PHYSICS 221 SPRING 2014

FINAL EXAM: May 6, 2014 7:00pm - 9:00pm 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. 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. Bubble answers 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. Either turn off your cell phone or leave it at home. Anyone answering a cell phone must hand in their work; their exam is over.

Best of luck,

Drs. Kai-Ming Ho, Eli Rosenberg, and Kerry Whisnant

55) In the figure on the right, a diatomic ideal gas is going clockwise through a cyclic process. Which of the following statements about the work done in the process is correct?

A) It is equal to the area under the curve abc. B) It is equal to the area under the curve adc. C) It is zero. D) It is equal to the area enclosed by the curve abcda. E) It is equal to the area under the curve ab minus the area under the curve dc. 56) A 20-g bullet has an initial speed of 200 m/s. After going through a 2.5 cm-

thick wall, it’s speed is 180 m/s. What is the average force on the bullet as it passes through the wall, in kN?

A) 11 B) 30 C) 19 D) 6.4 E) 3.0 57) An ice cube at 0°C is placed inside a large metal box at 70°C. Heat is

transferred and the ice melts and the box cools until both are at 40°C. Which statement is correct?

A. The entropy of the ice increases; the entropy of the metal box decreases; the total entropy is unchanged. B. The entropy of the ice increases; the entropy of the metal box decreases; the total entropy increases. C. The entropy of the ice increases; the entropy of the metal box decreases; the total entropy decreases. D. The entropy of the ice decreases; the entropy of the metal box increases; the total entropy is unchanged. E. The entropy of the ice decreases; the entropy of the metal box is unchanged; the total entropy deceases.

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74) In the figure on the right, a diatomic ideal gas is going clockwise through a cyclic process. Which of the following is an accurate statement? A) The work done in the process is equal to the area under the curve abc. B) The work done in the process is equal to the area enclosed by the cyclic process. C) The work done in the process is equal to the area under the curve adc. D) The work done in the process is zero. E) The work done in the process is equal to the area under ab minus the area under dc. 75) A heat engine takes 9.0 moles of a diatomic ideal gas through the reversible cycle abca, on the p-V diagram, as shown. The path bc is an isothermal process. The temperature at c is 640 K, and the volumes at a and c are 0.03 m3 and 0.22 m 3, respectively. In the figure on the right, for the path ab, the heat absorbed by the gas, in kJ, is closest to: A) 145 B) !100 C) zero D) !145 E) 100

58) A 73-kg mass is hung from a massless horizontal beam. The beam is attached to a wall at the left end and supported by a cable on the right end (see diagram). The angle θ is 300 and the length of the beam is 2.0 m. If the maximum tension the cable can withstand without breaking is 1000 N, what is the maximum distance x from the wall the mass can be hung, in m, that will not break the cable?

A) 0.50 B) 2.0 C) 1.4 D) 1.1 E) 0.70 59) Two boxes are connected by a massless string and are pulled along a

frictionless horizontal surface by a horizontal force (see figure). If mA = 2.0 kg, mB = 3.0 kg, and F = 18 N, what is the tension in the string, in N?

A) 7.2 B) 18 C) 11 D) 9.0 E) 0

60) Water at +50.0 °C with a mass of 0.231 kg is placed in a freezer whose temperature is kept at –50.0 °C. The water eventually turns to ice at –50.0 °C. How much heat is absorbed by the freezer, in kJ? The specific heat of ice is 2.10 kJ/kg·°C, the specific heat of liquid water is 4.19 kJ/kg·°C, and the latent heat of fusion of water is 334 kJ/kg.

A) 750

B) 600 C) 450 D) 300 E) 150

61) A Heat Pump with a coefficient of performance 4.0 deposits 8.0 J of heat into

a room. How much heat does it remove from the outside air, in J? A) 12 B) 10 C) 8.0 D) 6.0 E) 4.0 62) A 1500-kg car moves eastward with speed 65 mph. It hits an 8000-kg truck

that is traveling at 20 mph towards the southwest. If they stick together, what is the speed of the two vehicles immediately after the collision, in mph?

A) 12 B) 16 C) 20 D) 24 E) 28

The following information is used in problems 63 and 64. The transverse displacement of wave traveling down a stretched string of mass per unit length 1.0 gm/cm is described by the function

y(x,t ) = (5.00 cm) cos[(5.00 rad/m)x + (30.0 rad/s)t ], where x is the position in m and t is the time is seconds. 63) What is the wavelength of this wave, in m?

