Physics 121, Sections 1 and 2, Winter 2011 Instructor: Scott Bergeson Exam #3 April 16 April 21, 2011 RULES FOR THIS TEST: This test is closed book. You may use a dictionary. You may use your own calculator but you may not use your calculator s graphing or equation solving capabilities. This test is not timed. You may use any information written or printed onto one 8.5 11.0 inch sheet of paper. You may not discuss this test with anyone until after the end of finals week. 1. The nearest star to our Sun is Proxima Centauri. It is 4.0 10 16 meters from Earth. If you travel in a spaceship at 18,000 miles per hour, how long will it take for you to reach Proxima Centauri? a.) about 1,500 years b.) about 15,000 years c.) about 150,000 years d.) about 1,500,000 years e.) about 15,000,000 years 2. One day on your way to class you meet an alien from outer space who wants to measure your height. You say you are 5 feet 9 inches tall. But the alien says you are 62.5 froops tall because in her solar system all distances are measured in froops. You don t know how big a froop is, but you are pretty sure you can do some math to find out. Which of the following equations is true? a.) about 36 froops = 1 meter b.) about 14 froops = 1 meter c.) about 1 froops = 1 meter d.) about 0.07 froops = 1 meter e.) about 0.03 froops = 1 meter 1
3. A particle moves according to the equation x(t) = 2t 4 7, where x is in meters and t is in seconds. How fast is the particle moving when t = 2 seconds? a.) about 96 m/s b.) about 64 m/s c.) about 57 m/s d.) about 25 m/s e.) about 6 m/s 4. A particle is moving in the positive x-direction with an initial speed of 0.500 m/s. It experiences a constant acceleration of 1.000 m/s 2 in the negative x-direction for a time duration of t = 1.000 second. What is its new speed? a.) about -1.0 m/s b.) about -0.5 m/s c.) about 0.0 m/s d.) about 0.5 m/s e.) about 1.0 m/s 5. What is the angle between vector A = 3î + 3ĵ and B = 3î + 12ĵ? a.) about 45 degrees b.) about 50 degrees c.) about 55 degrees d.) about 60 degrees e.) about 65 degrees 6. A person walks the following path. He walks 100 m east, then 300 m south, then 150 m in a direction 30 south of west, and finally 200 m in a direction 60 north of west. What is the magnitude of his displacement? a.) about 110 m b.) about 150 m c.) about 240 m d.) about 350 m e.) about 750 m 2
7. A block slides down a frictionless inclined plane. The initial velocity is 1 m/s down the plane and the plane makes an angle of θ = 15 with respect to the horizontal. This occurs on Earth where g = 9.800 m/s 2 pointing straight downwards. How long does it take for the mass to slide 3 meters down the plane? a.) about 0.5 seconds b.) about 0.9 seconds c.) about 1.2 seconds d.) about 2.0 seconds e.) about 2.4 seconds 8. Johnny stands a distance d from a tall building. He kicks a ball at an angle θ above the horizontal. If the initial speed of the ball is v, at what height h does the ball strike the building? a.) h = [v sin(2θ i )]/g b.) h = d cos(θ) + v 2 /g c.) h = d tan(θ) (gd 2 )/[2v 2 cos 2 (θ)] d.) h = vg/2 sin(θ) e.) h = (v + v f )d tan(θ) 9. You are standing in an elevator, moving straight upwards at constant speed. Which is true? a.) There is no net force on you. b.) The floor pushes up on you with a force that is greater than your gravitational weight. c.) Your gravitational weight exceeds the force of the floor on you. d.) Because you are moving upwards there must be an unbalanced force on you in the upwards direction. e.) Even though you are moving in a straight line at constant speed, you are still accelerating. 10. A 10 kg mass experiences a force of 100 N. What is its acceleration? a.) 0.010 m/s 2 b.) 0.100 m/s 2 c.) 1.000 m/s 2 d.) 10.00 m/s 2 e.) 100.0 m/s 2 3
