PHYSICS 221 SPRING EXAM 2: March 30, 2017; 8:15pm 10:15pm

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1 PHYSICS 221 SPRING 2017 EXAM 2: March 30, 2017; 8:15pm 10:15pm Name (printed): Recitation Instructor: Section # Student ID# 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. Fill in questions 28 through 54 for this exam. 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 front of the exam. Other copies of the formula sheet are not allowed. If you need extra scratch paper, request it from the proctor. 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. Write and fill in the bubbles corresponding to: - Your last name, middle initial, and first name - ««Your ID number (the middle 9 digits on your ISU card) ««- Special codes K to L are your recitation section. Always use two digits (e.g. 01, 09, 11, 13). Honors sections: H1 02; H2 13; H3 24; H4 30; H Fill in questions 28 through 54 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 the table at the end of the exam and take them with you to compare with the posted answers. When you are finished with the exam, place all exam materials, including the bubble sheet, and the exam itself, and any scratch paper in your folder and return the folder to your recitation instructor. No cell phones, smart watches or other devices that can transmit data are allowed during the exam. Turn off any such device (don t just silence it or put it into sleep mode). Anyone using such a device must hand in their work; it will be considered academic dishonesty. Best of luck, Drs. Mohamad Al-Saqer, Kerry Whisnant, David Johnston, and Lekha Adhikari

2 28. Which of the following statements is (are) true? A. Work done by a non-conservative force is path dependent. B. Work done by a conservative force is path dependent. C. A potential energy function can be defined for a non-conservative force. D. A and C E. B and C 29. A putty ball with a mass of kg is thrown at a vertical wall with a speed of 20 m/s and sticks to the wall. The time interval from the time of first contact of the putty ball with the wall to the time that the putty ball stops moving is s. The magnitude of the average force exerted by the wall on the putty ball during the collision time is N. A. 10 B. 27 C. 43 D. 59 E A 2.0-kg mass hangs from a massless rope that is wrapped around one of several pulleys, each with the same radius. In each case, the hanging mass is 3.0 m above the ground and the mass-pulley system starts at rest. The rope does not slip on the pulley and the pulley rotates without friction about its symmetric axis. For which pulley will the mass have the highest speed as it hits the ground? 2.0 kg A. A uniform ring with mass 0.5 kg 3.0 m B. A uniform disk with mass 0.5 kg C. A uniform ring with mass 1.0 kg D. A uniform disk with mass 1.0 kg E. The mass will hit the ground with the same speed in all cases described above R

3 31. A particle is subjected to the force associated with the potential energy function U(x) shown below. The total mechanical energy is denoted by the horizontal line. Assume no other forces are exerted on the particle. For which set of the labeled points is the force experienced by the particle zero? A. A, C, D B. B, E, G C. B, D, G D. C, F, G E. A, C, F 32. What is the magnitude of the gravitational force, in N, on a 1000-kg satellite that is in a circular orbit around the Earth with orbital speed 2437 m/s? A B C D E Four masses comprising a system of particles are positioned with respect to an x-y coordinate system as shown. The position of the center of mass of the system is (x cm, y cm ) =. A. (2 m, 1 m) B. (2 m, 2 m) C. (3 m, 3 m) D. (1 m, 2 m) E. (3 m, 2 m)

4 34. An ice skater spins on one skate with arms stretched out. As she begins to pull her arms in towards her body, which one of the following statements is true? A. Her angular speed increases B. Her angular speed decreases C. She gains an additional transitional motion D. The normal force supporting her body decreases E. The normal force supporting her body increases 35. A record is dropped vertically onto a turntable that is freely rotating (undriven) with angular speed 4.7 rad/s. Frictional forces act to bring the record and turntable to a common angular speed. If the moment of inertia of the record is 0.30 kg-m 2 and the moment of inertia of the turntable is 0.59 kg-m 2, how much kinetic energy, in J, is lost during this process? A. 1.3 B. 3.6 C. 2.2 D. 4.9 E A hoop of mass M and radius R is at rest at the top of an inclined plane as shown below. The hoop rolls down the plane without slipping. When the hoop reaches the bottom, its angular momentum about its center of mass is A.! MR! gh B. MR gh C. M 2gh D. Mgh E.!! Mgh

