PHYSICS 221 Fall 2016 FINAL EXAM: December 12, :30pm 6:30pm. Name (printed): Recitation Instructor: Section #:

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1 PHYSICS 221 Fall 2016 FINAL EXAM: December 12, :30pm 6:30pm Name (printed): Recitation Instructor: Section #: INSTRUCTIONS: This exam contains 25 multiple-choice questions, plus two extra-credit questions, each worth 4 points. The last four questions are the laboratory final. Choose one answer only for each question. Choose the best answer to each question. Answer all questions. Allowed material: Pencils, erasers, rulers and your calculator. Everything else, including bags, coats, hats/caps etc., must be left in the front of the room. Headphones or earbuds are not allowed. There is a formula sheet attached to the exam. Other copies of the formula sheet are not allowed. Calculator: Normal graphic calculators are permitted. Electronic devices that can store large amounts of text, data or equations (like laptops, tablets, or phones) are NOT permitted. If you are unsure whether or not your calculator is allowed for the exam, ask your instructor. 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. Write and fill in the bubbles corresponding to: o Your last name, middle initial and first name. o Your ID number (the middle 9 digits on your ISU card) o Special codes K to L are your recitation section. Use two digits: 01, 02, etc. Honors section: enter 34. 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. All calculations are to be done on this exam booklet. If you need extra paper, request it from the instructors, and make sure that you turn that in with the rest of the exam. When you are finished with the exam: Make sure that your answers on your bubble sheet are what you intend them to be. Make sure that your answers are circle in this exam booklet. 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. The only paper you are allowed to take with you is this table with your answers. Nothing else should be written on this answer paper. Place all exam materials, including the bubble sheet, and the exam itself, into your folder and return the folder to your instructor. No cell phones or smartwatches allowed. Leave them in your bag. Anyone using a cell phone or a smartwatch in any manner must hand in their work immediately; their exam is over. Best of luck, Drs. Canfield, Herrera, Adhikari 1

2 Note: For all problems in this exam, assume that air resistance is negligible unless stated otherwise. NOTE THAT THE QUESTIONS ARE NUMBERED 55 THROUGH A block of mass m = 5.0 kg hangs at the end of a massless spring with constant k = 3000 N/m as shown in the figure. When the block is in equilibrium, the block is at position A. The block is then pulled down 4.0 cm, to position B, and released from rest. How much work is done by the spring as the block moves up from B to A? A. 0 J B J C J D. 2.0 J E. 2.4 J A B 56. Consider an L-shaped object made from two identical and uniform meter-sticks. This object can rotate about 3 different axes of rotation, as shown in the figure: Axis 1 runs along the vertical side of the L. Axis 2 is parallel to the vertical side of the L and intersects the middle of the horizontal side. Axis 3 is parallel to the vertical side of the L and intersects the right end of the horizontal side. Rank the moments of inertia of this object for rotations about these axes. A. I 1 = I 2 = I 3 B. I 1 = I 2 > I 3 C. I 1 = I 2 < I 3 D. I 1 < I 2 < I 3 E. I 1 > I 2 > I 3 Axis 1 Axis 2 Axis 3 2

3 57. Two blocks with masses 3m and 4m are connected by a massless, ideal string as shown below. The pulley is massless and rotates without friction about its axle. The incline is frictionless. The system is released from rest from the positions shown below. Let T be the tension in the string, and let N be the normal force by the inclined on the 3m block. Which of the following statements is correct? A. T 4 mg and N 3mg B. T 4 mg and N 3mg C. T 4 mg and N 3mg D. T 4 mg and N 3mg E. T 4 mg and N 3mg 58. A ball moving with velocity hits a rock, and bounces off with velocity v 2. The figure below shows the velocity vectors and directions to scale. v 1 Ball Before After Which of the vectors below best describes the direction of the impulse exerted by the rock on the ball during this collision? A B C D E 3

