PHYSICS 221 Fall 2007 EXAM 2: November 14, :00pm 10:00pm

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1 PHYSICS 221 Fall 2007 EXAM 2: November 14, :00pm 10:00pm 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. 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. (Honors section, please enter 24). Always use two digits (e.g. 01, 09, 11, 13) 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, Paul Canfield and Paula Herrera

2 28. Which of the following changes to an oscillating system will cause the smallest change in the system s period? A) For a spring / mass system, double the mass. B) For a spring / mass system, double the spring constant. C) For a simple pendulum (point mass on a string), double the length of the string. D) For a simple pendulum (point mass on a string), double the mass. E) All of the above changes affect the period in the same manner. 29. An insulating rod with charge Q is placed at distance d from an uncharged metal surface. The electrostatic force between the rods is: A) Zero. B) Attractive if Q > 0, repulsive if Q < 0. C) Attractive if Q < 0, repulsive if Q > 0. D) Attractive, independently of the sign of Q. E) Repulsive, independently of the sign of Q.

3 30. Four forces of equal magnitude F and different directions are applied at different points on a rod of length L as shown below. All the forces are in the plane of this page. What is the magnitude of the net torque about point P? A) 0.13FL B) 0.50FL C) 0.63FL D) FL E) 1.2FL P F 30 F F F L/2 L/2 31. An insulating, rod is balanced at its center of mass and is allowed to rotate in the horizontal plane, that we shall take as the xy plane. It has a positive charge on one end of the rod and an equally sized, negative charge on the other end of the rod. Taking the pivot as the origin, the positive end is located at (x, y) = (0, 1) and the negative end is located at (0, 1). For which direction will an applied field, of magnitude 1000 N/C, result in the largest potential energy of the system? A) Along the x axis, pointing in the positive direction B) Along the x axis, pointing in the negative direction C) Along the y axis, pointing in the positive direction D) Along the y axis, pointing in the negative direction E) Along the direction of the vector that runs from the origin to the (1,1) point.

4 32. Two particles of masses m and 2m move toward one another with speeds v and 2v, respectively, and collide. After the collision, they come out at a 45 angle as shown in the figure. v 2 m v 45 2v 2m v 1 What is the speed of the center of mass of the system after the collision? A) 5 3 v 2 B) 3 2 v C) v D) 3v E) 2v

5 33. Two charges +q and 3q are placed on the x-axis as shown. L (left), M (middle) and R (right) refer to the points along the x axis that are to the left of q, between the two charges, and to the right of 3q, respectively. q 3q L M R x The net electric field is of course zero at infinity, but there might be other points along the x axis where the net electric field is zero, too. In which region(s)? A) In region L B) In region R C) In regions L and R (there are two points where E = 0) D) In region M E) The net electric field is never zero on the x axis (except at ± ) 34. A point charge Q is at the center of a spherical metal shell of radii R and 2R. The shell has a net charge 3Q. The charge on the inner surface of the shell is: A) 2Q B) Q C) 0 D) Q E) 2Q

6 35. Pluto is a sphere of mass kg and radius km. If a 0.5-kg rock is released from a height of 10 m above the surface of Pluto, how long will the rock take to hit the ground? A) 1.4 s B) 2.2 s C) 4.2 s D) 5.5 s E) 6.7 s 36. A proposed low-budget carnival ride consists of a cabin hung from a vertical spring that shakes the passengers in the cabin with harmonic oscillations (see figure). The combined mass of the cabins and the passengers is 1000 kg, and the spring constant is 6000 N/m. For safety reasons, the acceleration of the passengers should never exceed 3g (g = 9.81 m/s 2 ). What is the maximum amplitude of the oscillations? A) 1.6 m B) 3.3 m C) 4.9 m D) 6.5 m E) 8.0 m

7 37. A non-uniform rod of mass 2.0 kg and length 2.0 m can rotate freely about an axis through a point P that is 1.0 m away from the center of mass of the rod. The rod is released from the horizontal position. When the rod is vertical, the angular speed of the rod is 3.0 rad/s. What is the moment of inertia of the rod about point P? A) 0.67 kg m 2 B) 2.2 kg m 2 C) 2.7 kg m 2 D) 3.6 kg m 2 E) 4.4 kg m 2 P CM CM 38. A cylinder is released from the top of an incline and rolls down without slipping. Which of the following statements about the friction force between the cylinder and the incline is true? A) There is no friction. B) The friction is kinetic and points up along the incline. C) The friction is kinetic and points down along the incline. D) The friction is static and points up along the incline. E) The friction is static and points down along the incline.

