PHYSICS 221 SPRING 2016 FINAL EXAM: May 2, 2016 4:30pm - 6:30pm Name (printed): ______________________________________________ Recitation Instructor: _________________________ Section #_______ 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 end of the exam. Other copies of the formula sheet are not allowed. 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. Wireless devices 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. You will continue to use the same bubble sheet that you already used for the first midterm exam. Fill in questions 55-81 on the bubble sheet 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 a piece of paper to take with you and compare with the posted answers. You may use the table at the end of the exam for this. When you are finished with the exam, place all exam materials, including the bubble sheet, and the exam itself, in your folder and return the folder to your recitation instructor. No cell phone calls allowed. Turn off your cell phone (don’t just silence it) or leave it at home. Anyone using a cell phone must hand in their work; it will be considered academic dishonesty.

Best of luck,

Drs. Kai-Ming Ho, David Johnston, Joseph Shinar, and Kerry Whisnant

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55. Two carts A and B with masses mA = 5 kg and mB = 3 kg are initially at rest and compressing a massless spring. After they are released, cart A has a final speed of 3 m/s. The final speed of cart B is ___ m/s. (Ignore friction.) A) 1 B) 2 C) 3 D) 4 E) 5

56. A force pulls on two blocks as shown in the figure at the right. The coefficient of static friction between blocks A and B is µS = 0.30 and the coefficient of kinetic friction is µK = 0.20. The mass of B is 6.0 kg and the mass of A is 1.5 kg. There is no friction between block B and the surface below it.

What is the maximum the force F can be, in N, if block A does not slip on Block B? A) 18 B) 22 C) 27 D) 32 E) 36 57. Rank the magnitude of the torques about point P due to the force F for the three cases shown: A) τ 3 = τ 2 < τ1 B) τ 2 < τ 3 < τ1 C) τ1 < τ 2 = τ 3 D) τ 3 < τ 2 < τ1 E) τ1 < τ 3 < τ 2

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58. A point particle of mass m is attached to a massless string of length L. The other end of the string is attached to a fixed pivot point. The particle moves in a vertical circle under the influence of gravity. The velocity of the particle at a particular instant of time is indicated in the figure. If the speed v of the particle at θ = 90˚ is one-half of the speed v0 at θ = 0, then v0 = ____. A) gL

B) 2gL

C) 8gL / 3

D) 3gL / 2

E) 3gL 59. Which of the following situations is impossible?

A) An object has constant non-zero acceleration and changing velocity. B) An object has constant non-zero velocity and changing acceleration. C) An object has velocity directed east and acceleration directed east. D) An object has velocity directed east and acceleration directed north. E) An object has zero velocity but non-zero acceleration. 60. A uniform ladder of mass 12 kg rests against a wall as shown, making an angle θ with respect to the wall. There is no friction between the wall and the ladder, but the coefficient of static friction between the ladder and the floor is µS = 0.42 . What is the maximum angle θ such that the ladder does not slip? A) 40o B) 28o C) 57o D) 35o E) 21o

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61. A speeder goes by a police car at a constant speed of 20 m/s. Five seconds after the speeder has passed the police car, the police car starts from rest with constant acceleration in the direction of the speeder. If the police car catches the speeder after accelerating for 20 s, what was the magnitude of the acceleration of the police car, in m/s2? A) 9.8 B) 8.2 C) 6.4 D) 4.1 E) 2.5 62. A simple pendulum with a length of 1.0 m swings back and forth from a suspension point on the surface of a hypothetical Planet X. If the period of small-amplitude oscillations is 4.0 s and the radius of Planet X is 3.5 x 106 m, what is the mass of Planet X, in kg? A) 7.5 x 1022 B) 1.9 x 1023 C) 4.5 x 1023

D) 8.4 x 1023 E) 1.2 x 1024 63. Two masses are attached to the ends of a massless string and the string is stretched over a massless, frictionless pulley, as shown. There is no friction between mass 2m and the incline. What is the acceleration of mass m (on the left), in m/s2?   A) 0.48, up B) 1.2, down C) 1.6, up D) 2.1, down E) 0

!

Find!acceleration!of!m!block.!