4 59. The plot below shows the net force on a 2.00-kg object moving in one dimension along the x direction. If the object has v x = 2.00 m/s at x = 0.00, what is its velocity when it passes x = 6.00 m? A m/s B m/s C m/s D m/s E m/s F x(n) x(m) 60. A playground merry-go-round can be treated as a uniform disk that rotates about its fixed axis. A child is on the edge of the merry-go-round. The system is initially at rest. The child then jumps off the merry-go-round with speed v, and the merry-go-round starts rotating with angular speed ω. Let: P : total linear momentum of the merry-go-round + child system KE : total kinetic energy of the merry-go-round + child system L : total angular momentum of the merry-go-round + child system Which of these quantities is/are conserved throughout the jump? A. P only B. KE only C. L only D. P and KE E. P, KE and L 4

5 61. The four masses shown below are linked by massless, ideal wires and are being pulled to the right by a constant horizontal force of F = 150 N. Which mass experiences the largest acceleration? A. 10 kg B. 20 kg C. 50 kg D. 70 kg E. All masses experience the same acceleration. 62. At t = 0 s, a block is at the origin and has a velocity v x = 2.0 m/s i. The acceleration of the block is shown in the plot below. What is the position x of the block at t = 8.0 s? A. 6 m B. 12 m C. 24 m D. 30 m E. 48 m a x (m/s 2 ) 4.0 t (s)

6 63. A block of mass m = 1.0 kg hangs from a massless rope from a selection of pulleys, each with identical radius R: Pulley A: A uniform disk of mass 1.0 kg Pulley B: A uniform ring of mass 1.0 kg Pulley C: A uniform disk of mass 2.0 kg Pulley D: A uniform ring of mass 2.0 kg R M In all cases, the system starts at rest with the block 2.0 m above the ground, and then the system is released so the block drops to the ground. The rope does not slip on the pulley. For which pulley will the block have the largest velocity as it hits the ground? A. Pulley A B. Pulley B C. Pulley C D. Pulley D E. The velocity of the block is the same with all pulleys. 2.0 m m 64. A 10.0-kg rock is on the surface of planet 1 with mass M 1. The velocity needed to launch this rock radially away from the center of the planet so that it never falls back to the planet is called the escape velocity. On planet 1, the escape velocity is v 1. Planet 2 has the same diameter as planet 1 but three times the mass, M 2 = 3M 1. What is the escape velocity for a 30.0-kg rock on planet 2? A. B. C. v1 3 v v D. 3 v E. 3v 1 1 6

7 65. A 25.0-g pebble is at rest until it is struck by a golf club. The club is in contact with the pebble for 5.00 ms. After the blow, the pebble has a speed of 20.0 m/s. What was the average force experienced by the pebble during its contact with the club? A N B N C. 100 N D. 143 N E N 66. A certain transverse wave that propagates along the x axis is described by the two separate graphs shown in the figure below: displacement y versus time t, and displacement y versus position x. Based on these two graphs, what is the speed of the wave propagation? A. 20 m/s B. 10 m/s C. 5.0 m/s D. 2.0 m/s E. 0.8 m/s y (cm) t (ms) y (cm) x (cm) 7

8 67. The intensity of a 70-decibel sound is times the intensity of a 40-decibel sound. A B. 30 C. 1,000 D. 3,000 E. 9, A 3.00-m long wire is fixed at both ends. The wire has a linear mass density = 50.0 g/m and is under a tension of 5.00 N. What is the wire s fundamental frequency? A Hz B Hz C Hz D Hz E Hz 69. A window is made out of glass. The glass is 3.0 m high, 2.0 m wide, and 4.0 mm thick. The temperatures at the inner and the outer surface of the glass are 25C and 25C, respectively. How much energy is lost each hour through the window? A J B J C J D J E J 8

