PHYSICS 221 SPRING 2015

FINAL EXAM: May 4, 2015 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. 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. Lekha Adhikari, Rana Biswas, Kai-Ming Ho, and Kerry Whisnant    

55. A force pulls on two blocks as shown in the figure at the right. The static coefficient of friction between blocks A and B is µS = 0.30 and the kinetic coefficient of friction is µK = 0.20. The mass of B is 7.5 kg and the mass of A is 2.5 kg. There is no friction between block B and the surface below it.

If the force F is strong enough that block A slips, what is the acceleration of block A, in m/s2? A) 2.9 B) 3.9 C) 2.0 D) 9.8 E) 4.9

56. In which of the following situations is there a nonzero net force acting on the body?

A) A box with slick, frictionless surfaces in the back of a truck as the truck accelerates forward on a level road at 9 m/s2. B) An airplane flying due north at a steady speed of 210 m/s. C) A car driving straight up a slope at a constant speed of 70 km/h. D) A hawk circling at a constant 15 km/h at a constant height above the ground. E) More than one of the above. 57. Two blocks of masses m1 = m and m2 = 4m are connected by a string and placed on a frictionless, horizontal surface. Block #1 and Block #2 are subjected to the horizontal forces of magnitude F and 3F respectively, as shown below. What is the magnitude of the force exerted on Block #2 by the string?

A) F B) 2F C) 3F/2 D) 4F/3 E) 7F/5

         

1   2   3F  F  

58. A car is travelling on a highway at a steady speed of 25 m/s (55 mph), when the driver sees a deer and slams on the brakes. The car comes to a stop after sliding 100 m. How long did it take the car to stop, in s? A) 2.0 B) 4.0 C) 6.0 D) 8.0 E) 16

59. An object is thrown from the top of a cliff with initial speed of 123 m/s at an angle of 53 degrees above the horizontal direction. The height of the cliff is 98 m above the sea. How much time does it take, in s, for the object to fall into the sea? [Ignore air resistance.]

A) 10 B) 21 C) 28 D) 16 E) 32

60. A horizontal, uniform disk of mass 6M and radius r rotates without friction about its axis of symmetry with angular velocity ω. Four weights, each with mass M, are dropped onto the edge of the disk, as shown in the figure, without introducing any external torque. What is the new angular velocity ω’ of the system? A) 6ω/5 B) ω/3 C) 3ω/5 D) ω/5 E) 3ω/7 61. A block of mass m = 4.0 kg hangs at the end of a massless rope that is wrapped around a pulley (see figure). The pulley is a uniform disc of mass M = 8.0 kg and radius R = 0.40 m that rotates without friction about an axis through its center. The rope does not slip on the pulley. Calculate the linear acceleration, in m/s2, when the mass m starts moving downward. A) 3.3 B) 9.8 C) 4.9 D) 9.0 E) 2.5

ω  

r  

ω '  

r  

Before  masses  added:   After  masses  added:  

62. If the net torque on an object is zero, then

A) the object can be both accelerating linearly and rotating about its center of mass B) it can be accelerating linearly but it cannot be rotating about its center of mass C) the object cannot be rotating about its center of mass D) the object is at rest E) the forces on it also add up to zero 63. A hoop of mass M and radius R is rest at the top of an inclined plane as shown. The hoop rolls down the plane without slipping. When the hoop reaches the bottom, its angular momentum around its center of mass is

A) MR gh

B) !!MR gh

C) MR 2gh

D) !!Mgh

E) Mgh 64. A gun with mass 450 g fires a 20-g bullet with muzzle velocity 200 m/s. The person holding the gun stops the gun after the gun recoils a distance of 3.0 cm. What was the average force required by the person to stop the gun, in N? A) 1.3x102 B) 5.9x102

C) 1.7x103

D) 5.1x103 E) 1.3x104

65. A block of mass 200 g is attached to a massless spring of force constant 3.2 N/m and set to oscillate on a horizontal, frictionless surface. The amplitude of the oscillation is 20 cm. What is the acceleration of the block, in m/s2, when the mass has a displacement of +15 cm from the equilibrium position? A) 2.4 B) 1.6 C) -1.6 D) -2.4 E) -3.2 66. The displacement of a transverse wave in a rope is described by

y(x, t) = (1.5 cm) sin[(6.0 m!1)x + (3.0 s!1)t] What is the wave velocity in the x direction, in m/s? A) −0.50 B) −1.6 C) +0.50 D) +1.6 E) +2.0 67. For sound waves, the intensity level β = 40 dB (decibels) is how many times as intense as the intensity level β = 20 dB?

