Phys1443-003, Fall04,Term 2 Exercise Problems Page 1 1. Two objects attract each other gravitationally with a force of 2.5 ð 10-10 N when they are 0.25 m apart. It their total mass is 4.0 kg, their individual masses are: a. 1.5 and 2.5 kg b. each 2 kg c. 0.5 and 3.5 kg d. need more information 2. Two objects have mass m and 2m respectively and are separated by a distance d. At what distance from the lighter object along the line joining the two objects would the net gravitational force on a third object be zero? a. 0.25 d b. 0.41 d c.0.5 d d. 0.81 d 3. Three 5 kg masses sit at the vertices of an equilateral triangle of side 1 m. The magnitude of the gravitational force on any of the masses due to the other two is a. 1.2 ð 10-11 N b. 2.5 ð 10-10 N c. 2.9 ð 10-9 N d. 3.4 ð 10-8 N 4. An object of mass 5 kg weighs 49 N at the surface of the Earth. At an altitude equal to twice the Earth's radius its weight is a. 12.3 N b. 24.5 N c.49 N d. 98 N 5. The gravitational acceleration g at the surface of two hypothetical planets has the same value, but planet #1 has twice the radius of planet #2. The ratio of the mass of planet #1 to that of #2 is a. 2:1 b. 1:2 c.4:1 d. 1:4 6. The period of a satellite orbiting the Earth 2000 km above the surface is a. 3.5 ð 103 s b. 7.6 ð 103 s 3 c. 8.5 ð 10 s d. 9.0 ð 103 s 7. A satellite orbits the Earth with a speed of 4500 m/s. Its period is a. 1.5 ð 103 s b. 2.1 ð 104 s c. 2.7 ð 104 s d. 3.5 ð 104 s 8. Which of the following statements is true regarding satellites in circular orbits about a planet? a. The period depends on the mass of the satellite b. The period is independent of the radius of the orbit c. The speed of the satellite can change as it maintains its circular orbit d. The period increases with increasing orbital radius 9. A satellite of mass 5000 kg orbits the Earth (mass = 6.0 ð 1024 kg) and has a period of 6000 s. The magnitude of the Earth's gravitational force on the satellite is a. 7.9 ð 10-3 N b. 7.9 ð 10-2 N c. 7.9 N d. 7.9 ð 103 N 10. The period of a satellite orbiting just above the Earth's surface is a. 2500 s b. 5040 s c. 7500 s d. 86,400 s 1 Phys1443-003, Fall04,Term 2 Exercise Problems 11. Two satellites are in circular orbits about the Earth, with satellite 2 in an orbit of larger radius than satellite 1. Which satellite has the longer period? a. satellite 1 b. satellite 2 c. need to know the masses of the satellites 12. Satellite #1 has three times the mass of satellite #2. Both are in circular orbits of the same radius about Earth. The ratio of the speed of satellite #1 to the speed of satellite #2 is a. 3:1 b. 1:3 c.2:1 d. 1:1 13. The speed of Halley's comet at its point of closest approach to the Sun is a. the same as its speed throughout its orbit b. greater than its value at any other point in its orbit c. less than its value at any other point in its orbit 14. Four equal masses are located at the corners of a square. The direction of the gravitational field at the midpoint of the lower side of the square is a. up b. down c.left d. right 15. The gravitational field at the center of the Earth has magnitude a. zero N/kg b. 6.67 ð 10-11 N/kg c. 9.8 N/kg d. infinity 16. If the inertial mass and the gravitational mass were not equal, which of the following principles would change? a. the inverse-square law of gravitation b. Kepler's Third Law c. Newton's Second Law A satellite of mass 5000 kg orbits the Earth (mass = 6.0 ð 1024 kg) and has a period of 6000 s. 17. In the above problem the altitude of the satellite above the Earth's surface is a. 7 ð 103 m b. 7 ð 105 m c.4 ð 106 m d. 5 ð 108 m Two objects attract each other gravitationally with a force of 2.5 ð 10-10 N when they are 0.25 m apart. 18. In the above problem if the two objects experience no forces other than their mutual gravitational attraction then their resulting accelerations are a. equal b. different Two satellites are in circular orbits about the Earth, with satellite 2 in an orbit of larger radius than satellite 1. 