 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 The work done by the gas, in SI units, is closest to: A) 13,000 B) 6,300 C) 9,400 D) 16,000 E) 19,000 Answer: A Var: 50+

41) An expansion process on a diatomic ideal gas (

= 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 The change in the internal energy of the gas, in SI units, is closest to: A) -2,900 B) -1,700 C) 2,900 D) 1,700 E) zero Answer: A Var: 50+ Figure 15.6

42) In Figure 15.6 is a cyclic process carried out in a gas. Which of the following is an accurate statement? A) The work done in the process is equal to the area enclosed by the cyclic process. B) The work done in the process is equal under the curve abc. C) The work done in the process is equal to the area under the curve adc. D) The work done in the process is equal to the area under ab minus the area under dc. E) The work done in the process is zero. Answer: A Var: 1

Figure 15.7

43) In Figure 15.7, an ideal gas is carried around the cyclic process. How much work is done in one cycle if and liters? A) 1,210 J B) 485 J C) 2,280 J D) 2,420 J E) 4,850 J Answer: A Var: 50+ 44) Which of the following is a FALSE statement? A) Heat is energy transferred into or out of a system as a result of a temperature difference between the system and its surroundings. B) The heat added to an ideal gas during the transition from state 1 to state 2 depends only on the initial and final states, 1 and 2, and not on the path by which the gas went from one to the other. C) When a gas goes from one state to another, the work done depends on the path followed. D) It does not make sense to refer to "the amount of heat in a body". E) When an ideal gas experiences a free expansion, its temperature doesn't change. Answer: B Var: 1

45) 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 The heat absorbed by the gas, in kJ, is closest to: A) -22 B) -17 C) 22 D) 17 E) -5.7 Answer: A Var: 50+ 46) 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 equals 0.70 times the initial volume. The molar heat capacity at constant volume of the gas is The change in the the internal energy of the gas, in kJ, is closest to: A) -28 B) -38 C) 28 D) 38 E) -9.7 Answer: A Var: 50+ 47) A cylinder contains 9 moles of an ideal gas at a temperature of 300 K. The gas is compressed at constant pressure until the final volume equals 0.68 times the initial volume. The molar heat capacity at constant volume of the gas is The adiabatic constant for the gas is closest to: A) 1.35 B) 1.40 C) 1.47 D) 1.56 E) 1.67 Answer: A Var: 50+

48) A sealed 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 1.9 times the initial pressure. The heat capacity at constant pressure of the gas is The heat absorbed by the gas, in kJ, is closest to: A) 110 B) 170 C) 230 D) -52 E) 7.0 Answer: A Var: 50+ 49) A sealed 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 1.4 times the initial pressure. The heat capacity at constant pressure of the gas is The change in the internal energy of the gas, in kJ, is closest to: A) 77 B) 100 C) 130 D) -50 E) -23 Answer: A Var: 50+ 50) A sealed tank contains 49 moles of an ideal gas, at an initial temperature of The pressure of the gas is increased until the final pressure equals 2.2 times the initial pressure. The heat capacity at constant pressure of the gas is The adiabatic constant of the gas is closest to: A) 1.42 B) 1.30 C) 1.73 D) 1.23 E) 1.19 Answer: A Var: 50+

51) 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) 1/2 v B) v C) 2v D) 4v E) v/4 Answer: C Var: 1 Situation 15.2 Twenty moles of a monatomic ideal gas (γ = 5/3) undergo an adiabatic process. The initial pressure is and the initial temperature is The final temperature of the gas is

52) In Situation 15.2, the final volume of the gas, in SI units, is closest to: A) 0.19 B) 0.23 C) 0.27 D) 0.31 E) 0.35 Answer: D Var: 1 53) In Situation 15.2, the heat absorbed by the gas, in kJ, is closest to: A) zero B) +32 C) +54 D) -32 E) -54 Answer: A Var: 1 54) In Situation 15.2, the change in the internal energy of the gas, in kJ, is closest to: A) zero B) +32 C) +54 D) -32 E) -54 Answer: D Var: 1

Situation 15.3 An adiabatic process is performed on 15 moles of an ideal gas. The initial temperature is 320 K and the initial volume is The final volume is The adiabatic constant for the gas is 1.44. 55) In Situation 15.3, the final temperature of the gas, in SI units, is closest to: A) 435 B) 450 C) 465 D) 480 E) 495 Answer: A Var: 1 56) In Situation 15.3, the heat absorbed by the gas, in kJ, is closest to: A) zero B) +14 C) +32 D) -14 E) -32 Answer: A Var: 1 57) In Situation 15.3, the work done by the gas, in kJ, is closest to: A) zero B) +14 C) +32 D) -24 E) -32 Answer: E Var: 1 58) In Situation 15.3, the heat capacity at constant pressure for the gas, in SI units, is closest to: A) 23 B) 25 C) 27 D) 29 E) 31 Answer: C Var: 1

59) For an ideal gas the internal energy U depends only on A) volume. B) temperature. C) pressure. Answer: B Var: 1 60) The internal energy of an ideal gas A) does not depend on how many moles of gas are in the system. B) depends on the volume of the gas. C) depends on the pressure of the gas. D) depends only on the temperature of the gas, and not on pressure or volume. E) More than one of the above are true. Answer: D Var: 1 Situation 15.4 A substance has a density of 2000 kg/ substance has a boiling point of has a density of

in the liquid state. At atmospheric pressure, the and a heat of vaporization of

The vapor

at the boiling point and at atmospheric pressure.

61) In Situation 15.4, the work done by 1.0 kg of the substance, as it vaporizes at atmospheric pressure, in kJ, is closest to: A) 20 B) 30 C) 40 D) 50 E) 60 Answer: A Var: 1 62) In Situation 15.4, the change in the internal energy of 1.0 kg of the substance, as it vaporizes at atmospheric pressure, in kJ, is closest to: A) 120 B) 140 C) 160 D) 180 E) 200 Answer: B Var: 1

63) When an ideal gas is expanded in volume at constant pressure, the average kinetic energy of the gas molecules A) increases. B) decreases. C) does not change. D) may either increase or decrease, depending on whether or not the process is carried out adiabatically. E) may or may not change, but insufficient information is given to make such a determination. Answer: A Var: 1 64) An ideal gas with γ = 1.67 is initially at 0°C in a volume of 10.0 liters at a pressure of 1.00 atm. It is expanded adiabatically to a volume of 10.4 liters. What then is the temperature? A) -7.10°C B) 2.53°C C) -22.7°C D) 67.8°C E) -19.5°C Answer: A Var: 1 15.2 Short Answer Questions Figure 15.8

1) In Figure 15.8, in a certain process 1,190 J of heat flows into a system, and at the same time the system expands against a constant external pressure of If the volume of the system increases from to calculate the change in internal energy of the system. If the internal energy change is nonzero, be sure to indicate whether the internal energy change is positive or negative. Answer: -3,010 J Var: 50+

2) 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 gas constant is Calculate: (a) the work W done by gas (b) the net change in the internal energy, ΔU, of the gas, and (c) the heat transfer Q. Answer: (a) W = -7,200 J (b) ΔU = -12,000 J (c) Q = -19,000 J Var: 50+ 3) 2.5 moles of an ideal gas is at an initial temperature of 30°C and has an initial volume of The gas expands adiabatically to a volume of For the gas, The gas constant is Calculate the internal energy change of the gas during this expansion. Answer: -5700 J Var: 1 4) If a certain sample of an ideal gas has a temperature of 104°C and exerts a pressure of on the walls of its container, how many gas molecules are present in each of volume? Assume that the gas is ideal. The gas constant is and Avagadro's number is

molecules/mol.

Answer: 4.5 × 1018 molecules Var: 50+

Figure 15.9

5) In Figure 15.9, an air pocket at the top of a vertical tube, closed at the upper end and open at the lower, occupies a volume of at the surface of a lake where the air pressure is and the temperature is What is the volume of the air in the pocket if the tube is taken to a depth of 56 meters, where the temperature is Assume that none of the air escapes from the tube. The density of the water in the lake is Answer: 78 Var: 50+ 6) What is the total translational kinetic energy in a classroom filled with nitrogen at and The dimensions of the classroom are Answer: 3.19 × 107 J Var: 50+ 7) A flask contains a mixture of argon and neon gases. The root-mean-square speed of the argon gas is determined to be 1210 m/s. What is the root-mean-square speed of the neon gas? The atomic masses are argon, 39.95 g/mole; neon, 20.18 g/mole. Answer: 1700 m/s Var: 1

College Physics, 11e (Young) Chapter 16 The Second Law of Thermodynamics 16.1 Multiple Choice Questions 1) A 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 for the air conditioner under these operating conditions, in SI units, is closest to: A) 3,600 B) 4,400 C) 5,100 D) 5,800 E) 6,600 Answer: A Var: 50+ 2) A 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 per second and maintains the room at a temperature of when the outside temperature is The power requirement for the heat pump under these operating conditions, in SI units, is closest to: A) 8,900 B) 7,100 C) 20,000 D) 15,000 E) 11,000 Answer: A Var: 50+ 3) A real (non-Carnot) heat engine, operating between heat reservoirs at temperatures of and performs 3.3 kJ of net work, and rejects of heat, in a single cycle. The thermal efficiency of this heat engine is closest to: A) 0.29 B) 0.26 C) 0.23 D) 0.32 E) 0.34 Answer: A Var: 50+

4) A real (non-Carnot) heat engine, operating between heat reservoirs at temperatures of and performs 4.1 kJ of net work, and rejects of heat, in a single cycle. The thermal efficiency of a Carnot heat engine, operating between the same heat reservoirs, in percent, is closest to: A) 62 B) 56 C) 50 D) 43 E) 37 Answer: A Var: 50+ 5) A 700 g quantity of an ideal gas undergoes a reversible isothermal compression at a temperature of The compression reduces the volume of the gas from initially, to finally. The molecular mass of the gas is SI units, is closest to: A) -150 B) -57 C) 150 D) 57 E) zero Answer: A Var: 50+

The entropy change for the gas, in

6) A 420 g quantity of ethanol, in the liquid state at its melting point of

is frozen at

atmospheric pressure. The heat of fusion of ethanol is and the molecular mass is The change in the entropy of the ethanol as it freezes, in SI units, is closest to: A) -280 B) -250 C) -310 D) 250 E) 280 Answer: A Var: 50+ 7) A Carnot heat engine operates between

and

What is its efficiency?

A) 0.38 B) 0.62 C) 0.61 D) 1.61 Answer: A Var: 50+ 8) A Carnot heat engine has an efficiency of 0.600. If it operates between a deep lake with a

constant temperature of A) 735 K B) 490 K C) 470 K D) 784 K Answer: A Var: 50+

and a hot reservoir, what is the temperature of the hot reservoir?

9) A 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+ 10) 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+ 11) A 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) 1,642 J B) 2,358 J C) 1,483 J D) 2,517 J Answer: A Var: 50+

12) A Carnot refrigerator with a COP of 5.0 cools to needed to operate this refrigerator? A) 61° C B) 1,395° C C) 6° C D) 30° C Answer: A Var: 50+

What is the high temperature, Th,

13) A heat pump with a COP of 4.9 absorbs heat from the atmosphere at a rate of what rate is it doing work? A) 6 kW B) 132 kW C) 105 kW D) 33 kW Answer: A Var: 50+

14) A Carnot engine operating between a warmer unknown temperature and a reservoir of boiling helium at has an efficiency of What is the warmer temperature? A) 2.93 K B) 0.0500 K C) 106 K D) 0.0400 K Answer: A Var: 16 15) A Carnot engine operating between a reservoir of liquid mercury at its melting point and a colder reservoir extracts of heat from the mercury and does of work during each cycle. What is the temperature of the colder reservoir? Mercury melts at A) 171 K B) 62 K C) 47 K D) 67 K Answer: A Var: 50+

16) What is the efficiency of a 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 atmosphere for both. A) 27% B) 0.27% C) 100% D) 1.0% Answer: A Var: 1 17) A Carnot engine operates between two reservoirs with unknown temperatures. If the Carnot engine operates at efficiency, what is the ratio of the kelvin temperatures of the reservoirs, A) 0.33 B) 0.0012 C) 0.0025 D) 0.67 Answer: A Var: 42 18) Figure 16.1 shows a cycle for a heat engine for which efficiency? Figure 16.1

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

=59 J. What is the thermal

19) A gas follows the pV trajectory shown in Figure 16.2. How much work is done per cycle by the gas if Figure 16.2

A) 220 J B) 440 J C) 870 J D) 1,100 J Answer: A Var: 50+

20)

Figure 16.3a

A heat engine takes 9.0 moles of an ideal gas through the reversible cycle abca, on the pV diagram, as shown. The path bc is an isothermal process. The temperature at c is and the volumes at a and c are volume, of the gas, is in kJ, is closest to: A) 55 B) 80 C) -55 D) -80 E) zero Answer: A Var: 50+

and

respectively. The molar heat capacity at constant In Figure 16.3a, for the path ab, the heat absorbed by the gas,

21)

Figure 16.3b

A heat engine takes 2.0 moles of an ideal gas through the reversible cycle abca, on the pV diagram, as shown. The path bc is an isothermal process. The temperature at c is and the volumes at a and c are volume, of the gas, is kJ, is closest to: A) 8.6 B) 17 C) -8.6 D) -17 E) zero Answer: A Var: 50+

and

respectively. The molar heat capacity at constant In Figure 16.3b, for the path bc, the work done by the gas, in

22)

Figure 16.3c

and

respectively. The molar heat capacity at constant In Figure 16.3c, for the path ca, the heat absorbed by the gas,

23)

Figure 16.3d

A heat engine takes 6.0 moles of an ideal gas through the reversible cycle abca, on the pV diagram, as shown. The path bc is an isothermal process. The temperature at c is and the volumes at a and c are volume, of the gas, is kJ, is closest to: A) -27 B) 27 C) -260 D) 260 E) zero Answer: A Var: 50+

and

respectively. The molar heat capacity at constant In Figure 16.3d, for the path ca, the work done by the gas, in

24)

Figure 16.3e

A heat engine takes 2.0 moles of an ideal gas through the reversible cycle abca, on the pV diagram, as shown. The path bc is an isothermal process. The temperature at c is and the volumes at a and c are volume, of the gas, is closest to: A) 0.14 B) 0.057 C) 0.24 D) 0.34 E) 0.54 Answer: A Var: 50+

and

respectively. The molar heat capacity at constant In Figure 16.3e, the thermal efficiency of the engine, is

Figure 16.4

A heat engine performs the reversible cycle abca with 9.0 moles of an ideal gas. Path ca is an adiabatic process. The temperatures at points a and b are and respectively. The volume at point c is

The adiabatic constant of the gas is 1.60.

25) In Figure 16.4, the heat absorbed by the gas in path ab, in kJ, is closest to: A) zero B) +25 C) +40 D) -25 E) -40 Answer: C Var: 1 26) In Figure 16.4, the heat absorbed by the gas in path ca, in kJ, is closest to: A) zero B) +10 C) +16 D) -10 E) -16 Answer: A Var: 1 27) In Figure 16.4, the work done by the gas in path ab, in kJ, is closest to: A) zero B) +15 C) +25 D) -15 E) -25 Answer: B Var: 1

Figure 16.5

28) In Figure 16.5, a gas initially at

is caused to change its volume and pressure

reversibly such that it moves along the path sketched here. In one cycle the net work done by the gas is thus A) B)

V∙2 -

(

D) ( E)

(

) )) (

)

Answer: D Var: 1 29) Which 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 30) 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

31) 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 is conserved, i.e. constant. D) Entropy can be measured in units of J/K. Answer: C Var: 1 32) Which of the following relationships are true for all types of heat engines? (There may be more than one correct choice.) A) e = 1 B) e =

C) e =

E) e = 1 Answer: B, C, E Var: 1 16.2 Short Answer Questions 1) A Carnot heat engine operates between reservoirs at

= 1,740 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: 2,760 J Var: 50+ 2) A Carnot refrigerator takes heat from water at 0°C and rejects heat to a room at Suppose that 78 grams of water at 0°C are converted to ice at 0°C by the refrigerator. Calculate the mechanical energy that must be supplied to the refrigerator. (Note: The heat of fusion of water is Answer: 1,900 J Var: 50+

3) A 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 °C. Answer: 626°C Var: 50+ 4) A 15.0 kg block of ice at 0.00°C falls into Lake Superior, which is a fresh water lake. The lake water is at 10.0°C, and the latent heat of fusion for ice is 3.34 × 105 J/kg. Find the change in entropy due to the melting of the ice (a) of the block of ice, (b) of the lake, and (c) of the system consisting of the lake and the ice. (d) Is your answer to part (c) consistent with the reversibility or irreversibility of the melting process? Answer: (a) +1.84 × 104 J/K, (b) –1.77 × 104 J/K, (c) +7.00 × 102 J/K, (d) The process is irreversible, so ΔS > 0. Var: 1 5) An automobile engine takes in 4000 J of heat and performs 1100 J 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) 2900 J Var: 1 6) A refrigerator has a coefficient of performance 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

College Physics, 11e (Young) Chapter 17 Electric Charge and Electric Field 17.1 Multiple Choice Questions 1) Suppose a van de Graaff generator builds a negative static charge, and a grounded conductor is placed near enough to it so that a of negative charge arcs to the conductor. Calculate the number of electrons that are transferred. A) 4.38 × 1013 B) 7.0 C) 1.12 × 10-18 D) 43.8 Answer: A Var: 6 2) A metal sphere is insulated electrically and is given a charge. If 50 electrons are added to the sphere in giving a charge, how many Coulombs are added to the sphere? A) -8.0 × 10-18 C B) -8.0 × 10-20 C C) -80 C D) -50 C Answer: A Var: 31 3) An asteroid has acquired a net negative charge of from being bombarded by the solar wind over the years, and is currently in equilibrium whereby it expels electrons at the same rate as it acquires them. How many more electrons does it have than protons? A) 9.19 × 1020 B) 919 C) 882 D) 1.47 × 10-17 Answer: A Var: 50+ 4) An asteroid of mass 58,000 kg carrying a negative charge of asteroid of mass carrying a negative charge of asteroids exert upon each other? A) 0.000040 N B) 0.0062 N C) 570,000 N D) 510,000 N Answer: A Var: 50+

is from a second What is the net force the and

5) Two electrons are passing

apart. What is the electric repulsive force that they exert

on each other? (The value of k is 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 6) A proton is located at x = 1.0 nm, and an electron is located at Find the attractive Coulombic force between them. (The value of k is 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 7) Two like charges of the same magnitude are apart. If the force of repulsion they exert upon each other is what is the magnitude of each charge? (The constant of proportionality for the Coulombic force is 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 8) Three charges of magnitude each are located at at and at The one in the middle is negative, while the other two are positive. What is the net Coulombic force exerted by them on a negative charge located at (The value of k is A) 87 N attractive B) 87 N repulsive C) 120 N attractive D) 120 N repulsive Answer: A Var: 9 9) 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?

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+ 10) The electric field 2.8 cm from a small object points toward the object with a strength of What is the object's charge? A) -16 nC B) +16 nC C) -17 nC D) +17 nC Answer: A Var: 50+ 11) What is the magnitude of an electric field that balances the weight of a plastic sphere of mass that has been charged to 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+ 12) Two equally charged spheres of mass 1.0 g are placed 2.0 cm apart. When released, they begin to accelerate at What is the magnitude of the charge on each sphere? A) 140 nC B) 120 nC C) 95 nC D) 75 nC Answer: A Var: 50+

13) In Figure 17.1 Q = 6.7 nC and all other quantities are exact. What is the magnitude of the electrical force on the charge Q? Figure 17.1

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+ 14) The charge in the bottom right corner of Figure 17.2 is Q = - 90 nC. What is the magnitude of the electrical force on Q? Figure 17.2

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

15) The charge at the bottom of Figure 17.3 is Q = +23 nC. What is the magnitude of the force on the charge Q? Figure 17.3

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 16) In Figure 17.4 the charge in the middle is in static equilibrium? Figure 17.4

A) 30 nC B) 15 nC C) 7.5 nC D) 60 nC Answer: A Var: 50+

For what charge q1 will charge q2 be

17) A plastic rod is charged up by rubbing a wool cloth, and brought to an initially neutral metallic sphere. 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 18) 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 19) A positive test charge q is released near a positive fixed charge Q. As q moves away from Q, it will move with A) constant velocity. B) constant acceleration. C) increasing acceleration. D) decreasing acceleration. Answer: D Var: 1

20) One charged plastic ball is vertically above another in a test tube as shown in Figure 17.5. The balls are in equilibrium a distance d apart. Figure 17.5

If the charge on each ball is doubled, the distance between the balls in the test tube would become A) d B) 2d C) 4d D) 8d Answer: B Var: 1

21) X and Y are two uncharged metal spheres on insulating stands, and are in contact with each other. A positively charged rod R is brought close to X as shown in Figure 17.6a. Figure 17.6a

Sphere Y is now moved away from X (Figure 17.6b). Figure 17.6b

What are the final charge states of X and Y, respectively? A) neutral and neutral B) positive and neutral C) neutral and positive D) negative and positive Answer: D Var: 1 22) Two identical small charged spheres are a certain distance apart, and each initially experiences an electrostatic force of magnitude F due to the other. With time, charge gradually diminishes on both spheres. When each of the spheres has lost half its initial charge, the magnitude of the electrostatic force will be A) 1/16 F B) 1/8 F C) 1/4 F D) 1/2 F Answer: C Var: 1

23) Two equal and opposite charges a certain distance apart are called an electric "dipole". A positive test charge is placed as shown in Figure 17.7, equidistant from the two charges. Figure 17.7

Which diagram below gives the direction of the net force on the test charge? A)

C) D) Answer: C Var: 1

24) Two identically charged balls are a certain distance apart. The vectors in Figure 17.8 show the magnitude and direction of the electrostatic force on each ball. Figure 17.8

Suppose the charge on the left ball is now doubled (represented by two plus signs). Which diagram below best represents the forces that now act on the two balls? A)

D) Answer: C Var: 1 25) 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 26) What is the strength of an electric field that a from a

positive charge? (The value of k is

A) 2.8 × 1015 N/C B) 7.0 × 1016 N/C C) 1.4 × 1015 N/C D) 2.8 × 1016 N/C Answer: A Var: 3

negative charge experiences

27) What is the electric field strength at and the other at

produced by two electrons, one at (The value of k is

A) 0 N/C B) 1.8 × 10-19 N/C C) 2.88 × 10-19 N/C D) 5.76 × 10-19 N/C Answer: A Var: 1 28) A 6.0 μC positive charge is located at the origin and a positive charge is located at Find the point between them where the electric field strength is zero. A) x = 0 m, y = 0.55 m B) x = 0 m, y = 0.67 m C) x = 0 m, y = 1.5 m D) x = 0 m, y = 0.60 m Answer: A Var: 35 29) An object with a 5.0 μC charge is accelerating at due to an electric field. If the object has a mass of what is the magnitude of the electric field? A) 2.0 N/C B) -2.0 N/C C) 0.0020 N/C D) -0.0020 N/C Answer: A Var: 50+

