PHYSICS 221 SPRING 2014

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1 PHYSICS 221 SPRING 2014 EXAM 2: April 3, :15-10:15pm 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: 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. Wireless devices 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. If for some reason you have to use a new bubble sheet 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 25, H4 06, H5 49. 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, Drs. Kai-Ming Ho, Eli Rosenberg, and Kerry Whisnant

2 28. The potential energy for a particle of mass 5.0 kg is shown in the figure. If the particle is released at point P with speed 4.0 m/s in the +x direction, what is its speed at the point where it is moving the slowest, in m/s? A) 0 B) 3.2 C) 4.0 D) 5.1 E) A baseball bat of mass 0.90 kg hits a baseball of mass 0.15 kg. The original velocity of the baseball is!27 î m/s, and after it is hit its velocity is 21 î m/s. If the average force exerted on the ball by the bat is 3000 N, for how long is the ball in contact with the bat, in ms? A) 2.4 B) 6.0 C) 10 D) 12 E) Assume a potential energy is given by the equation U = x 2 + y 2 3x + 2y + 5, where U is in J, and x and y are in m. What is the magnitude of the associated force, in N, at the point (x, y) = (3.0 m, 2.0 m)? A) 8.5 B) 5.0 C) 1.0 D) 6.2 E) 3.6

3 31. An elastic spring of (k = 22 N/m) is attached to a rigid wall at one end and to a 100 g block at the other end. The system is placed on a horizontal table and the block is pushed against the spring, compressing it by 10 cm from equilibrium. When the block is released it travels 17 cm before coming to a stop (at a point where the spring is stretched 7.0 cm from equilibrium). What is the coefficient of kinetic friction between the block and the table? A) 0.13 B) 0.21 C) 0.26 D) 0.34 E) Several forces F are applied to the two dimensional objects shown at right. All forces have equal magnitude. All the objects have the same mass, uniformly distributed. Which one of the following statements about the magnitude of the net torque about the center of mass of each system is true?? A) τ A < τ B < τ C B) τ C < τ B < τ A C) τ B < τ A < τ C D) τ B < τ C < τ A E) τ C = τ B < τ A

4 33. Consider a turntable to be a circular disk of moment of inertia I t = 0.85 kg-m 2 rotating at a constant angular velocity ω i = 3.5 rad/s around an vertical axis through the center and perpendicular to the plane of the disk. The motor of the turntable is off, so there is no external torque being applied to the axis. Another disk (a record) is dropped onto the first such that it lands coaxially (the axes coincide). The moment of inertia of the record is I r = 0.15 kg-m 2. The initial angular velocity of the second disk is zero. What is the final angular velocity of the two disks after they come to a common angular speed, in rad/s? A) 10 B) 20 C) 5.0 D) 3.0 E) A 75-kg man sits in a 40-kg, 3.5 m long boat that is floating on a lake. Initially he is at the right end of the boat, which is farthest from the dock (see diagram below). The man moves to the left end of the boat, intending to get off. How far from the dock does he end up, in m? Assume the boat floats without friction on the water. A) 1.2 B) 2.6 C) 0.0 D) 2.9 E) 2.3

5 35. A 1.0-kg block and a 2.0-kg block are pressed together on a horizontal frictionless surface with a compressed very light spring between them. They are not attached to the spring. After they are released and have both moved free of the spring, which one of the following statements is true? A) The heavier block will have more kinetic energy than the lighter block. B) Both blocks will have the same amount of kinetic energy. C) The lighter block will have more kinetic energy than the heavier block. D) Both blocks will have equal speeds. E) The magnitude of the momentum of the heavier block will be greater than the magnitude of the momentum of the lighter block. 36. A drawbridge of length L = 30 m and weight 9000 N is being held at rest by a cable attached to the right end (see diagram). The left end is attached to the wall by a frictionless pivot. What is the tension in the cable, in N? A) 4.5 x 10 3 B) 9.0 x 10 3 C) 1.5 x 10 3 D) 6.0 x 10 3 E) 3.0 x 10 3

6 37. A planet moves in a highly elliptical orbit about a star. If the angular speed of the planet is ω, the angular momentum L, and the total mechanical energy of the planet-star system E, which of the following quantities are constant as the planet orbits the star? A) only E B) L and E C) only ω D) L and ω E) only L 38. A motor has a power output of 45 kw when it rotates at an angular speed of 80 rpm. A drum of radius 1.2 m and negligible mass is attached to the motor shaft. A rope is wrapped around the drum and attached to a hanging weight. What is the weight, in N, if it is being lifted at constant speed? A) 2.8 x 10 4 B) 7.8 x 10 3 C) 4.7 x 10 2 D) 9.5 x 10 3 E) 4.5 x You are trying to move a dresser of height H = 1.6 m, mass m = 35 kg, and width L = 0.70 m. If the coefficient of kinetic friction is 0.20, what is the maximum height h, in m, that you can apply a force so that it moves at constant velocity and does not tip over? A) 0.70 B) 1.0 C) 1.2 D) 1.5 E) Any height less than H will not tip it over.

