Momentum, Impulse, Work, Energy, Power, and Conservation Laws

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1 Momentum, Impulse, Work, Energy, Power, and Conservation Laws 1. Cart A has a mass of 2 kilograms and a speed of 3 meters per second. Cart B has a mass of 3 kilograms and a speed of 2 meters per second. Compared to the inertia and magnitude of momentum of cart A, cart B has A) the same inertia and a smaller magnitude of momentum B) the same inertia and the same magnitude of momentum C) greater inertia and a smaller magnitude of momentum D) greater inertia and the same magnitude of momentum 2. What is the momentum of a kilogram car as it travels at 30. meters per second due east for 60. seconds? A) kg m/s, east B) kg m/s, west C) kg m, east D) kg m, west 3. Which is a unit of momentum? A) N-m/s 2 B) kg-m/s 2 C) N-m/s D) kg-m/s 4. A kilogram baseball, initially moving at 15 meters per second, is brought to rest in second by a baseball glove on a catcher's hand. The magnitude of the average force exerted on the ball by the glove is A) 2.2 N B) 2.9 N C) 17 N D) 56 N 5. In the diagram below, a 60.-kilogram rollerskater exerts a 10.-newton force on a 30.-kilogram rollerskater for 0.20 second. What is the magnitude of the impulse applied to the 30.-kilogram rollerskater? A) 50. N s B) 2.0 N s C) 6.0 N s D) 12 N s 6. During a collision, an 84-kilogram driver of a car moving at 24 meters per second is brought to rest by an inflating air bag in 1.2 seconds. The magnitude of the force exerted on the driver by the air bag is approximately A) N B) N C) N D) N 7. The velocity-time graph below represents the motion of a 3-kilogram cart along a straight line. The cart starts at t = 0 and initially moves north. What is the magnitude of the change in momentum of the cart between t = 0 and t = 3 seconds? A) 20 kg m/s B) 30 kg m/s C) 60 kg m/s D) 80 kg m/s

2 Base your answers to questions 8 through 11 on the diagram below which represents two objects at rest on a frictionless horizontal surface with a spring compressed between them. When the compressed spring is released, the two objects are pushed apart. 8. What kinetic energy does the 2.0-kilogram object have after gaining a velocity of 5.0 meters per second? A) 25 J B) 20. J C) 10. J D) 5.0 J 9. What is the total momentum of the two-object system after the expansion of the spring? A) 20. kg-m/s B) 10. kg-m/s C) 5.0 kg-m/s D) 0 kg-m/s 10. What is the velocity of the 2.0-kilogram object after being acted on by 10. Newton-seconds of impulse? A) 1.0 m/s B) 2.0 m/s C) 5.0 m/s D) 10. m/s 11. If the 1.0-kilogram object receives an impulse of +20.-newton-seconds, what impulse does the 2.0-kilogram object receive? A) 0 N-s B) 5.0 N-s C) 10. N-s D) 20. N-s 12. A rocket engine acquires motion by ejecting hot gases in the opposite direction. This is an example of the law of A) conservation of heat B) conservation of energy C) conservation of momentum D) conservation of mass 13. Base your answer to the following question on the information and diagram below. Block A moves with a velocity of 2 meters per second to the right, as shown in the diagram, and then collides elastically with block B, which is at rest. Block A stops moving, and block B moves to the right after the collision. What is the total change in momentum of blocks A and B? A) B) C) D)

