[1011b] physics 71 le 3

Name: Student Number: Lecturer:

Section: Course: College:

University of the Philippines College of Science

PHYSICS 71 SET A

2nd Semester AY 2010-2011 Third Long Examination

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2nd Semester AY 2010-2011Physics 71

National Institute of Physics

INSTRUCTIONS: Choose the best answer. Ignore air resistance, otherwise stated in the question.

Useful constants: G = 6.67 x 10-11 m3/kg s2 density of water = 1000 kg/m3 g near Earth surface = 9.81 m/s2 density of seawater = 1030 kg/m3 Mass of sun = 1.99 x 1030 kg Patm = 1 atm = 101325 Pa Mass of earth = 5.97 x 1024 kg Radius of earth = 6.38 x 106 m 1.

unless

EQUILIBRIUM. Which of the following depict/s a system in static equilibrium?

I. Two girls sitting on opposite ends of an unmoving see-saw I. A wheel rolling without slipping at a constant linear velocity II. A Ferris wheel undergoing uniform circular motion A. I only D. I and II B. II only E. I and III C. III only

For the next two questions: Shown on the right is a two-level mobile.

Assume that the masses of the strings and the rods are negligible, and that the strings are attached at the center of each rod. The lower and upper rods have lengths L and 2L, respectively. The mobile is in static equilibrium.

2.

MOBILE I. What should be the mass of star 2 (m2) if m1 = m3 = m4 = m?

A. B. C.

3.

2=12 2=23 2=34

D. E.

2=32 2=2

MOBILE II. How far from the center of the upper rod (x) should the lower rod be placed?

A. B. C.

=27 =14 =411

D. E.

A-2

=38 =52

2nd Semester AY 2010-2011Physics 71

National Institute of Physics

4.

STABLE ANGLE. A 4.0 m-long uniform plank with mass m = 0.60 kg is hinged on a wall, and is supported on the other end with a wire that makes an angle θ with respect to the plank (see figure).

The tension along the wire is 5.0 N. What is the value of θ if the plank is to support a box (M = 1.0 kg) placed 0.50 m from the wall?

A. 3.4° D. 36° B. 4.9° E. 56° C. 20°

For the next two questions: Consider a metal rod of cross sectional area A, original length l0, and Young’s modulus Y. When the metal is given a force along its length, it is stretched by a displacement from its original length according to the diagram at the right.

5.

No Money3. Which of the following scenarios will break the rod?

A. When the Young’s modulus of the rod becomes proportional to F1 / s1.

B. When you exert a force F1 on the rod.

C. When you stretch the rod by s1.

D. Both A and B are correct.

E. A, B and C are correct.

6.

A ONLY. What is the slope of the indicated straight line?

A. 0 D. B. E. C.

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2nd Semester AY 2010-2011Physics 71

National Institute of Physics

7.

Gravitation. Which of the following statements about Newton's Law of Gravitation is false?

A. The acceleration due to gravity of an object is independent of its mass.

B. The gravitational forces exerted by two bodies on each other are an action-reaction pair.

C. The mass of an object is larger at the surface of the Earth than at a height 5000 km above the surface.

D. The magnitude of the gravitational force exerted on a mass by another mass decreases when the distance between them increases.

E. At the earth's surface, an object's gravitational force exerted on the earth is equal in magnitude to the object's weight on earth.

8.

Masses Given three aligned masses as shown, what is the net gravitational force experienced by mass B [the positive direction is to the right]?

A. 3Gm2/2r2 B. 2Gm2/r2 C. Gm2/2r2 D. zero E. - Gm2/2r2

9.

Greatest On which of the following planets will an object have the greatest acceleration due to gravity at the surface? Let ME, and RE be the Earth's mass and radius respectively.

