PHYSICS 221, FALL 2010 FINAL EXAM MONDAY, DECEMBER 13, 2010

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1 PHYSICS 221, FALL 2010 FINAL EXAM MONDAY, DECEMBER 13, 2010 Name (printed): Nine-digit ID Number: Section Number: Recitation Instructor: INSTRUCTIONS: i. Put away all materials except for pens, pencils, erasers and your calculator. Turn off (not just silence) any electronic communication devices that you have with you. ii. Fill in your name, identification number, section number and recitation instructor above. iii This exam contains 15 multiple choice problems worth 4 points each (problems 61-75), and 15 multiple choice problems worth 2 points each (problems 76-90), for a total of 30 problems worth 90 course points. iv. In marking the multiple choice answer sheet use a number 2 pencil. Do NOT use ink. If you did not bring a pencil, ask for one. Fill in the appropriate circles completely. If you need to change any entry, you must completely erase your previous entry. v. Carefully read each problem completely and its five possible answers before beginning to work the problem. For each problem, select one answer that is closest to the correct one. vi. Please turn over or cover your answer sheet when you are not marking it. vii. Before handing in your exam, make sure that your answers on your bubble sheet are the ones you intend them to be. Copy down your answers on a piece of unused scratch paper for comparison with the answer key to be posted later. viii. When you are finished with the exam, please place all exam materials, including the answer sheet, the exam itself and scratch paper that you used for the exam, in your folder and return the folder to your recitation instructor. 1

2 Note: The unit vectors in the +x, +y, and +z directions of a right-handed Cartesian coordinate system are î, ĵ, and ˆk, respectively. In this exam, assume that the magnitude of the acceleration due to earth s gravity at the surface of the earth is g = 9.80 m/s 2. Problems 61 through 75 are worth 4 points each 61. A vector is given by A! =!(6.00 m/s)î + (3.00 m/s)ĵ! (5.00 m/s)ˆk. The unit vector that points in the direction of A! is. A. Â =!(0.72)î + (0.36)ĵ! (0.60)ˆk B. Â = (0.72)î! (0.36)ĵ + (0.60)ˆk C. Â =!(0.36 m/s)î + (0.72 m/s)ĵ! (0.30 m/s)ˆk D. Â = (0.36)î + (0.72)ĵ! (0.60)ˆk E. Â =!(0.72 m/s)î + (0.36 m/s)ĵ! (0.60 m/s)ˆk 62. A cannon ball is launched horizontally off a cliff of height h = 11.0 m above the ground with speed v 0 = 40.0 m/s as shown in the figure. The cannon ball goes a horizontal distance D = m before hitting the ground. Ignore any influence of air friction. A. 20 B. 40 C. 60 D. 80 E

3 63. A 2.00 kg wood block is sliding down an inclined plane that is at an angle of 45.0 with the horizontal. The coefficient of kinetic friction between the block and the inclined plane is The magnitude of the acceleration of the block is m/s 2. A. 8.0 B. 6.5 C. 5.0 D. 3.5 E A particle moves along the x-axis under the influence of a conservative force. The potential energy of the particle associated with this force is U(x) = (0.500 J/m)x + (0.250 J/m 2 )x 2. If the constant mechanical energy of the particle is 5.00 J, then the kinetic energy of the particle at x = 2.00 m is J. A. 2 B. 3 C. 4 D. 5 E A uniform solid sphere of mass M and radius R = m is attached to a thin massless rod tangent to its surface and is rotating at angular speed! = 4.00 rad/s about an axis through the center of the rod as shown in the figure. If the rotational kinetic energy of the sphere is 3.50 J, then the mass of the sphere is M = kg. [The moment of inertia of a uniform solid sphere about an axis through its center of mass is I cm = (2 / 5)MR 2 ] A. 2 B. 3 C. 4 D. 5 E. 6 3

4 66. A 1.00 kg particle is going around a circle of radius 2.00 m at constant speed v. If the magnitude of the angular momentum of the particle about the center of the circle is 8.00 kg! m 2 /s, then the speed of the particle is v = m/s. A. 1 B. 2 C. 3 D. 4 E A transverse traveling wave on a stretched string has the wave function y(x,t) = (1.00 cm)cos [(5.00 rad/m)x + (30.0 rad/s)t ], where t is the time is seconds. The velocity of the wave is. A. B. C. D. E.! v =!(6 m/s)î! v = (6 m/s)î! v =!(30 m/s)ĵ! v = (5 m/s)ĵ! v = (1 cm/s)ˆk 68. A pipe with length 1.00 m is in diatomic nitrogen (N 2 ) gas at a temperature of 385 K and has one end open and one end closed. The fundamental frequency of standing sound waves in the pipe is Hz. (For N 2 gas, the ratio of heat capacities is 1.40 and the molecular weight is 28.0 g/mol) A. 50 B. 100 C. 200 D. 400 E

