PHYSICS 221 SPRING 2017

FINAL EXAM: May 2, 2017; 4:30pm—6:30pm Name (printed): ______________________________________________ Recitation Instructor: _________________________ Section #_______ Student ID#_____________________ INSTRUCTIONS: This exam contains 25 multiple-choice questions plus 2 extra credit questions, each worth 4 points. Choose one answer only for each question. Choose the best answer to each question. Answer all questions. Fill in questions 55 through 81 for this exam. Allowed material: Before turning over this page, put away all materials except for pens, pencils, erasers, rulers and your calculator. There is a formula sheet attached at the front of the exam. Other copies of the formula sheet are not allowed. If you need extra scratch paper, request it from the proctor. Calculator: In general, any calculator, including calculators that perform graphing, is permitted. Electronic devices that can store large amounts of text, data or equations (like laptops, palmtops, pocket computers, PDA or e-book readers) are NOT permitted. If you are unsure whether or not your calculator is allowed for the exam, ask your TA. How to fill in the bubble sheet:

Use a number 2 pencil. Do NOT use ink. If you did not bring a pencil, ask for one. Write and fill in the bubbles corresponding to: - Your last name, middle initial, and first name - « « Your ID number (the middle 9 digits on your ISU card) « « - Special codes K to L are your recitation section. Always use two digits (e.g. 01, 09, 11, 13).

Honors sections: H1 → 02; H2 → 13; H3 → 24; H4 → 30; H5 → 42 - Fill in questions 55 through 81 for this exam

Please turn over your bubble sheet when you are not writing on it. If you need to change any entry, you must completely erase your previous entry. Also, circle your answers on this exam. Before handing in your exam, be sure that your answers on your bubble sheet are what you intend them to be. You may also copy down your answers on the table at the end of the exam and take them with you to compare with the posted answers. When you are finished with the exam, place all exam materials, including the bubble sheet, and the exam itself, and any scratch paper in your folder and return the folder to your recitation instructor. No cell phones, smart watches or other devices that can transmit data are allowed during the exam. Turn off any such device (don’t just silence it or put it into sleep mode). Anyone using such a device must hand in their work; it will be considered academic dishonesty.

Best of luck,

Drs. Mohamad Al-Saqer, Kerry Whisnant, David Johnston, and Lekha Adhikari

55. A block attached onto a spring undergoes simple harmonic motion with amplitude A = 0.25 m. If we increase amplitude to A = 0.75 m, the total energy of the system will:

A. Decrease by a factor of 9 B. Increase by a factor of 9 C. Stay the same D. Increase by a factor of 3 E. Decrease by a factor of 3 56. A massless cable is wound around a solid, uniform cylinder of mass M = 2.0 kg and radius R = 0.10 m. A force F = 0.90 N pulls on the end of the cable which unwinds from the cylinder without slipping. The magnitude of the angular acceleration of the cylinder is ____ rad/s2. A. 9.0 B. 18 C. 27 D. 36 E. 45 57. Consider a block that moves on a smooth surface with speed 25 m/s. It then enters a rough region of length 10 m. After it leaves the rough region, the speed is 24 m/s. What is the coefficient of kinetic friction 𝜇!?

A. 0.15 B. 0.20 C. 0.25 D. 0.30 E. Cannot be determined since the mass of the block is not given

Smooth Smooth

With  Kinetic  Friction 𝜇! =?

25  m/s 24  m/s

10𝑚

58. A uniform steel rod (linear expansion coefficient αS = 1.20x10-5/K) has a radius of 4.000 cm when it is at a temperature of 30.0 oC. A uniform brass ring (αB = 2.00x10-5/K) has an inner radius of 3.992 cm at a temperature of 30.0 oC. The rod and the ring are heated together. At which common temperature, in oC, does the rod just fit through the ring? A. 197 B. 93.0 C. 390 D. 200 E. 281 59. A ball bounces elastically off the floor as shown. There is no friction force on the ball by the floor during the collision. The direction of the impulse on the ball, Δp, due to the contact with the floor, is A. straight up ↑ B. straight down ↓ C. to the right → D. to the left ← E. the impulse is zero 60. Which one of the following five statements is false? A. If the net external torque on a system of particles about a given point is zero, then the

total angular momentum of the system about that point does not change with time. B. The parallel-axis theorem gives the relationship between the moments of inertia of a

body for rotations about two parallel axes, one of which passes through the center of mass of the body.

C. If a particle is moving along a straight line, its angular momentum about any point is zero.

D. If the line of action of an external force on a rigid body passes through a reference point, then the torque of the force about that point is zero.

E. In order for a rigid body to be in static equilibrium, both the net torque on the body about any point and the net external force on the body must be zero.

61. A particle is subject to the force associated with the following potential energy function. There are no other forces acting on the particle.