8 39. Consider the orbits of the planets in the solar system. Which of the following quantities is NOT constant throughout the orbit? A) Mechanical energy B) Angular speed C) Angular momentum about the sun. D) None of the quantities above are constant. E) All the quantities above are constant. 40. A 50 g bead is in equilibrium at the end of a spring with k = 2.5 N/m. At t = 0, the bead is pulled 0.30 m and released. A damping force F = bv acts on the bead, and the amplitude of the motion decreases to 0.10 m in 5.0 s. Find the magnitude of the damping constant b. A) kg/s B) 0.45 kg/s C) 1.7 kg/s D) 8.2 kg/s E) 38 kg/s

9 41. A point charge Q > 0 is at the center of three concentric spheres of radii r 1 = R, r 2 = 2R and r 3 = 4R. There are not other charges nearby. What is the relation between the electric fluxes through these spheres? (Φ i is the flux through the i th sphere). A) Φ 1 = 2Φ 2 = 4Φ 3 B) Φ 1 = 4Φ 2 = 16Φ 3 C) 16Φ 1 = 4Φ 2 = Φ 3 D) 4Φ 1 = 2Φ 2 = Φ 3 E) None of the above. 42. A uniform rod of mass m and length L has two small spheres of mass m attached to the ends. The system rotates with initial speed ω 0 in the horizontal plane, about the center of the rod. Suddenly, both spheres detach and drop from the rod. What is the angular speed of the rod right after the spheres drop? A) ω 0 /7 B) 2ω 0 /5 C) ω 0 D) 5ω 0 /2 E) 7ω 0

10 43. The figure below is made of eight uniform squares of side a. Find the x component of the center of mass. y x A) B) C) D) E) a 4 a 3 a 2 2a 3 3a 4

11 44. Below, the momentum vectors of two objects are shown before and after a collision on a frictionless air table. Which of the figures below is not physically possible?

12 45. Treat the orbits of Earth and Mercury as essentially circular. A spacecraft is in an orbit about the Sun with the perihelion point at the orbit of Mercury and the aphelion point at the orbit of the Earth. Calculate the flight time for the spacecraft to travel from Earth orbit to Mercury orbit. (The radius of Mercury s orbit is m and the radius of Earth s orbit is m. The masses of Mercury, Earth and the Sun are kg, kg, and kg respectively.) A) 365 days B) 208 days C) 104 days D) 88.0 days E) 27.3 days 46. A 2.00 m long rod with a mass of 15.0 kg is attached to the left wall by a hinge. It is supported on the other end by a massless string attached to the right wall. If the string makes an angle of 37.0 degrees with the wall, what is the tension in the string if the rod is horizontal and motionless? A) 46.0 N B) 73.5 N C) 92.0 N D) 122 N E) 147 N

13 47. The sketch below shows four identical masses attached by massless rods to form a rectangle of dimensions 2L L. For which axis of rotation will this rectangular object have the smallest rotational moment of inertia, I? 48. An electron with speed of cm/s enters an electric field of magnitude N/C, traveling along the field lines, as shown below. If the region with the electric field is 1.50 cm long, what is the electron s speed when it emerges from this region? A) cm/s B) cm/s C) cm/s D) cm/s E) 0 cm/s

14 49. A thin rod, one meter in length and with a mass of 100 g, is rotated about an axis located at one end. The rod is initially at rest. If a force of 15 N is applied perpendicular to the far edge of the rod (initially pointing into the page), what is the magnitude of the rod s angular velocity 3.0 seconds later? A) 45.0 s 1 B) 135 s 1 C) 450 s 1 D) 1350 s 1 E) 5400 s A kg iron mass slides down a frictionless incline, as shown. At the bottom of the incline the iron mass sticks to a 3.00 kg plastic mass, initially at rest, and the combined mass slides on a horizontal frictionless surface. The velocity of this combined mass is: A) m/s B) m/s C) 1.36 m/s D) 3.96 m/s E) None of the above

15 51. The graph below shows the time dependent force that a 3.00 kg mass, with an initial (t = 0 s) velocity of 5.00 m/s in the positive x direction, experiences. If the force is in the positive x direction, what is the mass s velocity at t = 1.00 s? A) 13.3 m/s B) 15.0 m/s C) 24.4 m/s D) 35.0 m/s E) 50.0 m/s 52. Let s look at two spring/mass systems. In system 1, a mass M 1 is hung from a vertical spring. In system 2, an identical, vertical spring has a mass M 2 = 2M 1 hung from it. The resonant frequencies of these systems are f 1 and f 2, respectively. What is the ratio between the two resonant frequencies, f 1 : f 2? A) 2 B) 1/2 C) 2 D) 1/ 2. E) None of the above

16 53. A 300 g mass is attached to a string that is wrapped around a pulley. The pulley has a radius of 20 cm and the string unwinds from the pulley without slipping. If the mass accelerates downward with a = 7.77 m/s 2, what is the rotational moment of inertia, I, of the pulley? A) kg-m 2 B) kg-m 2 C) kg-m 2 D) kg-m 2 E) kg-m A solid, uniform sphere with a radius of 30.0 cm and a mass of 4.00 kg is hung so that it rotates about a point on its edge. What is the period of the sphere s motion if it oscillates with a small amplitude? A) s B) 1.30 s C) 6.95 s D) 9.45 s E) 13.0 s

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