PHYSICS 221 Fall 2013 EXAM 2: November 6, 2013 8:15pm 10:15pm Name (printed): Recitation Instructor: Section #: INSTRUCTIONS: This exam contains 25 multiple choice questions, plus two 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, etc., must be left in the front of the room. 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, palmtops, pocket computers, PDA or e book readers) are NOT permitted. Phones cannot be used as calculators. 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. 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. In case you have 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 are your recitation section. (Honors section: please enter 24). Always use two digits (e.g. 01, 09, 11, 13) Besides entering your answers on the bubble sheet, circle your answers on this exam! Before handing in your exam, make sure that your answers are circled in the exam and that the 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 to take with you and compare with the posted answers. When you are finished with the exam, place all exam materials, including the bubble sheet, and the exam itself, into your folder and return the folder to your recitation instructor. No cell phones allowed. Either turn off your cell phone and place it in your backpack, or leave it at home. Anyone using a cell phone in any manner must hand in their work immediately; their exam is over. 1
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28. A very light string of length = 0.50 m and a small bob of mass m = 0.50 kg have been used to construct a pendulum. The pendulum is released from rest from a position such that the string makes an angle of 40 with the vertical. What is the kinetic energy of the bob when the string makes an angle of 10 with the vertical? A. 0.54 J B. 0.57 J C. 1.1 D. 1.9 J E. 2.4 J 29. A perfect sphere rolls without slipping down an incline. Air resistance is negligible. In this process, mechanical energy is conserved because: A. There is no friction between the sphere and the incline. B. There are no net external forces on the sphere. C. There is no torque on the sphere. D. There are no non conservative forces doing work on the sphere. E. Mechanical energy is always conserved. 3
For the next two problems, consider an shaped two dimensional object made with two uniform sticks. The thickness of the sticks is much smaller than their lengths and can be neglected. 30. Find the center of mass of this object in the reference frame given in the figure to the right. A. xcm ; ycm 4 2 B. xcm ; ycm 4 3 C. xcm ; ycm 6 3 D. xcm ; ycm 12 2 E. xcm ; ycm 12 3 31. The can rotate about three axes labeled 1, 2, 3 in the figure below. Compare the moments of inertia of this object for rotations about each of these axes. A. I 1 < I 2 < I 3 B. I 2 < I 1 < I 3 C. I 3 < I 1 < I 2 D. I 1 < I 3 < I 2 E. I 3 < I 2 < I 1 4
32. The container in the figure below is made of two cylinders connected through a tube at their base. The container is partially filled with water. Massless pistons close each of the cylinders. The pistons are wellfitted (no leaks) but can move up and down with negligible friction. The area of the pistons is A 1 and A 2. The system is of course in equilibrium when the pistons are located at the same height. Now a block of mass M is placed on the piston of the larger cylinder. The system reaches equilibrium when the difference in the water levels is h. If the area of the base of the smallest cylinder and the corresponding piston had been A 2 = A 2 /2, the new difference in the water levels, h, would be: A. h = h/4 B. h = h/2 C. h = h D. h = 2h E. h = 4h 33. A 0.25 kg particle moves on the xy plane at 4.0 m/s in a straight line from point A (3, 2) m to point B (1,0) m. Find the angular momentum of this particle relative to the origin. A. 1.0 kg m 2 /s, out of the page B. 0.71 kg m 2 /s, out of the page C. 0 D. 0.71 kg m 2 /s, into the page E. 1.0 kg m 2 /s, into the page 5