3 14. The diagram below shows an 8.0-kilogram cart moving to the right at 4.0 meters per second about to make a head-on collision with a 4.0-kilogram cart moving to the left at 6.0 meters per second. After the collision, the 4.0-kilogram cart moves to the right at 3.0 meters per second. What is the velocity of the 8.0-kilogram cart after the collision? A) 0.50 m/s left B) 0.50 m/s right C) 5.5 m/s left D) 5.5 m/s right Base your answers to questions 15 through 19 on the diagram below which represents carts A and B being pushed apart by a spring which exerts an average force of 50. Newtons for a period of 0.20 second. [Assume friction-less conditions.] 15. What is the average acceleration of cart B during the 0.20-second interaction? A) 0 m/s 2 B) 10. m/s 2 C) 25 m/s 2 D) 50. m/s What is the magnitude of the impulse applied by the spring on cart A? A) 5.0 N-sec B) 10. N-sec C) 50. N-sec D) 100 N-sec 17. Compared to the magnitude of the impulse acting on cart A, the magnitude of the impulse acting on cart B is A) one-half as great B) twice as great C) the same D) four times as great 18. Compared to the velocity of cart B at the end of the 0.20-second interaction, the velocity of cart A is A) one-half as great B) twice as great C) the same D) four times as great 19. Compared to the total momentum of the carts before the spring is released, the total momentum of the carts after the spring is released is A) one-half as great B) twice as great C) the same D) four times as great

4 20. In the diagram below, scaled vectors represent the momentum of each of two masses, A and B, sliding toward each other on a frictionless, horizontal surface. Which scaled vector best represents the momentum of the system after the masses collide? A) B) C) D) 21. The diagram below represents two masses before and after they collide. Before the collision, mass ma is moving to the right with speed v, and mass mb is at rest. Upon collision, the two masses stick together. 23. Satellite A has a mass of kilograms and is traveling east at meters per second. Satellite B is traveling west at meters per second. The satellites collide head-on and come to rest. What is the mass of satellite B? A) kg B) kg C) kg D) kg 24. Which action would require no work to be done on an object? A) lifting the object from the floor to the ceiling B) pushing the object along a horizontal floor against a frictional force C) decreasing the speed of the object until it comes to rest D) holding the object stationary above the ground 25. Base your answer to the following question on A box is pushed to the right with a varying horizontal force. The graph below represents the relationship between the applied force and the distance the box moves. Which expression represents the speed, v', of the masses after the collision? [Assume no outside forces are acting on ma or mb.] A) B) C) D) 22. As shown in the diagrams below, a lump of clay travels horizontally to the right toward a block at rest on a frictionless surface. Upon collision, the clay and the block stick together and move to the right. What is the total work done in moving the box from 3.0 to 6.0 meters? A) 9.0 J B) 18 J C) 6.0 J D) 36 J Compared to the total momentum of the clay and the block before the collision, the momentum of the clay-block system after the collision is A) less B) greater C) the same

5 26. The diagram below shows a 50.-kilogram crate on a frictionless plane at angle to the horizontal. The crate is pushed at constant speed up the incline from point A to point B by force F. 29. A block weighing 15 Newtons is pulled to the top of an incline that is 0.20 meter above the ground, as shown below. If angle were increased, what would be the effect on the magnitude of force F and the total work W done on the crate as it is moved from A to B? A) W would remain the same and the magnitude of F would decrease. B) W would remain the same and the magnitude of F would increase. C) W would increase and the magnitude of F would decrease. D) W would increase and the magnitude of F would increase. 27. In the diagram below, a 20.0-newton force is used to push a 2.00-kilogram cart a distance of 5.00 meters. If 4.0 joules of work are needed to pull the block the full length of the incline, how much work is done against friction? A) 1.0 J B) 0.0 J C) 3.0 J D) 7.0 J 30. In the diagram below, 400. joules of work is done raising a 72-newton weight a vertical distance of 5.0 meters. The work done on the cart is A) 100. J B) 200. J C) 150. J D) 40.0 J 28. A horizontal force of 40 Newtons pushes a block along a level table at a constant speed of 2 meters per second. How much work is done on the block in 6 seconds? A) 80 J B) 120 J C) 240 J D) 480 J How much work is done to overcome friction as the weight is raised? A) 40. J B) 360 J C) 400. J D) 760 J