A. Mplanet = 2ME, Rplanet = 2RE

D. Mplanet = ME/2, Rplanet = RE/2

B. Mplanet = 2ME, Rplanet = RE/2

E. Mplanet = ME, Rplanet = 2RE

C. Mplanet = ME/2, Rplanet = 2RE 10. Zhao. Comet Zhao was found to be in its perihelion last Dec. 6, 2007. It is found to have an orbital period of 2.34x108 s (7.40 years). What is the semimajor axis a of comet Zhao? [Mass of sun = 1.99 x 1030 kg] A. 9.22 x 108 m D. 5.69 x 1011 m 10 B. 3.71 x 10 m E. 8.31 x 1011 m C. 5.43 x 1010 m 11. At Aphelion. A hypothetical planet with mass of 1.500 x 1017 kg moves around the sun. When the planet is at perihelion, it has a speed of 2.650 × 104 m/s and is 2.067 × 1011m from the sun. The orbital radius increases to 2.492 × 1011 m at aphelion. What is the planet's speed at aphelion?

A. 1.482 x 102 m/s D. 7.800 x 105 m/s 4 B. 2.198 x 10 m/s E. 9.404 x 105 m/s C. 3.195 x 104 m/s

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2nd Semester AY 2010-2011Physics 71

National Institute of Physics

For the next two questions: Satellite Roemer with mass of 84.0 kg orbits around the earth at a constant height of 600. km from the earth’s surface.

12. Roemer 1. What is the period of satellite Roemer’s orbit?

A. 0.146 x 103 s D. 5.55 x 103 s 3 B. 1.70 x 10 s E. 5.81 x 103 s C. 5.07 x 103 s 13. Roemer 2. What is the total mechanical energy of the satellite Roemer?

A. -2.86 x 107 J D. -2.63 x 109 J B. -1.68 x 109 J E.-2.79 x 1010 J 9 C. -2.40 x 10 J 14. Torque on Planet N. Planet N orbits around the sun as shown in the figure. Which of the following positions I, II and III does planet N experiences the greatest torque about an axis passing through the sun and perpendicular to the plane of the orbit?

A. I only B. II only C. III only D. I and III only E. Torque is the same for I, II and III. 15. Cube face. Consider two cubes: cube A has mass m and side s while cube B has mass 2m and side 2s (as shown in the figure). The relationship of the density ρ between cubes A and B is A.ρA= (1/4)ρB B.ρA= (1/2)ρB C.ρA= ρB D.ρA= 2ρB E.ρA= 4ρB 16. Pressured. A tank with height 10.0 m diameter of 3.0 m is full of water. If a pressure gauge is attached exactly at the middle of the tank, what is the reading on the gauge? (ρwater is 1000 kg/m3) A. zero B.1.0 x 103 Pa C.5.0 x 103 Pa D.1.0 x 104 Pa E.5.0 x 104 Pa

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2nd Semester AY 2010-2011Physics 71

National Institute of Physics

17. Ice water. A large ice cube of side-length equal to 1.0 m is totally immersed under water. What is the buoyant force exerted by the water on the ice cube? [ρwater = 1000 kg/m3; ρice = 920 kg/m3] A.zero D. 9.8 x 103 N 2 B.7.8 x 10 N E. 1.9 x 104 N C.9.0 x 103 N

18. Donsol Sharks. Bob was swimming when he was bitten by a shark and pulled vertically 500 m below the surface of the sea (completely submerged). The shark then got tired and let Bob go. Assuming Bob has a mass of 50.0 kg and volume of 1.00 m3, how much force did the shark exert before releasing Bob? [ρseawater=1030kg/m3] A.zero D. 9.81 x 103 N 2 B.4.91 x 10 N E. 1.01 x 104 N 3 C.9.61 x 10 N 19. Sprinkler. A lawn sprinkler is made of a 1.00-cm diameter garden hose with one end closed and has 25 holes, each with a diameter of 0.0500 cm, cut near the closed end. If water flows at 2.00 m/s in the hose, the speed of the water leaving a hole is_________.

A. 2.00 m/s D. 600 m/s B. 32.0 m/s E. 800 m/s C. 40.0 m/s

20. Wave Consider the x-t plot of a wave on the right. What are the wave's

period

and

angular

frequency?