34. After an elegant landing on planet X (see figure below), Spaceman Spiff decides to do a quick estimation of the mass of the planet. As he was approaching the planet, he had the chance to measure the radius of the planet, R X = 3,000 km. Now he grabs a pebble and drops it from a height of 1.0 m (Spaceman Spiff s height). The pebble takes exactly 1.0 s to reach the ground. What is the mass of planet X? A. 2.7 10 23 kg B. 8.5 10 22 kg C. 2.7 10 17 kg D. 9.0 10 16 kg E. 9.0 10 14 kg 35. Two blocks A and B slide on a horizontal table along perpendicular directions, which we can take as the +x direction for block A and +y direction for block B. Block B has twice the mass of block A. The blocks collide and stick together. After the collision, the two blocks slide together for 3.00 m in the direction 30.0 from the +x axis before they come to a stop due to friction. The coefficient of kinetic friction between any of the two blocks and the table is 0.250. What was the speed of block A right before the collision? A. 4.92 m/s B. 5.75 m/s C. 6.64 m/s D. 9.97 m/s E. 11.5 m/s 6
36. Two identical balls are thrown off of a 20 m high building, with the same initial speed. Ball A is thrown at an angle of 55 above the horizontal and ball B is thrown at 55 below the horizontal. et v A and v B be the speeds of the balls just before they hit the ground. Which of the following choices will make the statements below correct? Ignoring air resistance, v A is (larger than, smaller than, identical to) v B. Taking air resistance into account, v A is (larger than, smaller than, identical to) v B A. identical to, smaller than B. identical to, larger than C. identical to, identical to D. larger than, larger than E. smaller than, smaller than 37. A uniform disk with radius R = 30 cm and mass M = 5.0 kg rotates at 30 revolutions per minute about its symmetry axis. Due to friction, it slows down and comes to a stop after a few turns. What is the work done by friction during this process? A. 1.1 J B. 2.2 J C. 3.3 J D. 4.4 J E. 5.5 J 7
38. A mass (M = 3.00 kg) is pushed against a spring with k = 1500 N/m so that it compresses the spring some distance x from its equilibrium position. The mass is then released and slides along a track without friction. The track includes a loop the loop with radius R = 2.00 m, as shown below. What is the minimum compression of the spring x that will ensure that the mass stays on the track at the top of the loop? A. 0.156 m B. 0.198 m C. 0.346 m D. 0.443 m E. 0.624 m 39. Two masses with masses m A = 1.0 kg and m B = 2.0 kg slide without friction along the x axis. Initially, A is located at x = 0.0 m and has a velocity of +8.0 m/s, and B is located at x = 1.0 m and has a velocity of +3.0 m/s. After they collide, A has a velocity of +4.0 m/s. How much kinetic energy was lost as a result of the collision? A. 33 J B. 12 J C. 8.0 J D. 4.0 J E. 0.0 J 8
40. A mass can move along the x axis and the only force that acts on it is the one associated to the potential energy depicted in the figure below. In two separate experiments, the mass is released from rest at points A (U = 40 J) and B (U = 30 J). Consider in each case the maximum kinetic energy that the mass will achieve, KE A max and KE B max. What is the difference between these maximum kinetic energies, KE A max KE B max? A. 0.0 J B. 10 J C. 20 J D. 30 J E. 40 J 41. A planet moves around a star along the elliptical orbit shown in the figure. Compare the speed of the planet and the magnitude of its angular momentum relative to the star when the planet is at points X and Y. A. v X = v Y ; X = Y B. v X < v Y ; X = Y C. v X < v Y ; X < Y D. v X > v Y ; X > Y E. v X > v Y ; X = Y 9
42. Consider the Moon as a static mass in space. A 10 kg object is to be launched straight upward. What minimum velocity does it need to have so that it reaches a distance 2R Moon above the surface of the Moon before falling back to the Moon s surface? M Moon = 7.35 10 22 kg R Moon = 1.74 10 6 m A. 1.68 km/s B. 1.94 km/s C. 2.37 km/s D. 5.10 km/s E. 11.2 km/s 43. A 7.00 kg lamp has a 60 W light bulb in it. If left on for 15.0 minutes, this bulb uses an energy equivalent to lifting the lamp to what height above the ground? A. 7.00 m B. 13.1 m C. 15.0 m D. 60.0 m E. 786 m 10
