PHYSICS 221 SPRING FINAL EXAM: May 2, :30pm 6:30pm

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1 PHYSICS 221 SPRING 2011 FINAL EXAM: May 2, :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. 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 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, Soeren Prell, Kai-Ming Ho and Anatoli Frishman.

2 55) If a particle travels at a constant speed along the track shown, what is the correct ordering of the magnitudes of the acceleration at the labeled points? Let a P be the acceleration at point P, etc. A) a R < a S < a P < a Q B) a P < a Q < a R < a S C) a R = a S = a P = a Q D) a P < a Q < a S < a R E) a R < a S < a Q < a P 56) Which of the following is an accurate statement about circular motion? A) The vector sum of the tangential acceleration and the centripetal acceleration can be zero for a point on the rim of a rotating disk. B) All points on a rotating disk have the same angular velocity. C) All points on a rotating disk have the same linear speed. D) All points on a car tire have zero acceleration if the car is moving with constant linear velocity. E) All points on a rotating disk experience the same radial acceleration. 57) A long distance swimmer is able to swim through still water at 4 km/h. She wishes to cross an ocean current that runs from west to east at 3 km/h. In what direction should she swim to cross the current along a straight line from the south shore to the north shore? A) 37 o east of north B) 41 o east of north C) 37 o west of north D) 49 o west of north E) 41 o west of north

3 58) In the figure, a constant external force P = 170 N is applied to a 20 kg box, which is on a rough horizontal surface. The angle between the force and the horizontal is 30 o.the force pushes the box a distance of 8.0 m, in a time interval of 6.0 s, and the speed changes from = 0.3 m/s to = 2.5 m/s. The work done by the external force P is closest to: A) 1180 J B) 810 J C) 1060 J D) 940 J E) 680 J 59) In the system shown in the figure, a 1kg block rests on a horizontal table. The coefficient of static friction between the block and the table is µ S = 0.6. The coefficient of kinetic friction between the block and the table is µ K = 0.3. The 1kg block is attached via an ideal massless string over an ideal massless pulley to a 3kg block, which can move vertically without resistance. Initially, the 1kg block is held fixed and is released at t = 0. What is the magnitude of the acceleration of the 1kg block after it is released? A) 0 m/s 2 B) 5.9 m/s 2 C) 6.6 m/s 2 D) 23.5 m/s 2 E) 26.5 m/s 2

4 60) A 10kg weight hangs from two ideal massless strings as shown in the figure. Give the tension in the left rope. A) 33 N B) 49 N C) 85 N D) 98 N E) 113 N 61) In the following, K = kinetic energy, U = potential energy, and W = work. In using the expression K 2 + U 2 = K 1 + U 1 + W other we recognize that A) we are assuming no friction is present. B) gravitational and elastic potential energies would be included in and. C) K and U can be either positive or negative, depending on the reference point chosen. D) is always positive. E) gravitational and elastic potential energies would be included in. 62) The potential energy function of a particle moving in one dimension is U = kx 2 e x2 a 2 where a = 7.80 nm and k = 20 ev. At what value of x is a point of stable equilibrium located? A) nm B) 7.80 nm C) nm D) 6.81 nm E) 0 nm

5 63) The figure to the right shows a graph of potential energy U versus position for a particle moving in a straight line. From this curve, for the region shown, we deduce that A) there are three positions of stable equilibrium. B) this could not represent an actual physical situation, since the drawing shows the potential energy going negative, which is not physically realizable. C) for a given value of x, the particle can have a total energy that lies either above or below the value given by the curve at that point. D) the force on the particle would be greatest when the particle is near point D. E) the force on the particle would be greatest when the particle is near the origin. 64) In the figure on the right, a bullet of mass 0.01 kg moving horizontally strikes a block of wood of mass 1.5 kg which is suspended as a pendulum. The bullet lodges in the wood, and together they swing upward a distance of 0.40 m. What was the velocity of the bullet just before it struck the wooden block? The length of the string is 2 meters. A) 366 m/s B) 423 m/s C) 646 m/s D) 66.7 m/s E) 34.4 m/s

6 65) The radius of a 3.0 kg wheel is 6.0 cm. The wheel is released from rest at point A on a 30 o incline. The wheel rolls without slipping and moves 2.4 m to point B in 1.20s. The angular acceleration of the wheel is closest to: A) 56 rad/s 2 B) 82 rad/s 2 C) 65 rad/s 2 D) 73 rad/s 2 E) 48 rad/s 2 66) If both the mass of a simple pendulum and its length are doubled, the period will A) increase by a factor of 4. B) be unchanged. C) decrease by a factor of D) increase by a factor of 2. E) increase by a factor of ) In the figure on the right, which of the curves best represents the variation of wave speed as a function of tension for transverse waves on a stretched string? A) A B) B C) C D) D E) E