A) 0.05 B) 1.26 C) 0.80 D) 4.80 E) 0.20 64) What is the tension on the string, in N? A) 0.0036 B) 0.020 C) 0.60 D) 3.6 E) 6.0 65) An object moves in a circular path at constant speed. Compare the directions

of the object’s velocity and acceleration vectors.

A) They are in the same direction. B) They are in the opposite direction. C) They are perpendicular. D) The acceleration vector is zero and has no direction. E) The velocity and acceleration vectors for this motion have no fixed relationship.

66) An unknown substance is in a container where the pressure is below the triple-point pressure of the substance. The temperature in the container can be varied. Which states of the substance can be observed as you vary the temperature?

A) Either gas, liquid, or solid B) Gas or liquid, but not solid C) Gas or solid, but not liquid D) Liquid or solid, but not gas E) Only gas 67) A baseball is hit with initial speed 40 m/s at an angle 300 above the

horizontal. Its initial height is 1.0 m above the ground. A 20-m high fence is 130 m away. How high up on the fence does the ball hit, in m? Neglect air resistance,

A) The baseball hits the ground before reaching the fence. B) 7.0 C) 12 D) 17 E) The baseball goes over the fence. 68) A police car siren emits sound that has frequency 2000 Hz and wavelength

0.172 m. A stationary observer measures a frequency of 1854 Hz. Relative to the observer the police car is moving

A) away from the observer at 27 m/s. B) towards from the observer at 27 m/s. C) away from the observer at 25 m/s. D) towards from the observer at 25 m/s. E) in a circle with angular velocity 5825 rad/s.

69) A bullet is fired horizontally, and at the same instant a second bullet is dropped from rest from the same height. Compare the times it takes for the two bullets to hit the ground.

A) The fired bullet hits the ground first. B) The dropped bullet hits the ground first. C) The two bullets hit the ground at the same time. D) The relative times cannot be determined without knowing the masses of the bullets. E) The relative times cannot be determined without knowing the speed of the fired bullet. The following information is used in problems 70 and 71. Eight moles of a diatomic ideal gas are compressed adiabatically from an initial pressure of 4.0 atm and an initial volume of 50.0 L to a final volume of 25.0 L. 70) What is the initial temperature of the gas, in °C? A) 3.0 B) 300 C) 2800 D) 28 E) -3.0 71) What is the final pressure of the gas, in atm? A) 2.00 B) 6.50 C) 10.6 D) 8.01 E) 1.50

72) A large pendulum consists of a massive bob suspended from the ceiling by a very light steel wire. The coefficient of linear expansion of steel is 1.2 x 10-5/K. At -400C the period of the pendulum is 5.000 s. By how much does the period of the pendulum change when it is heated to 1000C, in ms? [You can ignore the mass of the wire.]

A) 1.7

B) 4.2

C) 5.0

D) 8.4 E) 0 73) A 2.0-kg mass swings through an arc on the end of a

40-cm long massless string (see diagram). The speed of the mass is 4.0 m/s at the bottom of the arc. What is the tension in the string, in N, when the string is horizontal?

A) 41 B) 60 C) 33 D) 20 E) 10

74) A 2.5-kg particle is moving in a straight line with speed 2.0 m/s as shown, where d = 0.60 m. The angular momentum of the particle about the point O has magnitude _________ kg-m2/s and direction _______

A) 1.2, parallel to the velocity. B) 1.2, out of the page. C) 1.5, opposite to the velocity. D) 3.0, to the left. E) 3.0, into the page. 75) Two masses are attached to each other by a

long, massless string. The string runs over a massless pulley (see diagram). The coefficient of kinetic friction between m1 and the incline is 0.10 and the coefficient of static friction is 0.20. If there is no slipping of the string on the pulley, m1 = 3.0 kg, m2 = 1.0 kg, and α = 350, what is the acceleration of m2, in m/s2?

A) 0 B) 2.4, down C) 9.8, down D) 2.4, up E) 1.2, up

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51. A cylinder is rotating at an angular speed of 4.00 rad/s. If the moment of inertia of the cylinder

about its axis of rotation is 2.00 kg !m2 , the rotational kinetic energy of the cylinder is ____ J.