44. Four identical steel balls are shot off of the edge of a building that is built on a flat plain. The balls have all the same initial speed but are shot at different angles with respect to the horizontal as shown in the figure. Air resistance is negligible. Which ball has the largest total mechanical at the highest point of its trajectory? A. Ball A B. Ball B C. Ball C D. Ball D E. Balls A, B, C and D all have the same total mechanical energy at their highest points. 45. A Ping Pong ball is shot straight upward with a velocity of 300 m/s. If it rises to a maximum altitude of 50.0 m above its launching point, which of the above statements is correct? A. Mechanical energy is conserved. B. The momentum of the ball is conserved. C. The angular momentum of the ball is conserved. D. The ball takes 0.167 s to reach this height. E. There was work done on the ball by a non conservative force. 11
46. A particle can move in only one dimension, along the x axis, and is subject to a force F x that depends on position as shown in the graph below. Which of the points labeled on the curve is an unstable equilibrium point? 47. A brick of mass M falls from a height h and comes to a stop on a person s head in a time t. The average force on the person s head was 1200 N. Another brick with mass 2M falls from a height 4h and is in contact with the person s head for 10t. What is the average force on the person s head in this case? A. 4800 N B. 3000 N C. 2400 N D. 1200 N E. 480 N 12
48. Two masses move on a frictionless, one dimensional air track. Mass A (m A = 2.0 kg) has initial velocity v Ax = +2.0 m/s. Mass B (m B = 4.0 kg) has initial velocity v Bx = +1.0 m/s. The figure below shows their relative positions before they undergo a perfectly elastic collision. What is the velocity of mass A after they collide? A. 0.33 m/s B. 0.0 m/s C. +0.33 m/s D. +0.67 m/s E. +1.7 m/s 49. The three objects below have the same mass and the same radius: a solid cylinder (SC), a solid sphere (SS) a thin walled hollow sphere (HS). They each spin around an axis through their center of mass, as shown in the table on your equation sheet. They all have the same rotational kinetic energy. Rank their angular speed A. SC = SS = HS B. SC > SS = HS C. SC < SS = HS D. HS > SC > SS E. HS < SC < SS 13
50. Several forces F are applied to the two dimensional objects below. All forces have equal magnitude. All the objects have the same mass, uniformly distributed. Which of the following statements about the magnitude of the net torque about the center of mass of each system is true? A. A < B < C B. A > B > C C. B < A < C D. B > A > C E. B = C < A 51. A 25 kg log of wood is a solid cylinder with a 0.60 m diameter. It is rolling without slipping on a horizontal surface and the speed of its center of mass is 2.0 m/s. What is the log s total kinetic energy? A. 150 J B. 100 J C. 75 J D. 50 J E. 25 J 14
52. An object is made up of a rod of negligible mass and length = 1.00 m, and two point masses m. The point masses are initially at the ends of the rod. The system rotates without friction on a horizontal table, about an axis through the center of the rod, with constant angular velocity I (figure 1 below.) At a certain point, due to internal forces in the rod/mass system, the masses suddenly shift to new positions that are separated by = 0.40 m (figure 2). What is the final angular velocity of the system in terms of the initial angular velocity, i? A. 6.25 i B. 4.00 i C. 1.50 i D. i E. 0.40 i 15
Extra credit 53. A 30.0 kg cube has dimensions of 0.500 m on a side. A hand holds the cube at rest completely under water at a depth of 10.0 m below the surface. When released, what is the initial acceleration of the block? The density of water is 1000 kg/m 3. A. 9.81 m/s 2 downward B. 4.90 m/s 2 downward C. 4.90 m/s 2 upward D. 31.1 m/s 2 upward E. 40.8 m/s 2 upward 54. A light string is tightly wrapped around a cylinder of mass M and radius R that can rotate without friction about a fixed axle through its center. The mass in the cylinder is not uniformly distributed, and the moment of inertia of the cylinder for rotations about this axis is: I 1 2 3 MR A block with the same mass as the cylinder (M) is attached to the free end of the string as shown in the figure. Find the acceleration of the mass when the mass is released, assuming that the string does not slip on the cylinder. A. a = 1/3 g B. a = 2/3 g C. a = 3/4 g D. a = g E. a = 2 g 16
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. 31 41 51 32 42 52 33 43 53 34 44 54 35 45 36 46 37 47 28 38 38 29 39 39 30 40 50 17
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