19. In the above problem which satellite has the larger speed? a. satellite 1 b. satellite 2 c. need to know the masses of the satellites The period of a satellite orbiting just above the Earth's surface is 5040 s. 20. The mass of the satellite in the above problem is 2 Phys1443-003, Fall04,Term 2 Exercise Problems a. 5000 kg b. 9.8 kg 5 c. 2.5 ð 10 kg d. need more information 21. The speed of the satellite in the above problem is a. 3070 m/s b. 7780 m/s c.7900 m/s d. 8500 m/s Three 5 kg masses sit at the vertices of an equilateral triangle of side 1 m. 22. In a. b. c. the above example the force points away from the center of the triangle toward the center of the triangle along a line joining two of the masses Four equal masses are located at the corners of a square. 23. In the above problem if each mass is 1 kg and the square has side 0.5 m the strength of the gravitational field at the midpoint of a side is a. 1.6 ð 10-9 N/kg b. 2.5 ð 10-9 N/kg -9 c. 3.8 ð 10 N/kg d. 3.8 ð 10-10 N/kg 24. If you lift a box of mass 5 kg straight up at constant speed through a displacement of 1 m, the total work done on the box is a. zero J b. 49 J c.-49 J d. 25 J 25. The angle between a force F and a displacement d is 125ø. The work done by the force is a. zero b. positive c. negative d. the sign depends on the magnitudes of F and d. 26. A particle moves in uniform circular motion. The work done on it by the centripetal force is a. zero b. positive c. negative 27. A box of mass 5 kg is accelerated by a force across the floor at a rate of 2 m/s2 for 10 s. The work done by the force is a. 50 J b. 100 J c.1000 J d. 1500 J 28. A box of mass 10 kg slides down a plane inclined at an angle of 30ø with the horizontal. The coefficient of kinetic friction between the box and the incline is 0.2. The length of the incline is 5 m. The work done by friction is a. -9 J b. -98 J c.85 J d. -85 J 29. The dot product of vectors A and B equals 4. If A has magnitude 2 and B has magnitude 1.5 then the angle between the two vectors is a. 40ø b. 90ø c. 135ø d.the given information is inconsistent 30. Vectors A and B have components (1.5, 2.3) and (3.1, 4.5) respectively. Their dot product is a. 5.7 b. 15 c.-15 d. 11.4 31. A force F = 3i + 2j - 4k acts on an object moving it from a position i + 5j - 4k to a position 3i - 2j + 8k. The work done by F is a. 2 b. 56 c.-56 d. 48 3 Phys1443-003, Fall04,Term 2 Exercise Problems 4 Phys1443-003, Fall04,Term 2 Exercise Problems 32. If a. b. c. d. two vectors satisfy A ú B = -AB then they are parallel to each other they are antiparallel to each other they are perpendicular to each other they make an angle of 45ø with each other 33. A spring with k = 50 N/m hangs vertically next to ruler. The end of the spring is next to the 10 cm mark on the ruler. If a 2.5 kg mass is now attached to the end of the spring, the end will line up with a. the 10 cm mark b.the 39 cm mark c. the 49 cm mark d. the 59 cm mark 34. The work done by a force F = k³x³ on an object moving from x = -2 to x = 2 is a. zero b. 2 k c. 4 k d. 8 k 35. A particle moves from x = 2 to x = 3.5 subject to a force F = 5x + 7x2 which points in the y direction. The work done by F is a. zero b. 102 c. -102 d. 150 36. A box of mass 10 kg slides down a plane inclined at an angle of 30ø with the horizontal. The coefficient of kinetic friction between the box and the incline is 0.2. The length of the incline is 5 m. If the box is released from rest at the top of the incline, its speed at the bottom is a. 5.7 m/s b. 7.0 m/s c. 9.0 m/s d. 12.3 m/s 37. A platform is supported by a spring with k = 1.0 kN/m. The spring is compressed 1 cm due to the weight of the platform. A box of mass 20 kg is then placed on the