A. 2 sec, π rad/sec B. 2 sec, 1/2 rad/sec C. 4 sec, π/2 rad/sec D. 4 sec, π rad/sec E. 4 sec, 1/4 rad/sec

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2nd Semester AY 2010-2011Physics 71

National Institute of Physics

For the next three questions: A system is filled to a height h with a liquid of density ρ as shown at the right. The atmospheric pressure is Patm. The cross sectional area at 3 is half of that at 4 (A3 = A4/2). Assume that the fluid is incompressible and friction is negligible.

21. Liquid I. At which point is the speed greatest?

A. 1 D. 4 B. 2 E. The speed is the same at all points.

C. 3 22. Liquid II. At which point is the pressure greatest?

A. 1 D. 4 B. 2 E. The pressure is the same at all points.

C. 3 23. Liquid III. At which point is the volume flow rate greatest?

A. 1 D. 4 B. 2 E. The volume flow rate is the same at all points.

C. 3 24. M and m. A mass m is attached to a spring and is oscillating with a period T. When the mass is replaced by another mass M, the period becomes 3T. What is M in terms of m?

A. M = 9m D. M = m/3 B. M = 3m E. M = m/9 C. M = √3m 25. SHM. A ball moves in a circular path of 0.075-m radius with a constant angular speed of (2π/3) rad/s. Its shadow performs simple harmonic motion on the wall behind it. At the turning point, what is the acceleration and velocity of the shadow?

A. a = 0; v = 0.16 m/s D. a = 0; v = 0 B. a= 0.33 m/s2; v = 0.16 m/s E. a = 16 m/s2; v = 0 2 C. a = 0.33 m/s ; v = 0

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2nd Semester AY 2010-2011Physics 71

National Institute of Physics

26. SHM Experiment.

An experiment is done to measure the stiffness of a spring. The set-up is a vertical spring oscillator with a bob having a mass of 0.75 kg. The position versus time plot of the bob is acquired (see graph below).What is the spring constant?

A. 241 N/m B. 185 N/m C. 76.9 N/m D. 58.9 N/m E. 29.5 N/m 27. AMP! A 1.0kg block is attached to a spring (spring constant 200. N/m) on a frictionless floor as shown in the figure below. At the displacement x=0.010 m, its speed is 0.35 m/s. What is the amplitude of the block’s oscillation?

A. 7.1 x 10-4 m B. 2.7 x 10-2 m C. 3.5 x 10-1 m D. 3.8 x 10-1 m E. 5.0 m

28. Pendulums. Two simple pendulums have the same mass. However, pendulum I has length L, and pendulum II has length 4L. Compare the period of small oscillations of I (TI) and that of II (TII)?

A. TI = 4 TII D. TI = TII / 2 B. TI = 2 TII E. TI = TII / 4 C. TI = TII 29. Damping. Which of the following damping condition will the oscillation cease fastest? [All of the cases have the same initial condition] A. underdamping D. underdamping and critical damping B. critical damping E. critical damping and overdamping C. overdamping

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2nd Semester AY 2010-2011Physics 71

National Institute of Physics

30. Natural Rhythm. Consider an oscillator under forced oscillation. What will happen to the behavior of the oscillation when the frequency of the driving force nears the natural frequency of the system?

A. the oscillation will cease B. the oscillation’s period will increase C. the oscillation will be unpredictable D. the amplitude of oscillation will increase E. Choices A, B and C are correct.

31. Small Os 1. Consider the figure at the right.

If the three uniform rods with equal length L are released at a very small angle θ with respect to the vertical, which of the following shows the correct order of the period of the rods?

A. 1>2>3 D. 3>2>1 B. 1>3>2 E. 3>1>2 C. 1=2=3 32. Small Os 2 Consider the figure at the right. If the three uniform rods with lengths as shown are released at a very small angle θ with respect to the vertical, which of the following shows the correct order of the period of the rods?

A. 1>2>3 D. 3>2>1 B. 1>3>2 E. 3>1>2 C. 1=2=3

33. Resonance. What is the resonance frequency of the spring-mass system shown?

A.0.50 Hz D. 2.0 Hz B.0.63 Hz E. 3.2 Hz C.1.6 Hz

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2nd Semester AY 2010-2011Physics 71

National Institute of Physics

34. Ahon. By how much would the speed of a wave with frequency 500Hz be diminished if it is brought from water (where its wavelength is λ = 2.96m) to air (λ = 0.69m)?

