PHYSICS 221 Fall 2016 EXAM 2: November 02, :15pm 10:15pm. Name (printed): Recitation Instructor: Section #:

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1 PHYSICS 221 Fall 2016 EXAM 2: November 02, :15pm 10:15pm Name (printed): Recitation Instructor: Section #: INSTRUCTIONS: This exam contains 25 multiple-choice questions, plus 2 extra-credit questions, each worth 3 points. 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: 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, 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 allowed. Either turn off your cell phone or leave it at home. Anyone using a cell phone 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 QUESTIONS ARE NUMBERED 28 THROUGH Consider a particle that can move along the x axis, subject only to a conservative force. At which of the following points could the particle be in unstable equilibrium? A. At a local minimum of the potential energy versus x plot. B. At the zero crossing of the force versus x plot that has positive slope. C. At the zero crossing of the force versus x plot that has negative slope. D. At a local minimum of the force versus x plot. E. At a local maximum of the force versus x plot. 29. A massless, ideal spring with k = 600 N/m is mounted vertically. A 3.0-kg ball is placed on top of it. Let y = 0 be the position of the ball in this situation, when the spring+ball system is in its equilibrium position. The ball is then pushed downward, compressing the spring to y = 20 cm, and then released from rest, so the ball is launched straight up into the air. How high does the ball go above y = 0? A. 61 cm B. 41 cm C. 31 cm D. 21 cm E. 11 cm 2

3 The next two questions concern the figure below. A 5.00-kg mass slides along a frictionless track. It starts at rest from a height h = 2.00 m above the floor. M h R 30. Assuming that the mass remains in contact with the track at all times, what is its speed after it passes through the loop and reaches the far right end of the track? A m/s B m/s C m/s D m/s E. Cannot determine without knowing a value for R. 31. What is the largest radius R for the loop-the-loop such that the mass remains in contact with the track at all times as it moves along the track? A m B m C m D m E m 3

4 32. A 4.00-kg mass can move along the x axis and the only force acting on it is the one associated with the potential energy U that depends on x as shown in the diagram below. The mass is initially at 6.00 m and has a speed of 3.00 m/s. What is the maximum speed this mass can have? A m/s B m/s C m/s D m/s E m/s 33. An object is under the effects of the force associated with the potential energy described by the diagram below. The mechanical energy E of the object is indicated by the horizontal line in the plot. At which point(s) will this object experience a force with F x > 0? A. At all points A through H B. At none of the points A through H C. At points A and E D. At points B, D, F and H E. At points C and G 4

5 34. A 70-kg climber is sliding down a vertical rope and uses the friction between her hands and the rope to slow down the descent. When the climber is 30 m above the ground, she is dropping with a speed of 9.0 m/s. By the time she reaches the ground, the climber has a downward velocity of 15 m/s. How much work has been done by the friction between the hands and the rope? A. 21 kj B. 16 kj C. 14 kj D. 7.0 kj E. 5.0 kj 35. A 3.00-kg brick is dropped from rest from a point 10.0 m above the ground on the roof of a parked pickup truck. The roof of the pickup truck is 2.00 m above the ground. The brick comes to rest on the roof in s. What is the magnitude of the average force by the brick on the roof during this time? A. 16,800 N B. 15,000 N C. 8,400 N D N E N 5

6 36. The two masses (left mass = 5.0 kg and right mass = 2.0 kg) shown in the figure below are tied together with a massless string. The string runs over a massless and frictionless pulley. The left mass rests on a frictionless, horizontal surface. If both masses start at rest, what is the speed of the 2.0-kg mass after it has dropped by 1.0 m? A. 2.4 m/s B. 2.8 m/s C. 3.7 m/s D. 4.4 m/s E. 5.2 m/s 37. Two cars crash at an intersection. Car A, of mass M A = 2000 kg, initially headed west with a velocity of 10.0 m/s, collides with car B, of mass M B = 2500 kg, that was going south with a velocity of 12.0 m/s. After the crash, both cars stick together. How much kinetic energy was lost as a result of the collision? A kj B kj C. 136 kj D. 172 kj E. 236 kj 6