30) Four charged particles (two having a charge +Q and two having a charge -Q) are distributed as shown in Figure 17.9. Each charge is equidistant from the origin. In which direction is the net electric field at the point P, which is on the y axis? Figure 17.9

A) directly up (in the positive y direction) B) directly left (negative x direction) C) upwards, towards the left D) upwards, towards the right E) the net field is zero, so there is no direction Answer: C Var: 1

31) An electron is initially moving to the right when it enters a uniform electric field directed upwards. Which trajectory shown in Figure 17.10 will the electron follow? Figure 17.10

A) Trajectory W B) Trajectory X C) Trajectory Y D) Trajectory Z Answer: D Var: 1

32) Figure 17.11 shows electric field lines arising from two small charged particles P and Q. Figure 17.11

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 that on Q. Which of the above statements are true? A) Only i. B) Only ii. C) Both i and ii. D) Neither i nor ii. Answer: A Var: 1

33) Figure 17.12 shows two unequal charges +q and - Q, of opposite sign. Charge Q has greater magnitude than charge q. Point X is midway between the charges. Figure 17.12

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 34)

Figure 17.13a

A point charge Q = -600 nC and two unknown point charges, q1 and q2, are placed as shown. The electric field at the origin O, due to charges Q, q1 and q2, is equal to zero. In Figure 17.13a, the number of excess electrons in charge Q, is closest to: A) 3.3 × 102 B) 1.9 × 102 C) 3.8 × 102 D) -1.9 × 102 E) -3.3 × 102 Answer: A Var: 50+

35)

Figure 17.13b

A point charge Q = -900 nC and two unknown point charges, q1 and q2, are placed as shown. The electric field at the origin O, due to charges Q, q1 and q2, is equal to zero. In Figure 17.13b, the charge q1, in nC, is closest to: A) 210 B) 120 C) 250 D) –120 E) –210 Answer: A Var: 50+

36)

Figure 17.13c

A point charge Q = -600 nC and two unknown point charges, q1 and q2, are placed as shown. The electric field at the origin O, due to charges Q, q1 and q2, is equal to zero. In Figure 17.13c, the charge q2, in nC, is closest to: A) -91 B) -160 C) 91 D) 160 E) 180 Answer: A Var: 50+ 37)

Two point charges,

Figure 17.14a

= -3.0 μC and

number of excess electrons in charge

= +4.0 μC, are placed as shown. In Figure 17.14a, the is closest to:

A) 1.9 × 1013 B) 1.9 × 1014 C) 6.0 × 1011 D) 6.0 × 1012 E) 6.0 × 1013 Answer: A Var: 50+ 38)

Figure 17.14b

Two point charges,

= -4.0 μC and

= +4.0 μC, are placed as shown. In Figure 17.14b, the

x-component of the electric field, at the origin O, is closest to: A) 2,900 N/C B) 15,000 N/C C) -15,000 N/C D) -2,900 N/C E) -6,800 N/C Answer: A Var: 50+ 39)

Two point charges,

Figure 17.14c

= -4.0 μC and

= +2.0 μC, are placed as shown. In Figure 17.14c, the

y-component of the electric field, at the origin O, is closest to: A) -1,600 N/C B) -6,000 N/C C) 1,600 N/C D) 6,000 N/C E) zero Answer: A Var: 50+

40)

Two point charges,

Figure 17.14d

= -3.0 μC and

= +5.0 μC, are placed as shown. In Figure 17.14d, the

magnitude of the electric force on either charge is closest to: A) 0.028 N B) 0.022 N C) 0.034 N D) 0.040 N E) 0.046 N Answer: A Var: 50+ 41)

Two point charges,

Figure 17.14e

= -4.0 μC and

= +5.0 μC, are placed as shown. In Figure 17.14e, a

proton is released at the midpoint between the proton is closest to: A) -1.6 × 1013 m/ B) 1.7 × 1012 m/ C) -4.8 × 1012 m/ D) 1.6 × 1013 m/ E) -1.7 × 1012 m/ Answer: A Var: 50+

and

. The y-component of the acceleration of

Figure 17.15

A point charge Q = -12 μC, and two other charges, q1 and q2, are placed as shown. The electric force components on charge Q are and 42) In Figure 17.15, the number of excess electrons in charge Q is closest to: A) 5.5 × B) 6.5 × C) 7.5 × D) 8.5 × E) 9.5 × Answer: C Var: 1 43) In Figure17.15, charge q1, in nC, is closest to: A) +200 B) +400 C) +600 D) -200 E) -400 Answer: C Var: 1 44) In Figure 17.15, charge q2, in nC, is closest to: A) +320 B) +480 C) +640 D) -480 E) -640 Answer: E Var: 1

45) If you rub a balloon on your sweater and then press it to a wall, it will often stick there. Why does this happen? A) Rubbing removes a surface layer of grease, allowing the rubber to come in sufficiently close contact with the wall so that air pressure holds it there. B) Rubbing the balloon charges it electrostatically, and this charge on the balloon induces an opposite charge on the wall. The attraction between the induced charge and the charge on the balloon holds the balloon to the wall. C) A wall typically has a net electric charge on it, and rubbing the balloon charges it electrostatically. If the wall happens to have opposite charge to that on the balloon, the balloon will stick. D) Rubbing the balloon causes moisture to condense on it, and surface tension causes the balloon to stick to the wall. E) Rubbing the balloon surface causes it to become slightly conducting. When the balloon is touched to the wall, electrons flow from the balloon to the wall. This sets up an electric field which bonds the balloon weakly to the wall. Answer: B Var: 1 Figure 17.16

Two small insulating spheres are attached to silk threads. The spheres have equal masses of and have electric charges of and The spheres are brought into the initial positions shown in Figure (a), with a vertical separation of 15 cm between them. 46) In Figure 17.16, the tension in the lower thread in Figure (a) is closest to: A) 1.2 N B) 1.4 N C) 1.6 N D) 1.8 N E) 2.0 N Answer: A Var: 1

47) In Figure 17.16, the upper thread is slowly pulled upward, while point B is kept fixed. When point A has been raised through a height h, the lower sphere suddenly falls, as shown in Figure (b). The height h, is closest to: A) 9 cm B) 11 cm C) 13 cm D) 15 cm E) 17 cm Answer: D Var: 1 Figure 17.17

48) In Figure 17.17, a small 80 g insulating sphere is suspended from point P by a silk thread that is long. The sphere bears an unknown electric charge Q. A positive point charge is brought to a position directly below P, and the sphere is repelled to a new position, 30 cm to the right of q, as shown. The charge Q, in μC, is closest to: A) +1.5 B) +2.0 C) +2.5 D) +3.0 E) +3.5 Answer: D Var: 1

Situation 17.1 A 50 g insulating sphere carries a charge Q = -60 μC and is suspended by a silk thread from a fixed point. An external electric field which is uniform and vertical is applied. 49) In Situation 17.1, the applied electric field has a magnitude of 3000 N/c and is directed downward. The tension in the thread is closest to: A) 0.2 N B) 0.3 N C) 0.4 N D) 0.5 N E) 0.7 N Answer: B Var: 1 50) In Situation 17.1, the applied electric field holds the sphere in place above the fixed point of suspension, and the tension in the thread is The applied electric field, including direction, is closest to: A) 2000 N/C, upward B) 8000 N/C, upward C) 14,000 N/C, upward D) 8000 N/C, downward E) 14,000 N/C, downward Answer: E Var: 1

Figure 17.18

A pair of charged conducting plates produces a uniform field of right, between the plates. The separation of the plates is 40 mm.

directed to the

51) In Figure 17.18 , an electron is projected from plate A, directly toward plate B, with an initial velocity of The velocity of the electron as it strikes plate B is closest to: A) 1.2 ×

m/s

B) 1.5 ×

m/s

C) 1.8 ×

m/s

D) 2.1 ×

m/s

E) 2.4 × m/s Answer: B Var: 1 52) In Figure 17.18, an electron is projected from plate A, directly toward plate B, with an initial The closest approach of the electron to plate B is closest to: velocity A) 16 mm B) 18 mm C) 20 mm D) 22 mm E) 24 mm Answer: A Var: 1

53)

Figure 17.19

In Figure 17.19, a small spherical insulator of mass 10.00 × kg and charge +0.910 μC is hung by a thin wire of negligible mass. A charge of is held away from the sphere and directly to the right of it, so the wire makes an angle θ with the vertical (see drawing). What is the angle θ? A) 1.21° B) 1.44° C) 1.70° D) 1.97° E) 2.23° Answer: A Var: 50+

Figure 17.20

54) An electron is projected with an initial velocity

= 8.4 ×

m/s along the y-axis, which is

the center line between a pair of charged plates. The plates are 1.00 m long and are separated by A uniform electric field E, in the positive x-direction, is presented between the plates. The magnitude of the acceleration of the electron is magnitude of the electric field between the plates is closest to: 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+

In Figure 17.20, the

55) The electric field at point P due to a point charge Q a distance R away has magnitude E. In order to double the magnitude of the field at P, you could A) double the charge to 2Q. B) double the distance to 2R. 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: A Var: 1 56) A flat disk 1.0 m in diameter is oriented so that the plane of the disk makes an angle of radians with a uniform electric field. If the field strength is find the electric flux through the surface. A) 90 π N∙m2/C B) 620 N∙m2/C C) 2,500/π N∙m2/C D) 160 π N∙m2/C Answer: A Var: 50+ 57) A spherical conductor with radius

carries a charge of

What is the electrical

field strength at A) 1.7 × 109 N/C B) 88 × 109 N/C C) 25 × 109 N/C D) 780 × 109 N/C Answer: A Var: 50+

from the center of the conductor?

17.2 Short Answer Questions Figure 17.21

1) In Figure 17.21, charge is placed on the

= 2.2 x

C is placed at the origin and charge Where along the x-axis can a third charge

be placed such that the resultant force on this third charge is zero? Answer: 0.89 m Var: 50+ 2)

Figure 17.22

In Figure 17.22, a proton, mass 1.67 x kg, is projected horizontally midway between two parallel plates that are separated by with an electrical field with magnitude between the plates. If the plates are long, find minimum speed of the proton that just misses the lower plate as it emerges from the field. Answer: 6.16 × 106 m/s Var: 50+

Figure 17.23

An electric dipole consists of charges of ±6.00 µC that are 10.0 cm apart, as shown in Figure 17.23. Find the magnitude and direction of the electric field this dipole produces at point P, which is 7.00 cm from each charge. Answer: Magnitude: 1.57 × 107 N/C; Direction: To the left parallel to the line connecting the two charges. Var: 1 4)

Figure 17.24

Two point charges q = –8.50 µC are fixed 10.0 cm apart along a horizontal bar. Their electrical forces will be used to suspend a very small sphere carrying a charge Q = +15.0 µC, 10.0 cm from each of them, as shown in Figure 17.24. What is the greatest mass this sphere can have without falling? Answer: 20.3 kg Var: 1 5) A nonconducting sphere of mass 18.5 kg and diameter 25.0 cm has 8.10 × 1015 electrons removed from it. The points of removal are spread uniformly throughout the volume of this sphere. A tiny neutral plastic ball of mass 0.120 g is placed just outside the surface of the large sphere and released. How many electrons must be removed from the plastic ball so that its initial acceleration just after being released will be 1525 m/s2? (You can neglect gravity.) Answer: 1.53 × 109 electrons Var: 1

Figure 17.25

6) In Figure 17.25, a conducting sphere of radius spherical conducting shell of inner radius sphere carries a charge of

= 0.050 m is placed at the center of a and outer radius

The inner

The outer spherical shell carries a net charge of

Calculate the magnitude of the electric field at the following distances from the center of the spheres: (a) r = 0.075 m (in the air space between spheres), (b) r = 0.120 m (in the metal of the spherical shell), and (c) r = 0.200 m (outside the spherical shell). Answer: (a) 6.4 × N/C (b) 0 (c) 2.3 × N/C Var: 1

College Physics, 11e (Young) Chapter 18 Electric Potential and Capacitance 18.1 Multiple Choice Questions 1)

Point charges,

Figure 18.1a

= +46 nC and

= -59 nC, are placed as shown. In Figure 18.1a, an external

force transports an electron from point A to point B. The work done by the external force is closest to: A) +630 eV B) +530 eV C) +420 eV D) -630 eV E) -420 eV Answer: A Var: 50+

Figure 18.1b

Point charges,

= +55 nC and

= -97 nC, are placed as shown. In Figure 18.1b, an electron

is released from rest at point C. The speed of the electron as it arrives at infinity is closest to: A) 1.7 × 107 m/s B) 1.8 × 107 m/s C) 2.0 × 107 m/s D) 1.5 × 107 m/s E) 1.3 × 107 m/s Answer: A Var: 50+ 3)

Figure 18.1c

Point charges,

= +40 nC and

the positive y-axis lies on the units, is closest to: A) 0.41 B) 0.39 C) 0.42 D) 0.44 E) 0.45 Answer: A Var: 50+

= -88 nC, are placed as shown. In Figure 18.1c, a point on equipotential surface. The y-coordinate of the point, in SI

Figure 18.2

In Figure 18.2, four charges are placed at the corners of a square of side 8 cm. What is the electrostatic potential energy of this system relative to infinity? A) -24 J B) -18 J C) -43 J D) -47 J E) -37 J Answer: A Var: 50+ 5) A proton with a speed of 2.0 x increases its speed to 4.0 x A) 630 V B) 210 V C) 840 V D) 1,000 V E) 100 V Answer: A Var: 24

m/s falls through a potential difference V and thereby

m/s. Through what potential difference did the proton fall?

6) A proton with speed 1.5 × m/s falls through a potential difference of 100 volts, gaining speed. What is the speed reached? A) 4.56 × m/s B) 2.04 ×

m/s

C) 3.55 ×

m/s

D) 8.80 ×

m/s

E) 1.55 × Answer: B Var: 1

m/s

7) A proton is projected toward a fixed nucleus of charge +Ze with velocity

. Initially the two

particles are very far apart. When the proton is a distance R from the nucleus its velocity has decreased to How far from the nucleus will the proton be when its velocity has dropped to A) 1/16 R B) 1/4 R C) 1/2 R D) 4/5 R E) None of these. Answer: D Var: 1 8) An electron is released from rest at a distance of 9 cm from a proton. How fast will the electron be moving when it is 3 cm from the proton? A) 75 m/s B) 106 m/s C) 130 m/s D) 1.06 × m/s E) 4.64 × Answer: B Var: 1

m/s

9) Two conductors are joined by a long copper wire. Thus A) each conductor carries the same free charge. B) each conductor must be at the same potential. C) the electric field at the surface of each conductor is the same. D) no free charge can be present on either conductor. E) the potential on the wire is the average of the potential of each conductor. Answer: B Var: 1 10) Two isolated copper plates, each of area 0.4

, carry opposite charges of magnitude

coulombs. They are placed opposite each other in parallel alignment, with a spacing What will be the potential difference between the plates when their spacing is increased

of to A) 0.4 V B) 3.04 V C) 3.2 V D) 7.6 V E) 8 V Answer: E Var: 1

11) A 6.0 μC negative charge is attracted to a large, well-anchored, positive charge. How much kinetic energy does the negatively charged object gain if the potential difference through which it moves is A) 18 nJ B) 0.50 kJ C) 0.50 J D) 6.0 μJ Answer: A Var: 30 12) A space probe approaches a planet, taking measurements as it goes. If it detects a potential difference of between the altitudes of and above the planet's surface, what is the approximate electric field strength produced by the planet at above the surface? Assume the electric field strength is approximately constant at these altitudes. A) 260.87 N/C B) 0.26087 N/C C) -260.87 N/C D) 493.14 μN/C Answer: A Var: 50+ 13) A sphere with radius 2.0 mm carries a charge. What is the potential difference, between point B from the center of the sphere and point A from the center of the sphere? (The value of k is A) 1,500 V B) -1,500 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 A third point is located at What is the potential at this third point relative to infinity? (The value of k is A) 11,000 V B) 9,000 V C) 14,000 V D) 3,400 V Answer: A Var: 30

15) A 6.9 μC negative point charge has a positively charged object in a elliptical orbit about it. If the mass of the positively charged object is and the distance varies from to between the charges, what is the maximum potential difference through which the positive object moves? A) 12 MV B) 3.9 MV C) -5.2 MV D) 19 MV Answer: A Var: 50+ 16) A 7.0 μC point charge and a work does it take to bring the point charge to A) 95 J B) 190 J C) 63 J D) 16 J Answer: A Var: 12

point charge are initially infinitely far apart. How much point charge to and the

17) A dipole with ±5.0 μC 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 charge from infinity to a position A) 23 J B) 110 J C) 19 J D) 49 J Answer: A Var: 50+ 18) A charge of 4.0 μC and a second charge are initially far apart. If it takes of work to bring them to a final configuration in which the is at and the other charge is at find the magnitude of the unknown charge. A) 1.50 μC B) 3.00 μC C) 7.50 μC D) 3.00 nC Answer: A Var: 50+

19) Consider the group of charges in Figure 18.3. All three charges have their electric potential energy?

What is

Figure 18.3

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: 50+ 20) An electron was accelerated from rest through a potential difference of 1,500 V. What is its speed? 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+

21) Three charges shown in Figure 18.4 form an equilateral triangle with 4.9 cm long sides. What is the electric potential at the point indicated with the dot? Figure 18.4

A) zero B) 1,300 V C) 640 V D) 1,900 V Answer: A Var: 50+

22) Figure 18.5 shows an arrangement of two

charges each separated by 5.0 mm

from a proton

If the two

charges are

held fixed at their locations and the proton is set into motion, what is the escape speed of the proton? Figure 18.5

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+

23) Four charged particles (two having a charge +Q and two having a charge -Q) are distributed on the xy-plane, as shown in Figure 18.6. The charges are equidistant from the origin. The voltage is zero at infinity. The voltage at location P, which is on the z axis, is Figure 18.6

A) zero. B) positive. C) negative. D) impossible to determine based on the information given. Answer: A Var: 1 24) Four charged particles (two having a charge +Q and two having a charge -Q) are distributed on the xy-plane, as shown in Figure 18.6. The charges are equidistant from the origin. The voltage is zero at infinity. The amount of work required to move a positively charged particle from point P to point O (which is on the z-axis, below the origin) is A) zero. B) positive. C) negative. D) depends on the path in which the charged is moved. Answer: A Var: 1 25) A hydrogen atom consists of a proton and an electron. If the orbital radius of the electron increases, the potential energy of the electron A) increases. B) decreases. C) remains the same. D) depends on the zero point of the potential. Answer: A Var: 1 26) 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, it would gain a speed A) 8v0 B) 4v0 C) 2v0 D) v0 Answer: D Var: 1 27) Each plate of a parallel-plate air capacitor has an area of 0.0040

, and the separation of the

plates is An electric field of is present between the plates. The potential difference across the capacitor is closest to: A) 350 V B) 233 V C) 467 V D) 583 V E) 700 V Answer: A Var: 50+ 28) Each plate of a parallel-plate air capacitor has an area of 0.0040 plates is An electric field of density between the plates is closest to: A) 300 J/

, and the separation of the

is present between the plates. The energy

B) 200 J/ C) 400 J/ D) 500 J/ E) 610 J/ Answer: A Var: 50+ 29) Each plate of a parallel-plate air capacitor has an area of 0.0020 plates is

An electric field of

charge density on the plates, in A) 19 B) 39 C) 9.3 D) 28 E) 47 Answer: A Var: 50+

, and the separation of the

is present between the plates. The surface is closest to:

30) Each plate of a parallel-plate air capacitor has an area of 0.0010

, and the separation of the

plates is An electric field of capacitance of the capacitor, in pF, is closest to: A) 180 B) 120 C) 300 D) 240 E) 360 Answer: A Var: 50+ 31) Two parallel circular plates with radius densities of plates have? A) 78 nJ B) 25 nJ C) 7.9 nJ D) 250 nJ Answer: A Var: 36

is present between the plates. The

carrying equal-magnitude surface charge

are separated by a distance of

How much stored energy do the

32) Two parallel plates that are initially uncharged are separated by What charge must be transferred from one plate to the other if of energy are to be stored in the plates? The area of each plate is A) 56 μC B) 40 μC C) 80 μC D) 6.0 mC Answer: A Var: 50+ 33) Two parallel plates are separated by If the potential difference between them is what is the magnitude of their surface charge densities? A) 27 nC/m2 B) 0.16 mC/m2 C) 53 nC/m2 D) 0.33 mC/m2 Answer: A Var: 5

34) A 3.0 pF capacitor consists of two parallel plates that have surface charge densities of If the potential between the plates is find the surface area of one of the plates. A) 69 mm2 B) 0.014 mm2 C) 35 mm2 D) 0.0072 mm2 Answer: A Var: 50+ 35) A 300.0 pF capacitor consists of two circular plates of radius plates? (The value of

How far apart are the

A) 0.0083 μm B) 0.0042 μm C) 0.00094 μm D) 0.00047 μm Answer: A Var: 28 36) A 5.0 μF capacitor has a potential difference of potential difference across its plates is increased to capacitor store? A) 98 μJ B) 200 μJ C) 23 μJ D) 45 μJ Answer: A Var: 28

applied across its plates. If the how much additional energy does the

37) A 5.0 μF, and 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) 36 μF C) 5.0 μF D) 14 μF Answer: A Var: 50+

38) 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 the three capacitors? A) 33 μF B) 13 μF C) 16 μF D) 38 μF Answer: A Var: 50+ 39) Two capacitors, one a 4.0 μF capacitor, C1, and the other a 7.0 μF capacitor, C2, are connected in series. If a 90.0 V voltage source is applied to the capacitors, as shown in Figure 18.7, find the voltage drop across the 4.0 μF capacitor. Figure 18.7

A) 54 V B) 36 V C) 60 V D) 9.0 V Answer: A Var: 1

40) A potential difference of 100.0 V is applied across two capacitors in series, as shown in Figure 18.8. If capacitance of

is a

capacitor and has a voltage drop of

across it, what is the

A) 18 μF B) 1.5 μF C) 4.5 μF D) 2.0 μF Answer: A Var: 10 41) Three capacitors of equal capacitance are arranged as shown in Figure 18.9. The voltage drop across is What is the voltage drop across Figure 18.9