platform and the system begins to oscillate up and down. Calculate how far the platform descends below its initial position. a. 15 cm b. 16 cm c. 17 cm d. 25 cm 38. A box is given a push across a table so that its initial speed is vo. The box travels a distance d and is brought to rest by friction. If instead the box is given an initial speed of 2vo, the box will travel a distance a. d b. 2d c.3d d. 4d 39. An object of mass 10 kg is released from the top of a building 100 m high. If the average force of air resistance experienced by the object is 15 N, its speed when it hits the ground is a. 22 m/s b. 30 m/s c. 41 m/s d. 52 m/s 40. A box is given an initial velocity of 5 m/s. It slides across a rough surface coming to rest in 2 m. The coefficient of kinetic friction is a. 0.2 b. 0.4 c. 0.6 d. 0.7 41. A spring attached to 2 kg mass is compressed 10 cm and released from rest. When the spring is compressed 5 cm, the mass is moving at 1.5 m/s. The spring constant is a. 450 N/m b. 600 N/m c. 750 N/m d. 1000 N/m 42. A block of mass 10 kg is attached to a spring with spring constant 1000 N/m. The spring is compressed 2 cm and released from rest. The speed of the block as it passes through the equilibrium position of the spring is 5 Phys1443-003, Fall04,Term 2 Exercise Problems a. 0.2 m/s b. 0.4 m/s c. 0.6 m/s d. 0.8 m/s 43. A block of mass 5 kg is subject to a force F = 3x + 5x2 (in N). The block is initially at rest at x = 1. Its speed when it has moved to x = 5 is a. 9.8 m/s b. 19.6 m/s c. 97 m/s d. 105 m/s 44. A block of mass 10 kg moves on a frictionless table at 2 m/s and strikes a spring attached to a wall. After the collision the spring is compressed to a maximum distance of 0.9 m. The spring constant of the spring is a. 100 N/m b. 74 N/m c. 49 N/m d. need more information 45. A block of mass 1 kg is placed against a compressed spring of constant 500 N/m at the bottom of frictionless plane inclined at 30ø. When the spring is released the block travels 1.5 m up the plane, losing contact with the spring. The spring was initially compressed by a distance of a. 10 cm b. 13 cm c. 15 cm d. 17 cm 46. How much work is done in accelerating an electron (mass = 9.1 ð 10-31 kg) from 0.5c to 0.9c? a. 9.3 ð 10-31 J b. 9.3 ð 10-14 J c. 2.3 ð 10-14 J d. 1.5 ð 10-14 J Vectors A and B have components (1.5, 2.3) and (3.1, 4.5) respectively. 47. The angle between the vectors in the above problem is a. 15ø b. 29ø c. 35ø d. not enough information given A box is given an initial velocity of 5 m/s. It slides across a rough surface coming to rest in 2 m. 48. The mass of the box in the above problem is a. 5 kg b. 10 kg d. not enough information provided c. 25 kg A block of mass 10 kg moves on a frictionless table at 2 m/s and strikes a spring attached to a wall. After the collision the spring is compressed to a maximum distance of 0.9 m. 49. In the above problem what is the speed of the block when the spring is compressed 0.5 m? a. 1.2 m/s b. 1.7 m/s c. 2.3 m/s d. need more information A block of mass 1 kg is placed against a compressed spring of constant 500 N/m at the bottom of frictionless plane inclined at 30ø. When the spring is released the block travels 1.5 m up the plane, losing contact with the spring. 50. In the above problem what is the speed of the block when it has traveled 0.9 m up the plane? a. 1.7 m/s b. 3.4 m/s c. 4.1 m/s d. 5.2 m/s 6 Phys1443-003, Fall04,Term 2 Exercise Problems A box of mass 10 kg slides down a plane inclined at an angle of 30ø with the horizontal. The coefficient of kinetic friction between the box and the incline is 0.2. The length of the incline is 5 m. 51. The work done by the normal force in the above problem is a. zero b. 49 J c. 123 J d. 250 52. For the potential energy function U(x,y) = 3xy + 5x2 + 6y3, the force is given by a. F = 5x2i + 6y3j b. F = 3xyi + 3xyj c. F = (-3y - 