A) 2 B) 20 C) 100 D) 400 E) 104

68. Which one of the following statements is false? A) If a system slowly decreases its volume while remaining at constant pressure, work is done on the gas by the surroundings. B) The internal energy of an ideal gas depends only on its temperature. C) The first law of thermodynamics is a statement of conservation of energy. D) One statement of the second law of thermodynamics is that the entropy of an isolated system can never decrease as time passes. E) The heat capacity of an ideal gas at constant pressure is smaller than the heat capacity of the same gas at constant volume. 69. The ”A” strings of two identical guitars have a mass of 10 g and length 60 cm. While tuning the guitars, a tension of 174 N was applied to the first and 170 N to the second. If the first harmonic was excited in each of the two guitar strings, a sound beat will be heard. What is the beat frequency, in Hz? A) 0.49 B) 0.98 C) 1.5 D) 2.0 E) 2.5 70. A steel bridge with 50-m long sections is built at 10oC. No expansion joints were made. On a hot summer day the temperature rises to 30oC. What is the thermal stress on each section of the bridge, in N/m2? [The coefficient of linear expansion and Young’s modulus of steel are 1.2x10-5/K and 2.0x1011 N/m2, respectively.] A) There is not enough information to determine the thermal stress B) 2.4x106 C) 2.4x109 D) 1.2x108 E) 4.8x107

71. Two separate containers filled with ideal diatomic gases are in thermal equilibrium with each other. One contains hydrogen gas and the other contains oxygen gas. Let v and K be the root-mean-square speed and the average kinetic energy of a molecule in the gas. Which of the following is true?

A) vH2 > vO2 and KH2

= KO2

B) vH2 < vO2 and KH2= KO2

C) vH2 < vO2 and KH2< KO2

D) vH2 > vO2 and KH2> KO2

E) vH2 = vO2 and KH2= KO2

72. One end of an insulated metal rod is maintained at 100 0C, and the other end is maintained at 0.00 0C by an ice-water mixture. The rod is 1.00 m long and has a cross-sectional area of 1.23 cm2. The heat conducted by the rod melts 8.50 g of ice in 10.0 min. (The insulated rod does not lose heat to the surroundings.) Find the thermal conductivity k of the metal, in W/m-K. A) 50.2 B) 109 C) 205 D) 385 E) 406 73. An ideal gas initially has 1.0 moles at 450 K. Later it has 1.2 moles at 300 K. Which of the following might describe what happened to the pressure and volume of the gas? A) Both the pressure and the volume went down by 10% B) The pressure went down by 50% and the volume went up by 60% C) The pressure went up by 20% and the volume went down by 40% D) All of the above E) None of the above

74. A chamber of volume 0.50 m3 contains diatomic nitrogen (N2) gas at a pressure of 1.0x105 Pa. The gas is allowed to expand isothermally to twice the initial volume. How much heat flows into the gas, in kJ? A) 0 B) 15 C) 35 D) 56 E) 71 75. 4.0 mol of a diatomic ideal gas goes through a thermodynamic cycle in which it absorbs 1400 J in net heat and does 2300 J of net work. What is the change in temperature of the gas, in K?

A) 45 B) -11 C) 28 D) -18 E) 18

76. A Carnot refrigerator does 240 J of work in keeping its interior at -10 °C by removing 2100 J of heat from the refrigerator and releasing it into the room. What is the temperature of the room, in °C?

A) -11 B) 0 C) 11 D) 20 E) 24 77. A glass of hot water (W) at temperature 80 °C is placed in a cold room (R) at temperature 20 °C. after some time the water has cooled to the temperature of the room. Which of the following statements represents the entropy changes:

A) ΔS(W) > 0 ; ΔS(R) < 0; ΔS(total) > 0

B) ΔS(W) < 0 ; ΔS(R) > 0; ΔS(total) > 0

C) ΔS(W) < 0 ; ΔS(R) > 0; ΔS(total) = 0

D) ΔS(W) > 0 ; ΔS(R) < 0; ΔS(total) = 0

E) ΔS(W) < 0 ; ΔS(R) > 0; ΔS(total) < 0  

   

Laboratory final exam      78. A cart moves at constant speed along a straight track. We measure both the mass of the cart and its velocity. The results are shown below, along with the uncertainty (standard error) of the measurements:

( )( )460 3  g

58 2  m/s

m

v

= ±

= ±

Determine the kinetic energy of the cart, in J, along with the corresponding standard error. !"##$$%±&

'"##$$%±(

)"##$$*±+*

,"##$$*±&*

-"##$$*±.*

         

79. A cart moves on a straight track as shown in the figure below. 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.

The system collects position data every 0.1 s. The computer software uses the data to calculate numerical derivatives, so we are provided with data for position, velocity and acceleration every 0.1 s. The graph below shows the velocity versus time data for a certain data run.  

                     Which of the following best describes the motion of the cart in this data run?

A. The cart is moving away from the motion detector and speeding up. B. The cart is moving away from the motion detector and slowing down. C. The cart is moving toward the motion detector and speeding up. D. The cart is moving toward the motion detector and slowing down. E. The cart is moving toward the motion detector at constant speed.

   

     

Motion  detector  

To  computer  

Reflective  plate  

Cart  

Track  

Table  

Force  probe  

Motion  detector  

Plate  

Spring  

80. In one of the labs, we studied the oscillations of a plate at the end of a vertical spring. As shown in the figure to the right, the spring was hung from a force probe, and the position of the plate was recorded by an ultrasonic motion detector placed on the floor, directly underneath the oscillating plate.

A plot of the force versus the position of the plate yields the following graph:  

   

                           

   

Use the graph to determine the spring constant of the spring, in N/m. A. 0.3 B. 0.8 C. 1 D. 3 E. 8  

     

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 mass of each of the sliding weights, in g? A. 50 B. 84 C. 170 D. 340 E. 250  

 

Sliding  weight  

Axis  of  rotation  

r  

Rod  

        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