A) 20 V B) 10.0 V C) 40 V D) 30 V Answer: A Var: 10 42) Three capacitors are arranged as shown in Figure 18.10.

has a capacitance of

and

has a capacitance of

across the entire arrangement if the voltage drop across

Find the voltage drop

Figure 18.10

A) 1,500 V B) 1,000 V C) 470 V D) 430 V Answer: A Var: 50+ 43) A parallel-plate capacitor consists of two parallel, square plates that have dimensions by If the plates are separated by and the space between them is filled with teflon, what is the capacitance? (The dielectric constant for teflon is 2.1.) A) 1.9 pF B) 0.44 pF C) 2.1 pF D) 0.89 pF Answer: A Var: 5

44) Suppose a region of space has a uniform electric field, directed toward the right, as shown in Figure 18.11. Which statement is true? Figure 18.11

A) The voltage at all three locations is the same. B) The voltage at points A and B are equal, and the voltage at point C is higher than the voltage at point A. C) The voltage at points A and B are equal, and the voltage at point C is lower than the voltage at point A. D) The voltage at point A is the highest, the voltage at point B is the second highest, and the voltage at point C is the lowest. E) None of the above Answer: C Var: 1 45) If the voltage at a point in space is zero, then the electric field must be A) negative. B) zero. C) uniform. D) positive. E) impossible to determine based on the information given. Answer: E Var: 1 46) A parallel-plate capacitor having circular plates of diameter D and 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

Figure 18.12

47) The capacitive network shown is assembled with initially uncharged capacitors. A potential difference, is applied across the network. The switch S in the network is kept open throughout. In Figure 18.12, the total energy stored in the seven capacitors, in mJ, is closest to: A) 48 B) 72 C) 96 D) 120 E) 144 Answer: B Var: 1

Figure 18.13

48) The network shown is assembled with uncharged capacitors X , Y, and Z, with and

and open switches,

and

. A potential difference

is applied between points a and b. After the network is assembled, switch

is closed, but switch

is kept open. In Figure 18.13, the energy stored in capacitor X, in mJ, is closest to: A) 29 B) 0.48 C) 0.24 D) 58 E) 0.96 Answer: A Var: 50+ 49) The network shown is assembled with uncharged capacitors X , Y, and Z, with and

and open switches,

and

. A potential difference

is applied between points a and b. After the network is assembled, switch

is closed, but switch

is kept open. In Figure 18.13, the charge on capacitor Y, in μC, is closest to: A) 110 B) 54 C) 81 D) 140 E) 160 Answer: A Var: 50+

50) The network shown is assembled with uncharged capacitors X , Y, and Z, with and

and open switches,

and

. A potential difference

is applied between points a and b. After the network is assembled, switch

is closed, but switch

is kept open. In Figure 18.13, the voltage across capacitor Z, in SI units, is closest to: A) 100 B) 600 C) 55 D) 38 E) 29 Answer: A Var: 50+ 51) The network shown is assembled with uncharged capacitors X , Y, and Z, with and

and open switches,

and

. A potential difference

is applied between points a and b. After the network is assembled, switch is kept open. In Figure 18.13, switch voltage across capacitor X, in A) 84 B) 77 C) 70 D) 63 E) 56 Answer: A Var: 50+

is opened, and then switch

units, is closest to:

is closed, but switch is closed. The final

Figure 18.14

52) In the circuit shown in Figure 18.14 the capacitors are initially uncharged. The switch is first thrown to position A for a long time and then to position B. Let the charges on the capacitors be , , and and the potential difference across them be , and . With the switch kept in position B: A) = = B)

Answer: B Var: 1 53) The square plates of a 5,000 pF capacitor measure 50 mm by 50 mm and are separated by a dielectric which is thick. The voltage rating of the capacitor is The maximum energy that can be stored in the capacitor, in mJ, is closest to: A) 0.40 B) 0.50 C) 0.60 D) 0.70 E) 0.80 Answer: A Var: 50+ 54) The square plates of a 3,000 pF capacitor measure 40 mm by 40 mm and are separated by a dielectric which is thick. The voltage rating of the capacitor is The dielectric constant of the dielectric is closest to: A) 61 B) 56 C) 50 D) 45 E) 67 Answer: A Var: 50+

55) The capacitance of a capacitor depends on A) the charge on it. B) the potential difference across it. C) the energy stored in it. D) More than one of these. E) None of these. Answer: E Var: 1 56) Two capacitors, identical except for the dielectric material between their plates, are connected in parallel. One has a material with a dielectric constant of 2, while the other has a material with a dielectric constant of 3. What is the dielectric constant that a material would need to have if the material were to replace the current dielectrics without changing the capacitance of the entire arrangement? A) B) 5 C) D) Answer: A Var: 1 57) A uniform electric field has the strength of field? (The value of

What is the electric energy density of the

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 58) A small object carries a charge of If the object is so small that it can be regarded as a point charge, what is the energy density at a distance of from the charge? (The value of k is A) 0.050 mJ/m3 B) 0.20 mJ/m3 C) 0.81 mJ/m3 D) 3.2 mJ/m3 Answer: A Var: 40 18.2 Short Answer Questions

1) Three point charges are placed at the following (x, y) coordinates: charge

charge at and charge at Calculate the electrical potential at the origin due to these three point charges. Take the zero of potential to be at infinity. Answer: 33,000 volts Var: 50+ 2) A small metal sphere of mass 4.8 g and charge 9.9 μC is fired with an initial speed of directly toward the center of a second metal sphere carrying charge This second sphere is held fixed. If the spheres are initially a large distance apart, how close do they get to each other? Treat the spheres as point charges. Answer: 3.0 meters Var: 50+ Figure 18.15

3) In Figure 18.15, two point charges, q1 = +56.0 nC and q2 = -46.0 nC, are separated by A third charge of is placed at the point A, 0.18 m to the left of q2. Find the work needed to move the third charge to point B, 0.40 m to the left of q1. Answer: 8.2 × 10-5 J Var: 50+ 4) An oil droplet with 9 excess electrons is held stationary in a field of

What is

the radius of the oil drop? (The density of the oil is Answer: 8.32 × 10-7 m Var: 50+ 5) A parallel-plate air capacitor is made from two plates 0.070 m square, spaced 9.2 mm apart. What must the potential difference between the plates be to produce an energy density of Answer: 1,100 volts Var: 50+

6) An isolated parallel-plate capacitor (not connected to a battery) has a charge of The separation between the plates initially is and for this separation the capacitance is Calculate the work that must be done to pull the plates apart until their separation becomes if the charge on the plates remains constant. The capacitor plates are in a vacuum. Answer: 130 J Var: 50+ 7) A network of capacitors is connected across a potential difference V0, as shown in Figure 18.16. Figure 18.16

(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 (b) 13.5 µJ Var: 1

College Physics, 11e (Young) Chapter 19 Current, Resistance, and Direct-Current Circuits 19.1 Multiple Choice Questions 1) The resistivity of gold is at a temperature of 20°C. A gold wire, 0.5 mm in diameter and 44 cm long, carries a current of 380 ma. The number of electrons per second passing a given cross section of the wire, is closest to: A) 2.4 × 1018 B) 2.4 × 1017 C) 1.2 × 1022 D) 2.8 × 1014 E) 6.3 × 1015 Answer: A Var: 50+ 2) 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. The power dissipated in the wire is closest to: A) 0.31 mW B) 0.077 mW C) 0.14 mW D) 0.19 mW E) 0.25 mW Answer: A Var: 50+ 3) How much current will be flowing through a if it is connected to a source supplying A) 1300 A B) 5.9 × 108 A C) 25 nA D) 770 A Answer: A Var: 50+

length of copper wire with radius (The resistivity of copper is

4) A 1.0 m length of metal wire is connected to a

battery, and a current of

flows

through it. What is the diameter of the wire? (The resistivity of metal is A) 12 μm B) 6.0 μm C) 24 μm D) 2.2 μm Answer: A Var: 38 5) A component with a 17 Ω resistor is rated for use at power levels not exceeding 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+ 6) A device experiences a voltage drop of across it while a current of through it. How much power does it dissipate? A) 50 mW B) 500 μW C) 2.5 kW D) 0.50 kW Answer: A Var: 35 7) A battery is rated that it provides current can it deliver? A) 0.11 mA B) 81 kA C) 0.33 mA D) 9.1 kA Answer: A Var: 41 8) A device with a resistance of does the device use? A) 0.50 mW B) 20,000 kW C) 0.050 mW D) 2,000 kW Answer: A Var: 10

How

flows

of power at

when fully charged. How much

is connected to a

battery. How much power

9) A 6.0 V battery that can store of energy is connected to a resistor. How much electrical charge must flow between the battery's terminals to completely drain the battery if it is fully charged? A) 83 C B) 0.01 C C) 3,000 C D) 0.07 C Answer: A Var: 50 10) Each of the resistors in the circuit shown in Figure 19.1 has a resistance of the equivalent resistance of the circuit? Figure 19.1

A) 450.0 Ω B) 720.0 Ω C) 540.0 Ω D) 180.0 Ω Answer: A Var: 41

What is

11) The resistors in the circuit shown in Figure 19.2 each have a resistance of equivalent resistance of the circuit? Figure 19.2

What is the

A) 700 Ω B) 2,800 Ω C) 175 Ω D) 1,400 Ω Answer: A Var: 9 12) What current will a 3.0 V battery cause to flow if it is short circuited? The internal resistance of the battery is A) 0.21 A B) 42 A C) 4.7 A D) 130 A Answer: A Var: 50+ 13) A 10.0 V battery is connected across two resistors in series. If the resistors have resistances of and what is the voltage drop across the resistor? A) 4.1 V B) 5.9 V C) 14 V D) 7.0 V Answer: A Var: 50+ 14) A 7.0 Ω resistor is connected across the terminals of a flows, what is the internal resistance of the battery? A) 13 Ω B) 20 Ω C) -10.8 Ω D) 27.0 Ω Answer: A Var: 7

battery. If

15) In the circuit shown in Figure 19.3, what current does the ammeter read?

of current

Figure 19.3

A) 0.044 A B) 0.033 A C) 0.18 A D) 0.11 A Answer: A Var: 50+ 16) What is the current through resistor R1 in the circuit shown in Figure 19.4? Figure 19.4

A) 0.08 A B) 0.05 A C) 0.00 A D) 3.68 A Answer: A Var: 50+

17) What is the current through resistor R1 in the circuit in Figure 19.5? Figure 19.5

A) 0.043 A B) 0.16 A C) 0.035 A D) 0.0095 A Answer: A Var: 50+ 18) A resistor is made out of a low wire having a length L. Each end of the wire is attached to a terminal of a battery having a constant voltage Vo. 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 to the battery (the end of both wires attached to one terminal, and the other ends attached to the other terminal), what would be the total current flowing through the two wires? A) 4I B) 2I C) I D) I/2 Answer: A Var: 1

19) A 9 Volt battery is hooked up to two resistors in series. One has a resistance of 5 Ohms, and the other has a resistance of 10 Ohms. Several locations along the circuit are marked with letters, as shown in Figure 19.6. Which statement about this circuit is true? Figure 19.6

A) The current at A is equal to the current at B, which is equal to the current at C, which is equal to the current at 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. Answer: A Var: 1 20) A 9 Volt battery is hooked up to two resistors in series. One has a resistance of 5 Ohms, and the other has a resistance of 10 Ohms. Several locations along the circuit are marked with letters, as shown in Figure 19.6. Through which resistor is energy being dissipated at the higher rate? A) The 10 Ohm resistor. B) The 5 Ohm resistor. C) Energy is being dissipated by both resistors at the same rate. Answer: A Var: 1

21) Identical light bulbs are attached to identical batteries, as shown in Figure 19.7. The ranking (from lowest to highest) of the total power emitted from the light bulb(s) is Figure 19.7

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

22) Identical batteries are connected in different arrangements to the same light bulb, as shown in Figure 19.8. For which arrangement will the bulb shine the brightest? Figure 19.8

A) A B) B C) C Answer: C Var: 1 23) The heater element of a 120 V toaster is a 5.4 m length of nichrome wire, whose diameter is 0.48 mm. The resistivity of nichrome at the operating temperature of the toaster is The toaster is operated at a voltage of 120 V. The power drawn by the toaster is closest to: A) 370 W B) 360 W C) 380 W D) 400 W E) 410 W Answer: A Var: 50+

24)

Figure 19.9a

The emf and the internal resistance of a battery are as shown. In Figure 19.9a, a current of 6.4 A is drawn from the battery when a resistor is connected across the terminals. The power dissipated by the resistor is closest to: A) 350 W B) 440 W C) 410 W D) 380 W E) 470 W Answer: A Var: 50+ 25)

Figure 19.9b

The emf and the internal resistance of a battery are as shown. In Figure 19.9b, when the terminal voltage is equal to 15.6 V, the current through the battery, including direction, is closest to: A) 1.2 A, from b to a B) 1.7 A, from b to a C) 1.2 A, from a to b D) 1.7 A, from a to b E) 2.9 A, from b to a Answer: A Var: 50+

Figure 19.10

The emf and the internal resistance of a battery are as shown. 26) In Figure 19.10, a current of 6.0 A is drawn from the battery. The terminal voltage of the battery is closest to: A) zero B) +12 V C) +24 V D) -12 V E) -24 V Answer: A Var: 1 27) In Figure 19.10, a 3.0 ohm cable is connected across the battery. The rate at which chemical energy in the battery is depleted is closest to: A) 24 W B) 27 W C) 29 W D) 32 W E) 34 W Answer: C Var: 1

Figure 19.11

A circuit has two batteries and a resistor as shown. 28) In Figure 19.11, the terminal voltage of the 6 V battery is closest to: A) +1.2 V B) +2.4 V C) +3.6 V D) -1.2 V E) -2.4 V Answer: D Var: 1 29) In Figure 19.11, the terminal voltage of the 12 V battery is closest to: A) 8.4 V B) 9.6 V C) 10.8 V D) 13.2 V E) 15.6 V Answer: A Var: 1 30) If the length and diameter of a wire of circular cross section are both doubled, the resistance is A) unchanged. B) doubled. C) increased fourfold. D) halved. E) None of these are true. Answer: D Var: 1

31) Nichrome wire, often used for heating elements, has resistivity of 1.0 x Ω ∙ m at room temperature. What length of No. 30 wire (diameter 0.250 mm) is needed to wind a resistor that has 50 ohms at room temperature? A) 3.66 m B) 2.45 m C) 0.61 m D) 6.54 m E) 22.4 m Answer: B Var: 1 Figure 19.12

32) Three light bulbs, A, B, and C, have electrical ratings as follows: Bulb A - 96 W, 1.7 A Bulb B - 80 V, 205 W Bulb C - 120 V, 0.4 A The three bulbs are connected in a circuit, which is across a 150-V line, as shown. Assume the filament resistances of the light bulbs are constant and independent of operating conditions. In Figure 19.12, the equivalent resistance of the circuit is closest to: A) 62 Ω B) 49 Ω C) 74 Ω D) 86 Ω E) 98 Ω Answer: A Var: 50+

33)

Figure 19.13a

A multiloop circuit is given. It is not necessary to solve the entire circuit. In Figure 19.13a, the current is closest to: A) -0.7 A B) 0.7 A C) 5 A D) -5 A E) zero Answer: A Var: 50+ 34)

Figure 19.13b

A multiloop circuit is given. It is not necessary to solve the entire circuit. In Figure 19.13b, the current is closest to: A) -5 A B) 5 A C) 13 A D) -13 A E) zero Answer: A Var: 50+

35)

Figure 19.13c

A multiloop circuit is given. It is not necessary to solve the entire circuit. In Figure 19.13c, the emf is closest to: A) -36 V B) 36 V C) 76 V D) 79 V E) -79 V Answer: A Var: 50+ 36)

Figure 19.13d

A multiloop circuit is given. It is not necessary to solve the entire circuit. In Figure 19.13d, the potential difference is closest to: A) -4 V B) 36 V C) -36 V D) -52 V E) 52 V Answer: A Var: 50+

Figure 19.14

37) In Figure 19.14, the resistor R has a variable resistance. As R is decreased A) remains unchanged, increases. B)

decreases,

decreases.

decreases,

increases.

increases,

decreases.

increases,

increases.

Answer: C Var: 1 Figure 19.15

38) In Figure 19.15, the current of the circuit in the 8 ohm resistor is 0.5A. What is the current in the 2 ohm resistor? A) 2.25 A B) 0.75 A C) 4.5 A D) 9.5 A E) 6.4 A Answer: D Var: 1

Figure 19.16

39) In Figure 19.16, what is the power dissipated in the 2 ohm resistance in the circuit? A) 5.33 W B) 8.0 W C) 6.67 W D) 2.67 W E) 3.56 W Answer: E Var: 1 Figure 19.17

A multiloop circuit is given. Some circuit quantities are not labeled. It is not necessary to solve the entire circuit. 40) In Figure 19.17, the current A) zero B) +0.2 A C) +0.4 A D) -0.2 A E) -0.4 A Answer: B Var: 1

is closest to:

41) In Figure 19.17, the emf ε is closest to: A) +3 V B) +18 V C) -3 V D) -10 V E) -18 V Answer: B Var: 1 42) In Figure 19.17, the current

is closest to:

A) +0.1 A B) +0.3 A C) +0.5 A D) -0.1 A E) -0.3 A Answer: E Var: 1 43)

Figure 19.18a

Initially, for the circuit shown, the switch S is open and the capacitor is uncharged.The switch S is closed at time In Figure 19.18a, when the time t is equal to 8.0 s, the charge on the capacitor, in μC, is closest to: A) 240 B) 190 C) 280 D) 330 E) 380 Answer: A Var: 50+

44)

Figure 19.18b

Initially, for the circuit shown, the switch S is open and the capacitor is uncharged.The switch S is closed at time In Figure 19.18b, when the time t is equal to 20.0 s, the potential difference across the resistor is closest to: A) 6.6 V B) 7.9 V C) 9.2 V D) 11 V E) 12 V Answer: A Var: 50+ 45)

Figure 19.18c

Initially, for the circuit shown, the switch S is open and the capacitor is uncharged.The switch S is closed at time In Figure 19.18c, at a given instant, the potential difference across the capacitor is twice the potential difference across the resistor. At that instant, the charge on the capacitor, in is closest to: A) 1,200 B) 1,000 C) 900 D) 670 E) 450 Answer: A Var: 50+

46)

Figure 19.19a

Initially, for the circuit shown, the switch S is open and the capacitor voltage is 80 V. The switch S is closed at time In Figure 19.19a, the charge on the capacitor, when the current in the circuit is , in is closest to: A) 970 B) 910 C) 850 D) 790 E) 740 Answer: A Var: 50+ 47)

Figure 19.19b

Initially, for the circuit shown, the switch S is open and the capacitor voltage is 80 V. The switch S is closed at time In Figure 19.19b, the capacitor voltage when the time t is equal to 40.0 s is closest to: A) 66 V B) 75 V C) 83 V D) 91 V E) 100 V Answer: A Var: 50+ 48) A 1.0 μF capacitor is charged until it acquires a potential difference of across its plates, then the emf source is removed. If the capacitor is then discharged through a resistance of a circuit, what is the voltage drop across the capacitor later? A) 880 V B) 920 V C) 16 V D) -16 V Answer: A Var: 50+ Figure 19.20

49) The capacitor shown in the circuit in Figure 19.20 is initially uncharged when the switch S is suddenly closed. After one time constant, the current through the resistor will be closest to: A) 0.00 A B) 0.74 A C) 1.0 A D) 1.3 A E) 2.0 A Answer: B Var: 1 50) For the circuit shown in Figure 19.20, the switch S is suddenly closed with the capacitor uncharged. After one time constant, the charge on the capacitor is closest to: A) 0.00 mC B) 0.74 mC C) 1.0 mC D) 1.3 mC E) 2.0 mC Answer: D Var: 1 19.2 Short Answer Questions 1) A heating element of resistance (at its operating temperature) 148 Ω is connected to a battery of emf 523 V and unknown internal resistance r. It is found that heat energy is being generated in the heater element at a rate of 66.0 W. What is the rate at which heat energy is being generated in the internal resistance of the battery? Answer: 283 watts Var: 50+ 2) When a thin copper wire of length 178.0 m is connected between the terminals of a 1.2 V battery, of negligible internal resistance, a current of 2.0 amps is produced. What is the diameter of the wire? (The resistivity of copper is Answer: 2.5 × Var: 1

3) When an external resistor of resistance

= 14 Ω is connected to the terminals of a battery, a

current of 6.0 A flows through the resistor. When an external resistor of resistance connected instead, the current is 2.0 A. Calculate: (a) the emf of the battery and (b) the internal resistance of the battery. Answer: (a) 150 volts (b) 11 Ω Var: 1

Figure 19.21

4) In Figure 19.21, consider the circuit sketched. Note that two currents are shown. Calculate the emf's and . Answer:

= 28 volts

= 44 volts Var: 1

Figure 19.22

5) In Figure 19.22, consider the circuit sketched. The battery has emf internal resistance. The four resistors have resistances of Calculate the rate at which heat is being generated in the resistor

and negligible and .