10x)i + (-3x - 18y2)j d.F = (3y + 10x)i + (-3x - 18y2)j 53. A spring is compressed a distance x and used to vertically launch a mass m placed against its end. The mass reaches a height h. If the spring is instead compressed a distance 2x, the height reached by the mass will be a. h b. 2h c. 3h d. 4h 54. A 1.5 kg mass rests atop a spring with spring constant 500 N/m. The spring is compressed a distance 25 cm and released. The ball will ascend to a height a. 0.5 m b. 0.6 m c. 0.8 m d. 1.0 m 55. A block of mass 5 kg starts from rest at the top of a ramp which is 5 m high. It descends to the bottom of the ramp and then rises to the top of a second ramp which is 2.5 m high. The speed of the block at the top of the second ramp is a. 3.5 m/s b. 7 m/s c. 14 m/s d.21 m/s 56. A toy car of mass 1.5 kg traveling on a level surface approaches a loop-the-loop with radius 1.5 m. The minimum speed of the car required to traverse the loop-the-loop is a. 1. 5 m/s b. 3.8 m/s c. 4.6 m/s d. 12.3 m/s 57. Three balls start at the same vertical position but follow different frictionless paths as they descend a height h. Which of the following statements is true? a. The balls all reach the lower level at the same time. b. The balls all reach the lower level with the same speed but at possibly different times. c. The ball that takes the longer path reaches the bottom with the lowest velocity d. The balls all reach the lower level with the same speed and at the same time. 58. A roller coaster car starts from rest and descends 40 m before rising 20 m to the top of a hill. The passenger of mass 75 kg at the top of the hill feels a normal force of 368 N. The radius of curvature of the hill is a. 10 m b. 20 m c. 30 m d. 40 m 59. A small block falls from the rim of a bowl down towards the bottom, 15 cm below. The maximum speed of the block neglecting friction is a. 1.3 m/s b. 1.5 m/s c. 1.7 m/s d. need to know the mass of the block 7 Phys1443-003, Fall04,Term 2 Exercise Problems 60. A mass of 2 kg is placed on an inclined plane (making an angle of 30ø with the horizontal) and connected to a spring fastened at the top of the plane. The spring has spring constant 50 N/m. The mass is released from rest with the spring initially unstretched. The block moves a distance 25 cm before coming to rest. The coefficient of kinetic friction between the block and the plane is a. 0.1 b. 0.2 c. 0.3 d. 0.4 61. A 5 kg block slides on a rough horizontal surface with speed 2.0 m/s. It makes contact with a spring and momentarily stops when the spring is compressed 5 cm. The work done by friction from the moment the block contacts the spring until it momentarily stops is -2.0 J. The spring constant of the spring is a. 2000 N/m b. 4000 N/m c. 6400 N/m d. 9600 N/m 62. An object is projected vertically upward from a planet of radius R with a velocity equal to one half the escape velocity. The maximum altitude attained by the object is a. 0.3 R b.0.5 R c. 1.3 d. 1.5 R 63. A person ascends a flight of stairs in 20 s. The person weighs 500 N and the vertical height of the stairs is 9 m. The person's power output is a. 150 W b. 225 W c. 325 W d. 450 W 64. An object moves with a potential energy given by U(x) = 2x2. If the particle's energy is 2 then turning points of the motion are a. 0 and infinity b. 1 and -1 c. 1 and infinity d.