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64. A 30-g bullet has initial velocity 300 m/s perpendicular to a board. After passing completely through the board (thickness 2.0 cm), its speed has been reduced to 184 m/s. What was the average force acting on the bullet, in N, while it was passing through the board? You may assume that the acceleration of the bullet in the board is constant. A) 9.5 x 104 B) 6.1 x 105 C) 2.3 x 105 D) 4.2 x 104

E) 8.7 x 103 65. Four equal point masses are placed at the corners of a square. Axes A, B, and C are in the plane of the paper, while axis D goes through the center of the square and is perpendicular to the plane of the paper. For which axis of rotation shown is the moment of inertia the largest? A) Axis A B) Axis B C) Axis C D) Axis D E) Both axes A and D 66. A child plays with a toy of mass 0.50 kg that hangs at the end of a vertical spring. Initially, the child pulls the toy 0.10 m below the equilibrium position. Starting from rest, the toy is released and undergoes simple harmonic motion in the vertical direction. The spring constant is k = 1.5 N/m. What is the maximum speed of the toy, in m/s? A) 0.17 B) 0.26 C) 0.14 D) 0.21 E) 0.10

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67. A uniform disk of radius R is suspended at its edge as shown above. It is free to swing back and forth in the plane of the disk. What is the frequency of small oscillations of this disk?  

A) !!!

!!!

B)   !!!

!!!!

C) !!!

!!!!

D) !!!

!!

E) !!!

!!!!

68. A siren at the top of a tall pole emits sound waves. Assume the sound wave propagates uniformly in all directions. One detects the sound intensity to be 0.23 W/m2 at 20 m away from the siren. The sound intensity detected by another listener 10 m away from the siren is ___ W/m2. A) 0.65 B) 0.46 C) 1.30 D) 0.92

E) 0.33

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69. Two identical wires of length 1.4 m and mass 30 g are each fixed at both ends. When the wires are plucked, they both vibrate at the fundamental frequency of 100 Hz. Which of the following increases in the tension of one of the wires, in N, would lead to a beat frequency of 2 Hz between the two wires?

A) 40 B) 68 C) 80 D) 24 E) 12 70. On a day when there is no wind, you are at rest and a source of sound waves is moving toward you. Compared to what you would hear if the source were not moving, the sound that you hear has A) a higher frequency and a shorter wavelength B) the same frequency and a shorter wavelength C) a higher frequency and the same wavelength D) the same frequency and the same wavelength E) a lower frequency and a longer wavelength 71. A solid object has a hole in it. Which of the illustrations more correctly shows how the size of the object and the hole change as the temperature increases?   A) Illustration #1 B) Illustration #2 C) The answer depends on the material of which the material is made D) The answer depends on how much the temperature increases E) Both C and D are correct

!

!

3!Mechanics!problem!!!!2numerical,!one!conceptual!

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72. Eight grams of ice at 0 °C are added to 36 g of hot coffee inside a thermos (thermally-isolated container) that is then tightly closed. After the system reaches equilibrium, the temperature of the mix is 20 °C. What was the initial temperature of the coffee? (The heat of fusion for water is 334 kJ/kg, and assume both water and coffee have a specific heat capacity of 4186 J/kgoC.) A) 24 °C B) 33 °C C) 42°C D) 54 °C E) 100 °C 73. Three moles of a diatomic ideal gas are initially at a temperature of 𝑇 = 25℃ and at a pressure of 𝑃 = 1.0 ∗ 10! Pa. The gas is heated through an isochoric process until its pressure is 1.07 x 105 Pa. What is the change in internal energy of the system, in J? Assume the molecules can translate and rotate, but not vibrate. A) 9.2 x 102 B) 2.5 x 103 C) 7.8 x 102 D) 3.5 x 103 E) 1.3 x 103     74. Which one of the following five statements is false? A) In a reversible adiabatic expansion of an ideal gas, the gas cools. B) The number density of an ideal gas (the number of molecules per unit volume) is proportional to the pressure of the gas divided by its absolute temperature. C) For a system undergoing a single cycle on a p-V diagram, the change in the internal energy of the system is zero. D) A diatomic molecule such as N2 has three rotational degrees of freedom. E) During an isothermal expansion of an ideal gas, the heat absorbed by the gas is equal to the work done by the gas.