Answer: 120 watts Var: 50+ 6) A resistor with resistance 360 Ω is in a series circuit with a capacitor of capacitance 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 x F Var: 50+ 7) In the circuit shown in Figure 19.23, all the capacitors are initially uncharged when the switch S is suddenly closed. Find (a) the maximum reading of the ammeter and (b) the maximum charge on the 5.00 µF capacitor. Figure 19.23

Answer: (a) 2.50 A, (b) 458 µC Var: 1

College Physics, 11e (Young) Chapter 20 Magnetic Field and Magnetic Forces 20.1 Multiple Choice Questions 1) Alpha particles (charge = +2e, mass = 6.68 × kg) are accelerated in a cyclotron to a final orbit radius of The magnetic field in the cyclotron is The period of circular motion of the alpha particles is closest to: A) 0.16 μs B) 0.25 μs C) 0.33 μs D) 0.40 μs E) 0.49 μs Answer: A Var: 50+ 2) Alpha particles (charge = +2e, mass = 6.68 × kg) are accelerated in a cyclotron to a final orbit radius of The magnetic field in the cyclotron is The kinetic energy of an alpha particle in the final orbit is closest to: A) 3.0 MeV B) 2.6 MeV C) 3.4 MeV D) 3.9 MeV E) 4.3 MeV Answer: A Var: 50+

3) A positive charge in Figure 20.1 is moving to the right and experiences a vertical (upward) magnetic force. In which direction is the magnetic field? Figure 20.1

A) to the right B) to the left C) upward D) out of the page E) into the page Answer: E Var: 1 4) 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

Figure 20.2

5) In Figure 20.2 is a velocity selector that can be used to measure the speed of a charged particle. A beam of particles is directed along the axis of the instrument. A parallel plate capacitor sets up an electric field E which is oriented perpendicular to a uniform magnetic field B. If the plates are separated by 3 mm and the value of the magnetic field is 0.3 T, what voltage between the plates will allow particles of speed to pass straight through without deflection? A) 450 V B) 1,400 V C) 2,800 V D) 140 V E) 70 V Answer: A Var: 50+ 6) Which of the following is an accurate statement? A) Magnetic field lines have as their sources north and south poles. B) A magnetic field line is, by definition, tangent to the direction of the magnetic force on a moving charge at a given point in space. C) The magnetic force on a moving charge does not change its energy. D) The magnetic force on a current carrying wire is greatest when the wire is parallel to the magnetic field. E) A current carrying loop of wire tends to line up with its plane parallel to an external magnetic field in which it is positioned. Answer: C Var: 1

Figure 20.3

A uniform magnetic field of magnitude 0.80 T in the negative z-direction is present in a region of space. A uniform electric field is also present. In Figure 20.3, the electric field is set at 20,800 V/m in the positive y-direction. An electron is projected with an initial velocity in the positive x-direction. The of the initial force on the electron is closest to: A) -7 ×

B) +7 ×

C) -3 ×

D) +3 × E) zero Answer: A Var: 50+

Figure 20.4

A mass spectrograph is operated with deuterons, which have a charge of +e and a mass of Deuterons emerge from the source, which is grounded with negligible velocity. The velocity of the deuterons as they pass through the accelerator grid is A uniform magnetic field of magnitude directed out of the plane, is present at the right of the grid. 8) In Figure 20.4, the deuterons are in circular orbit in the magnetic field. The radius of the orbit and the initial sense of deflection are closest to: A) 60 mm, upward B) 70 mm, upward C) 60 mm, downward D) 70 mm, downward E) 80 mm, downward Answer: E Var: 1 9) In Figure 20.4, the angular velocity of the deuterons in the magnetic field is closest to: A) 1.6 × rad/s B) 4.0 ×

rad/s

C) 1.0 ×

rad/s

D) 2.5 ×

rad/s

E) 6.3 × rad/s Answer: C Var: 1

10)

Figure 20.5a

A rigid rectangular loop, which measures 0.30 m by 0.40 m, carries a current of 9.9 A, as shown. A uniform external magnetic field of magnitude 1.8 T in the negative x-direction is present. Segment CD is in the x-z plane and forms a 19° angle with the z-axis, as shown. In Figure 10.5a, the y-component of the magnetic force on segment AB is closest to: A) +5.1 N B) -5.1 N C) +1.7 N D) -1.7 N E) zero Answer: A Var: 1

11)

Figure 20.5b

A rigid rectangular loop, which measures 0.30 m by 0.40 m, carries a current of 5.5 A, as shown. A uniform external magnetic field of magnitude 2.9 T in the negative x-direction is present. Segment CD is in the x-z plane and forms a 35° angle with the z-axis, as shown. In Figure 20.5b, an external torque applied to the loop keeps it in static equilibrium. The magnitude of the external torque is closest to: 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

12)

Figure 20.5c

A rigid rectangular loop, which measures 0.30 m × 0.40 m, carries a current of 7.7 A, as shown. A uniform external magnetic field of maggitude 2.6 T in the negative x-direction is present. Segment CD is in the x-z plane and forms a 33° angle with the z-axis, as shown. In Figure 20.5c, the magnitude of the magnetic moment of the loops is closest to: A) 0.92 A ∙ m2 B) 0.77 A ∙ m2 C) 0.62 A ∙ m2 D) 0.46 A ∙ m2 E) 0.31 A ∙ m2 Answer: A Var: 1 13) A 5 meter length of wire carrying a current of 5 A lies on a horizontal table with a rectangular top of dimensions The ends of the wire are attached to opposite ends of a diagonal of the rectangle. A vertical magnetic field of 0.30 T is present. What magnetic force acts on this segment of wire? A) 0.75 N B) 1.1 N C) 7.5 N D) zero E) The force cannot be determined without knowing the shape of the length of wire. Answer: A Var: 50+

14) A circular coil of wire of 200 turns and diameter 6 cm carries a current of 7 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 torque on the coil? A) 3.1 N ∙ m B) 1.8 N ∙ m C) 5.9 N ∙ m D) 8.2 N ∙ m E) 1.5 N ∙ m Answer: A Var: 50+ 15) An electron enters a magnetic field of with a velocity perpendicular to the direction of the field. At what frequency does the electron traverse a circular path? (The mass of an electron is and the charge of an electron is A) 1.9 × 1010 Hz B) 5.3 × 10-7 Hz C) 1.9 × 1014 Hz D) 5.3 × 10-11 Hz Answer: A Var: 50+ 16) 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) 2,500 C Answer: A Var: 50+ 17) An electron in a magnetic field has a cyclotron frequency of magnetic field strength? (The mass of an electron is is A) 110 T B) 12 T C) 0.084 T D) 0.0093 T Answer: A Var: 8

What is the and the charge of an electron

18) A square wire 2.0 cm on each side is oriented so that a angle with the normal to the plane of the square. If a on the wire, how many loops does the wire make? A) 3.2 × 1010 B) 3.2 × 106 C) 1.6 × 1010 D) 4.5 × 1010 Answer: A Var: 20

magnetic field makes a current causes a torque

19) The magnitude of a magnetic field a distance from a wire is How much current is flowing through the wire. Assume the wire is the only contributor to the magnetic field. A) 30 mA B) 188 mA C) 19 mA D) 377 mA Answer: A Var: 50+ 20) A wire carrying a current is shaped in the form of a circular loop of radius If the magnetic field strength at its center is with no external magnetic fields contributing to it, what is the magnitude of the current that flows through the wire? A) 7.0 A B) 28 A C) 14 A D) 17 A Answer: A Var: 30 21) A very long wire generates a magnetic field of What is the magnitude of the current? A) 1.0 mA B) 2.0 mA C) 4,000 mA D) 3,100 mA Answer: A Var: 27

at a distance of

22) Two parallel, straight wires are 7.0 cm apart and each carries 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 force does the wire pull on the cart? Both wires are long. A) 4,600 dynes B) 370 dynes C) 660 dynes D) 9,300 dynes Answer: A Var: 50+ 23) A 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+ 24) A solenoid 3.0 cm long consists of 5,748 loops of wire. If the magnetic field inside the solenoid is what is the magnitude of the current that flows through it? A) 4.2 A B) 0.24 A C) 52 A D) 3.0 A Answer: A Var: 50+

25) A negatively charged particle is moving to the right, directly above a wire having a current flowing to the right, as shown in Figure 20.6. In which direction is the magnetic force exerted on the particle? Figure 20.6

A) into the page B) out of the page C) downward D) upward E) The magnetic force is zero since the velocity is parallel to the current. Answer: D Var: 1 26) A ring with a clockwise current (as seen from above the ring) is situated with its center directly above another ring, which has a counter-clockwise current, as shown in Figure 20.7. In what direction is the net magnetic force exerted on the top ring? Figure 20.7

A) upward B) downward C) The net force is zero. D) Impossible to determine Answer: A Var: 1

27) 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) only contain a north pole. B) still contain a north pole on the right and a new south pole on the left. C) only contain a south pole. Answer: B Var: 1 28) A charged particle moving within a static 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) None of the above statements are true. Answer: C Var: 1 29) Consider a solenoid of length L, N windings, and radius b (L is much longer than b). A current I is flowing through the wire. If the radius of the solenoid were doubled (becoming 2b), and all other quantities remained the same, the magnetic field A) would remain the same. B) would become twice as strong. C) would become one half as strong. Answer: A Var: 1 30) Consider a solenoid of length L, N windings, and radius b (L is much longer than b). A current I is flowing through the wire. If the length of the solenoid became twice as long (2L), and all other quantities remained the same, the magnetic field inside the solenoid would A) stay the same. B) become twice as strong as initially. C) become half as strong as initially. Answer: C Var: 1

Figure 20.8

31) A circular loop of radius 10 cm and three long straight wires carry currents of and

respectively, as shown. Each straight wire is 20 cm from the

center of the loop. In Figure 20.8, the the loop is closest to: A) -54 μT B) -60 μT C) -50 μT D) +60 μT E) +50 μT Answer: A Var: 50+

of the resultant magnetic field at the center of

32) A circular loop of radius 10 cm and three long straight wires carry currents of and

respectively, as shown. Each straight wire is 20 cm from the

center of the loop. In Figure 20.8, the the loop is closest to: A) -360 μT B) +360 μT C) -40 μT D) +40 μT E) -170 μT Answer: A Var: 50+

of the resultant magnetic field at the center of

33)

Figure 20.9

A long straight wire on the z-axis carries a current of 5.0 A in the positive direction. A circular loop in the of radius 10 cm, carries a 8.0 A current, as shown. Point P, at the center of the loop, is 25 cm from the In Figure 20.9, an electron is projected from P with a velocity of in the negative x-direction. The closest to: A) -8.0 × 10-18 N B) +8.0 × 10-18 N C) -4.0 × 10-18 N D) +4.0 × 10-18 N E) zero Answer: A Var: 50+

of the force on the electron is

Figure 20.10

34) A solenoid is wound with 470 turns on a form 4 cm in diameter and 50 cm long. The windings carry a current in the sense that is shown. The current produces a magnetic field, of magnitude at the center of the solenoid. In Figure 20.10, the current in the solenoid windings is closest to: A) 3.5 A B) 3.0 A C) 2.6 A D) 4.3 A E) 3.9 A Answer: A Var: 50+ Figure 20.11

35) Three very long, straight, parallel wires each carry currents of 4 A, directed out of the page in the drawing in Figure 20.11. The wires pass through the vertices of a right isosceles triangle of side What is the magnitude of the magnetic field at point P at the midpoint of the hypotenuse of the triangle? A) 4.42 × T B) 1.77 ×

C) 5.66 ×

D) 1.26 ×

E) 1.77 × Answer: C Var: 1

36) A metallic weight is suspended from a metal spring. If now a current is passed through the

spring, A) the spring will contract, raising the weight. B) the spring will extend, lowering the weight. C) the weight will not move. D) whether or not the weight moves up or down depends on what the weight is made of (i.e. whether or not it is magnetizable). E) None of these are true. Answer: A Var: 1 37) 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 of A) 16d B) 8d C) 4d D) 2d E) d Answer: C Var: 1 20.2 Short Answer Questions 1) A wire along the z-axis carries a current of 4.9 A in the positive z direction. Find the force (magnitude and direction) exerted on a 3.3 cm long length of the wire by a uniform magnetic field with magnitude 0.43 T in the -x direction. Answer: 0.070 N, -y direction Var: 50+ 2) A proton, with mass 1.67 ×

kg and charge +1.6 ×

C, is sent with velocity

in the into a region where there is a uniform electric field of magnitude in the y direction. What is 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 xcomponent. Neglect gravitational effects. Answer: 3.4 × 10-2 T, +z direction Var: 50+

Figure 20.12

3) In Figure 20.12, a small particle of charge q = -1.9 x velocity

C and mass

has

as it enters a region of uniform magnetic field. The particle is

observed to travel in the semicircular path shown, with radius (a) magnitude and (b) direction of the magnetic field in the region. Answer: (a) B = 0.26 T (b) directed into the paper Var: 50+

Calculate the

Figure 20.13

4) In Figure 20.13, the rectangular loop is pivoted about one side (of length 0.060 m), that coincides with the The end (length 0.020 m) of the loop that lies in the makes an angle of with the as shown in the sketch. The loop carries a current of in the direction shown. (In the side of the loop that is along the the current is in the +y direction.) If there is a uniform magnetic field of magnitude in the -x direction, find the magnitude of the torque that the magnetic field exerts on the loop. Answer: 6.4 × 10-1 N ∙ m Var: 50+

Figure 20.14

5) In Figure 20.14, 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 is the magnitude and direction of the magnetic field at point P, that is a distance below the lower wire? (NOTE:

= 4π ×

T ∙ m/A.)

Answer: B = 7.7 × 10-6 T, directed out of the plane of the paper. Var: 50+ Figure 20.15

6) In Figure 20.15, a rectangular current loop is carrying current indicated near a long wire carrying a current

= 7.0 A, in the direction

. 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 (a) magnitude and (b) direction (from top to bottom or from bottom to top in the sketch) of the current in the wire? (NOTE: Answer: (a) 0.18 A (b) from bottom to top Var: 50+

7) An ideal toroidal solenoid containing 825 equally spaced coils is shown in Figure 20.16. (a) How large must the current I be so that the magnetic field within the coils at a distance of 17.0 cm from the center is 0.0250 T? (b) What is the magnetic field strength in the region outside the coils? Figure 20.16

Answer: (a) 25.8 A, (b) zero Var: 1

College Physics, 11e (Young) Chapter 21 Electromagnetic Induction 21.1 Multiple Choice Questions 1) A 2.0 m conductor is formed into a square and placed in the horizontal A magnetic field is oriented above the horizontal with a strength of What is the magnetic flux through the conductor? A) 0.12 T ∙ m2 B) 0.22 T ∙ m2 C) 0.25 T ∙ m2 D) 2.0 T ∙ m2 Answer: A Var: 10 2) A circular conducting loop with a radius of and a small gap filled with a resistor is oriented in the If a 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 conductor? A) 0.00054 A B) 0.0031 A C) 0.0054 A D) 0.00058 A Answer: C Var: 50+ 3) What is the radius of a tightly wound solenoid of circular cross-section that has 180 turns if a change in its internal magnetic field of causes a current to flow? The resistance of the circuit that contains the solenoid is The only emf source for the circuit is the induced emf. A) 0.25 m B) 0.014 m C) 0.54 m D) 0.043 m Answer: A Var: 50+

4) A closed loop conductor with radius is located in a changing magnetic field. If the maximum emf induced in the loop is what is the maximum 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 5) A conductor is formed into a loop that encloses an area of The loop is oriented at a angle with the A varying magnetic field is oriented parallel to the If the maximum emf induced in the loop is what is the maximum 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+ Figure 21.1

6) In Figure 21.1, a wire and a 10 ohm resistor are used to form a circuit in the shape of a square, 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 decreased from 2.70 T to 0.90 T in a time interval of 96 ms. The average induced current and its direction through the resistor, in this time interval, are closest to: 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+ Figure 21.2

7) In Figure 21.2, a coil of 8 turns is wound on a square frame, 25 cm by 25 cm. The resistance of the coil is The coil is initially in a horizontal plane and a uniform vertical magnetic field B is present. Two views of the initial orientation of the coil are given in figs (a) and (b). Points P and Q are initially of the left and right sides of the frame, respectively. The coil is flopped over about axis through 180 degrees, to the final horizontal orientation, shown in fig (c). The time interval, during which the coil is flipped over, is 0.50 s. The average induced current in the coil during the 0.50 s time interval is 88 ma. The magnitude of the magnetic field which is present is closest to: A) 0.23 T B) 0.46 T C) 0.92 T D) 1.8 T E) 3.7 T Answer: A Var: 50+

Figure 21.3

A long vertical wire carries a steady 40 A current. A pair of rails are horizontal and are apart. A 20 ohm 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 velocity of as shown. The bar and the rails have negligible resistance. At a given instant , the bar is from the wire, as shown. In Figure 21.3, at time t1, the induced current and its direction through the resistor are closest to: A) 0.12 μA, from a to b B) 0.12 μA, from b to a C) 0.060 μA, from a to b D) 0.060 μA, from b to a E) 0.36 μA, from b to a Answer: A Var: 50+ Figure 21.4

9) In Figure 21.4, a coil of wire is placed on the axis of a solenoid carrying a DC current. Which of the following will NOT result in an EMF being induced 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

10) A circular coil of 20 turns and radius 5 cms is placed with its plane oriented at 90° to a magnetic field of The field is now increased at a steady rate, reaching a value of after 4 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+ Figure 21.5

11) In Figure 21.5, a straight wire carries a steady current I. A bar is in contact with a pair of circular rails, and rotates about the straight wire. The induced current through the resistor R is: A) zero B) from a to b C) from b to a Answer: A Var: 1 Figure 21.6

12) In Figure 21.6, a bar magnet moves away from the solenoid. The induced current through the resistor R is: A) zero B) from a to b C) from b to a Answer: B Var: 1 Figure 21.7

13) In Figure 21.7, a bar is in contact with a pair of parallel rails and is in motion with velocity ν. A uniform magnetic field is present. The induced current through the resistor R is: A) zero B) from a to b C) from b to a Answer: A Var: 1 Figure 21.8

14) In Figure 21.8, one end of a bar is in contact with a circular rail and the other end is pivoted at P. A steady, uniform, magnetic field B is present. The bar rotates about P. The induced current through the resistor R is: A) zero B) from a to b C) from b to a Answer: C Var: 1

Figure 21.9

15) In Figure 21.9, two parallel wires carry a current I in opposite directions. A rectangular loop is midway between the wires. The current I is decreasing. The induced current through the resistor R is: A) zero B) from a to b C) from b to a Answer: B Var: 1 Figure 21.10

16) In Figure 21.10, a bar is in contact with a pair of parallel rails. A steady, uniform, magnetic field, perpendicular to the plane of the rails, is present. The bar is in motion with velocity ν. The induced current through the resistor R is: A) zero B) from a to b C) from b to a Answer: B Var: 1

Figure 21.11

17) In Figure 21.11, a loop carries a steady current I. A bar is in contact with a pair of circular rails, and rotates about the center of the loop. The induced current through the resistor R is: A) zero B) from a to b C) from b to a Answer: C Var: 1 Figure 21.12

18) In Figure 21.12, two solenoids are side by side. The switch S, initially open, is closed. The induced current through the resistor R is: A) zero B) from a to b C) from b to a Answer: C Var: 1

Figure 21.13

19) In Figure 21.13, a long bar slides on two contact points and is in motion with velocity ν. A steady, uniform, magnetic field B is present. The induced current through the resistor R is: A) zero B) from a to b C) from b to a Answer: A Var: 1 Figure 21.14

20) In Figure 21.14, a battery supplies a steady current to the solenoid on the left. The two solenoids are moving toward each other. The induced current through the resistor R is: A) zero B) from a to b C) from b to a Answer: B Var: 1

Figure 21.15

21) In Figure 21.15, a straight wire carries a current I. The wire passes through the center of a toroidal coil. The current is quickly reduced to zero. The induced current through the resistor R is: A) zero B) from a to b C) from b to a Answer: C Var: 1 Figure 21.16

22) In Figure 21.16, a C-shaped conductor is in a uniform magnetic field B, which is increasing. 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

Figure 21.17

23) In Figure 21.17, a bar is in contact with a pair of parallel rails. A steady, uniform, magnetic field B is present. The bar is in motion with velocity 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: A Var: 1 Figure 21.18

24) In Figure 21.18, two solenoids are in line. The switch S, initially closed, is opened. 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: B Var: 1

25) A circular wire ring is situated above a long straight wire, as shown in Figure 21.19. The straight wire has a current flowing to the right, and the current is increasing in time at a constant rate. Which statement is true? Figure 21.19

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 26) A loop of wire is situated inside a large solenoid, with the plane of the loop initially perpendicular to the axis of the solenoid. Current can be made to flow through the loop of wire if A) a constant current is flowing through the solenoid wire. B) the current flowing through the solenoid is decreasing with time. C) the loop of wire is rotating within the solenoid, and a constant current is flowing through the solenoid wire. D) All of the above statements are true. E) Only two of the above statements are true. Answer: E Var: 1

27) While a magnet is moved toward the end of a solenoid (as shown in Figure 21.20), a voltage difference is induced between the two ends of the solenoid wire. The voltage difference would be larger if Figure 21.20

A) the speed of the magnet were increased. B) the solenoid contained more loops (while having the same length). C) The bar magnet produced a stronger magnetic field. D) All of the above statements are true. E) Only two of the above statements are true. Answer: D Var: 1 Figure 21.21

28) In Figure 21.21, a straight wire carries a steady current I. A bar is in contact with a pair of rails and is in motion with velocity 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

Figure 21.22

29) In Figure 21.22, an electromagnetic flowmeter is useful when it is desirable not to interrupt the system in which the fluid is flowing (e.g. for the blood in an artery during heart surgery). Such a device is illustrated. The conducting fluid moves with velocity v in a tube of diameter d perpendicular to which is a magnetic field B. A voltage V is induced between opposite sides of the tube. Given and a measured voltage of determine the speed of the blood. A) 2.0 m/s B) 11 m/s C) 0.075 m/s D) 1.1 m/s E) 7.5 × 102 m/s Answer: A Var: 50+ 30) 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 for a wild goose with a wingspan of flying due south at at a point where the earth's magnetic field is horizontal by The expected voltage would be about A) 0.50 mV B) 0.60 mV C) 0.78 mV D) 0.060 mV E) 0.25 mV Answer: A Var: 50+

T directed downward from

31) If you hold a sheet of copper in a strong permanent magnet, with the plane of the sheet perpendicular to the magnetic field, and quickly jerk it out, A) you will experience a magnetic force opposing your action. B) you will experience a magnetic force assisting your action. C) you will feel no magnetic force. D) any force you feel will be due mainly to iron impurities in the copper, since copper itself is not magnetic. E) None of these are true. Answer: A Var: 1 32) The current flowing through a circuit is changing at a rate of a inductor, what is the emf across the inductor? A) 1,140 V B)

If the circuit contains

D) 31 V Answer: A Var: 50+ 33) A solenoid with 3,000.0 turns is radius? (The value of

long. If its self-inductance is

what is its

A) 0.02219 m B) 0.00199 m C) 327 m D) 52 m Answer: A Var: 50+ 34) A series RL circuit has a 1 k Ω resistor and a the circuit? A) 5 μs B) 5 s C) 1.61 μs D) 1.61 s Answer: A Var: 42

inductor. What is the time constant for

35) An 87 mH solenoid inductor is wound on a form 0.80 m in length and 0.10 m in diameter. A coil is tightly wound around the solenoid at its center. The coil resistance is 6.1 ohms. The mutual inductance of the coil and solenoid is At a given instant, the current in the solenoid is and is decreasing at the rate of The number of turns in the winding of the solenoid is closest to: A) 2,700 B) 2,600 C) 2,800 D) 2,900 E) 3,000 Answer: A Var: 50+ 36) An 85 mH solenoid inductor is wound on a form 0.80 m in length and 0.10 m in diameter. A coil is tightly wound around the solenoid at its center. The coil resistance is 8.1 ohms. The mutual inductance of the coil and solenoid is At a given instant, the current in the solenoid is and is decreasing at the rate of At the given instant, the induced emf in the solenoid is closest to: A) 210 mV B) 230 mV C) 190 mV D) 170 mV E) 150 mV Answer: A Var: 50+ 37) A 66 mH solenoid inductor is wound on a form 0.80 m in length and 0.10 m in diameter. A coil is tightly wound around the solenoid at its center. The coil resistance is 4.3 ohms. The mutual inductance of the coil and solenoid is At a given instant, the current in the solenoid is and is decreasing at the rate of At the given instant, the magnetic energy of the solenoid, in is closest to: A) 9,300 B) 8,200 C) 7,000 D) 5,700 E) 4,600 Answer: A Var: 50+