If the particle has kinetic energy 1 J at x = x0, at which x value will the speed be zero? A. xA B. xB C. xC D. xD E. xE 62. Some ice initially at −10oC is added to 500 g of liquid water at 50oC in a thermos with negligible mass. If the ice completely melts and the system reaches a common temperature of 30oC, find the mass of the melted ice, in g. [Specific heat capacities of liquid water and ice are 4186 J/kg K and 2100 J/kg K, respectively, and latent heat of fusion of ice is 3.34 ×105 J/kg.]

A. 118 B. 87 C. 29 D. 58 E. 100

(Ch.7%Conceptual)%A%particle%moves%in%a%region%of%space%with%the%following%potential%energy%function.%There%is%NO%dissipative%force%in%this%system.%

%

Consider%the%particle%with%kinetic%energy%1J%at%point%X.%At%which%point%will%the%speed%be%zero?%

A%B%C%D%E%

Solution:%Total%energy%is%!!"! = !" ! + 1! = !" ! %

So%at%point%E,%no%KE%thus%zero%speed.% %

!(!)

!(!)

1!J

1!J

x0 xA xB xC xD xE

63. A 4.00-kg box sits atop a 10.0-kg box on a horizontal table. There is friction between the two boxes, but no friction between the lower box and the table. A horizontal pull to the right is exerted on the lower box, as shown in the figure, and the boxes move together. What is the friction force on the UPPER box? A. 31.4 N to the right B. 31.4 N to the left C. 23.5 N to the right D. 42.9 N to the left E. 42.9 N to the right 64. Which of the following statements is FALSE? A. The internal energy of the system changes if the system absorbs heat and/or does

work on its environment. B. It is possible for any process to have as its sole result the transfer of heat from a

cooler to a hotter body without the input of work. C. It is impossible to reach absolute zero in any thermodynamic process. D. In an isolated system, any thermodynamic process causes the entropy of the system

to stay the same or increase. E. No engine can be more efficient than a Carnot engine if both engines operate

between the same two temperatures. 65. Consider the waves on a vibrating guitar string and the sound waves the guitar produces in the surrounding air. The waves on the string and the sound waves must have the same _______. A. wavelength B. speed C. frequency D. amplitude E. None of the above is true

66. A flower pot of mass M is hanging from the end of a horizontal massless rod of length L that is attached at the left to a pivot point O on a wall. The pot is supported by a massless cable at an angle θ with respect to the horizontal. The tension T in the cable is given by ____. A. Mg B. Mg sinθ C. Mg cosθ D. Mg / sinθ E. Mg / tanθ 67. Three different ideal gases, monatomic helium (He), diatomic nitrogen (N2), and monatomic argon (Ar), are heated so that the temperature of each gas increases by 30 K. The gases are held at constant volume during the process. Let Q1 be the amount of heat required to change the temperature of 5 moles of He gas. Let Q2 be the amount of heat required to change the temperature of 3 moles of N2 gas. Let Q3 be the amount of heat required to change the temperature of 3 moles of Ar gas. Which of the following relations is true?

A. Q1 = Q2 = Q3 B. Q1 = Q2 < Q3 C. Q1 < Q2 = Q3 D. Q1 = Q2 > Q3 E. Q1 > Q2 = Q3

68. Which one of the following five statements about thermodynamics is false? A. The First Law of Thermodynamics is a statement of conservation of energy. B. The entropy statement of the Second Law of Thermodynamics is that the entropy of

any system must always decrease during any thermodynamic process. C. In a thermodynamic process from an initial state to a final state of a system, the work

done by the system in general depends on the path the system takes from the initial to the final state.

D. The internal energy and the entropy of a system only depend on the variables of state and not on how the system came to be in that state.

E. The entropy of a system is a measure of the amount of disorder in the system.

69. Two objects (A and B) with masses MA = 5.0 kg and MB = 10 kg can be launched from the surface of a planet of mass M and radius R. Let vA and vB be the magnitudes of escape velocities for objects A and B, respectively, on the surface of the planet. Which of the following is true about the magnitudes of the velocities? A. vB = vA B. vB =2 vA C. vB = 2 vA D. vB =

!! vA

E. vB =!! vA

70. A sound source emits 20.0 W of acoustical power spread equally in all directions. What is the sound intensity level 30.0 m from the source, in dB? A. 92.5 B. 81.5 C. 70.3 D. 63.4 E. 55.8 71. Two moles of an ideal gas undergo an isothermal expansion at a temperature of 300 K from an initial volume of 1.00 L to a final volume of 2.73 L. The heat absorbed by the system during this process is ___ J. A. 1.00x103

B. 2.00x103

C. 3.00x103

D. 4.00x103

E. 5.00x103

72. A uniform disc of radius R = 20 cm, initially at rest (at t = 0 s), rotates about its symmetry axis with constant angular acceleration 0.50 rad/s2. What is the magnitude of the tangential velocity, in m/s, of a point on the disc’s edge after 10 seconds?