7 38. Two blocks (M 1 = 4.0 kg and M 2 = 3.0 kg) move on a frictionless, horizontal floor. Initially, block 1 moves with a velocity of 4.0 m/s to the right (+x direction) and block 2 moves with a velocity of 5.0 m/s to the left ( x direction). The blocks collide in an elastic, one-dimensional collision. Find the velocity of block 1 after the collision. A. 4.9 m/s to the right B. 4.9 m/s to the left C. 3.7 m/s to the left D. 2.0 m/s to the left E m/s to the right 39. Three horizontal forces (F 1, F 2, and F 3) are applied on a flat square plate with dimension L as shown in the figure. Let all forces have the same magnitude, and let τ i be the magnitude of the torque exerted by force F i about point O. Which of the following is true? A. τ 2 < τ 1 < τ 3 B. τ 2 < τ 1 = τ 3 C. τ 1 = τ 2 = τ 3 D. τ 1 < τ 2 < τ 3 E. τ 2 < τ 3 < τ 1 O L F 1 F 2 F 3 7

8 40. Two identical and uniform thin rods with mass M and length L are joined to make a T-shaped object as shown below. The horizontal rod lies on the x-axis with its left end at the origin and the other rod is parallel to the y-axis, with its center at the x-axis. What is the position of the center of mass of this object? A. x cm = 1/2 L, y cm = 0 B. x cm = 1/2 L, y cm = 1/2 L C. x cm = 3/4 L, y cm = 1/2 L D. x cm = 3/4 L, y cm = 0 E. x cm = 3/4 L, y cm = L y L/2 L x 41. Two uniform and identical solid spheres with mass M = 1.00 kg and radius R = 25.0 cm are connected by a uniform thin rod of length L = 1.00 m and mass m = 1.00 kg. The center of each sphere lies on the extrapolation of the rod s length and the combined system (the rod and the spheres) rotates in a horizontal plane. Find the moment of inertia of the system for rotations about the vertical axis that passes through the center of the rod. A kg m 2 B kg m 2 C kg m 2 D kg m 2 E kg m 2 M axis of rotation M 0.50 m 8

9 42. A uniform, thin, metallic disc of radius R is on the plane of this paper and rotates in the clockwise direction about its axis of symmetry. At t = 0, the disc has non-zero angular velocity ω, and it is in the process of slowing down with angular acceleration α. Which of the following is true? A. ω points out of the page; α points into the page B. ω points into the page; α points out of the page C. ω points into the page; α points into the page D. ω points out of the page; α points out of the page E. ω and α both lie in the plane of the paper and point in opposite directions. 43. Three different objects, a uniform solid cylinder, a uniform solid sphere, and a uniform hollow sphere, each of mass M and radius R, roll without slipping on a horizontal table and then up an incline. All objects start at the bottom of the incline with the same velocity of the center of mass. Which object is the highest along the incline when it stops? A. Uniform solid cylinder B. Uniform hollow sphere C. Uniform solid sphere D. They all reach the same height E. Not enough information is provided to allow for a conclusion V CM 9

10 44. Two blocks, initially sliding on a horizontal air track without friction, collide in an elastic, one-dimensional collision. Let P, KE, and V cm be the total linear momentum of the blocks, the total kinetic energy of the blocks, and the velocity of the center of mass of the blocks, respectively. Consider the following statements: 1. P is the same before and after the collision. 2. KE is the same before and after the collision. 3. V cm is the same before and after the collision. Which of the following is true? A. Only (1) is true B. Only (2) is true C. Only (1) and (2) are true D. Only (1) and (3) are true E. All three statements are true 45. A wooden stick with a mass of 160 g and a length of 1.0 m has the tip of one end on a table, while the other end (point P) is held by a hand, in such a way that the stick is initially horizontal. Suddenly, the hand lets go of the stick. What is the angular acceleration of the stick right after it is released? P A. 9.8 rad/s 2 B. 15 rad/s 2 C. 21 rad/s 2 D. 29 rad/s 2 E. 59 rad/s 2 10