7 68) Two loudspeakers placed 6.0 m apart are driven in phase by an audio oscillator, whose frequency range is 1032 Hz to 1396 Hz. A point P is located 5.3 m from one loudspeaker and 3.6 m from the other. The speed of sound is 343 m/s. The frequency produced by the oscillator, for which constructive interference of sound occurs at point P is closest to: A) 1265 Hz B) 1211 Hz C) 1315 Hz D) 1366 Hz E) 1164 Hz 69) A train is approaching a signal tower at a speed of 40 m/s. The train engineer sounds the 1020 Hz whistle and a switchman in the tower responds by sounding the 1215 Hz siren. The air is still and the speed of sound is 343 m/s. The wavelength of the train whistle tone reaching the switchman is given by: A) 0.30 m B) 0.36 m C) 0.32 m D) 0.34 m E) 0.38 m 70) A 23.4-kg solid aluminum cylindrical wheel of radius 0.41 m is rotating about its axle on frictionless bearings with angular velocity ω = 32.8 rad s. If its temperature is now raised from 20.0 C to 75.0 C, what is the fractional change in (The coefficient of linear expansion of aluminum is C A) B) C) D) E) ( ) 1.)

8 71) Approximately how long should it take 11.0 kg of ice at 0 C to melt when it is placed in a carefully sealed Styrofoam ice chest of dimensions 25 cm 35 cm 55 cm whose walls are 1.5 cm thick? Assume that the heat conductivity of Styrofoam is 0.023J/ s m C A) 10h B) 12h C) 16h D) 18h E) 25h J/kg, and that the outside temperature is 32 C. ( ), latent heat of fusion of ice is 72) A sample of some material is contained in a closed, well-insulated container. Heat is added at a constant rate and the sample temperature is recorded. The resulting data is sketched in the figure. Which of the following conclusions is justified from the data given? A) The heat of fusion is greater than the heat of vaporization. B) At t = 23 minutes the sample was all liquid. C) The heat capacity of the solid phase is greater than that of the liquid phase. D) The sample never boiled. E) At t = 7 minutes the sample was a mixture of solid and liquid. 73) During an isobaric volume expansion of an ideal gas, the average kinetic energy of the gas molecules A) increases. B) does not change. C) decreases. D) may either increase or decrease, depending on whether or not the gas is monatomic. E) may or may not change, but insufficient information is given to make such a determination.

9 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 m 3 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

10 76) One and one-half moles of an ideal monatomic gas expand adiabatically, performing 7500 J of work in the process. What is the change in temperature of the gas during this expansion? A) 200K B) 200K C) 400K D) 400K E) 0 77) A Carnot engine whose high-temperature reservoir is at 620 K takes in 550 J of heat at this temperature in each cycle and gives up 335 J to the lowtemperature reservoir. What is the temperature of the low-temperature reservoir? A) 224 K B) 310 K C) 340 K D) 378 K E) 412 K 78) A force probe is constructed in such a way that the force F applied results in a potential difference V that can be read in a voltmeter. The relation between the force and the potential difference is linear. To calibrate the probe, we observe that when the probe is hanging ready to use but with nothing attached to the hook, the reading is 10 volts. When 5.0 kg are hung from the hook, the reading is 60 volts. When we hang a mass M from the hook, the reading is 120 volts. What is the value of M? A) 9.0 kg B) 10 kg C) 11 kg D) 12 kg E) 13 kg

11 79) Two scales 1 and 2 are used to measure the weight of an object. The results are shown below, with the maximum errors (the real value is within the quoted range with 100% probability). Scale 1: 50 N ± 4% Scale 2: 45 N ± E What is the minimum value of the error E in case 2 that would allow us to conclude that these measurements are consistent with one another? A) 2 N B) 3 N C) 4 N D) 5 N E) 6 N 80) In the Rotational Motion experiment, you observed the rotation of a disk about its axis. Shown below are three graphs of angular velocity versus time. In which case(s) is the disk always moving in the same direction? ω ω ω t t t Case 1 Case 2 Case 3 A) Case 1 alone. B) Case 2 alone. C) Case 3 alone. D) Cases 1 and 2. E) All of them.

12 81) A glass flask full of air sealed with a well-fitting cap is sitting in a cold-water bath. Hot water is slowly added to the bath, in small amounts and stirred well in between additions. The flask is submerged during the whole process. Air Cold water Which of the following graphs best describes the contents of the flask? p p V A V B T C T p p D V E T