5 69. A 50.0 g ice cube (solid water) at its melting temperature of 0.0 C is dropped into 50.0 g of liquid water at 89.7 C inside a massless insulated calorimeter. After the calorimeter reaches thermal equilibrium, the temperature inside the calorimeter is C. (The specific heat of liquid water is 4.19 J/g! C and the heat of fusion of water is 334 J/g) A. 35 B. 25 C. 15 D. 5 E A car is driving along a straight road parallel to and next to straight railroad tracks at a speed of 30.0 m/s in still air. A train is far ahead of the car and is moving in the same direction as the car at a speed of 20.0 m/s. The train emits a whistle with a frequency of 360 Hz. The frequency of the whistle heard by the driver of the car is Hz. (The speed of sound in air is 340 m/s). A. 350 B. 355 C. 360 D. 365 E A certain molecule at a given high temperature has three translational degrees of freedom, three rotational degrees of freedom, and three vibrational degrees of freedom. The molar heat capacity at constant volume of an ideal gas of these molecules at the given high temperature is J/mol K. A. 46 B. 37 C. 29 D. 21 E. 12 5

6 72. Two moles of a monatomic ideal gas undergo an expansion at a constant pressure of 2.00 atm from an initial volume of 25.0 L to a final volume of 50.0 L. The change in the internal energy of the gas is L atm. A. 75 B. 100 C. 125 D. 150 E A heat engine operates using an ideal gas as the operating fluid and follows a cycle consisting of the following four steps: (i) Isothermal expansion at T = 400 K, (ii) adiabatic expansion, (iii) isothermal compression at T = 160 K, and (iv) adiabatic compression back to the original temperature, pressure, and volume. The thermal efficiency of this heat engine in converting heat into work is %. A. 20 B. 40 C. 60 D. 80 E An ideal gas consists of diatomic molecules that can translate and rotate but not vibrate. The gas is expanded adiabatically from an initial pressure of 10.6 atm and an initial volume of 25.0 L to a final volume of 50.0 L. The final pressure of the gas is atm. A. 3 B. 4 C. 5 D. 6 E A sample of 28.2 g of liquid water is heated from 290 K to 300 K. The change in the entropy of the water is J/K. Hint: dq = mc dt and you need to do an integral. (The specific heat of liquid water is 4.19 J/g! K ) A. 1 B. 2 C. 3 D. 4 E. 5 6

7 Problems 76 through 90 are worth 2 points each 76. A disk is spinning clockwise with a particle attached to its circumference as shown. The angular speed of the disk is decreasing. The angular acceleration of the particle is pointed A. upward on the page. B. downward on the page. C. toward the right on the page. D. out of the page. E. into the page. 77. Car #1 is going along a horizontal flat straight road at a steady 60 mph. Car #2 passes Car #1 going a steady 75 mph. Which one of the following five statements is true? A. The only force acting on either car in the vertical direction is the gravitational force. B. There are no external friction forces exerted on either car. C. There are no vertical forces exerted on either car. D. The magnitude of the net force on Car #2 is larger than the magnitude of the net force on Car #1. E. The net force on each car is zero. 78. A wood block is sliding down an inclined plane that is at an angle of 30 with the horizontal. A kinetic friction force is exerted on the block by the inclined plane. Over a given time interval as the block slides down the inclined plane, which one of the following five statements is false? A. The work done by the kinetic friction force of the inclined plane on the block is positive. B. The work done by the normal force of the inclined plane on the block is zero. C. The work done by the gravitational force on the block is positive. D. The net work done on the block equals the change in the kinetic energy of the block. E. The magnitude of the acceleration of the block is less than g. 79. A uniform square plate of side-length 2L has one quarter of it cut out. The center of mass of the remaining plate shown in the figure is at position. A. 2 B. 4 C. 1 D. 3 E. 5 7

