Physics 201, Exam 3 -- Summer 2017 Name (printed) On my honor as a Texas A&M University student, I will neither give nor receive unauthorized help on this exam. The fill-in-the-blank and multiple-choice problems carry no partial credit. Put your answer in the underlined space below each fill-in-the-blank problem. Circle the correct answer or answers for each multiple-choice problem. (An answer is approximately correct if it is correct to 2 significant figures.) Name (signed) In the work-out problems, you are graded on your well-organized work, with partial credit. (The answer by itself is not enough, and you receive credit only for your work.) Be sure to include the correct units in the answers, and give your work in the space provided. 1. (5) In the figure, cart A has mass 1 kg and is initially moving to the left. It elastically collides with cart B, which has mass 4 kg and is initially at rest. After the collision cart B is moving to the left with a speed that is 0.40 times the initial speed of cart A. Cart A will (a) continue to move to the left. (b) remain stationary (c) move back to the right. 2. (5) Four objects are allowed to roll (without slipping) down a wide inclined plane, all starting from rest at the same time: a solid cylinder, a thin-walled hollow cylinder, a solid sphere, and a thin-walled hollow sphere. Each has a mass M and a radius R. Which is the LAST to reach the bottom? Moment of inertia = 2 5 MR2 for solid sphere = 1 2 MR2 for solid cylinder = 2 3 MR2 for thin-walled hollow sphere (a) solid sphere (b) solid cylinder (c) thin-walled hollow sphere (d) thin-walled hollow cylinder (e) They all arrive at the same time. = MR 2 for thin-walled hollow cylinder 3. (5) A uniform beam is suspended horizontally, as shown in the figure. It is attached to the wall by a small hinge. The force that the hinge exerts on the beam has components (a) downward and to the left (b) downward and to the right (c) upward and to the left (d) upward and to the right 1
4. (5) Two identical merry-go-rounds are rotating at the same speed. One is crowded with children and the other is nearly empty. If both merry-go-rounds are initially moving with exactly the same speed, and they both lose rotational kinetic energy at the same rate through friction, which will take longer to stop? (a) the crowded merry-go-round (b) the empty merry-go-round (c) the same time for both Credit for photo: http://www.bluegrassplaygrounds.com/merry-go-round.html 5. (5) An omnidirectional loudspeaker produces sound waves uniformly in all directions. The total power received by a sphere of radius 3.0 m centered of the speaker is 500 W. A sphere of radius 6.0 m will receive a total power of: (answer) 6. (5) Our Foucault pendulum in the Mitchell Institute Building next door has a mass of 180 kg, and it swings with an amplitude of about 2 m. Its length is about 26 m. Calculate its period of oscillation. (Then check your answer by going next door and timing it.) (a) about 2 s (b) about 4 s (c) about 6 s (d) about 8 s (e) about 10 s (f) about 12 s (g) none of the above Texas A&M students at the Leaning Tower of Pisa (in Study Abroad Program) On the left is the cathedral of Pisa, where Galileo, as a 20 year old student watching the chandelier, and using his pulse as a clock, discovered the law of the pendulum. 2
7. (10) A diver comes off a board with arms straight up and legs straight down, giving her a moment of inertia about her rotation axis of 20 kg m 2. She then tucks into a small ball, decreasing this moment of inertia to 4 kg m 2. While tucked, she makes 3 complete revolutions in the 1.5 s from board to water. If she had not tucked at all, how many revolutions would she have made in this same 1.5 s? (Recall that you are always graded on your work in calculating the answer. The number of revolutions is not necessarily an integer, of course.) Answer: number of revolutions = 3
8. Two train whistles, A and B, each have a frequency of 500 Hz. A is stationary and B is moving away from A (toward the right) at a speed of 40 m/s. A listener is between the two whistles and is moving toward the right with a speed of 20 m/s. (a) (6) Calculate the frequency from A as heard by the listener. Answer: frequency from A as heard by the listener = (b) (6) Calculate the frequency from B as heard by the listener. Answer: frequency from B as heard by the listener = 4
9. The relevant vibrating string of a particular string instrument is 60.0 cm in length, and it has a mass of 2.00 g. The string vibrates at 440 Hz (A 4 note) when played. We will take the string to always vibrate in its fundamental mode. (a) (5) The player can change the length of the vibrating string to a different length L by placing a finger a distance L from the bridge. What should L be to change the frequency to 587 Hz (D 5 note)? Answer: For 587 Hz, length L from finger to bridge = (b) (5) Without retuning, is it possible to achieve a frequency of 392 Hz (G 4 note)? Explain. (c) (2) How can you retune to achieve different notes with the same length? 5
10. A 0.50 kg glider on an air track is attached to the end of an ideal spring with force constant 450 N/m. It undergoes simple harmonic motion with an amplitude of 0.040 m. Calculate the following: (a) (3) maximum speed of the glider Answer: maximum speed = (b) (3) speed of the glider when it at x = 0.015 m Answer: this speed = (c) (3) magnitude of maximum acceleration of glider Answer: magnitude of maximum acceleration = (d) (3) total mechanical energy of glider Answer: total mechanical energy = 6
11. A knight, who weighs 1000 N, has stopped 1/3 of the way up a ladder that is 6.0 m long. The ladder has a uniform density and a weight of 200 N, and it makes an angle of 53 o with the horizontal. The ladder-wall interface is frictionless, and everything is in static equilibrium. (a) (3) Calculate the normal force on the ladder at its base. Answer: normal force at base = (b) (3) Calculate the normal force on the ladder at its top. Answer: normal force at top = (c) (3) Calculate the friction force on the ladder at its base. Answer: friction force = (d) (3) Calculate the minimum coefficient of static friction needed to prevent slipping at the bottom. Answer: minimum coefficient of static friction = 7
12. In this problem use conservation of energy and ignore all friction. Also ignore the handle, so that the only relevant constants are the mass M of the cylinder, the radius R of the cylinder, the mass m of the bucket, the acceleration of gravity g, and the distance h that the bucket falls from the top until it hits the water level below. Let v be the velocity of the bucket and ω be the angular velocity of the cylinder as the bucket hits the water. (a) (6) In terms of the above quantities ( m, v, M, R, ω, g, h ), write down the equation expressing the fact that the total energy at the bottom, when the bucket hits the water, is equal to the total energy at the top, when the bucket is released from rest. (Recall that moment of inertia = 1 2 MR2 for solid cylinder.) (b) (6) Obtain a simple result for the velocity v of the bucket at the bottom, in terms of g, h, and the ratio M / m. 8