7 40. A rod of length 2.4 m and mass 7.5 kg is hinged at one end so that the rod can rotate without friction as shown. If the rod is released from rest in the horizontal position, what is its angular velocity, in rad/s, when it reaches the vertical position? ;0,1) A) 2.8 B) 2.0 C) 5.5 D) 3.5 E) A 3.0-kg mass moving with velocity 5.0 m/s in the +x direction collides elastically with a 4.0-kg mass moving with velocity 2.0 m/s in the +x direction (the first mass is overtaking the second mass). If the collision is head-on and the final velocities are both along the x direction, what is the x component of the velocity of the 3.0-kg mass after the collision, in m/s. A) 3.3 B) 5.4 C) 2.5 D) 1.6 E) 4.5

8 42. Three objects, each of mass m, are dropped from a height h. One falls straight down (left diagram below), one slides down a frictionless incline (middle diagram), and one swings down as a pendulum at the end of a massless string (right diagram). What is the relationship among their speeds when they reach the ground? A) v F > v I > v P B) v P > v I > v F C) v F = v I = v P D) v F > v P > v I E) v F = v P > v I und? h v F v I v P 43. A block of mass 3.5 kg is attached to a very light string, which is wrapped around a uniform, solid cylinder of radius 0.40 m and mass 2.0 kg. The cylinder is suspended from the ceiling by a fixed cable. When the block is released and allowed to fall, what is the tension in the string, in N? A) 17 B) 7.6 C) 34 D) 9.1 E) 54 v > v > v B. v > v > v C. v = v 44. A ball moving horizontally at a constant speed strikes a pendulum hanging on a string from the ceiling. If the ball sticks to the pendulum, what quantities are conserved for the ball-pendulum system in this collision? A) Mechanical energy B) Total angular momentum about the ceiling anchor C) Total linear momentum D) All of the above E) None of the above

9 45. A wheel (uniform cylinder) of radius 1.00 m and mass 0.50 kg is spun with a constant tangential force of 3.50 N acting at the rim (see figure). If the wheel is initially at rest, what is the angular velocity, in rad/s, after the wheel has undergone an angular displacement of 2.5 revolutions? A) 14 B) 21 C) 30 D) 47 E) Planet X s mass has been determined to be 4.8 x kg from the period of its moons. The acceleration of gravity at the surface of the Planet X is 14 m/s 2. What is the radius of the planet, in m? A) 1.5 x 10 7 B) 6.4 x 10 6 C) 2.4 x 10 7 D) 7.9 x 10 6 E) 4.3 x When you ride a bicycle in the forward direction, in what direction is the angular momentum of the wheels? A) To your right B) Forwards C) Down D) To your left E) Backwards

10 48. Skater A, who has mass 70 kg and is moving at 9.0 m/s, collides with Skater B, who has mass 60 kg and is at rest. Immediately after the collision, Skater A moves with speed 2.5 m/s at an angle of 30 o with respect to his original direction. What is the change in kinetic energy during this collision, in J? A) x 10 2 B) x 10 2 C) x 10 2 D) 0 E) x Two balls, one of mass m and the other of mass 2m, are thrown directly upward with the same velocity at the same time from ground level. Which statement about these balls is true? Assume there is no air resistance and that the gravitational potential energy is zero at ground level. A) The lighter ball will have a larger maximum height. B) At their highest point, both balls have the same gravitational potential energy. C) At its highest point, the heavier ball will have twice as much gravitational potential energy as the lighter one. D) The heavier ball will have a larger maximum height. E) The heavier ball will land sooner. 50. An 85-kg diver stands at the edge of a uniform diving board of mass 10 kg and length 4.0 m. The diving board is attached at two points A and B as shown. What is the magnitude and direction of the force at point A, in N? A) 3.5 x 10 3, up B) 1.5 x 10 3, up C) 9.2 x 10 2, up D) 2.6 x 10 3, down E) 2.1 x 10 3, down

11 The next two problems use the diagram at the right. The length L is 6.0 m and the total mass of the object is 6.0 kg. The object has uniform density. 51. What is the center of mass position of the object (x CM, y CM ), in m? A) (1.5, 2.0) B) (0.50, 2.0) C) (1.5, 3.0) D) (1.0, 2.0) E) (0.50, 3.0) 52. What is the moment of inertia of the object, in kg-m 2, for rotation about an axis through the right end and perpendicular to the plane of the paper? A) 90 B) 78 C) 42 D) 66 E) 54

12 53. A circular steel wire 2.4 m long must stretch no more than 3.6 mm if it is being used to hang a 400 kg mass at rest. What minimum radius is required for the wire, in mm? The Young s Modulus of steel is 1.8 x N/m 2. A) 2.1 B) 1.4 C) 2.7 D) 3.4 E) Four objects, each with mass M and radius R, roll without slipping down an inclined plane that makes a 30 o angle with the horizontal. Which object takes the longest time to reach the bottom? A) They all reach the bottom in the same amount of time. B) Hollow spherical shell C) Uniform, solid cylinder D) Uniform, solid sphere E) Hollow cylindrical shell

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