11 46. The metal slab in the figure can rotate without friction about a horizontal axle that goes through a hole in the slab, as shown. A putty ball moving with velocity v hits the slab and sticks to it. Let: KE = total kinetic of the ball + slab system P = total linear momentum of the ball + slab system L = total angular momentum of the ball + slab system Which of these quantities is conserved during the collision? A. KE only B. P only C. L only D. KE and P only E. KE and L only 47. When a solid plastic sphere is placed in water (density = 1000 kg/m 3 ), it floats with 2/5 of its volume submerged. What is the density of this plastic? A. 200 kg/m 3 B. 250 kg/m 3 C. 400 kg/m 3 D. 600 kg/m 3 E. 750 kg/m 3 11

12 Mars has two moons, Phobos and Deimos. Phobos takes 7 hours and 39 minutes to go around Mars, in an orbit that can be approximated as a circle. The mass and mean radius of both Mars and Phobos are given in the table below. Mass Mean radius Mars kg 3390 km Phobos kg 11.3 km 48. What is the average distance between the center of Mars and Phobos? A km B km C km D km E km 49. What is the magnitude of the acceleration due to gravity on the surface of Mars? A. 3.7 m/s 2 B. 4.5 m/s 2 C. 5.2 m/s 2 D. 8.7 m/s 2 E. 9.8 m/s 2 12

13 50. An underwater exploration chamber is to be lowered into the water from a ship by a chain. Figures 1 and 2 below show two different positions of the chamber. Chamber Figure 1 Figure 2 Compare the tension in the chain and the pressure exerted by the water on the bottom surface of the chamber in both figures. A. T 1 < T 2 and p 1 < p 2 B. T 1 < T 2 and p 1 = p 2 C. T 1 = T 2 and p 1 < p 2 D. T 1 = T 2 and p 1 = p 2 E. T 1 > T 2 and p 1 > p Pluto s orbit is an ellipse, so its distance to the Sun is not constant. When Pluto is at the closest point to the Sun, its distance to the Sun is m. Mass of Pluto: kg Mass of the Sun: kg At that point, what is the magnitude of the torque with respect to the Sun of the gravitational force by the Sun on Pluto? A. 0 B N m C N m D N m E N m 13

14 52. At t = 0, a 2.0-kg particle with velocity v 3.0iˆ 4.0 ˆj m/s is at r ˆj momentum of this particle with respect to the origin. 2 A. L 20 k kg m /s 2 B. L 12 k kg m /s C. L 0 2 D. L 12 k kg m /s 2 E. L 20 k kg m /s ˆ ˆ ˆ ˆ 2.0 m. Find the angular Extra-credit questions 53. A solid sphere of radius R = 10 cm and mass M = 1.5 kg is released from rest at the top of an incline that makes an angle of 30 with the horizontal. The sphere rolls down without slipping along the incline. Determine the magnitude of the frictional force. A. 2.1 N B. 2.9 N C. 5.9 N D. 7.4 N E. This cannot be determined without knowing the coefficient of friction between the sphere and the incline. 14

15 54. A crate with a mass m = 30.0 kg is to be pulled using a rope, pulley, and crank system. The pulley is a solid disk of mass M = 20.0 kg and radius R = 30.0 cm and rotates about its frictionless axle. A force of magnitude F needs to be applied tangentially to the free end of the crank to make the pulley turn and raise the crate. The crank s mass is negligible and its length is L = 40.0 cm. The rope is light and it does not slip on the pulley. Find the force F required to raise the crate vertically upward with a constant acceleration of 1.00 m/s 2. A. 251 N B. 243 N C. 236 N D. 206 N E N F m L M 15

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17 You may record your answers on this page and take it with you after the exam to compare to the solutions that will be posted online

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