11. A mangy old dog chews on a bone. Which is true? a.) The force of the dog s teeth on the bone exceeds the force of the bone on the dog s teeth. b.) The force of the bone on the dog s teeth exceeds the force of the dog s teeth on the bone. c.) The force of the dog s teeth on the bone is equal to the force of the bone on the dog s teeth. d.) You can t say anything about the relative strengths of the two forces unless you know if the teeth are accelerating after they come in contact with the bone. 12. A 1000 kg car moving on a flat horizontal road drives around a curve. The radius of curvature for the road is 32.5 m. The coefficient of static friction between the tires and the road is µ s = 0.200. Find the maximum speed for which the car can drive through the curve without sliding. a.) You can t calculate this because the coefficient of kinetic friction is not given. b.) about 6 m/s v c.) about 7 m/s d.) about 8 m/s e.) about 9 m/s R 13. An object of mass m = 0.500 kg is suspended from the ceiling of an accelerating truck. The object makes an angle θ = 10 with respect to the vertical. What is the acceleration of the truck? a.) about 1.5 m/s 2 b.) about 1.7 m/s 2 θ c.) about 1.9 m/s 2 d.) about 2.1 m/s 2 e.) about 2.3 m/s 2 4
14. A baseball outfielder throws a 0.150 kg baseball at a speed of 40.0 m/s and an initial angle of 30.0 with respect to the horizontal. What is the kinetic energy of the baseball at the highest point of its trajectory? a.) about 30 J b.) about 60 J c.) about 90 J d.) about 120 J e.) about 150 J 15. (Warning: This problem is somewhat challenging.) A particle of mass m = 1.000 kg is attached between two identical springs on a frictionless, horizontal tabletop with L = 1.000 m. Both springs have spring constant k = 100.000 N/m. They are unstressed when the particle is at x = 0. What force is required to pull the mass to the point x = 0.1 m? a.) about 1.0 N b.) about 0.1 N c.) about 0.01 N d.) about 0.001 N e.) about 0.0001 N L x=0 L x 16. A 1.000 kg mass is initially at rest on an inclined plane. The plane makes an angle of θ = 5.37 with respect to the horizontal. The first 1.000 meter of the plane is frictionless, but after that the plane is roughened and the coefficient of kinetic friction between the mass and the plane is µ k = 0.19. How far does the mass slide on the roughened surface before it comes to a complete stop? a.) 0 meters. It stops immediately. b.) about 1 meter c.) about 2 meters d.) about 3 meters e.) Because of the slope it never stops sliding. µ k = 0 θ µ k > 0 5
17. A 1.000 kg mass slides on a frictionless tabletop with a horizontal velocity of 4.000 m/s. The table top is 1.000 meter from the ground. What is the kinetic energy of the mass right before it lands? a.) about 6 J b.) about 10 J c.) about 15 J d.) about 28 J e.) about 36 J 18. A 2.000 kg mass and a 4.000 kg mass are released from rest at a height of h = 5.000 m on a frictionless track as shown. When they meet on the level portion of the track they undergo a head-on elastic collision. Which is true? a.) The masses will return to the exact same heights after the collision. b.) The masses will return to the same heights, but on opposite sides of the track. h c.) The small mass will reach a height greater than 5 meters. d.) The large mass will reach a height greater than 5 meters. e.) The two masses will stick together and reach a height less than 5 meters. 19. A 1.25 kg wooden block rests on a table over a large hole as shown. A 5.00 g bullet with an initial velocity v i is fired upward into the bottom of the block and remains in the block after the collision. The block and bullet rise to a maximum height of 22.0 cm after the collision. What is the speed of the bullet right before the collision? a.) about 260 m/s b.) about 325 m/s c.) about 390 m/s v i d.) about 455 m/s e.) about 520 m/s 6