38) An 73 mH solenoid inductor is wound on a form 0.80 m in length and 0.10 m in diameter. A coil is tightly wound around the solenoid at its center. The coil resistance is 7.7 ohms. The mutual inductance of the coil and solenoid is At a given instant, the current in the solenoid is and is decreasing at the rate of At the given instant, the induced current in the coil is closest to: A) 6.2 μA B) 4.9 μA C) 7.4 μA D) 8.6 μA E) 9.9 μA Answer: A Var: 50+ 39)

Figure 21.23a

An R-L circuit has a 60 V battery, a 50 H inductor, a 11 ohm resistor, and a switch S, in series, as shown. Initially, the switch is open, and there is no magnetic flux in the inductor. At time the switch is closed. In Figure 21.23a, when the time the current in the circuit is closest to: A) 3.2 A B) 2.7 A C) 2.2 A D) 4.3 A E) 5.5 A Answer: A Var: 50+

40)

Figure 21.23b

An R-L circuit has a 60 V battery, a 42 H inductor, a 24 ohm resistor, and a switch S, in series, as shown. Initially, the switch is open, and there is no magnetic flux in the inductor. At time the switch is closed. In Figure 21.23b, when the resistor voltage is equal to the inductor voltage, the current in the circuit is closest to: A) 1.3 A B) 0.50 A C) 1.0 A D) 0.75 A E) 1.5 A Answer: A Var: 50+ 41)

Figure 21.24a

An R-L circuit is shown, with a 19 ohm resistor and an ideal 42 H inductor, that has zero resistance. At time there is a current in the circuit. In Figure 21.24a, at time the rate of change of the current is closest to: A) -5.4 A/s B) -11 A/s C) -16 A/s D) -21 A/s E) -27 A/s Answer: A Var: 50+

42)

Figure 21.24b

An R-L circuit is shown, with a 23 ohm resistor and an ideal 41 H inductor, that has zero resistance. At time there is a current in the circuit. In Figure 21.24b, when the magnetic energy of the inductor is the rate of dissipation in the resistor is closest to: A) 1,800 W B) 450 W C) 900 W D) 1,300 W E) 2,200 W Answer: A Var: 50+ 43)

Figure 21.24a

An R-L circuit is shown, with a 20 ohm resistor and an ideal 41 H inductor, that has zero resistance. At time there is a current in the circuit. In Figure 21.24c, when the time t is equal to the inductor emf is closest to: A) 21 V B) 19 V C) 17 V D) 23 V E) 24 V Answer: A Var: 50+ 44) A 5 H inductor carries a current of 2 amps. How can a self-induced EMF of 50 volts be made to appear across the inductor? A) Change the current at the rate of 10 amps/sec. B) Change the current to 10 amps. C) Break the circuit instantaneously. D) Change the current uniformly to zero in 20 seconds. E) None of these. Answer: A Var: 1 45) What resistance should be added in series with a 6.0 H inductor to complete an

circuit

with a A) 2.0 k Ω B) 18 Ω C) 2.0 Ω D) 2.9 Ω Answer: A Var: 28

time constant?

46) An RL circuit consists of a switch, an emf source If the potential across the resistor is emf, .

resistor, and a

inductor.

after the switch is closed, find the source

A) 71 V B) 36 V C) 76 V D) 56 V Answer: A Var: 50+ 47) A 3.0 A current passes through an inductor. If the inductor stores inductance? A) 4.44 H B) 90 H C) 60 H D) 3.7 H Answer: A Var: 44

of energy, what is the

48) A large electromagnet has a 22 T magnetic field between its poles. What is the magnetic energy density between the poles? A) 190 J/cm3 B) 88 J/cm3 C) 240 J/cm3 D) 30,000 J/cm3 Answer: A Var: 11

Situation 21.1 A series circuit contains an 80 μF capacitor, a 20 mH inductor, and a switch. The resistance of the circuit is negligible. Initially, the switch is open, the capacitor voltage is and the magnetic energy of the inductor is zero. At time the switch is closed. 49) In Situation 21.1, the time t at which the magnetic energy of the inductor first reaches its maximum value is closest to: A) 2 ms B) 4 ms C) 6 ms D) 8 ms E) 10 ms Answer: A Var: 1 50) In Situation 21.1, the maximum current in the circuit is closest to: A) 2.2 A B) 2.4 A C) 2.8 A D) 3.0 A E) 3.2 A Answer: E Var: 1 51) In Situation 21.1, when the current is 1.5 A, the charge on the capacitor, in μC, is closest to: A) 2000 B) 2500 C) 3000 D) 3500 E) 4000 Answer: D Var: 1 52) In Situation 21.1, when the capacitor voltage is 30 V, the rate of change of the current is closest to: A) 1000 A/s B) 1500 A/s C) 2000 A/s D) 2500 A/s E) 3000 A/s Answer: B Var: 1

21.2 Short Answer Questions Figure 21.25

1) In Figure 21.25, a uniform magnetic field B is confined to a cylindrical volume of radius 0.05 m. B is directed into the plane of the paper and is increasing at a constant rate of Calculate the magnitude and direction of the current induced in a circular wire ring of radius and resistance that encircles the magnetic field region. Answer: 1.0 × 10-3 A, counterclockwise Var: 50+ Figure 21.26

2) In Figure 21.26, there is a uniform magnetic field of magnitude B = 2.8 T and directed into the plane of the paper in the region shown. Outside this region the magnetic field is zero. A rectangular loop by and of resistance 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 required to move the loop at a constant speed of The mass of the loop is Answer: (a) counterclockwise 6 × 10-1 N (b) Var: 50+

Figure 21.27

3) In Figure 21.27, a large cylindrical loop of 269 turns and radius 67.0 cm carries a current of A small square loop of 31 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 in find the induced emf in the small loop. (Assume that the magnetic field in the region of the square loop is uniform.) Answer: 1.30 × 10-3 V Var: 50+ Figure 21.28

4) In Figure 21.28, the current in a solenoid is decreasing at a rate of -5.5 A/s. The self-induced emf in the solenoid is found to be 9.5 volts. (a) What is the self-inductance of the solenoid? (b) If the current is in the direction from b to a in the sketch, which point, a or b is at higher potential? The solenoid has negligible resistance. Answer: (a) 1.7 H (b) point a Var: 50+

Figure 21.29

5) Consider the circuit sketched above. The battery has emf ε = 27 volts and negligible internal resistance. The inductance is and the resistances are and Use Figure 21.29 to answer the following questions: (a) Initially the switch S is open and no currents flow. Then the switch is closed. What is the current in the resistor just after the switch is closed? (b) After leaving the switch closed for a long time, it is opened again. Just after it is opened, what is the current in ? Answer: (a) 2.3 A (b) 3.0 A Var: 50+ 6) An LC circuit consists of a capacitor with C = 3.4 ×

F and an inductor with

At the capacitor has charge and the current in the inductor is zero. The circuit oscillates at its angular frequency ω. (a) How long after t = 0 will the current in the circuit be maximum? (b) What will be this maximum current? Answer: (a) 8.2 × seconds (b) 1.0 × Var: 1

7) A toroidal solenoid has a mean radius of 0.210 m, a cross-sectional area of 631 turns. What current is required to produce a stored energy of (NOTE:

and

Answer: 8.89 A Var: 1 8) The mutual inductance between two coils is 0.0100 H. The current in the first coil changes uniformly from 2.70 A to 5.00 A in 0.160 s. If the second coil has a resistance of what is the magnitude of the induced current in the second coil? Answer: 0.240 A Var: 1 9) You need a 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. (a) How many windings should the secondary circuit contain? (b) What is the effective resistance of the secondary circuit? Answer: (a) 22 windings, (b) 1500 Ω Var: 1

College Physics, 11e (Young) Chapter 22 Alternating Current 22.1 Multiple Choice Questions 1) An alternating current is supplied to an electronic component with a rating that it be used only for voltages below What is the highest 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 2) 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

3) At 8.543 kHz the reactance in a circuit of a magnitude. What is the value of the inductor? A) 0.000039 μH B) 0.0000016 mH C) 0.000039 mH D) 0.0000016 H Answer: A Var: 50+ 4) What is the resonance frequency of an inductor? A) 0.15 kHz B) 0.9 kHz C) 6.9 kHz D) 6 kHz Answer: A Var: 50+

What is the capacitance?

capacitor and an inductor are equal in

circuit consisting of a

capacitor and a

5) An LC circuit has a resonance frequency of of 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: 50+

If the inductor in the circuit has a value

6) A circuit has a resistance of 4.0Ω; a reactance, due to the capacitance, of reactance, due to the inductance, of Find the impedance of the circuit. A) 9.8 Ω B) 31 Ω C) 13 Ω D) 47 Ω Answer: A Var: 50+

and a

7) An RLC circuit has a sinusoidal voltage supplied to it at with a peak voltage of a resistance; a capacitance; and a inductance. What is the peak current for this circuit? A) 6.3 μA B) 11 μA C) 26 μA D) 30 μA Answer: A Var: 50+ 8) For an RLC circuit with a resistance of a capacitance of what frequency is needed to minimize the impedance? A) 0.010 kHz B) 0.064 kHz C) 12 kHz D) 2.1 kHz Answer: A Var: 50+

and an inductance of

9) An RLC circuit has a resistance of a capacitance of and an inductance of If the frequency of the alternating current is what is the phase shift between the current and the voltage? A) -1.5 rad B) -1.6 rad C) 36 rad D) 3.1 rad Answer: A Var: 50+ 10) An RLC circuit has voltage supplied to it at a frequency of with a phase difference between the current and the voltage of magnitude If the circuit has a capacitance of and an inductance of find the resistance of the circuit. A) 11 k Ω B) 0.05 k Ω C) 10 k Ω D) 0.20 k Ω Answer: A Var: 50+ 11) A series RLC circuit has a peak voltage of and a peak current of lags the voltage by what is the average power of the circuit? A) 71 W B) 142 W C) 148 W D) 296 W Answer: A Var: 50+

If the current

12) An RLC circuit has a reactance, due to its capacitance, of a reactance, due to its inductance, of and a resistance of What is the power factor of the circuit? A) 0.96 B) 0.27 C) 1.04 D) 0.48 Answer: A Var: 50+

13) A series RLC circuit has a peak current of with a frequency of If the resistance of the circuit is the capacitance of the circuit is and the inductance of the circuit is determine the average power of the circuit over one cycle. A) 260,000 W B) 780,000 W C) 78,000 W D) 42,000 W Answer: A Var: 50+ 14)

Figure 22.1a

The 60 Hz ac source of a series circuit has a voltage amplitude of 120 V. The capacitive and inductive reactances are and respectively. The resistance is In Figure 22.1a, the capacitance, in μF, is closest to: A) 3.3 B) 6.3 C) 9.5 D) 13 E) 20 Answer: A Var: 50+

15)

Figure 22.1b

The 60 Hz ac source of a series circuit has a voltage amplitude of 120 V. The capacitive and inductive reactances are and respectively. The resistance is In Figure 22.1b, the inductance, in mH, is closest to: A) 560 B) 1,300 C) 2,100 D) 2,600 E) 3,500 Answer: A Var: 50+ 16)

Figure 22.1c

The 60 Hz ac source of a series circuit has a voltage amplitude of 120 V. The capacitive and inductive reactances are and respectively. The resistance is In Figure 22.1c, the rms current in the circuit is closest to: A) 0.089 A B) 0.098 A C) 0.11 A D) 0.12 A E) 0.14 A Answer: A Var: 50+

17)

Figure 22.1d

The 60 Hz ac source of a series circuit has a voltage amplitude of 120 V. The capacitive and inductive reactances are and respectively. The resistance is In Figure 22.1d, the phase angle is closest to: A) -53° B) 53° C) -76° D) 76° E) -14° Answer: A Var: 50+ 18)

Figure 22.1e

The 60 Hz ac source of a series circuit has a voltage amplitude of 120 V. The capacitive and inductive reactances are and respectively. The resistance is In Figure 22.1e, the resistance is changed from its original value so that the power factor is now 0.80. The original values of capacitance, inductance, and frequency remain unchanged. The new resistance is closest to: A) 750 Ω B) 670 Ω C) 600 Ω D) 500 Ω E) 420 Ω Answer: A Var: 50+

19)

Figure 22.2a

A series ac circuit is shown. The inductor has a reactance of 60 ohms and an inductance of 150 mH. A 50 ohm resistor and a capacitor whose reactance is 90 ohms are also in the circuit. The rms current in the circuit is 1.5 A. In Figure 22.2a, the rms voltage of the source is closest to: A) 87 V B) 84 V C) 81 V D) 78 V E) 75 V Answer: A Var: 50+ 20)

Figure 22.2b

A series ac circuit is shown. The inductor has a reactance of 80 ohms and an inductance of 180 mH. A 50 ohm resistor and a capacitor whose reactance is 120 ohms are also in the circuit. The rms current in the circuit is 1.6 A. In Figure 22.2b, the capacitance of the capacitor is closest to: A) 19 μF B) 20 μF C) 17 μF D) 16 μF E) 15 μF Answer: A Var: 50+

21)

Figure 22.2

A series ac circuit is shown. The inductor has a reactance of 90 ohms and an inductance of 240 mH. A 50 ohm resistor and a capacitor whose reactance is 70 ohms are also in the circuit. The rms current in the circuit is 1.9 A. In Figure 22.2c, the phase angle of the circuit is closest to: A) 22° B) -22° C) +90° D) 68° E) -68° Answer: A Var: 50+ 22)

Figure 22.2d

A series ac circuit is shown. The inductor has a reactance of 60 ohms and an inductance of 150 mH. A 80 ohm resistor and a capacitor whose reactance is 70 ohms are also in the circuit. The rms current in the circuit is 2.1 A. In Figure 22.2d, the voltage amplitude across the capacitor is closest to: A) 210 V B) 150 V C) 260 V D) 320 V E) 88 V Answer: A Var: 50+

23)

Figure 22.2e

A series ac circuit is shown. The inductor has a reactance of 50 ohms and an inductance of 200 mH. A 70 ohm resistor and a capacitor whose reactance is 110 ohms are also in the circuit. The rms current in the circuit is 1.5 A. In Figure 22.2e, the peak magnetic energy in the inductor is closest to: A) 0.45 J B) 0.23 J C) 0.68 J D) 0.90 J E) 1.1 J Answer: A Var: 50+ 24)

Figure 22.2f

A series ac circuit is shown. The inductor has a reactance of 80 ohms and an inductance of 230 mH. A 90 ohm resistor and a capacitor whose reactance is 70 ohms are also in the circuit. The rms current in the circuit is 1.9 A. In Figure 22.2f, the capacitor is changed so that the circuit is in resonance. The voltage of the source is adjusted so that the rms current of 1.9 A is maintained. The new voltage amplitude of the source is closest to: A) 240 V B) 210 V C) 170 V D) 280 V E) 310 V Answer: A Var: 50+

25) The inductor in a radio receiver carries a current of amplitude 200 mA when a voltage of amplitude 2.4 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 26)

Figure 22.3a

A series circuit has a 50 Hz ac source, a 40 ohm resistor, a 0.30 H inductor, and a 40 μF capacitor, as shown. The rms current in the circuit is 1.7 A. In Figure 22.3a, the voltage amplitude of the source is closest to: A) 100 V B) 88 V C) 72 V D) 59 V E) 51 V Answer: A Var: 50+

27)

Figure 22.3b

A series circuit has a 50 Hz ac source, a 80 ohm resistor, a 0.50 H inductor, and a 20 μF capacitor, as shown. The rms current in the circuit is 3.5 A. In Figure 22.3b, the power factor of the circuit is closest to: A) 1.00 B) 0.95 C) 0.90 D) 0.85 E) 0.80 Answer: A Var: 50+ 28)

Figure 22.3c

A series circuit has a 50 Hz ac source, a 80 ohm resistor, a 0.90 H inductor, and a 40 μF capacitor, as shown. The rms current in the circuit is 2.7 A. In Figure 22.3c, the capacitance is changed so that the circuit is in resonance. The original resistor and inductor are retained. The voltage and frequency of the source are kept at the original values. The new capacitance, in μF, is closest to: A) 11 B) 12 C) 13 D) 15 E) 16 Answer: A Var: 50+

29)

Figure 22.4

An ac source whose rms voltage is 80 V is in series with a 100 ohm resistor and a capacitor whose reactance is 200 ohms at the frequency of the source. In Figure 22.4, the rms voltage across the capacitor is closest to: A) 66 V B) 68 V C) 70 V D) 72 V E) 74 V Answer: D Var: 1 Figure 22.5

30) In Figure 22.5, 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

22.2 Short Answer Questions 1) An ac series circuit consists of a voltage source, a resistance R = 810 Ω and an inductance L. (There is no capacitance in the circuit.) The current amplitude is 0.40 A, and the phase angle between the source voltage and the current has magnitude (a) Does the source voltage lag or lead the current? (b) What is the voltage amplitude of the source? Answer: (a) The source voltage leads the current. (b) 330 volts Var: 50+ 2) An ac series circuit consists of a voltage source of frequency f = 60 Hz and voltage amplitude V, a resistor of resistance and a capacitor of capacitance What must the source voltage amplitude V be for the average electrical power consumed in the resistor to be 529 watts? There is no inductance in the circuit. Answer: 1,200 volts Var: 50+ 3) A series ac circuit consists of a voltage source of frequency f = 60 Hz and source voltage amplitude 345 volts, a resistor of resistance a capacitor of capacitance and an inductor of inductance L. (a) What must be the value of L for the phase angle Φ to be zero? (b) When L has the value calculated in (a), what is the current amplitude in the circuit? Answer: (a) 2.6 H (b) 0.878 A Var: 50+ 4) In an L-R-C series circuit L = 0.440 H, R = 380.0 Ω, and C = 5.70 μF. The voltage amplitude of the source is Find the rms voltage across the capacitor when the source operates at resonance. Answer: 129 V Var: 50+

College Physics, 11e (Young) Chapter 24 Geometric Optics 24.1 Multiple Choice Questions 1) As you walk away from a plane mirror on a wall, 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 2) Suppose you place your face in front of a concave mirror. A) If you position yourself between the center of curvature and the focal point of the mirror, you will not be able to see your image. B) No matter where you place yourself, a real image will be formed. C) Your image will always be inverted. D) Your image will be diminished in size. E) None of these is true. Answer: A Var: 1

Figure 24.1a

A thin hemispherical bowl of clear plastic floats on water in a tank. The radius of the bowl is 50 cm and the depth of the bowl in water is 10 cm. The depth of the water in the tank is 740 cm. An object 8.0 cm long is on the bottom of the tank directly below the bowl. The object is viewed from directly above the bowl. Ignore the refractive effects of the plastic. In Figure 24.1a, the position of the image below the water level, in cm, is closest to: A) 130 B) 120 C) 220 D) 160 E) 210 Answer: A Var: 50+ 4)

Figure 24.1b

A thin hemispherical bowl of clear plastic floats on water in a tank. The radius of the bowl is 50 cm and the depth of the bowl in water is 10 cm. The depth of the water in the tank is 620 cm. An object 8.0 cm long is on the bottom of the tank directly below the bowl. The object is viewed from directly above the bowl. Ignore the refractive effects of the plastic. In Figure 24.1b, the character of the image is: A) virtual and erect B) real and inverted C) real and erect D) virtual and inverted E) indeterminate Answer: A Var: 50+

Figure 24.1c

A thin hemispherical bowl of clear plastic floats on water in a tank. The radius of the bowl is 50 cm and the depth of the bowl in water is 10 cm. The depth of the water in the tank is 210 cm. An object 8.0 cm long is on the bottom of the tank directly below the bowl. The object is viewed from directly above the bowl. Ignore the refractive effects of the plastic. In Figure 24.1c, the size of the image, in cm, is closest to: A) 3.9 B) 5.9 C) 7.8 D) 12 E) 14 Answer: A Var: 50+ 6) A fish appears to be 9.00 m below the surface of a pond when viewed almost directly above by a fisherman. What is the actual depth of the fish? A) 11.97 m B) 0.15 m C) 6.77 m D) 0.08 m Answer: A Var: 9 7) A fisherman in a stream 30 cm deep looks downward into the water and sees a rock on the stream bed. How deep does the stream appear to the fisherman? Assume that the index of refraction of the water is 1.33. A) 23 cm B) 40 cm C) 26 cm D) 35 cm Answer: A Var: 44

8) The radius of curvature of the curved side of a plano-convex lens made of glass What is the focal length of the lens? A) 52 cm B) -52 cm C) 21 cm D) -21 cm Answer: A Var: 39

9) A double-concave lens has equal radii of curvature of An object placed from the lens forms a virtual image from the lens. What is the index of refraction of the lens material? A) 1.98 B) 2.06 C) 1.90 D) 1.84 Answer: A Var: 50+ 10) A thin double convex lens is to focus the image of an object onto a screen so that the image is life-sized. The lens has equal radii of and the refractive index is (a) What is the distance d from image to screen? (b) What is the total distance L between object and image? A) (a) d = 138 cm (b) L = 276 cm B) (a) d = 276 cm (b) L = 552 cm C) (a) d = 69 cm (b) L = 35 cm D) (a) d = -138 cm (b) L = -276 cm Answer: A Var: 50+ 11) A double convex thin glass lens has equal radii of curvature. The focal length of the lens is +37.3 cm and the index of refraction of the glass is 1.52. The radius of curvature of each convex surface, in cm, is closest to: A) 39 B) 35 C) 31 D) 43 E) 46 Answer: A Var: 50+