-1 and infinity 65. The potential energy of a particle is given by U = x3 exp (-x2). The point of stable equilibrium is given by a. x = 0 b. x = 1.2 c. x = 2.4 d. there is no point of stable equilibrium A 5 kg block slides on a rough horizontal surface with speed 2.0 m/s. It makes contact with a spring and momentarily stops when the spring is compressed 5 cm. The work done by friction from the moment the block contacts the spring until it momentarily stops is -2.0 J. 66. In the above problem the coefficient of kinetic friction is a. 0.3 b. 0.5 c. 0.6 d. 0.8 67. In the above problem when the spring pushes the block back the block's velocity when it loses contact with the spring is a. 1.5 m/s b. 2.0 m/s c. 2.5 m/s d. 3.5 m/s A roller coaster car starts from rest and descends 40 m before rising 20 m to the top of a hill. The passenger of mass 75 kg at the top of the hill feels a normal force of 368 N. 68. Suppose the roller coaster in the above problem starts with a speed of 5 m/s. Its speed at the top of the next hill is a. 16 m/s b. 21 m/s c. 25 m/s d. 30 m/s An object moves with a potential energy given by U(x) = 2x2. 69. The maximum kinetic energy of the object in the above problem is a. 1.125 b. 0 c. 2 d.not enough information 8 Phys1443-003, Fall04,Term 2 Exercise Problems 70. The equilibrium position of the object in the above problem is located at a. x = 0 b. x = -0.5 c. x = -1.25 d. x = -2 71. The equilibrium position located in the above problem is a. stable b. unstable c. not enough information 72. A particle moving in the x direction feels a force of F(t) = 3t + 4 Newtons where t is in seconds. What is the momentum change between t = 0 and t = 2. s? a. -2. N-s b. 0. N-s c. 12. N-s d. 14. N-s 73. Two railroad cars collide on a level track and lock together. The collision: a. was elastic b. reduced momentum c. was inelastic d. conserved kinetic energy 74. Assume a rocket is far enough in space that the acceleration due to gravity is negligible. If the mass ratio, initial mass/final mass, changes from 10 to 20 for the same exhaust velocity, by what factor does the increase of velocity change? a. 2.0 b. 0.50 c. 0.69 d. 1.3 75. Which of the following units may be used to describe momentum? a. N-s b. N/s c. N-m d. N/m 76. A 200. Megagram rocket on the launchpad consists of 190. Megagrams of fuel which is burned at the rate of 2.0 Megagrams/second with an exhaust speed of 3.0 km/s. What thrust is produced by the engines? a. 2.0 ð 106 N b. 4.0 ð 106 N c. 6.0 ð 106 N d.8.0 ð 106 N 77. The pitcher throws a 44. m/s fastball. The bat reverses the ball's velocity and it leaves the bat at 56. m/s. What was the average force on the 0.145 kg baseball during the contact time of 15. ms? a. 0.43 KN b. 0.54 KN c. 0.97 KN d. 1.45 KN 78. As the bullet enters the wood block of a ballistic pendulum, which is/are conserved? a. kinetic energy and momentum b.kinetic energy but not momentum c. momentum but not kinetic energy d.neither kinetic energy nor momentum 79. A particle moves with momentum p. Which of the following describe its kinetic energy? a. p/m b. 1/2 mp2 c. p2/2m d. 1/2 p/m 80. A 3500. kg parked car, with brakes off and free to move, is bumped from the rear by a 2000. kg car moving 4.0m/s and they lock bumpers. What percentage kinetic energy is lost in the collision? a. 36 b. 48 c. 64 d. 77 81. In an inelastic collision, the ______ is less after the collision than before. a. momentum b. total energy c. kinetic energy 82. Three masses are positioned thus: 2.0 kg at (0,0), 3.0 kg at (10,20), 5.0 kg at (-10,30). Where is the cm? 9 Phys1443-003, Fall04,Term 2 Exercise Problems a. (-2, 21) b.(2, 21) c.(-2.5, 26) d.(2.5, 26) 83. Consider two astronauts initially at rest "floating" next to each other in space. The 80. kg astronaut pushes the 100. kg astronaut. How far apart are they when the heavier astronaut has moved 10. meters? a. 8.0 m b. 18. m c. 12.5 m d.22.5 m 84. Suppose you were to throw a firecracker straight up and it exploded into 2 pieces when it reached its maximum height of 6.5 meters. Both pieces are initially flung horizontally but then fall to the ground. The 37. gram piece hits the ground 1.9 meters to your left. How far to your right does the 63. gram piece hit the ground? a. 0.93 m b.1.1 m c. 1.8 m d. 3.2 m 85. How long would a force have to act starting from zero and linearly increasing with time such that 20. kg-m/s