A. 8 B. 10 C. 12 D. 14 E. 16

52. A massless ideal cable is wound around the outside of a uniform solid

cylinder with a mass M = 20.0 kg and radius R = 0.500 m. The

cylinder rotates on a frictionless axle pointing into the page, as shown

in the figure. A force with magnitude F pulls horizontally on the

cable, as shown. If the magnitude of the angular acceleration of the

cylinder is 5.00 rad/s2, then F = ____ N.

[The moment of inertia of a uniform solid cylinder about its

continuous rotation symmetry axis is Icm

= (1 / 2)MR2 ]

A. 5 B. 10 C. 15 D. 20 E. 25

53. A particle with mass m = 0.500 kg is moving in a straight line with speed v = 6.00 m/s as shown, where the distance d shown is d = 0.667 m. The angular momentum of the particle about the point O has a magnitude of

____ kg !m2 /s and has a direction pointing ____

A. 0, the direction is not defined. B. 2, out of the page. C. 2, into the page. D. 4, upwards on the page. E. 4, downwards on the page.

76) A 0.500 kg mass on a spring is displaced 0.25 m from its equilibrium position and begins to oscillate with simple harmonic motion about equilibrium. The spring constant of the spring is k = 200 N/m. What is the speed of the mass when it passes through its equilibrium position, in m/s?

A) 0.0125 B) 5.0 C) 0.50 D) 2.5 E) 0.25

77) Three forces act on a 2.5-kg, uniform, cylindrical wheel as shown, where r = 40 cm and R = 80 cm. If the forces are F1 = 20 N, F2 = 10 N, and F3 = 25 N, through how many complete revolutions does the wheel rotate in 1.7 s if the wheel is initially at rest? A) 1.4 B) 5.7 C) 8.2 D) 2.9 E) 4.1

Laboratory  final  exam  

 78) To estimate the height of a cliff, Sam drops a stone that can be clearly heard as it hits the water at the bottom of the cliff. Using a stopwatch, he measures the time that the stone spends in the air. After several attempts, he computes the average value and standard uncertainty of his measurements:

( )2.3 0.1  st = ±

Thus, the estimated height of the cliff is:

( )( )22 21 19.81  m/s 2.3  s 26  m

2 2h gt= = =

What is the uncertainty in the height due to the uncertainty in the time?

A. ± 0.5 m B. ± 1 m C. ± 2 m D. ± 3 m E. ± 4 m

       

79) In one of this semester’s experiments, a cart was pulled on a track as shown in the figure below. The force probe was fastened to the body of the cart, and the whole system (cart + probe) was pulled through a string attached to the probe’s hook.

   In any experiment, it is very important to know exactly what each sensor measures. In this setup, which of the following is the best description of the force measured by the probe when the system is in motion? A. The net force on the cart B. The net force on the cart and probe system C. The weight of the hanging mass D. The tension in the string E. The friction between the cart and the track            

   

Cart  

Force  probe  Pulley  

Hanging  mass  

80) A motion detector like the ones we used in the labs is placed on the floor, facing up. A ball is thrown vertically up right above the detector, and its position is measured while it is in the air (trajectory shown in the figure to the right). Remember that these detectors measure the distance of the object to the detector, so the positive x axis is as shown in the figure.  

 The detector sends the position and time data to the computer, where the software uses a numerical derivative to obtain the corresponding velocity vx as a function of time. Which of the plots below is closest to the graph you will obtain for the motion of this ball?  

 

   

vx  

t  0  

A  

vx  

t  0  

B  

vx  

t  0  

C  

vx  

t  0  

D  

vx  

t  0  

E  

Motion  detector  

+x  

 81) In the setup shown in the figure to the right, the syringe is slowly pushed in while the pressure in the sample of gas is measured with a pressure sensor. The whole system is submerged in icy water, so the temperature in the gas remains constant at 273K.

 The graphs below show the volume markings in the syringe as the piston is pushed versus the pressure, and versus the inverse of the pressure. The latter is a linear graph, as expected. How many moles of gas are there in the sample? A. 0.2 moles B. 0.4 moles C. 2 moles D. 4 moles E. It cannot be determined unless

we know which gas this is.      

           

                                   

55         64         73      

56         65         74        

57           66         75      

58         67         76      

59         68         77      

60         69         78      

61         70         79      

62         71         80      

63         72         81