12) A double convex thin glass lens has equal radii of curvature. The focal length of the lens is +31.2 cm and the index of refraction of the glass is 1.52. The lens is replaced with a planoconvex glass lens of the same focal length and thickness. The radius of curvature of the convex surface is 13.0 cm. The index of refraction of the glass of the plano-convex lens is closest to: A) 1.42 B) 1.44 C) 1.40 D) 1.38 E) 1.36 Answer: A Var: 50+ Situation 24.1 An erect object is 50 cm from a concave mirror of radius 60 cm. 13) In Situation 24.1, the character of the image is: A) real and erect B) real and inverted C) virtual and erect D) virtual and inverted E) indeterminate Answer: B Var: 1 14) In Situation 24.1, the distance of the image from the mirror, in cm, is closest to: A) 19 B) 35 C) 60 D) 75 E) 120 Answer: D Var: 1 15) In Situation 24.1, the lateral magnification of the image is closest to: A) +0.4 B) +0.7 C) +1.5 D) -0.7 E) -1.5 Answer: E Var: 1

16) In Situation 24.1, the object is moved to a new position, such that the new lateral magnification is +2.5. The new object distance, in cm, is closest to: A) 18 B) 24 C) 30 D) 36 E) 42 Answer: A Var: 1 17) Suppose you wanted to start a fire using sunlight and a mirror. 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 18) An amateur astronomer grinds a double convex lens whose surfaces have radii of curvature of 40 cm and 60 cm. The glass has an index of refraction of 1.54. What is the focal length of this lens in air? A) 42.5 cm B) 126 cm C) 88.8 cm D) 44.4 cm E) 222 cm Answer: D Var: 1 19) An object is placed 15.0 cm to the left of a double-convex lens of focal length 20.0 cm. The image of this object is located A) 60.0 cm to the right of the lens. B) 60.0 cm to the left of the lens. C) 8.57 cm to the right of the lens. D) 8.57 cm to the left of the lens. E) 30.0 cm to the left of the lens. Answer: B Var: 1

20) 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. Answer: C Var: 1 21) Which statement about thin lenses is correct? In each case, we are considering only a single lens. 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 erect image. D) A diverging lens always produces a virtual erect image. E) A diverging lens produces a virtual erect image only if the object is located within the focal point of the lens. Answer: D Var: 1 22) Which statement about images is correct? 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 24.2 Short Answer Questions 1) When an object is placed 118 cm from a diverging thin 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 is the same in absolute value 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+ 2) An object 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+

3) The left-hand end of a glass rod is ground to a spherical surface. The glass has index of refraction 1.50. A small object 4.00 mm tall is placed in the axis of the rod, 11.0 cm to the left of the vertex of the spherical surface. The image is formed in the rod, 17.0 cm to the right of the vertex. (a) What is the magnitude of the radius of curvature of the spherical surface at the end of the rod? (b) What is the height of the image? Answer: (a) 2.79 cm (b) 4.12 mm Var: 50+ 4) A tank contains benzene, which has index of refraction 1.50. A dime is on the bottom of the tank. When viewed at normal incidence the dime appears to be 61 cm below the surface of the benzene. What is the actual depth of the benzene? Answer: 92 cm Var: 50+

5) As part of a piece of optical apparatus to be used in air, you need to design a thin lens having faces with radii of curvature of magnitude 24.0 cm each. When an object 32.0 mm tall is placed 30.0 cm from this lens, it must form a real image 60.0 cm from the lens. (a) What must be the index of refraction of the lens material? (b) What is the height of the image of the object? Is it erect or inverted; real or virtual? Answer: (a) 1.60, (b) 64.0 mm, inverted, real Var: 1 6) Figure 24.2

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 Figure 24.2. The magnitude of the focal length of the converging lens is 25.0 cm, while the magnitude of the focal length of the diverging lens is 40.0 cm. An object 8.25 cm tall is placed 35.0 cm to the left of the converging lens. (a) Where is the final image produced by this combination of lenses? (b) Compared to the object, is the final image erect or inverted? Is it real or virtual? Answer: (a) 9.52 cm to the left of the diverging lens, (b) inverted, virtual Var: 1

College Physics, 11e (Young) Chapter 25 Optical Instruments 25.1 Multiple Choice Questions 1) A 35 mm camera equipped with a 45 mm focal length lens is used to photograph a tree 15 m tall. The aperture of the lens is set at f/2. The aperture diameter at f/2, in mm, is closest to: A) 23 B) 14 C) 18 D) 27 E) 32 Answer: A Var: 50+ 2) A 35 mm camera equipped with a 40 mm focal length lens is used to photograph a tree 17 m tall. The aperture of the lens is set at f/8. A 32 mm high image of the tree on the film is required. The required distance, between the tree and the camera, to take the photograph is closest to: A) 21 m B) 22 m C) 23 m D) 24 m E) 26 m Answer: A Var: 50+ 3) A simple camera lens with focal object length object on a photographic film located a distance moves away from the lens and the new focal distance is move? (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+

perfectly focuses the image of an away from the lens. The object now (a) How far did the object

4) The image of a tree on a 35 mm color slide is high. It is to be projected onto a screen from the slide, and is to appear high. (a) What focal length lens (in meters) is needed? (b) What is the distance in meters between the lens and the slide? (c) What is the magnification of the system? A) (a) 0.02 m (b) 0.02 m (c) 329 B) (a) 0.02 m (b) 7.98 m (c) 0.00 C) (a) 0.02 m (b) -0.02 m (c) 0.00 D) (a) 0.02 m (b) -8.02 m (c) 0.00 Answer: A Var: 50+ 5) A lens of focal length 45 mm is mounted on a 35 mm camera. The lens aperture is set at f/2 and the shutter speed set at The aperture diameter, in mm, is closest to: A) 23 B) 16 C) 19 D) 26 E) 29 Answer: A Var: 50+ 6) A lens of focal length 40 mm is mounted on a 35 mm camera. The lens aperture is set at f/5.6 and the shutter speed set at A different camera has a lens of focal length 56 mm in place. The shutter speed is set at The lens aperture setting, for the closest matching film exposure, is: A) f/5.6 B) f/8 C) f/11 D) f/16 E) f/22 Answer: D Var: 1

7) A lens of focal length 90 mm is used as a magnifier. The object being viewed is 9.9 mm long, and is positioned at the focal point of the lens. The angle subtended by the image at infinity, in milliradians, is closest to: A) 110 B) 73 C) 37 D) 147 E) 183 Answer: A Var: 50+ 8) 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. The angular magnification of the magnifier is closest to: A) 6.3 B) 5.6 C) 6.9 D) 7.5 E) 8.1 Answer: A Var: 50+ 9) A lens of focal length 45 mm is used as a magnifier. The object being viewed is 6.8 mm long, and is positioned at the focal point of the lens. The lens is moved closer to the object, so that the image is now 25 cm from the lens. The distance the lens has been moved, in cm, is closest to: A) 0.69 B) 0.76 C) 0.62 D) 0.55 E) 0.48 Answer: A Var: 50+ 10) A farsighted boy has a near point at 2.3 m and requires eyeglasses to correct his vision. Corrective lenses are available in increments in power of 0.25 diopters. The eyeglasses should have lenses of the lowest power for which the near point is no further than 25 cm. The correct choice of lens power for eyeglasses, in diopters, is: A) +3.75 B) +3.50 C) +3.25 D) +4.00 E) +4.25 Answer: A Var: 18

11) A farsighted boy has a near point at 2.0 m and requires eyeglasses to correct his vision. Corrective lenses are available in increments in power of 0.25 diopters. The eyeglasses should have lenses of the lowest power for which the near point is no further than 25 cm. The boy borrows eyeglasses that have a power of +2.75 diopters. With these eyeglasses, the near point of the boy, in cm, is closest to: A) 31 B) 28 C) 33 D) 37 E) 40 Answer: A Var: 50+ 12) A myopic girl wears eyeglasses that allow her to have clear distant vision. The power of the lenses of her eyeglasses is -3.00 diopters. Without eyeglasses, the far point of the girl is closest to: A) 0.33 m B) 0.25 m C) 0.17 m D) 0.42 m E) 0.50 m Answer: A Var: 12 13) A machinist with normal vision has a near point at 25 cm. The machinist wears eyeglasses in order to do close work. The power of the lenses is +4.25 diopters. With these eyeglasses, the near point of the machinist, in cm, is closest to: A) 12 B) 10 C) 7 D) 15 E) 17 Answer: A Var: 14 14) In a 35 mm single lens reflex camera (SLR) the distance from the lens to the film is varied in order to focus on objects at varying distances. Over what range must a lens of 45 mm focal length vary if the camera is to be able to focus on objects ranging in distance from infinity down to 1.4 m from the camera? A) 1.49 mm B) 1.20 mm C) 4.48 mm D) 5.98 mm E) 2.09 mm Answer: A Var: 50+

Situation 25.1 The objective of a microscope has a focal length of 2.4 mm and the eyepiece has an angular magnification of 15. The object is positioned 0.06 mm beyond the focal point of the objective. The focal point of the eyepiece is positioned at the real image formed by the objective. 15) In Situation 25.1, the overall magnification of the microscope is closest to: A) 400 B) 450 C) 500 D) 550 E) 600 Answer: E Var: 1 16) In Situation 25.1, the separation between the objective and the eyepiece, in mm, is closest to: A) 98 B) 102 C) 107 D) 111 E) 115 Answer: E Var: 1 Situation 25.2 The objective 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. The final image is viewed at infinity. The near point of the microscope user is at 25 cm. 17) In Situation 25.2, the distance between the object and the focal point of the objective, in mm, is closest to: A) 0.13 B) 0.18 C) 0.23 D) 0.28 E) 0.33 Answer: A Var: 1

18) In Situation 25.2, the distance between the objective and the real image produced by it, in mm, is closest to: A) 116 B) 120 C) 124 D) 128 E) 132 Answer: C Var: 1 19) In Situation 25.2, the overall magnification of the microscope is closest to: A) 250 B) 300 C) 350 D) 400 E) 450 Answer: B Var: 1 Situation 25.3 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. 20) In Situation 25.3, the focal length of the objective, in cm, is closest to: A) 137 B) 138 C) 139 D) 140 E) 141 Answer: D Var: 1 21) In Situation 25.3, the angle subtended by the final image of the tower is closest to: A) 0.15 rad B) 0.17 rad C) 0.19 rad D) 0.21 rad E) 0.23 rad Answer: B Var: 1

22) 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 and the distance from Earth at the time of observation is m rad, is closest to: A) 0.9 B) 1.1 C) 1.3 D) 1.5 E) 1.7 Answer: A Var: 1

The angle subtended by the final telescopic image of Neptune, in

23) 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 for example such a person wanted to read a book at a distance of 25 cm, he would have to wear eyeglasses whose diopter power was approximately A) +2.78 diopters B) +3.33 diopters C) -1.78 diopters D) +4.00 diopters E) -4.00 diopters Answer: D Var: 1 24) 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 + , where is the lateral magnification of the objective and is the angular magnification of the eyepiece. E) the image of the objective serves as the object for the eyepiece. Answer: E Var: 1

25) 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 (near point at 25 cm). What is the angular magnification of the microscope? A) 72 B) 88 C) 180 D) 219 E) 115 Answer: A Var: 50+ 26) The objective lens of an astronomical telescope has a focal length of 60 cm and the eyepiece has a focal length of 2 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 27) An astronomical 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 if the telescope is viewed by 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+

25.2 Short Answer Questions 1) A 35 mm 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 film? 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 mm × 36 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) What power (in diopters) of corrective lens is required to correct the vision of a myopic eye whose far point is at 170 cm? Answer: -0.59 diopters Var: 29 4) A zoom lens is adjusted to change its focal length from 38 mm to 304 mm. If the same amount of light is to be admitted to the lens, what is the final f-number if the original f-number was 2.0? Answer: 16 Var: 50+ 5) A compound microscope consists of an objective of focal length

and an eyepiece with

magnification 25. The microscope is designed so that the object is focused in a plane 28.0 cm away from the focal point of the objective lens. When properly adjusted, the eyepiece and the objective are 29.9 cm apart. What is ? (Assume that the eyepiece magnification is based on an image at infinity and a near point at 25 cm.) Answer: 0.9 cm Var: 50+

College Physics, 11e (Young) Chapter 26 Interference and Diffraction 26.1 Multiple Choice Questions 1) 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. The smallest angle, reckoned east of north from the antennas, at which constructive interference of two radio waves occurs, is closest to: A) 50° B) 55° C) 45° D) 40° E) 35° Answer: A Var: 50+ 2) 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. The smallest angle, reckoned north of east from the antennas, at which destructive interference of the two radio waves occurs, is closest to: A) 13° B) 6.4° C) 9.7° D) 16° E) 19° Answer: A Var: 50+ 3) Two radio antennas are 10 km apart on a north-south axis on a seacoast. The antennas broadcast identical AM radio signals, in phase, at a frequency of 4.70 MHz. A steamship, 200 km offshore, travels due north at a speed of 15 km/hr 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. The time interval until the next occurrence of maximum reception is closest to: A) 5.1 min B) 3.8 min C) 6.4 min D) 7.7 min E) 8.9 min Answer: A Var: 50+

4) 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 double slit whose spacing is A) 10 B) 9 C) 8 D) 11 E) 12 Answer: A Var: 50+ Situation 26.1 A 360 nm thick oil film floats on the surface of the water. The indices of refraction of the oil and the water are 1.50 and 1.33, respectively. The surface of the oil is illuminated from above at normal incidence with white light. 5) In Situation 26.1, the two wavelengths of light in the 400 nm to 800 nm wavelength band that are most strongly reflected, in nm, are closest to: A) 410 and 700 B) 430 and 720 C) 450 and 740 D) 470 and 760 E) 490 and 780 Answer: B Var: 1 6) In Situation 26.1, the wavelength of light in the 400 nm to 800 nm wavelength band that is most weakly reflected, in nm, is closest to: A) 520 B) 540 C) 560 D) 580 E) 600 Answer: B Var: 1

Situation 26.2 A pair of narrow slits, separated by 1.8 mm, is illuminated by a monochromatic light source. Light waves arrive at the two slits in phase. A fringe pattern is observed on a screen 4.8 m from the slits. 7) In Situation 26.2, there are 5.0 bright fringes/cm on the screen. The wavelength of the monochromatic light is closest to: A) 550 nm B) 600 nm C) 650 nm D) 700 nm E) 750 nm Answer: E Var: 1 8) In Situation 26.2, monochromatic light of 450 nm wavelength is used. The angular separation between adjacent dark fringes on the screen, measured at the slits, in m rad, is closest to: A) 0.15 B) 0.20 C) 0.25 D) 0.30 E) 0.36 Answer: C Var: 1 Situation 26.3 Two optically 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 index of the glass plates is 1.55. The plates are illuminated at normal incidence with monochromatic light, and fringes are observed. 9) In Situation 26.3, the monochromatic light has a wavelength of 580 nm. The number of bright fringes which are visible is closest to: A) 60 B) 70 C) 80 D) 90 E) 100 Answer: E Var: 1

10) In Situation 26.3, the spacing of the dark fringes is 2.0 mm. The wavelength of the monochromatic light, in nm, is closest to: A) 425 B) 475 C) 525 D) 675 E) 725 Answer: E Var: 1 11) An oil film (n = 1.48) of thickness 290 nm floating on water is 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 12) A double slit illuminated with light of wavelength forms a diffraction pattern on a screen away. The slit separation is What is the distance Δx between orders and A) 6.94 × 107 nm B) 129.64 × 107 nm C) 13.88 × 107 nm D) 3.47 × 107 nm Answer: A Var: 50+ 13) An optical engineer needs to ensure that the bright fringes from a double-slit are apart on a detector that is from the slits. If the slits are illuminated with 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+

light, how

14) A 2-slit arrangement with 60.3 μm separation between the slits is illuminated with light. Assuming that a viewing screen is located 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) 57.2 mm B) 38.1 mm C) 76.3 mm D) 26.9 mm Answer: B Var: 50+ 15) A grating with 396 lines/mm is illuminated with light of wavelength angular separation between the two lines formed in order A) 31.5° B) 15.8° C) 32.9° Answer: A Var: 50+ 16) What is the angular separation of two spectral lines of wavelengths formed in order with a grating? A) 34.84° B) 24.82° C) 0° Answer: A Var: 50+

What is the

and

17) A single slit forms a diffraction pattern, with the first minimum at an angle of 40° from central maximum. Monochromatic light of 410 nm wavelength is used. The same slit, illuminated by a different monochromatic light source, produces a diffraction pattern with the second minimum at a 60° angle from the central maximum. The wavelength of this light, in nm, is closest to: A) 276 B) 293 C) 309 D) 326 E) 342 Answer: A Var: 33

18) A single slit forms a diffraction pattern, with the first minimum at an angle of 40° from central maximum. Monochromatic light of 530 nm wavelength is used. The width of the slit, in nm, is closest to: A) 825 B) 791 C) 757 D) 723 E) 689 Answer: A Var: 33 19) A single slit, 1,400 nm wide, forms a diffraction pattern when illuminated by monochromatic light of 490 nm wavelength. The largest angle from the central maximum at which the intensity is zero is closest to: A) 44° B) 41° C) 38° D) 35° E) 32° Answer: A Var: 50+ 20) A single slit forms a diffraction pattern with monochromatic light. The fourth minimum of the pattern occurs at an angle of 32° from the central maximum. The angle at which the fifth minimum of the pattern occurs is closest to: A) 41.5° B) 41.0° C) 40.5° D) 42.0° E) 42.5° Answer: A Var: 40 21) An 18 mm wide diffraction grating has rulings of 710 lines per mm. Light is incident normally on the grating. Monochromatic light of 506 nm wavelength is used. The largest angle from the normal at which an intensity maximum is formed is closest to: A) 46° B) 44° C) 42° D) 40° E) 38° Answer: A Var: 50+

22) A 17 mm wide diffraction grating has rulings of 530 lines per mm. Light is incident normally on the grating. The longest wavelength that forms an intensity maximum in the fifth order is closest to: A) 377 nm B) 352 nm C) 402 nm D) 427 nm E) 452 nm Answer: A Var: 50+ 23) The spacing of ruled lines on a diffraction grating is 1,900 nm. The grating is illuminated at normal incidence with a parallel beam of white light in the 400 nm to 700 nm wavelength band. The angular width of the gap between the first order spectrum and the second order spectrum is closest to: A) 3.3° B) 4.3° C) 5.3° D) 6.3° E) 2.3° Answer: A Var: 50+ 24) The spacing of ruled lines on a diffraction grating is 1,770 nm. The grating is illuminated at normal incidence with a parallel beam of white light in the 400 nm to 700 nm wavelength band. The longest wavelength that appears in the third order spectrum is closest to: A) 590 nm B) 570 nm C) 550 nm D) 530 nm E) 610 nm Answer: A Var: 50+

Situation 26.4 A metallic sheet has a large number of slits, 5.0 mm wide and 20 cm apart, and is used as a diffraction grating for microwaves. A wide parallel beam of microwaves is incident normally on the grating. 25) In Situation 26.4, the microwave wavelength is 6.0 cm. The largest angle from the normal, at which an intensity maximum occurs, is closest to: A) 64° B) 69° C) 74° D) 79° E) 84° Answer: A Var: 1 26) In Situation 26.4, the smallest microwave frequency for which only the central maximum occurs is closest to: A) 0.5 GHz B) 0.7 GHz C) 1.0 GHz D) 1.5 GHz E) 2.0 GHz Answer: D Var: 1 27) In Situation 26.4, intensity maxima occur two degrees apart in the central region. The wavelength of the microwaves is closest to: A) 5 mm B) 6 mm C) 7 mm D) 8 mm E) 9 mm Answer: C Var: 1 28) Light of wavelength 560 nm illuminates a single slit placed 60 cm from a screen. The separation between the first and third minima in the diffraction pattern is 2.8 mm. What is the slit width? A) 0.72 mm B) 0.24 mm C) 1.16 mm D) 3.8 × m E) 0.082 mm Answer: B Var: 1

Situation 26.5 Certain planes of a crystal of halite have a spacing of 0.399 mm. 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. 29) In Situation 26.5, the wavelength of the x-rays, in nm, is closest to: A) 0.14 B) 0.17 C) 0.21 D) 0.24 E) 0.27 Answer: E Var: 1 30) In Situation 26.5, the angle the beam makes with the planes for second order constructive interference to occur is closest to: A) 37° B) 40° C) 43° D) 46° E) 49° Answer: C Var: 1 31) A diffraction grating has 450 lines per mm. What is the highest order 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 32) 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) None of these. E) More than one of these. Answer: A Var: 1 33) The lattice spacing of the principal Bragg planes in sodium chloride is 0.282 nm. For what wavelength will the first order diffracted beam be deviated by 70°?