A. 1.0 B. 2.0 C. 4.0 D. 5.0 E. 10

73. A heavy stone of mass M is hung from the ceiling by a thin wire of mass m = 8.25 g that is 65.0 cm long. When you gently pluck the upper end of the wire, a pulse travels down the wire and reaches the lower end 3.92 ms later. The stone is heavy enough to prevent the lower end of the wire from moving. What is the mass M of the stone, in kg? A. 8.90 B. 23.1 C. 35.6 D. 227 E. 349 74. In a Carnot heat engine, the cold reservoir is at 27˚C and the thermal efficiency of the engine is 40.0%. The temperature of the hot reservoir is ___ ˚C. A. 293 B. 461 C. 354 D. 409 E. 227

75. Two blocks (A and B) are moving on a horizontal track without friction. Block A of mass 1.0 kg initially moving with velocity 3.0 m/s to the right (+x direction) collides with block B of mass 2.0 kg initially moving with velocity 5.0 m/s to the left (−x direction). Find the velocity of block A after the collision if the collision is elastic and one-dimensional. A. 3.0 m/s to the right B. 9.0 m/s to the left C. 5.7 m/s to the left D. 7.7 m/s to the left E. 3.0 m/s to the left

76. As you stand by the side of the road, a car approaches you at a constant speed, sounding its horn, and you hear a frequency of 80 Hz. After the car goes by, you hear a frequency of 60 Hz. What is the speed of the car, in m/s? The speed of sound in air is 343 m/s. A. 16 B. 25 C. 36 D. 49 E. 64

77. Find the moment of inertia, in kg-m2, of a thin, 3.0-kg rectangular sheet (length 40 cm, width 20 cm) rotating about an axis that is perpendicular to the plane of the sheet and that goes through one corner of the sheet. A. 0.050 B. 0.15 C. 0.20 D. 0.60 E. 0.82

Laboratory final exam    78. In a certain experiment, we want to find the velocity of a puck moving across a frictionless, horizontal table. We will measure both the speed of the puck and the angle of its trajectory with respect to one of the sides of the tables, which we take as the x axis. The results of the measurements are quoted below, along with the standard errors:

Using the equations for propagation of standard error, determine the value of the x component of the velocity, along with its corresponding standard error.

   

                           

( )( )θ

= ±

= ± °

71 3  cm/s

57 1

v

( )( )( )( )( )

±

±

±

±

±

A.       38 2  cm/s

B.       38 3  cm/s

C.       39 1  cm/s

D.       39 2  cm/s

E.       39 3  cm/s

79. A 0.50-kg puck moves at constant speed on the plane of the paper and leaves a mark on the surface with a frequency of 60 Hz. Each of these marks is a circle in the figure below. The distance between the first and last circle is 35 cm. Find the linear momentum of the puck.  

A. 1.2 kg m/s B. 1.3 kg m/s C. 1.7 kg m/s D. 2.2 kg m/s E. 2.9 kg m/s

80. A cart moves along a track. Its position is measured with an ultrasound motion detector clamped to one end of the track. The results are plotted below.

  What is the velocity of the cart, in m/s, at time t = 4.0 s?  

A. 4.0 B. 1.5 C. 1.0 D. −1.5 E. −1.0

3"

3. A"cart"moves"along"a"track."Its"position"is"measured"with"an"ultrasound"motion"detector"clamped"to"one"end"of"the"track."The"results"are"plotted"below.""

""" What"is"the"velocity"of"the"cart"at"t"="4.0"s?"4. "

A. −1.0"m/s"B. −1.5"m/s"C. 1.0"m/s"D. 1.5"m/s"E. 4.0"m/s"

""

" "

Position"(m

)"

Time"(s)

35  cm  

81. The figure below shows a horizontal rod that can rotate about the central vertical axle. Two sliding weights can be fixed at different distances r from the rotation axis.  

 In our experiment, the two weights are always in symmetric positions about the rotation axis (i.e., distance r is always the same for both sides), and we measure the total moment of inertia of the rod-and-weights system, for different values of r. The results are displayed in the graph below.

 

   

Based on this data, what is the moment of inertia of the rod by itself, in g-m2? A. 1 B. 6 C. 90 D. 150 E. 240  

   

Sliding  weight  

Axis  of  rotation  

r  

Rod  

Physics 221 Final Exam - KEY             61         71         81      

        62         72          

          63         73          

        64         74          

55         65         75          

56         66         76          

57         67         77          

58         68         78          

59         69         79          

60         70         80