20. A massless string is wound around a uniform cylindrical spool of radius 0.500 m and mass 1.000 kg. The spool is mounted on a frictionless axle and is initially at rest. The string is pulled from the spool with a constant acceleration of magnitude 1.500 m/s 2. How long does it take the spool to reach an angular speed of 9.000 rad/s? Note: I CM = 1 2 MR2 for a uniform cylindrical spool. a.) about 0.7 seconds b.) about 1.2 seconds c.) about 1.5 seconds d.) about 2.2 seconds e.) about 3.0 seconds 21. A solid sphere of mass 1.000 kg and radius 0.200 m starts from rest and rolls down an inclined plane. The plane is 2.000 m long and makes an angle of 30 with respect to the horizontal. How fast is the sphere rolling when it gets to the bottom of the plane? Note: I CM = 2 5 MR2 for a solid sphere. a.) about 3.7 m/s b.) about 4.4 m/s c.) about 5.1 m/s d.) about 5.8 m/s e.) about 6.5 m/s 22. An ice skater spins with her arms outstretched. Her initial angular speed is 3.14 rad/s. She pulls her arms in and her angular speed increases to 31.4 rad/s. If her initial moment of inertia is 100 kg m 2 when her arms are outstretched, what is her final moment of inertia when her arms are pulled in? a.) about 10 kg m 2 b.) about 32 kg m 2 c.) about 100 kg m 2 d.) about 320 kg m 2 e.) about 1000 kg m 2 7
23. A wooden block of mass M resting on a frictionless horizontal surface is attached to a rigid rod of length l and of negligible mass. The rod is pivoted at the other end. A bullet of mass m traveling parallel to the horizontal surface and perpendicular to the rod with speed v hits the block and becomes embedded in it. What is the angular momentum of the bullet-block system about a vertical axis through the pivot? a.) L = mvl b.) L = (m + M)vl c.) L = (M m)vl d.) L = mvl/m e.) L = m 2 vl/2(m + m) v i (top view) 24. The figure shows a cross member of a bridge lying in the xy plane of the page. The mass of the member is M = 15.000 kg and its center of mass is at its geometrical center. Two forces F and R each have x and y components and act at points A and O, as shown. The angle θ = 41.7 and R y = +2Mg. What is R x? a.) Mg b.) Mg/2 c.) 0 d.) +Mg/2 F y F x e.) +Mg R y Rx 8
25. The figure shows a cross member of a bridge lying in the xy plane of the page. The mass of the member is M = 15.000 kg and its center of mass is at its geometrical center. Two forces F and R each have x and y components and act at points A and O, as shown. The angle θ = 41.7 and R y = +2Mg. What is F y? a.) Mg b.) Mg/2 c.) 0 d.) +Mg/2 F y F x e.) +Mg R y Rx 26. A binary star system consists of two equal mass stars that revolve in circular orbits about their center of mass. The period of the motion is T = 23.5 days and the orbital speed is v = 220 km/s. What is the mass of each star? Use G = 6.67 10 11 N m 2 kg 2. a.) about 1.00 10 32 kg b.) about 1.33 10 32 kg c.) about 1.67 10 32 kg d.) about 2.00 10 32 kg e.) about 2.33 10 32 kg 27. A planet with mass m = 2.00 10 24 kg and a second mass with M = 5.00 10 24 kg are separated by a distance d = 4.76 10 11 m. There is a place between these two planets where the gravitational force equal zero. Where is that? Give your answer in meters, measured from the LARGER planet. a.) about 2 10 11 m b.) about 2.5 10 11 m c.) about 3 10 11 m d.) about 3.5 10 11 m e.) about 4. 10 11 m 9
28. A small satellite orbits the Earth at a height of R E above the surface of the Earth. What is its orbital speed? G = 6.67 10 11 N m 2 kg 2, R E = 6.38 10 6 m, and M e = 5.97 10 24 kg. a.) about 5000 m/s b.) about 5200 m/s c.) about 5400 m/s d.) about 5600 m/s e.) about 5800 m/s 29. A particle experiences simple harmonic motion according to the equation z(t) = A cos(ωt+φ). At time t = 0 the particle is at the position z = 3.000 cm with velocity v = +1.234 cm/s. The frequency is ω = 3.14 rad/s. What is the phase angle φ? a.) about -7E-5 m b.) about -3E-5 m c.) about 0 m d.) about +3E-5 m e.) about +7E-5 m 30. A mass of 1.000 kg hangs vertically downwards on a spring with k = 100.000 N/m. The mass is pulled down a small distance and released. What is the oscillation period? a.) about 6 s b.) about 3 s c.) about 1 s d.) about 0.3 s e.) about 0.6 s 10