A) 0.323 nm B) 0.530 nm C) 0.662 nm D) 0.150 nm E) 0.680 nm Answer: A Var: 1 34) A camera set with f-number f/4 has a focal length of 50 nm. What is the minimum spacing of two objects positioned 12 meters from the lens if the objects are barely resolved in the image? Assume the light wavelength is 500 nm. A) 1.66 mm B) 4.72 mm C) 0.024 mm D) 4.9 × m E) 0.58 mm Answer: E Var: 1 35) A camera used for aerial surveillance has a lens with a 30 cm maximum aperture and a 42 cm focal length. Assume light of 550 nm wavelength is used and that the resolution of the camera is limited solely by diffraction. The angular resolution of the camera at maximum aperture, in mrad, is closest to: A) 1.6 B) 2.2 C) 3.2 D) 4.5 E) 6.3 Answer: B Var: 1 36) A single slit with width 644 nm is illuminated with light of wavelength minima occur in the angular range from to A) 1 minima B) 0.5 minima C) 0.79 minima D) 1.52 minima Answer: A Var: 50+

How many

37) Light of wavelength 500 nm illuminates a 0.50 mm diameter hole. A screen is placed 6.0 m behind the slit. What is the width of the central maximum on the screen? A) 15 mm B) 260 μm C) 7.3 mm D) 3,700 μm Answer: A Var: 50+ 38) Light from a He-Ne laser of wavelength 633 nm passes through a circular aperture. It is observed on a screen 4.0 m behind the aperture. The width of the central maximum is 1.1 cm. What is the diameter of the hole? A) 560 μm B) 9.8 μm C) 32,000 μm D) 4,700 μm Answer: A Var: 50+ 39) A 0.85 mm diameter hole is illuminated by infrared light of wavelength 2.5 μm What is the angle of the first dark fringe? 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+ 40) Astronomers are proud of their telescopes, and often say they can "resolve a dime at so many miles." How many miles can you move a disk from a telescope mirror and just resolve it using light of wavelength A) 19 mi B) 9.7 mi C) 40 mi D) 190,000,000 mi Answer: A Var: 50+

26.2 Short Answer Questions 1) Light of wavelength 519 nm passes through two slits. In the interference pattern on a screen 4.6 m away, adjacent bright fringes are separated by 4.0 mm. What is the separation of the two slits? Answer: 0.60 mm Var: 50+ 2) Light is incident perpendicularly from air onto a liquid film that is on a glass plate. The liquid film is 199 nm thick, and the liquid has index of refraction 1.60. The glass has index of refraction 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. (Note: Assume that the visible spectrum lies between 400 and 700 nm.) Answer: 637 nm Var: 50+ 3) A soap bubble, when illuminated with light of 463 nm, appears to be especially reflective. If the index of refraction of the film is 1.35, what is the thinnest thickness the soap film can be? Answer: 85.7 nm Var: 50+ Figure 26.1

4) In Figure 26.1, a slit 0.3 × m wide 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+ 5) 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 a 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 this light? Answer: 529 nm Var: 50+

6) Treat each of your eyes 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 resolved by your eye? Assume that the resolution is diffraction limited and use Rayleigh's criterion. Answer: 4.9 × 10-2 m Var: 50+ 7) A researcher is investigating a cubic crystal with x rays. He is looking at Bragg reflection from the planes parallel to the cube faces. He finds that when using x rays 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 the crystal? Answer: 0.207 nm Var: 1

College Physics, 11e (Young) Chapter 27 Relativity 27.1 Multiple Choice Questions 1) Two fixed navigation beacons mark the approach lane to a star. The beacons are in line with the star and are 40 Mm apart. A spaceship approaches the star with a relative velocity of 0.30 c and passes the beacons. The passage of the ship between the beacons is timed by observers on the beacons. The time interval of the passage is closest to: A) 440 ms B) 470 ms C) 420 ms D) 250 ms E) 170 ms Answer: A Var: 50+ 2) Two fixed navigation beacons mark the approach lane to a star. The beacons are in line with the star and are 49 Mm apart. A spaceship approaches the star with a relative velocity of 0.50 c and passes the beacons. The passage of the ship between the beacons is timed by an observer on the ship. The time interval of the passage is closest to: A) 280 ms B) 330 ms C) 380 ms D) 170 ms E) 110 ms Answer: A Var: 50+ 3) Two fixed navigation beacons mark the approach lane to a star. The beacons are in line with the star and are 65 Mm apart. A spaceship approaches the star with a relative velocity of 0.90 c and passes the beacons. As the ship passes the first beacon the ship emits a short radar pulse toward the second beacon, and the radar echo is received at the ship. The time interval between the emission of the radar pulse and the reception of the radar echo is closest to: A) 230 ms B) 520 ms C) 150 ms D) 99 ms E) 60 ms Answer: A Var: 50+

Figure 27.1a

A right-angled construction frame ABC, when measured at rest, has dimensions as follows: and The frame is given a velocity of 0.85 c, relative to the space platform, in a direction parallel to AC. The dimensions of the moving frame are measured simultaneously by observers on the platform. In Figure 27.1a, the length BC measured by these observers is closest to: A) 17 m B) 15 m C) 13 m D) 11 m E) 19 m Answer: A Var: 50+ 5)

Figure 27.1a

A right-angled construction frame ABC, when measured at rest, has dimensions as follows: and The frame is given a velocity of 0.77 c, relative to the space platform, in a direction parallel to AC. The dimensions of the moving frame are measured simultaneously by observers on the platform. In Figure 27.1b, the length AB measured by these observers is closest to: A) 22.7 m B) 23.4 m C) 22.1 m D) 21.5 m E) 24.0 m Answer: A Var: 50+

Figure 27.2a

System S' has a velocity u = +0.58 c relative to system S, as shown. The clocks of S and S' are synchronized at when the origins 0 and 0' coincide. An event is observed in both systems. The event takes place at and at time as measured by an observer in S. In Figure 27.2a, the of the event, measured by an observer in S' is closest to: A) -900 B) -740 C) -820 D) -750 E) -600 Answer: A Var: 50+ 7)

Figure 27.2b

System S' has a velocity u = +0.57 c relative to system S, as shown. The clocks of S and S' are synchronized at when the origins 0 and 0' coincide. An event is observed in both systems. The event takes place at and at time as measured by an observer in S. In Figure 27.2b, the time t' of the event, measured by an observer in S' is closest to: A) 7.1 μs B) -6.9 μs C) 6.5 μs D) 4.8 μs E) 6.0 μs Answer: A Var: 50+

Figure 27.2c

System S' has a velocity u = +0.69 c relative to system S, as shown. The clocks of S and S' are synchronized at when the origins 0 and 0' coincide. An event is observed in both systems. The event takes place at and at time as measured by an observer in S. In Figure 27.2c, a rod which is stationary in S has a proper length of 27 m. The length of the rod measured by an observer in S' is closest to: A) 20 m B) 37 m C) 18 m D) 14 m E) 12 m Answer: A Var: 50+ 9)

Figure 27.2d

System S' has a velocity u = +0.68 c relative to system S, as shown. The clocks of S and S' are synchronized at when the origins 0 and 0' coincide. An event is observed in both systems. The event takes place at and at time as measured by an observer in S. In Figure 27.2d, a stopwatch which is stationary in S' records a proper time interval of 92 s. The time interval, measured by an observer in S is closest to: A) 130 s B) 67 s C) 140 s D) 160 s E) 170 s Answer: A Var: 50+

10)

Figure 27.3

The captain of spaceship A observes enemy spaceship E escaping with a relative velocity of 0.40 c. A missile M is fired from ship A, with a velocity of 0.77 c relative to ship A. In Figure 27.3, the relative velocity of approach of missile M, observed by the crew on ship E, is closest to: A) 0.53 c B) 0.37 c C) 0.49 c D) 0.45 c E) 0.41 c Answer: A Var: 50+ 11) If you were in a spaceship traveling at a speed 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 is different than normal. C) your pulse rate is different than normal. D) None of these effects occur. E) More than one of these effects occur. Answer: D Var: 1 12) A spaceship approaching an asteroid at a speed of 0.6 c launches a scout rocket with speed 0.4 c. At what speed is the scout rocket approaching the asteroid? A) 0.81 c B) 1.00 c C) 0.76 c D) 0.64 c E) 0.96 c Answer: A Var: 1

13)

Figure 27.4

Three spaceships A, B, and C are in motion. The commander on ship B observes ship C approaching with a relative velocity of 0.60 c. The commander also observes ship A, advancing in the rear, with a relative velocity of 0.48 c. In Figure 27.4, the velocity of ship C, relative to an observer on ship A, is closest to: A) 0.84 c B) 0.093 c C) 1.5 c D) 0.17 c E) 1.1 c Answer: A Var: 50+ Situation 27.1 A proton (rest energy = 938 MeV) has a speed of 0.80 c. 14) In Situation 27.1, the ratio of the kinetic energy of the proton to its rest energy is closest to: A) 0.60 B) 0.67 C) 0.80 D) 1.2 E) 1.7 Answer: B Var: 1 15) In Situation 27.1, the momentum of the proton in kg ∙ m/s is closest to: A) 4.0 x B) 4.4 x C) 5.0 x D) 5.8 x E) 6.7 x Answer: E Var: 1

Situation 27.2 An electron has a kinetic energy equal to twice its rest energy. 16) In Situation 27.2, the speed of the electron is closest to: A) 0.84 c B) 0.87 c C) 0.89 c D) 0.91 c E) 0.94 c Answer: E Var: 1 17) In Situation 27.2, the relativistic mass of the electron is closest to: A) 1.8 x kg B) 2.3 x

C) 2.7 x

D) 3.2 x

E) 3.6 x Answer: C Var: 1

18) Consider three galaxies, Alpha, Beta and Gamma. An observer in Beta sees the other two galaxies each moving away from him in opposite directions at speed 0.7 c. At what speed would an observer in Alpha see the galaxy Beta moving? A) 0.82 c B) 0.70 c C) 0.94 c D) 0.35 c E) 0.57 c Answer: B Var: 1 19) Consider three galaxies, Alpha, Beta and Gamma. An observer in Beta sees the other two galaxies each moving away from him in opposite directions at speed 0.7 c. At what speed would an observer in Alpha see the galaxy Gamma moving? A) 0.7 c B) 1.4 c C) 0.82 c D) 0.94 c E) 0.98 c Answer: D Var: 1 20) Free neutrons (unlike those in the nucleus of an atom) decay spontaneously into a proton, an

electron and an antineutrino. The masses of these particles are (approx.) mn = 1.67492 × kg mp = 1.67262 ×

me = 9.10939 × kg The mass of the neutrino is zero (or nearly so). How much energy is released in this decay? A) 1.01 × J B) 1.25 ×

C) 4.66 ×

D) 7.08 ×

E) 5.61 × Answer: B Var: 1

Situation 27.3 A relativistic proton has a momentum of 1.0 × 0.150 nJ.

kg ∙ m/s. The rest energy of a proton is

21) In Situation 27.3, the kinetic energy of the proton, in nJ, is closest to: A) 0.13 B) 0.16 C) 0.19 D) 0.22 E) 0.25 Answer: C Var: 1 22) In Situation 27.3, the speed of the proton is closest to: A) 0.87 c B) 0.89 c C) 0.91 c D) 0.93 c E) 0.95 c Answer: B Var: 1

23) The special theory of relativity predicts that there is an upper limit to the speed of a particle. It thus follows that there is also an upper limit on the following property of a particle. A) The kinetic energy B) The total energy C) The linear momentum D) More than one of these E) None of these Answer: E Var: 1 24) Astronaut Spud Nick is space-travelling from planet X to planet Y at a speed of When he is precisely halfway between the planets, a distance of 1 light-hour from each, nuclear devices are detonated. The explosions are simultaneous in the frame of the planets. What is the difference in time of arrival of the flashes from the explosions as observed by Spud? A) 420 min B) 210 min C) 110 min D) 0 min Answer: A Var: 50+ 25) Astronaut Mark Uri is space-travelling from planet X to planet Y at a speed of When he is precisely halfway between the planets, a distance of 1 light-hour from each, nuclear devices are detonated. The explosions are simultaneous in Mark's frame. What is the difference in time of arrival of the flashes from the explosions as observed by Mark? A) 0 min B) 160 min C) 78 min D) 310 min Answer: A Var: 50+ 26) In their common rest frame, two stars are apart. If they appear to be spaceship, how fast is the spaceship moving? Express your answer in terms of c. A) 0.646 c B) 0.604 c C) 0.558 c D) 0.505 c Answer: A Var: 50+

apart to a

27) A particle in a 799 m-long particle accelerator is moving at particle accelerator appear to the particle? A) 387 m B) 1,039 m C) 184 m D) 1,651 m Answer: A Var: 50+

How long does the

28) A spaceship is moving between two distant stars at To someone in the ship, the distance between the two stars appears to be What is the distance between the stars in the stars' rest frame? A) 72.8 ly B) 9.57 ly C) 21.1 ly D) 55.4 ly Answer: A Var: 50+ 29) As measured in Earth's rest frame, a spaceship traveling at takes to travel between planets. How long does the trip appear to take for someone on the spaceship? A) 2.79 y B) 6.83 y C) 39.5 y D) 28.8 y Answer: A Var: 50+ 30) An astronaut on a spaceship moving at 0.927 c says that the trip between the two 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+

31) Someone in Earth's rest frame says that a spaceship's trip between two planets took while an astronaut on the space ship says that the trip took Find the velocity of the spaceship in terms of the speed of light. A) 0.816 c B) 0.735 c C) 0.975 c D) 0.384 c Answer: A Var: 50+ 32) In an "atom smasher," two particles collide head on at relativistic speeds. If the velocity of the first particle is to the left, and the velocity of the second particle is to the right (both of these speeds are measured in Earth's rest frame), how fast are the particles moving with respect to each other? A) 0.916 c B) 1.284 c C) 0.934 c D) 0.834 c Answer: A Var: 50+ 33) Calculate the speed at which a 0.723 kg object has the same momentum as a moving A) 0.734 c B) 0.712 c C) 0.981 c D) 0.592 c Answer: A Var: 50+

object

34) A particle is moving at about 0.86 c. By what 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

35) Calculate the kinetic energy of an electron moving at A) 280 keV B) 240 keV C) 320 keV D) 370 keV Answer: A Var: 50+ 36) The total energy of a moving electron is terms of c? A) 0.739 c B) 0.794 c C) 0.306 c D) 0.933 c Answer: A Var: 50+

Express your answer in

What is the speed of the electron in

37) An electron has a speed of 0.783 c. Through what potential difference would the electron need to be accelerated in order to reach this speed? Assume that the electron was initially at rest. A) 310 kV B) 260 kV C) 360 kV D) 400 kV Answer: A Var: 50+ 38) Assume that a typical city consumes electrical energy at a rate of How many kilograms of matter would have to be converted entirely into energy in order to keep this city running for 14 weeks? A) 0.19 kg B) 0.21 kg C) 0.27 kg D) 0.32 kg Answer: A Var: 17 39) Calculate the amount of energy needed to accelerate an electron from Express your answer in A) 2.71 MeV B) 1.90 MeV C) 4.61 MeV D) 5.69 MeV Answer: A Var: 50+

40) A particle has speed 0.95 c and total energy 4.8 × 10-10 J. What is its momentum? A) 1.5 × 10-18 kg ∙ m/s B) 2.5 × 10-15 kg ∙ m/s C) 5.6 × 10-13 kg ∙ m/s D) 1.0 × 10-9 kg ∙ m/s Answer: A Var: 50+ 41) A star is moving toward the Earth with a speed of 0.9 c (90% the speed of light). It emits light, which moves away from the star at the speed of light. Relative to us on Earth, the speed of the light moving towards us (emitted by the star) is A) c B) 1.9 c C) 1.2 c D) 0.98 c Answer: A Var: 1 42) A spaceship is moving in a straight line at a speed of 0.8 c (relative to Earth). It launches a missile that moves away from the spaceship (traveling in the same direction as the spaceship) at a speed of 0.6 c. Relative to Earth, the speed of the missile is A) greater than 0.8 c and less than c. B) 1.4 c. C) c. D) greater than c and less than 1.4 c. Answer: A Var: 1 43) The kinetic energy of an object moving at 10% the speed of light is A) slightly higher than that given by (1/2) m v2. B) slightly less than that given by (1/2) m v2. C) exactly equal to (1/2) m v2. Answer: A Var: 1

27.2 Short Answer Questions 1) A spacecraft is measured by an observer 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 observer on the ground, this time while the spacecraft is at rest relative to him. What result does he now get for the length? (Use for the speed of light.) Answer: 1.4 × 102 m Var: 50+ 2) How much work must be done to accelerate a particle of mass

(rest mass) from

a speed of light.) Answer: 630 J Var: 50+

for the speed of

to a speed of

(Use

3) Two spaceships are approaching one another, each at a speed of 0.31 c relative to a stationary observer on earth. What speed does an observer on one spaceship record for the other approaching spaceship? Answer: 0.57 c Var: 50+ 4) A 50.0 kg object is pushed in the direction it is moving by a 100.0 N force. Find the acceleration this force produces if the object has a speed of (a) 25.0 m/s, (b) 2.50 × m/s. (c) In parts (a) and (b), find the momentum of the object. Answer: (a) 2.00 m/s2, (b) 0.338 m/s2, (c) 1250 kg ∙ m/s, 2260 kg ∙ m/s Var: 1

College Physics, 11e (Young) Chapter 28 Photons, Electrons, and Atoms 28.1 Multiple Choice Questions 1) Find the energy (in eV) of an optical photon of frequency A) 2.66 eV B) 1.62 eV C) 1.94 eV D) 3.27 eV Answer: A Var: 50+ 2) Find the wavelength (in nm) of a A) 196 nm B) 167 nm C) 216 nm D) 233 nm Answer: A Var: 50+

photon.

3) The work function of a particular substance is wavelength for this material? A) 473 nm B) 308 nm C) 393 nm D) 554 nm Answer: A Var: 50+

What is the photoelectric cutoff

4) Upon being struck by 240 nm photons, a material ejects electrons with a maximum kinetic energy of What is the work function of this material? A) 2.60 eV B) 2.18 eV C) 3.02 eV D) 3.43 eV Answer: A Var: 50+

5) 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. The range of the wavelength band in this white light illumination for which photoelectrons are not produced, in nm, is closest to: A) 430 to 700 B) 400 to 480 C) 430 to 480 D) 400 to 430 E) 480 to 700 Answer: A Var: 10 6) A photocathode whose work function is 2.5 eV is illuminated with white light that has a continuous wavelength band from 360 nm to 700 nm. The stopping potential for this white light illumination is closest to: A) 0.94 V B) 0.85 V C) 1.0 V D) 1.1 V E) 1.2 V Answer: A Var: 50+ 7) A photocathode has a work function of 2.4 eV. The photocathode is illuminated with monochromatic radiation whose photon energy is 3.5 eV. The wavelength of the illuminating radiation is closest to: A) 350 nm B) 330 nm C) 300 nm D) 380 nm E) 410 nm Answer: A Var: 50+ 8) A photocathode has a work function of 2.4 eV. The photocathode is illuminated with monochromatic radiation whose photon energy is 3.4 eV. The maximum kinetic energy of the photoelectrons produced is closest to: 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+

9) A photocathode has a work function of 2.8 eV. The photocathode is illuminated with monochromatic radiation whose photon energy is 4.0 eV. The threshold frequency for photoelectron production is closest to: 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+ 10) A phototube has a stopping potential of 2.80 V when the cathode is illuminated with bichromatic light of 400 nm and 600 nm wavelengths. The maximum speed of the emitted photoelectrons, in SI units, is closest to: A) 9.9 × 105 B) 9.3 × 105 C) 1.1 × 106 D) 1.2 × 106 E) 1.3 × 106 Answer: A Var: 50+ 11) 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 the maximum kinetic energy will increase. B) the rate of ejected electrons will remain the same but the maximum kinetic energy will increase. C) the rate of ejected electrons will increase and the maximum kinetic energy will increase. D) the rate of ejected electrons will remain the same but the maximum kinetic energy will decrease. Answer: A Var: 1 12) A blue photon A) has a smaller wavelength than a red photon and travels with the same speed. B) has a smaller wavelength than a red photon and travels with a greater speed. C) has a longer wavelength than a red photon and travels with the same speed. D) has a longer wavelength than a red photon and travels with a greater speed. Answer: A Var: 1

13) Monochromatic light is incident on a metal surface. The ejected electrons give rise to a current in the circuit shown in Figure 28.1. The maximum energy of the ejected electrons is determined by applying a reverse ('stopping') potential, sufficient to reduce the current in the ammeter to zero. Figure 28.1

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 14) Monochromatic light is incident 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 15) Increasing the brightness of a beam of light without changing its color will increase A) the number of photons emitted by light every second. B) the average energy of each photon. C) the speed of the photons. D) Two of the above statements are true. Answer: A Var: 1

16) 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 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) all of the above E) two of the above Answer: A Var: 1 17) What is the wavelength of the light emitted by atomic Hydrogen according to Balmer's formula with and ? A) 22,300 nm B) 12,400 nm C) 52,500 nm D) 10,500 nm Answer: A Var: 44 18) What is the frequency of the light emitted by atomic Hydrogen according to Balmer's formula with and ? A) 1.65 × 1014 Hz B) 1,820 Hz C) 1,460 nm D) 1.46 × 10-6 m Answer: A Var: 44 19) 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

20) In the spectrum of Hydrogen the lines obtained by setting m = 1 in Balmer's formula is called the Lyman series. Calculate the wavelength of the spectral line of the 16th member of the Lyman series. A) 91.6 nm B) 371 nm C) 102 nm D) 83.2 nm Answer: A Var: 15 21) Find 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 22) Calculate the radius of the n = 4 Bohr orbit in removed). A) 106 pm B) 74 pm C) 85 pm D) 95 pm Answer: A Var: 9

state to the

(oxygen with 7 of its 8 electrons

23) When a metal is illuminated by light, photoelectrons are observed provided the light's wavelength is less than 520 nm. What is the metal's work function? A) 2.4 eV B) 2.6 eV C) 2.8 eV D) 3.0 eV Answer: A Var: 50+ 24) 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 detected emission? A) 7,510 nm B) 4,670 nm C) 12,400 nm D) 4,380 nm Answer: A Var: 44

25) A Hydrogen atom is excited to the n = 9 level. Its decay to the n = 6 level is detected in a photographic plate. What is the frequency of the light photographed? A) 5.08 × 1013 Hz B) 5,910 Hz C) 5,910 nm D) 3.28 × 10-9 km Answer: A Var: 44 26) A hydrogen atom makes a downward transition from the the wavelength of the emitted photon. A) 2.56 μm B) 1.54 μm C) 2.05 μm D) 3.07 μm Answer: A Var: 15 27) 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

state to the

excited state in a hydrogen atom.

state. Find

28) Part of the energy level diagram of a certain atom is shown in Figure 28.2. 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. Figure 28.2

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 29) The longest wavelength of a photon that can be emitted by a hydrogen atom, for which the final state is is closest to: A) 39,000 nm B) 22,000 nm C) 7,400 nm D) 16,000 nm E) 28,000 nm Answer: A Var: 9 30) The shortest wavelength of a photon that can be emitted by a hydrogen atom, for which the initial state is is closest to: A) 92 nm B) 82 nm C) 72 nm D) 62 nm E) 52 nm Answer: A Var: 10