8 80. A block of mass m 1 is attached to a spring with spring constant k and is undergoing simple harmonic motion with a period T. In order to increase T to two times its original value, the block must be replaced by a block with mass m 2 =. A. 4 m 1 B. 2 m 1 C. m 1 D. m 1 / 2 E. m 1 / A transverse wave pulse on a stretched string is moving along the x-axis in the +î direction at constant speed v and with a constant shape. The wave function of the pulse at time t = 0 is A y(x,t = 0) =, where A and B are positive constants. At a later time t, the wave function is 2 B + x. A. y(x,t) = B. y(x,t) = C. y(x,t) = D. y(x,t) = E. y(x,t) = A B + x 2 + vt A B + x 2 + (vt) 2 A B + x 2! (vt) 2 A B + (x! vt) 2 A B + (x + vt) Two pipes are in air at room temperature. Pipe #1 has both ends open and has a length L 1. Pipe #2 has one end open and one end closed. In order for the fundamental frequencies of standing sound waves in the two pipes to be the same, the length of Pipe #2 would have to be L 2 =. A. L 1 /4 B. L 1 /2 C. L 1 D. 2 L 1 E. 4 L 1 8

9 83. A temperature of 238 F on the Fahrenheit temperature scale corresponds to a temperature of C on the Celsius temperature scale. A. 150 B. 175 C. 200 D. 225 E Which one of the following five statements about ideal gases is false? A. An ideal gas is defined to be a gas in which the potential energy of interaction between the gas molecules is negligible compared to the translational kinetic energy of the molecules. B. In an adiabatic process, no heat is absorbed or given off by the gas. C. The work done by an ideal gas when it expands from a given initial volume and pressure to a given final volume is larger for an isothermal expansion than for an adiabatic expansion. D. The speed of sound in an ideal monatomic gas at a given temperature is larger than the rms translational speed of the atoms in the same gas at the same temperature. E. If a gas is taken around a closed cycle on a p-v diagram in a counterclockwise direction, the net work done by the gas during the cycle is negative. 85. An ideal gas goes around one complete cycle in a clockwise direction on a p-v diagram as shown in the figure, where the initial point 1 on the cycle is the same as the final point 2. The net work done by the gas during the cycle is L atm. A. 8 B. 8 C. 12 D. 12 E A refrigerator operating in a cycle extracts 2.00 J of heat from inside the refrigerator each cycle, which takes J of work per cycle to do. The coefficient of performance of the refrigerator is. A. 4 B. 2 C. 1 D. 1 / 2 E. 1 / 4 9

10 Laboratory Final Exam: Four 2-Point Problems 87. In the Rotational Motion experiment, a brass disk was able to rotate with very little friction about its vertical axis. The disk had two hubs, small (S) and large (L), attached to it, with diameters D S = 3.0 cm and D L = 9.0 cm. A mass m was attached at one end of the string that went over a pulley. The other end of the string was wrapped around either the small hub or the large hub, as shown in the figure. When the mass was released at time t = 0, the string exerted a torque on the disk with a constant magnitude. Pulley Large hub Small hub Brass wheel The experiment was repeated for the string wound first around one hub (L or S) and then around the other. Which one of the following graphs of the angular speed ω of the brass disk versus the time t is the correct one? Weight (m) 10

11 88. A flask full of air is connected to a syringe, which together form a sealed system. The volume of the flask plus syringe system is changed by moving the piston in the syringe. The process is done slowly, so the air in the system is always in thermal equilibrium with the room at constant temperature T. The pressure inside the system in units of atm is measured for different values of the volume in the syringe in units of cm 3. Shown below is a plot of the pressure in the system versus volume of the syringe, including a fit of the data points (filled black circles) by a straight line. What can you conclude from this graph? A. The slope of the linear fit is proportional to the temperature. B. There is something wrong with the calibration of the pressure meter, because the graph should not intersect the p axis at a nonzero value. C. The intersection of the line with the pressure axis represents the pressure that the system would have at temperature T = 0 K. D. There is something wrong with the data, because the pressure should decrease as the volume of the syringe increases, rather than increase as the volume of the syringe increases. E. There is something wrong with the data, because the change in the pressure is too large. 11

12 89. In the Free Oscillations lab, you studied the vertical oscillation of a plate. The y-component of the position of the plate is measured as the height above the motion detector on the floor, which is underneath the oscillating system, as shown in the figure to the right. The positive y-axis points upwards. The y-component of the velocity versus time for a data run is plotted in the graph below. Using this information, the plate is at its lowest position (i.e., the position closest to the motion detector) at the time t =. spring plate A s B s C s D s E s motion detector 90. The measurements of the magnitude F and of the direction θ with respect to the vertical of the force! F in the figure are measured to be: F = (44 ± 1) N θ = (30 ± 5) degrees. The horizontal x-component of the force, including the error in its value, is F x =. A. (22 ± 1) N B. (22 ± 2) N C. (22 ± 3) N D. (22 ± 4) N E. (22 ± 6) N 12