A. 3.44 x 102 m/s D. 1.69 x 102 m/s 2 B. 7.25 x 10 m/s E. 5.56 x 102 m/s 3 C. 1.14 x 10 m/s For the next 2 numbers: A certain wave can be described by

,

=0.5

cos2

−1

−

−1

35. PS. What is the speed of propagation of the wave?

A. 0.5 m/s D. 3 m/s B. 1 m/s E. 6 m/s C. 2 m/s 36. Fastest. Which of the following points on the string would have the greatest transverse speed after 1s? [Hint: It’s a sin to speed!!!]

A. 0 m D. 3/4 m B. 1/3 m E. 1 m C. 1/2 m 37. Transfer. A force is applied to a string with mass per unit length µ to give it wave with a propagating speed v. To have a transverse wave on a new material with propagating speed 2v using the same force, the mass per unit length of the new material should be A. 2µ

D.

B. µ

E. µ/4

C. µ/2 38. Antinode. A standing wave has three antinodes. The first node (from the left) is at x=0. The third antinode (from the left) is at x = 5L/2. What is its wavelength?

A. L/2 D. 2L B. L E. 5L/2 C. 3L/2 39. Harmonic. A string fixed at both ends is set to vibrate in its 4th harmonic frequency equal to 400 Hz. What is its fundamental frequency?

A. 100 Hz D. 800 Hz B. 200 Hz E. 1600 Hz C. 400 Hz

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2nd Semester AY 2010-2011Physics 71

National Institute of Physics

40. Sitting wave. Which of the following situations will a standing wave be impossible to obtain?

A. A vibrating string with fixed ends.

B. A vibrating string with only one end fixed.

C. A vibrating string with stationary nodes.

D. Superposition of two identical waves travelling with the same speed towards each other.

E. Superposition of two identical waves propagating on the same direction.

41. Audio Book. A rope is supplied an average power P producing a wave with amplitude A, frequency f and speed v. How much power is needed to make the same rope produce a wave of amplitude 2A, frequency f and speed 0.5v?

A. 0.25P D. 2P B. 0.50P E. 4P C. P 42. Dim Sound. You are listening to an audio book 2.0 m away from the 40.W speaker in order to have just the right intensity. If the speaker’s power is changed to 10. W, how far from the speaker do you have to be in order to listen to the book at the right intensity?

A. 0.5m D. 2.0m B. 1.0m E. 2.5m C. 1.5m 43. Counting Red Cars. While resting on a lazy afternoon, you heard an annoying frequency of f0 from an approaching Volkswagen. The hunchbacked car then passed you, but you can still hear it at a frequency of 0.9 f0. If v is the speed of sound, what is the speed of the car? Assume that the car was moving at a constant speed. [Hint: f0 will cancel!]

A. 0.9 v D. v / 19 B. v / 0.9 E. v / 23 C. v / 11 44. Launch! A 700 kg satellite is launched with an initial speed of 4.00x103 m/s from the surface of the earth. What is the satellite’s speed as it reaches a height of 20.0 km from the surface of the earth?

A. 3.95 x 103 m/s D. 1.56 x 107 m/s 3 B. 4.05 x 10 m/s E. 1.64 x 107 m/s C. 1.53 x 104 m/s

A-11

2nd Semester AY 2010-2011Physics 71

National Institute of Physics

45. Superman 1.5. In order to force Clark to come out of the closet and reveal his true identity, Lois decided to jump out of the Daily Planet building while screaming at a constant frequency of 500Hz [she had opera lessons]. Clark, upon hearing the soprano voice from Lois (at t=0s), immediately changed costumes, jumped out of the building and caught Lois. Which of the following frequency (f) vs time plot could describe what Clark’s super-ear sensed?[Note: Clark is Superman, he can fly and has super-hearing ability.]

A

B

D

C

E

Physics 71 Finals: April 1, (Friday) 9:15am - 11:15 am (no joke!)

 END OF EXAM 

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