5 37. Which one of the following five statements is false? A. An elastic collision of two particles is a collision in which the kinetic energy of each of the colliding particles does not change as a result of the collision B. The center of mass velocity of a system of two colliding particles does not change as a result of the collision C. An inelastic collision is one in which the total kinetic energy of the colliding particles changes as a result of the collision D. The total momentum of two colliding particles is the same before and after the collision E. A completely inelastic collision between two particles is one in which the particles stick together after the collision 38. Two carts A and B with masses m A = 1.0 kg and m B = 3.0 kg are initially at rest compressing an ideal spring. After they are released and become separated from each other, cart B has a speed of 4.0 m/s. The final speed of cart A is m/s. A. 4.0 B. 8.0 C. 12 D. 16 E A particle is subjected to a potential energy function of the form U(x) = (5.0 J/m 5 ) x 5 + (1.0 J/m 2 ) x J, What is the magnitude of the force, in N, associated with this function at x = 0.28 m? A. 2.1 B. 1.3 C D. 1.7 E. 0.71

6 40. If a body is not rotating during some nonzero time interval, which one of the following statements would always be true over this time interval? A. The net force on the body is zero B. The net linear momentum of the body is zero C. The total kinetic energy of the body is zero D. The net torque on the body about any point is zero E. The total moment of inertia of the body about any axis is zero 41. A uniform, thin ring, of mass m = 5.0 kg and radius R = 30 cm, is attached to the right edge of a massless rod of length L = 1.0 m, as shown in the figure. The center of the ring lies on the extrapolation of the rod s length. The rod-ring system is allowed to rotate in a plane about an axis through the left edge of the rod that is perpendicular to the plane of the page. Find the moment of inertia of the system for such rotations, in kg m 2. m = 5.0 kg A. 14 B. 7.3 C. 2.3 D. 3.7 E. 8.9 axis of rotation L = 1.0 m R 42. Planet X has a mass equal to 1/2 that of Mars and a radius equal to 1/2 that of Mars, and is spherically symmetric. With g M representing the acceleration due to gravity on the surface of Mars, the acceleration due to gravity, g X, on the surface of planet X is: A. 1/2 g M B. 1/4 g M C. 2 g M D. 4 g M E. 1/6 g M

7 43. Consider a uniform solid sphere of radius R and mass M rolling without slipping. Which contribution to its kinetic energy is larger, translational or rotational? A. Its translational kinetic energy is larger than its rotational kinetic energy B. Its rotational kinetic energy is larger than its translational kinetic energy C. The two contributions to the kinetic energy are equal D. The answer depends on the radius of the sphere E. The answer depends of the speed of the sphere 44. A uniform, solid sphere of mass M = 2.0 kg and radius R = 50 cm is pulled to the right by horizontal force F = 14 N that passes through the center of the sphere as shown. The sphere, initially at rest, rolls without slipping on the horizontal floor. Find the angular speed of the sphere, in rad/s, when its center moves a distance of 2.0 m. A. 8.9 B. 17 C. 13 D. 10 E. 6.5 R F

8 45. Particle A with mass 2.0 kg and Particle B with mass 3.0 kg collide. Just before they collide, their velocities are! v A = (7.0 m/s) î (3.0 m/s) ĵ! v B = ( 3.0 m/s) î + (4.0 m/s) ĵ. Just after they collide, the center-of-mass velocity of the system is: A. (2.0 m/s) î + (2.0 m/s) ĵ B. (0.8 m/s) î (0.3 m/s) ĵ C. (0.2 m/s) î + (0.4 m/s) ĵ D. (0.4 m/s) î + (0.2 m/s) ĵ E. (1.0 m/s) î + (1.2 m/s) ĵ 46. Which one of the following statements is true? A) The acceleration of an object due to the gravitational force of the earth does not depend on the distance of that object from the surface of earth B) The center of gravity of an object always lies within the object C) The magnitude of acceleration of the Moon and the magnitude of acceleration of the Earth, due to their mutual gravitational attraction, are equal D) The escape speed from the surface of Mars is the same for objects with different mass E) The planets move in elliptical orbits with the Sun at the center of the ellipse 47. A 40.0-kg mass sits on a uniform bench of length 5.00 m and mass 10.0 kg. The mass is 1.00 m from the left support, and the bench supports are 4.00 m apart, as shown in the figure. What is the magnitude of the left support force acting on the bench, in N? A. 216 B. 278 C. 452 D. 343 E. 404