is the momentum change produced (dF/dt = 5.0 N/s)? a. 2.8 s b. 4.0 s c. 8.0 s d. 9.2 s 86. What is the angular speed of rotation of the earth? a. 6.94 ð 10-4 rpm b. 4.36 ð 10-3 radian/s c. 7.27 ð 10-5 rpm d. 8.34 ð 10-4 degree/s 87. A Ferris Wheel has a diameter of 25.0 meters. How far does a person on the rim travel when the wheel rotates 120. degrees? a. 8.33 m b. 3.00 ð 103 m c. 26.2 m d. 52.4 m 88. A 30.cm diameter wheel rolls without slipping at 120. rpm. The point of contact with the ground has an instantaneous speed of: a. 5.2 mm/s b. 1.04 cm/s c. 2.6 m/s d. zero 89. Which of the following is not a vector? a. angular velocity b. angular acceleration c. angle d. torque 90. A spinning ice skater draws her arms in closer to her body. As she does so the: a. angular speed decreases b. angular momentum increases c. torque on the skater decreases d. angular momentum is constant 91. An in a. c. old 33 1/3 rpm record player starts from rest and reaches operating speed 2.0 seconds. Through what angle did it turn in those 2.0 s? 0.56 radian b. 0.56 revolution 3.5 radians d. 3.5 revolutions 92. At a point 1.2 m out from the hinge, 14. Newtons is exerted at an angle of 27.ø to the radius in a plane which is perpendicular to the door. What magnitude torque is exerted? a. 7.6 N-m b. 9.7 N-m c. 15. N-m d. 17. N-m 93. Estimate the rotational kinetic energy of the rotating earth (assume earth is a uniform sphere of mass 6.0 ð 1024 kg and radius 6.4 ð 103 km). a. 2.6 ð 1025 J b. 2.6 ð 1027 J c. 2.6 ð 1029 J d. 2.6 ð 1031 J 10 Phys1443-003, Fall04,Term 2 Exercise Problems 94. What is the ratio of angular momentum of earth orbiting the sun and the angular momentum of the moon orbiting the earth? earth/moon mass = 81.; earth-sun/earth-moon distance = 391.; moon period = 27.3 days a. 2.4 ð 103 b. 9.2 ð 105 c. 1.7 ð 108 d. 6.1 95. A 200. hp automobile engine delivers what torque at 3000. rpm? a. 0.637 N-m b. 77.3 N-m c. 475. N-m d. 950. N-m 96. What is the ratio of the kinetic energy per unit mass of the earth orbiting the sun and the kinetic energy per unit mass of the moon orbiting the earth? earth/moon mass = 81.; earth-sun/earth-moon distance = 391.; moon period = 27.3 days a. 85. b. 8.5 ð 102 c. 8.5 ð 103 d. 8.5 ð 104 97. A yoyo is placed so it can roll on the floor without slipping and its string (wound around its central small radius peg) is pulled horizontally such that the string is below the center of mass. Does the yoyo roll toward the person pulling (thus shortening the string) or does it roll away from the person pulling (thus lengthening the string)? a. toward b.away 98. A yoyo is placed so it can roll on the floor without slipping and its string (wound around its central small radius peg) is pulled horizontally such that the string is above the center of mass. Does the yoyo roll such that it lengthens the string or does it roll such as to shorten the string? a. lengthens b. shortens 99. In the presence of frictional forces, the total mechanical energy always decreases. True or false? a. True b. False 100. Two blocks of different masses are projected up a rough inclined plane with the same initial speed. True or false: Both blocks reach the same height. a. True b. False 11 Phys1443-003, Fall04,Term 2 Exercise Problems Answer keys! The answers have not been checked. So please use these with a grain of salt!! 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. a b c a c b c d c b b d b a a b b b a d c b d a c a c d d b c b d c a a b d c c b a a c d b b d b b a c d 12 Phys1443-003, Fall04,Term 2 Exercise Problems 54. d 55. b 56. b 57. b 58. b 59. c 60. b 61. c 62. a 63. b 64. b 65. b 66. d 67. a 68. b 69. c 70. a 71. a 72. d 73. c 74. d 75. a 76. c 77. c 78. c 79. c 80. c 81. c 82. a 83. d 84. b 85. a 86. a 87. c 88. d 89. c 90. d 91. d 92. a 93. c 94. b 95. c 96. b 97. a 98. a 99. True 100. False 13