9 70. A uniform, square sheet with side L = 16.0 cm is made out of copper. The copper sheet has a centered circular hole of radius R = 4.00 cm, as shown in the figure below. The copper sheet is initially at 300K. It is then heated to a temperature of 500 K. What is the new area of the circular hole at a temperature of 500 K? L = 16.0 cm A cm 2 B cm 2 C cm 2 D cm 2 E cm 2 O R 71. Two separate containers filled with ideal monoatomic gases are in thermal equilibrium with each other. One contains helium gas and the other contains neon gas. The molar mass of He is 4.00 g/mole and the molar mass of Ne is 20.2 g/mole. Let v He and v Ne be the root-mean-square speeds of a helium atom and a neon atom, respectively. What is the ratio v He / v Ne? A B C D E

10 72. A 10-mole sample of an ideal monoatomic gas has 3 possible thermodynamic states indicated by A, B, and C in the pressure (P) versus volume (V) graph below. Let U A, U B, and U C be the internal energy of the gas sample at states A, B, and C, respectively. Which of the following relations is true? A. U A < U B <U C B. U A > U C > U B C. U A = U B = U C D. U A = U B < U C E. U A > U C = U B P B A C V 73. A 2.0-kg sample of solid nitrogen at 210C melts and becomes liquid nitrogen at 210C. What is the change of entropy of the nitrogen as a result of this process? A. 0.0 J/K B. 240 J/K C. 400 J/K D. 810 J/K E J/K 10

11 74. Initially, a thermally insulated container contains 3.0 m 3 of an ideal diatomic gas at a pressure of 1.0 atm. The gas is suddenly compressed adiabatically to a final volume of 1.0 m 3. What is the final pressure of the gas? 5 7 For a diatomic gas, CV R, Cp R 2 2 A. 6.2 atm B. 4.7 atm C. 3.0 atm D. 1.0 atm E atm 75. A Carnot engine operates between two reservoirs at temperatures T C and T H, respectively. The efficiency of the Carnot engine is 25%. If we used this engine as a refrigerator operating between the same two reservoirs, how much work would be required to remove 1200 J of heat from the cold reservoir? A. 300 J B. 400 J C. 600 J D J E J 11

12 Extra credit questions 76. A 100-kg person, standing on the floor of a room, applies an upward force on a 20-kg mass that is initially on the floor. During this time, the normal force by the floor on the person is 1100 N. Which of the following best describes what is happening to the 20-kg mass while the person is pulling? For this problem, take the gravitational acceleration near the surface of earth to be 10.0 m/s 2. A. The mass remains on the floor. B. The mass moves upward with a constant velocity of 5 m/s. C. The mass accelerates upward with an acceleration of 110 m/s 2. D. The mass accelerates upward with an acceleration of 10 m/s 2. E. The mass accelerates upward with an acceleration of 5 m/s Initially, a thermally insulated container of negligible mass has 500 g of liquid water at a temperature of 50.0C. Then, 100 g of ice at a temperature of 10.0C are added to the water in the container. What is the final temperature of the mixture after it reaches thermal equilibrium? A. 27.5C B. 30.1C C. 33.6C D. 40.8C E. 50.0C 12

13 Laboratory final exam Note that there is a data analysis formula sheet at the end of the regular formula sheet 78. A force F is applied at an angle with the x axis. We measure both quantities and obtain the following values and standard uncertainties: F N 48 1 Determine the value of the x component of this force, along with its corresponding standard uncertainty. A N B N C N D N E N 13

14 79. In one of the labs, a microphone was used to capture the sound produced when we pluck a steel wire under tension. The signal was then fed onto an oscilloscope. The image to the right shows a screenshot of one of the oscilloscope displays obtained in the experiment. The horizontal scale is shown in the figure. What is the fundamental frequency of this wave? A. 100 Hz B. 200 Hz C. 300 Hz D. 400 Hz E. 500 Hz 2 ms 14

15 80. A group of engineering students needs 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, 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 g m 2 B g m 2 C g m 2 D. 1.1 g m 2 E. 1.6 g m 2 15

16 81. A cart moves on a straight track. The position of the cart is tracked with a motion detector that measures how far the cart 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. Motion detector Reflective plate To computer Cart Track Which of the graphs in the next page corresponds to the described experiment? 16

17 A B C D E 17