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75. One mole of an ideal gas with an initial pressure of 1.0 atm is compressed adiabatically from an initial volume of 20 L to a final volume of 2.0 L. The ratio of the heat capacity at constant pressure to that at constant volume is 1.40. The final temperature of the gas is ____ K. [R = 0.0821 L atm/(mol K)] A) 720 B) 280 C) 500 D) 390 E) 610 76. Which one of the following statement is false? A) The change in internal energy of a system is equal to the amount of heat absorbed by the system minus the amount of work done by the system on its surroundings. B) It is impossible for any process to transfer heat from a cooler body to a hotter body without the input of work. C) The entropy of an isolated system may increase but never decrease.

D) The total entropy change during any reversible cycle is zero. E) The entropy of any system may increase but never decrease.

77. A Carnot engine takes in 1.5x104 J of heat at 650 K in each cycle and rejects heat at a temperature of 350 K in each cycle. The engine completes 240 cycles in 1 minute. What is the power output of the engine, in W?

A) 1.5 x 104 B) 1.9 x 104 C) 2.8 x 104

D) 3.1 x 104 E) 3.7 x 104

 

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Laboratory final exam 78. A force F is applied at an angle θ with the x axis. We measure both quantities and obtain the following values and standard uncertainties:

( )( )250 2  N

34 1

F

θ

= ±

= ± °

Determine the value of the x component of this force, along with its corresponding standard uncertainty.

( )( )( )( )( )

A.       207 1  N

B.       207 2  N

C.       207 3  N

D.       207 4  N

E.       207 5  N

±

±

±

±

±

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79. A group of engineering students need to determine the moment of inertia of the helicopter model they are designing. They decide to resort to the apparatus they remember using in the Rotational Motion experiment in their PHYS 221 class.

They mount the helicopter model on a horizontal rotating base (in such a way that it rotates about the axis they are interested in). The system is set in motion by applying a horizontal constant force F through a string wrapped around the rotating base, of known radius. By measuring the magnitude of F, the group has a measurement of τ, the torque applied on the helicopter+base system.

The rotating base is screwed onto a rotary motion sensor that measures the angle as a function of time. The appropriate computer software uses this data to calculate numerical derivatives, thus providing values for the angular acceleration.

The experiment is repeated for several different torques that result in different angular accelerations. The resulting data is shown in the graph. What is the moment of inertia of the helicopter+base system for this particular axis of rotations?

A. 0.40 g m2 B. 0.55 g m2 C. 0.60 g m2 D. 1.1 g m2 E. 1.6 g m2

Force  F  Rotary  motion  

sensor  

Rotating  base  

Table  Side  view Top  view

Force  F

Rotating  base

Sensor

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80. The image below shows the positions every 10 ms for two objects, “C” and “T”. The positions of object C are represented with circles; the positions of object T, with triangles. The initial position of each object is indicated with a black circle/triangle.

Which of the following can be inferred from this data? A. The total linear momentum of the system (C+T) is conserved.

B. The total kinetic energy of the system (C+T) is conserved. C. None of the two quantities (total linear momentum and total linear kinetic energy) are

conserved. D. The mass of C is larger than the mass of T.

E. The mass of C is smaller than the mass of T.

t  =  0

t  =  0 C

T

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81. A cart moves on a straight track. The position of the cart is tracked with a motion detector that measures how far an object is from the detector with ultrasonic pulses that bounce off a reflective plate attached to the cart. Using numerical derivatives, the software computes the velocity of the cart as a function of time.

When the track is perfectly horizontal, if the cart is given an initial push, it is observed to slow down at a uniform rate and come to a stop, so the system has a non-negligible amount of friction.

In the experiment shown in the figure below, the track is tilted so the motion detected is on the highest end. The cart is given an initial impulse at the lowest part of the track, so it moves up along the track and toward the motion detector. Before reaching the detector, the cart comes to a stop and rolls back down.

Which of the velocity versus time graphs below corresponds to the described experiment?

Motion  detector  

To  computer  

Reflective  plate  

Track  

Cart  

A B

C D

E

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        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