9 48. A time-dependent force in the +x direction is given by F x (t) = (5.0 N/s 2 ) t 2. This force acts on a 2.0 kg object for 3.0 s. The object is traveling in the x direction at 3.5 m/s when t = 0. What is the velocity of the object at t = 3.0 s, in m/s? A. 7.0 B. 19 C. 22 D. 25 E At some instant in time, a uniform solid cylinder is rolling without slipping up an incline with angular!!! velocity ω and angular acceleration α, and is the static friction force exerted on the cylinder by the incline. Which one of the following statements is true at that instant? A.! F f points down the incline ;! ω points out of the page;! α points out of the page B.! F f points down the incline ;! ω points out of the page;! α points into the page C.! F f points up the incline ;! ω points out of the page;! α points out of the page D.! F f points up the incline ;! ω points into the page;! α points into the page E.! F f points up the incline ;! ω points out of the page;! α points into the page 50. A 4.0-kg mass slides along a horizontal frictionless surface with speed 30 cm/s. It then pushes against a horizontal spring. If the speed of the mass is 15 cm/s after the spring has compressed 10 cm, what is the spring constant of the spring, in N/m? A. 11 B. 88 C. 27 D. 67 E. 50 F f

10 51. A box is being pulled upwards using a rope, pulley, and crank system. The pulley is a solid disk of mass M = 20 kg and radius R = 35 cm, and rotates without friction about its axle. A force of magnitude F tan = 200 N is applied to the free end of the crank, to make the pulley turn and pull the box upward, as shown in the figure. The direction of the force varies so that it is always perpendicular to the crank. The crank s mass is negligible and its length is L = 60 cm. The rope is light and does not slip on the pulley. Find the mass of the hanging box, in kg, if it is raised vertically upward with constant velocity. A. 12 B. 10 C. 117 D. 35 E. 50 F tan M R L m 52. A 5.0-kg mass is moving initially in the +x direction on a frictionless horizontal surface with speed 4.0 m/s. It collides with a 10-kg mass at rest. After the collision, the two masses move off at the angles shown in the figure. What is the speed of the 5.0-kg mass after the collision, in m/s? A. 5.6 B. 2.5 C. 4.0 D. 1.3 E. 3.2

11 53. A massless ladder that is 2.50 m long is placed against a smooth vertical wall and reaches to a height of 2.10 m, as shown in the figure. The base of the ladder rests on a rough horizontal floor; the coefficient of static friction is large enough so that the ladder does not slip on the floor. An 80.0-kg bucket of concrete is suspended from the top of the ladder, right next to the wall, as shown in the figure (i.e., assume the bucket has zero distance from the wall). What is the magnitude of the friction force that the floor exerts on the ladder, in N? A. 506 B. 738 C D. 833 E A planet of mass 4.5x10 23 kg is in an elliptical orbit (period 250 days) around a star of mass 6.0x10 30 kg. Its closest approach to the star is 7.5x10 10 m. What is the planet s farthest distance from the star, in m? A. 5.8x10 10 B. 2.6x10 11 C. 9.4x10 10 D. 1.2x10 12 E. 7.3x10 11

12 Physics 221 midterm exam 2 - KEY

13 Physics 221 midterm exam 2 - KEY 31 D 41 E 51 D 32 A 42 C 52 C 33 B 43 A 53 A 34 A 44 A 54 B 35 C 45 E 36 B 46 D 37 A 47 D 28 A 38 C 48 B 29 E 39 E 49 E 30 B 40 D 50 C

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