31) The longest wavelength of a photon that can be emitted by a hydrogen atom, for which the initial state is is closest to: A) 550 nm B) 575 nm C) 600 nm D) 625 nm E) 650 nm Answer: E Var: 1 32) The shortest wavelength of a photon that can be emitted by a hydrogen atom, for which the initial state is is closest to: A) 820 nm B) 850 nm C) 880 nm D) 910 nm E) 940 nm Answer: A Var: 1 33) The energy required to remove the electron from a hydrogen atom in the closest to: A) 0.11 eV B) 0.094 eV C) 0.080 eV D) 0.17 eV E) 0.14 eV Answer: A Var: 9 34) A doubly-ionized lithium atom 3Li++ undergoes a state transition from wavelength of the photon which is emitted is closest to: A) 350 nm B) 450 nm C) 550 nm D) 650 nm E) 750 nm Answer: B Var: 1

state is

The

35) What is the longest wavelength radiation that will emit photoelectrons from sodium metal for which the work function is 2.28 eV? A) 580 nm B) 499 nm C) 633 nm D) 668 nm E) 544 nm Answer: E Var: 1 36) 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? A) 4.0 × 1018 B) 9.9 × 1019 C) 4.8 × 1019 D) 1.6 × 1017 E) 3.2 × 1017 Answer: A Var: 50+ 37) 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? A) 1.7 × 1018 B) 2.1 × C) 2.6 × D) 3.1 × Answer: A Var: 50+ 38) Light excites atomic hydrogen from its lowest level to the the light? A) 13.7 eV B) 32.2 eV C) 61.4 eV D) 91.8 eV Answer: A Var: 9

level. What is the energy of

39) Light shines through atomic Hydrogen gas. It is seen that the gas absorbs light readily at a wavelength of 91.33 nm. What is the level to which the Hydrogen is being excited by the absorption of light of this wavelength? Assume that the most of the atoms in the gas are in the lowest level. A) 25 B) 27 C) 22 D) 32 Answer: A Var: 12 40) The Bohr model of the hydrogen atom predicts an ionization energy of 13.6 eV. With this model one would expect the ionization energy of the Li++ ion to be A) 122.4 eV B) 40.8 eV C) 54.4 eV D) 27.2 eV E) 79.6 eV Answer: A Var: 1 41) A 29.0 pm wavelength photon is scattered by a stationary electron. The maximum energy loss of the photon is closest to: A) 4 KeV B) 6 KeV C) 10 KeV D) 12 KeV E) 15 KeV Answer: B Var: 1 42) An 18.0 pm wavelength photon is scattered by a stationary electron through an angle of 120°. The wavelength of the scattered photon, in pm, is closest to: A) 19.2 B) 20.4 C) 21.6 D) 22.9 E) 24.1 Answer: C Var: 1

43) For what wavelength does a 100 mW laser deliver 1.6 × 1017 photons in one second? A) 320 nm B) 330 nm C) 340 nm D) 350 nm Answer: A Var: 25 44) An electron's de Broglie wavelength is 2.4 μm. What is its speed? 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+ 45) An electron has the same de Broglie wavelength as a 390 nm photon. The speed of the electron is closest to: A) 1,900 m/s B) 2,100 m/s C) 1,700m/s D) 1,500 m/s E) 540 m/s Answer: A Var: 50+ 46) A proton has a speed of 7.2 x m/s. The energy of a photon that has the same de Broglie wavelength as the proton is closest to: A) 230 keV B) 150 keV C) 300 keV D) 370 keV E) 440 keV Answer: A Var: 50+

47) An electron has the same de Broglie wavelength as a 1.8 eV photon. The speed of the electron is closest to: A) 1,100 m/s B) 980 m/s C) 910 m/s D) 840 m/s E) 770 m/s Answer: A Var: 50+ 48) The spacing of the surface planes of a crystal is 159 pm. A beam directed normally at the surface of the crystal undergoes first order diffraction at an angle of 58° from the normal. The diffraction is done with a beam of monoenergetic neutrons. The energy of the neutrons is closest to: A) 0.045 eV B) 0.039 eV C) 0.050 eV D) 0.056 eV E) 0.061 eV Answer: A Var: 50+ 49) A molecule of roughly spherical shape has a mass of 1.80 x kg and a diameter of 0.6 nm. The uncertainty in the measured position of the molecule is equal to the molecular diameter. The minimum speed of the molecule is closest to: A) 1 m/s B) 10 m/s C) 100 m/s D) 0.1 m/s E) 0.01 m/s Answer: A Var: 50+ 50) A laser produces a beam of 4000 nm light. A shutter allows a pulse of light, 30 ps in duration, to pass. The uncertainty in the energy of a photon in the pulse is closest to: A) 2 × eV B) 2 ×

C) 2 ×

D) 2 ×

E) 2 × eV Answer: B Var: 1 28.2 Short Answer Questions

1) 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. (Note: and Answer: 1.39 eV Var: 50+ 2) X-rays of energy 3.5 x

eV are Compton-scattered through an angle of 105°. What is the

energy of the scattered X-rays, in electron volts? (Note: and the mass of the electron is Answer: 3.2 × 104 eV Var: 50+ 3) When a photoelectric surface is illuminated with light of wavelength 437 nm, the stopping potential is 1.67 V. (a) What is the work function of the metal in eV? (b) What is the maximum speed of the ejected electrons? (Note: h = 6.626 × J ∙ s, me = 9.110 x kg, e = 1.602 × c) Answer: (a) 1.17 Ev (b) 7.66 × m/s Var: 1 4) Calculate the energy in eV of a neutron (mass 1.675 ×

kg) that has de Broglie

wavelength of (Note: Answer: 16 eV Var: 50+

and

5) An unstable particle produced in a high-energy collision is measured to have an energy of 483 MeV and an uncertainty in energy of 29 KeV. Use the Heisenberg uncertainty principle to estimate the lifetime of this particle. (Note: h = 6.626 × J ∙ s, c = 3.00 × m/s, and e = 1.602 × C.) Answer: 1.4 × 10-19 seconds Var: 50+

6) A small dust particle m = 8.50 × g is being observed under a magnifying lens. Its position is determined to be within 0.0060 mm. (a) Find the velocity limit implied by the uncertainty of its position. (b) Assuming the dust particle is moving at this speed, how many years would it take for the particle to move 1 mm? Answer: 3.6 × 10-21 m/s (a) 8.9 × 109 yrs (b) Var: 50+ 7) Recall that the energy levels of the hydrogen atom are given by =

, where R = 1.097 ×

What wavelength photon is emitted when the atom undergoes a transition from the level? Answer: 2.63 × 10-6 meters Var: 21

to the

College Physics, 11e (Young) Chapter 29 Atoms, Molecules, and Solids 29.1 Multiple Choice Questions Situation 29.1 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. 1) In Situation 29.1, the magnitude of the orbital angular momentum of the atom is closest to: A) 1.0 B) 1.2 C) 1.4 D) 1.7 E) 2.0 Answer: C Var: 1 2) In Situation 29.1, a magnetic field is applied. The set of possible angles between the magnetic field and the orbital angular momentum is: A) 45° B) 90° C) 45°, 90° D) 45°, 135° E) 45°, 90°, 135° Answer: E Var: 1 3) The total number of electron states (including spin states), for which ℓ = 1 in the K, L, and M shells is equal to: A) 6 B) 8 C) 10 D) 12 E) 16 Answer: D Var: 1

4) The only valid electron state and shell designation among the following is: A) 1p, K B) 2s, K C) 1s, L D) 2p, L E) 3f, M Answer: D Var: 1 5) The only invalid electron state and shell designation among the following is: A) 1s, K B) 2s, L C) 2d, L D) 3s, M E) 3d, M Answer: C Var: 1 6) The correct ground state electron configuration of boron (Z = 5) is: A) 2p B) C)

E) Answer: A Var: 1 7) Consider an atom with the electron configuration 1s22s22p63s23p6. Which of the following is an accurate statement concerning this atom? A) The atomic number of this atom is Z = 11. B) This atom is in an excited state. C) This atom has a non-zero angular momentum. D) This atom is most likely to give rise to an ion with charge +2e. E) This atom would probably be very inert chemically. Answer: E Var: 1

8) A highly ionized atom with Z = 5 has only one electron left around it, in its ground state. How much more energy is required to finish the job and have a bare nucleus? A) 340.0 eV B) 68.0 eV C) 10.9 eV D) 13.1 eV Answer: A Var: 5 9) 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 10) Within how many degrees of the z-axis (or any other you choose) can the orbital angular momentum of an electron in the state lie? A) 30.0° B) 41.4° C) 60.0° D) 45.0° Answer: A Var: 3 11) How many electrons can be found with principal quantum number atom? A) 18 B) 6 C) 20 D) 9 Answer: A Var: 3 12) Estimate the most energetic X-ray you can get from a heavy atom with A) 118 keV B) 0.865 eV C) 164 MeV D) 5.19 × 107 eV Answer: A Var: 15

in a suitably heavy

13) Radioastronomers 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 What is the energy difference between the hyperfine levels? A) 5.92 × 10-6 eV B) 5.92 × 10-25 J C) 1.66 × 10-24 J D) 4.73 × 10-25 J Answer: A Var: 1 14) How many 2d electron states can an atom have? A) 0 B) 4 C) 6 D) 8 E) 10 Answer: A Var: 1 15) How many 3d electron states can an atom have? A) 0 B) 4 C) 6 D) 8 E) 10 Answer: E Var: 1 16) Neon has 10 electrons. The element of next higher Z that has chemical properties very similar to those of neon has Z equal to A) 11 B) 17 C) 18 D) 19 E) 36 Answer: C Var: 1

17) In a transition from one vibrational state to another, a molecule emits a photon of wavelength 5.56 µm. The energy difference between these two states is closest to A) 0.223 eV B) 2.23 MeV C) 13.6 eV D) 13.6 MeV E) 0.223 MeV Answer: A Var: 1 18) A proton and an electron are 1.00 Å apart. (Å is the Ångstrom unit, which is 10-10 m.) The potential energy of this pair of charges is closest to A) 14.4 J B) 1.44 eV C) 14.4 eV D) 144 eV E) 14.4 keV Answer: C Var: 1 29.2 Short Answer Questions 1) 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 2) An atom with atomic number 3 is in its ground state. How many electrons are in its outermost shell? Answer: 1 Var: 8 3) Write out the electron configuration for the ground state of the phosphorus atom, for which Z = 15. Answer: 1s2, 2s2 2p6, 3s2 3p3 Var: 1 4) For an electron in the M 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. Answer: (a) 2.58 × 10-34 kg ∙ m2/s, p subshell, (b) 0, s subshell Var: 1 5) In an excited hydrogen atom, the electron is in the 4d state. If this atom is in an external

magnetic field, what are the smallest and largest possible angles between the orbital angular momentum and the direction of the magnetic field (or any other direction, for that matter)? Answer: 35.3°, 145° Var: 1

College Physics, 11e (Young) Chapter 30 Nuclear and High-Energy Physics 30.1 Multiple Choice Questions 1) In a head-on collision, an alpha particle of energy bounces straight back from a nucleus of charge How close were the centers of the objects at closest approach? 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) The diameter of an atom is 1.4 × 10-10 m and the diameter of its nucleus is 1.0 × What fraction of the atom's volume is occupied by mass? A) 3.6 × 10-13 B) 7.1 × 10-5 C) 5.1 × 10-9 D) 2.6 × 10-17 Answer: A Var: 19 3) Estimate the radius of a nucleus with mass 50 atomic mass units. A) About 4.42 × 10-15 m B) About 8.49 × 10-15 m C) About 3.68 × 10-15 m D) About 6.17 × 10-15 m Answer: A Var: 50+ 4) Estimate the mass of a nucleus with radius A) About 2.11 × 10-26 kg B) About 7.53 × 10-27 kg C) About 2.29 × 10-26 kg D) About 4.72 × 10-26 kg Answer: A Var: 13

5) How much energy is released when

have decayed to

Use

and A) 1.02 × 104 J B) 5.12 × 103 J C) 3.41 × 103 J D) 3.07 × 104 J Answer: A Var: 11 6) A summary of the nuclear reactions that power our sun can be written as with masses of for p, for helium, and electrons. If this is the reaction that occurs, how much energy is released? A) 24.69 MeV B) 28.3 MeV C) 2790.13 MeV D) 279.01 MeV Answer: A Var: 1 7) The following masses are known: n

1.008665 u

1.007825 u Rn 222.017571 u

The binding energy of A) 1,700 B) 1,900 C) 2,100 D) 2,300 E) 2,400 Answer: A Var: 12

Rn, in MeV, is closest to:

for

8) A proton is projected at a stationary

Ra aluminum target. The proton momentarily comes

to a halt at a distance from the center of an aluminum nucleus, equal to twice the nuclear radius. Assume that the nucleus retains its spherical shape and that the nuclear force on the proton is negligible. The initial kinetic energy of the proton, in MeV, is closest to: A) 8.7 B) 5.8 C) 2.9 D) 13 E) 17 Answer: A Var: 14 9) Rubidium

Rb is a naturally occurring nuclide which undergoes beta-minus decay. The

nuclide, which is the product of the decay, is: A)

Answer: E Var: 1

10) Neodymium 144Nd is a nuclide which undergoes alpha decay. The nuclide which is the product of the decay is: A)

Answer: B Var: 1 11) Scandium 44Sc decays by emitting a positron. The nuclide which is the product of the decay is: A)

Answer: A Var: 1

12) A radioactive source of a single nuclide emits 2.4 MeV neutrons at the rate of 7,100 neutrons per second. The number of atoms in the source is The activity of the source, in nCi, is closest to: A) 190 B) 1,900 C) 19 D) 71 E) 710 Answer: A Var: 50+ 13) The decay constant of a radioactive nuclide is 4.6 × minutes, is closest to: A) 2.5 B) 3.6 C) 3.1 D) 1.4 E) 2.0 Answer: A Var: 50+

. The half-life of the nuclide, in

14) The decay constant of a radioactive nuclide is 3.1 x . At a given instant, the activity of a specimen of the nuclide is 70 mCi. The time interval required for the activity to decline to 10 mCi is closest to: A) 630 s B) 690 s C) 750 s D) 820 s E) 880 s Answer: A Var: 50+ 15) The decay constant of a radioactive nuclide is 1.6 ×

. At a given instant, the number

of atoms of the radioactive nuclide is The number of atoms of the nuclide that remain after a time interval of 30 minutes is closest to: A) 1.04 × B) 1.14 × C) 1.26 × D) 1.38 × E) 1.52 × Answer: A Var: 1

16) A nuclear bomb explosion results in a mass decrease of about the final ingredients. How much energy is released? A) 1.89 × 1014 J B) 6.30 × 105 J C) 1.89 × 1013 J D) 2.25 × 1012 J Answer: A Var: 28

between the initial and

17) An archaeologist finds the 14C in a sample of of material to be decaying at 107 counts per second. A modern sample of the same material decays at 151 counts per second. The half-life of is 5730 years. How old is the sample? A) 8,980 years B) 6,230 years C) 17,000 years D) 8,530 years Answer: A Var: 17 18) About how many days are required for a radioactive sample, with an initial activity of to decay to an activity of The half-life of the material is 4.5 days. A) About 45 days B) About 36 days C) About 54 days D) About 31 days Answer: A Var: 41 19) A hospital patient has been given (half-life = 8.04 days) which decays at 5.9 times the acceptable level for exposure to the general public. How long must the patient wait to reach the acceptable level? Assume that the material merely decays and is not excreted. A) 21 days B) 14 days C) 9.9 days D) 8.9 days Answer: A Var: 31

20) The material used in nuclear bombs is with a half-life of about 20,000 years. How long must we wait for a buried stockpile of this substance to decay to of its original mass? A) 133 thousand years B) 92 thousand years C) 64 thousand years D) 0.2 thousand years Answer: A Var: 5 21) Why do heavy nuclei contain more neutrons than protons? A) Neutrons dilute the electric repulsion of the protons. B) Neutrons are lighter than protons. C) Neutrons are heavier than protons. D) Neutrons are radioactive, and so are heavy nuclei. Answer: A Var: 1 22) Modern nuclear bomb tests have created an extra high level of

in our atmosphere. When

future archaeologists date samples from this era, without knowing of this testing, will their dates be too young? Too old? Correct? If correct, why? A) Too young. B) Too old. C) Correct, since from bomb tests is different from that produced naturally. D) Correct, because modern biological materials do not gather

from bomb tests.

Answer: A Var: 1 23) The primary reason very large nuclei are unstable is due to A) the cumulative repulsive force amongst the protons. B) the cumulative attractive force between the protons and the orbiting electrons. C) the repulsive force between the neutrons and the protons. Answer: A Var: 1 24) Neutrons are slightly more massive than protons. If the mass of a neutron were smaller than its actual value, yet still more massive than a proton, a nucleus with a very high atomic number would most likely contain A) more neutrons than the actual number. B) fewer neutrons than the actual number. C) the same number of neutrons as the actual number. Answer: C Var: 1 25) In massive stars, three helium atoms fuse together, forming a carbon nucleus. 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 (mass is always conserved). Answer: A Var: 1 26) Suppose the half-life of some element is 2 days. If you purchase 10 grams of the element (which was produced in a laboratory 4 days ago), how much of this element would you have 3 days after you purchased it? 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: C Var: 1 27) A radioactive nuclide of atomic number Z emits an alpha particle and the daughter nucleus then emits a beta particle. What is the atomic number of the resulting nuclide? A) Z-1 B) Z+1 C) Z-2 D) Z-3 Answer: A Var: 1 28) A radioactive nuclide of atomic number Z emits an electron, then the daughter nuclide emits a gamma ray. What is the atomic number of the resulting nuclide after both processes? A) Z+1 B) Z-1 C) Z-2 D) Z-3 Answer: A Var: 1 29) 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) Attractive nuclear forces in the nucleus counteract 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. Answer: A Var: 1 30) Nuclei that are all isotopes of an element all have the same A) number of protons.

B) mass. C) number of nucleons. D) number of neutrons. Answer: A Var: 1 31) The half-life of cobalt-60 is 5.3 years, while that of strontium-90 is 28 years. Suppose you have a sample of each, such that they initially contain equal numbers of atoms of these nuclides. How will the activities (number of decays per unit time) 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 32) The half-lives of cobalt-60 and strontium-90 are 5.3 years and 28 years respectively. Suppose that samples of cobalt-60 and strontium-90 are such that they initially have the same activity. What will be true of the numbers of cobalt-60 and strontium-90 nuclei in these samples? A) There will be more strontium-90 than cobalt-60 nuclei. B) There will be equal numbers of cobalt-60 and strontium-90 nuclei. C) There will be 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

33) The stability of

C with respect to alpha, beta-plus and beta-minus decay is to be

determined. The following atomic masses in amu are known: He

4.002603

7.016928

11.009305

11.011433

11.026742

The

C nuclide 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

34) The stability of

Cl with respect to alpha, beta-plus and beta-minus decay is to be

determined. The following atomic masses in amu are known: He

4.002603

31.973907

35.967081

35.968307

35.967546

The

Cl nuclide is

35) 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 in amu are known: He

4.002603

Tl 207.981998 Pb 211.991871 Bi 211.991255 Po 211.988842

The

Bi nuclide 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 36) The maximum permissible workday dose for occupational exposure to radiation is 18 mrem. A 54 kg laboratory technician absorbs 2.6 mJ of 0.3 MeV gamma rays in a work day. The relative biological efficiency (RBE) for gamma rays is 1.00. The ratio of the equivalent dosage received by the technician to the maximum permissible equivalent dosage is closest to: A) 0.27 B) 0.29 C) 0.32 D) 0.35 E) 0.37 Answer: A Var: 50+

37) 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 efficiency (RBE) for gamma rays is 1.00. The number of gamma-ray photons absorbed by the technician in a workday is closest to: A) 3 × 1010 B) 3 × 109 C) 3 × 108 D) 1 × 109 E) 1 × 108 Answer: A Var: 50+ 38) A 70 kg researcher absorbs 4.5 × neutrons in a work day. The energy of the neutrons is 1.2 MeV. The relative biological efficiency (RBE) for fast neutrons is 10. The equivalent dosage of the radiation exposure, in mrem, is closest to: A) 1.2 B) 0.39 C) 0.77 D) 3.7 E) 12 Answer: A Var: 50+ 39) A beryllium-8 atom at rest undergoes double alpha decay as follows: Be →

He + He

The atomic masses are: He

4.002603 amu

8.005305 amu

The kinetic energy of each departing alpha particle, in keV, is closest to: A) 46 B) 65 C) 92 D) 130 E) 180 Answer: A Var: 1 40) 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 amu

3.016029 amu

4.002603 amu

The reaction energy, in MeV, is closest to: A) 11 B) 13 C) 15 D) 17 E) 19 Answer: B Var: 1

Situation 30.1 An excited

U* nucleus undergoes fission into two fragments.

U* →

Ba +

The following atomic masses are known: Kr

91.926270 amu

143.922845 amu

236.045563 amu

41) In Situation 30.1, the reaction energy, in MeV, is closest to: A) 150 B) 160 C) 170 D) 180 E) 190 Answer: D Var: 1 42) In Situation 30.1, assume, at a given instant, that the two fragments are spherical and barely in contact. At that instant, the electrostatic interaction energy of the two fragments, in MeV, is closest to: A) 230 B) 240 C) 250 D) 260 E) 270 Answer: C Var: 1

Table 30.1

43) In Table 30.1, 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 here. The accident occurred at 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 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+ 44) The attractive force between quarks is mediated by particles called A) stickons. B) gluons. C) adhesivons. D) chromons. E) forcons. Answer: B Var: 1 45) Redshift measurements on a constellation show that it is receding with a velocity of 7,240 km/s. How far away is the galaxy if Hubble's constant has the value 2.11 × 10-18 s-1? A) 3.4 × 1024 m B) 1.2 ×

C) 1.2 × 1024 m D) 4.1 × 1023 m E) 2.0 × 1022 m Answer: A Var: 50+

46) Which of the following is not true of the nuclear force? A) The nuclear force has a short range, of the order of nuclear dimensions. B) For two protons in close proximity, the nuclear force and the electric force have comparable 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 favors binding of pairs of protons or neutrons with opposite spin angular momenta. Answer: B Var: 1 47) In the nuclear reaction here, which of the following is the missing nuclear product? B +

He →

Answer: C Var: 1

H + ?

30.2 Short Answer Questions 1) If the radius of a nucleus is given by R = density of a nucleus that has Answer: 2.31 × Var: 50+

where

calculate the

The mass of a nucleon (proton or neutron) is

kg/

2) 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 × decays per second, what is the decay rate after 37 days? Answer: 2.2 × 1017 decays per second Var: 50+ 3) Consider the fusion reaction: H+ H+ H →

He +

H +

The atomic masses are: H, 2.01410 u ; He, 4.00260 u; H, 1.00783 u; and n, 1.008665 u, where 1u = 1.6606 ×

kg. What mass of deuterium { H} fuel is used up in producing

of energy by this reaction? Answer: 1.6 × 101 kg Var: 50+ 4) A hypothetical particle has mass 510 MeV/c2. If such a particle at rest decays into two gamma-ray photons, what is the wavelength of each photon? (Note: and Answer: 4.86 × 10-15 m Var: 50+ 5) If a Σ- at rest decays into an n and π- , what is the total kinetic energy of the decay products? (The masses of Σ- , n and π- are 1,197, 940, and respectively.) Answer: 117 MeV Var: 4

6) The earth's radius is 6380 km and its mass is 5.97 × 1024 kg. The gravitational constant is (a) If Hubble's constant has the experimental value (although this can change due to future measurements), calculate the critical density of the universe needed to stop the expansion of the universe. (b) If the earth had this density, what would be its radius? Express your answer in meters and as a multiple of its present radius. Answer: (a) 5.8 × 10-27 kg/m3 (b) 6.3 × 1016 m, 9.8 × 109 times its present radius Var: 1