6 31. A student pulls a block 3.0 meters along a horizontal surface at constant velocity. The diagram below shows the components of the force exerted on the block by the student. 33. The graph below represents the relationship between the work done by a student running up a flight of stairs and the time of ascent. How much work is done against friction? A) 18 J B) 24 J C) 30. J D) 42 J 32. As shown in the diagram below, a child applies a constant 20.-newton force along the handle of a wagon which makes a 25 angle with the horizontal. How much work does the child do in moving the wagon a horizontal distance of 4.0 meters? A) 5.0 J B) 34 J C) 73 J D) 80. J What does the slope of this graph represent? A) impulse B) momentum C) speed D) power 34. Which unit is equivalent to a watt, the SI unit of power? A) joule/second B) joule/volt C) joule/ohm D) joule/coulomb 35. A student running up a flight of stairs increases her speed at a constant rate. Which graph best represents the relationship between work and time for the student's run up the stairs? A) B) C) D)

7 36. In the diagram below, it takes a force of 40. Newtons to pull back the string of a bow 0.60 meter. As the arrow, leaves the bow, its kinetic energy is A) 24 J B) 6.0 J C) 12 J D) 33 J 37. Which energy transformation occurs in an operating electric motor? A) B) C) D) 38. The diagram below shows a moving, 5.00-kilogram cart at the foot of a hill 10.0 meters high. For the cart to reach the top of the hill, what is the minimum kinetic energy of the cart in the position shown? [Neglect energy loss due to friction.] 39. As the pendulum swings from position A to position B as shown in the diagram above, what is the relationship of kinetic energy to potential energy? [Neglect friction.] A) The kinetic energy decrease is more than the potential energy increase. B) The kinetic energy increase is more than the potential energy decrease. C) The kinetic energy decrease is equal to the potential energy increase. D) The kinetic energy increase is equal to the potential energy decrease. 40. A cart of mass M on a frictionless track starts from rest at the top of a hill having height h1, as shown in the diagram below. A) 4.91 J B) 50.0 J C) 250. J D) 491 J What is the kinetic energy of the cart when it reaches the flat, having height h3? A) mgh1 B) Mg(h1-h2) C) Mg(h2-h3) D) Mg(h1-h3) E) 0 J

8 41. A wound spring provides the energy to propel a toy car across a level floor. At time ti,the car is moving-at speed vi across the floor and the spring is unwinding, as shown below. At time tf, the spring has fully unwound and the car has coasted to a stop. 43. The wrecking crane shown below is moving toward a brick wall which is to be torn down. Which statement best describes the transformation of energy that occurs between the ti and tf? A) Gravitational potential energy at ti is converted to internal energy at tf. B) Elastic potential energy at ti is converted to kinetic energy at tf. C) Both elastic potential energy and kinetic energy at ti are converted to internal energy at tf. D) Both kinetic energy and internal energy at ti are converted to elastic potential energy at tf. 42. The graph below represents the kinetic energy, gravitational potential energy, and total mechanical energy of a moving block. Which best describes the motion of the block? A) accelerating on a flat horizontal surface B) sliding up a frictionless incline C) falling freely D) being lifted at constant velocity At what point in the swing of the wrecking ball should the ball make contact with the wall to make a collision with the greatest kinetic energy? A) 1 B) 2 C) 3 D) Which device transforms mechanical energy into electrical energy? A) generator B) motor C) transformer D) mass spectrometer 45. During an emergency stop, a kilogram car lost a total of joules of kinetic energy. What was the speed of the car at the moment the brakes were applied? A) 10. m/s B) 14 m.s C) 20. m/s D) 25 m/s 46. If the velocity of a moving object is doubled, the object's kinetic energy is A) unchanged B) halved C) doubled D) quadrupled 47. A shopping cart slows as it moves along a level floor. Which statement describes the energies of the cart? A) The kinetic energy increases and the gravitational potential energy remains the same. B) The kinetic energy increases and the gravitational potential energy decreases. C) The kinetic energy decreases and the gravitational potential energy remains the same. D) The kinetic energy decreases and the gravitational potential energy increases.

9 48. Two students of equal weight go from the first floor to the second floor. The first student uses an elevator and the second student walks up a flight of stairs. Compared to the gravitational potential energy gained by the first student, the gravitational potential energy gained by the second student is A) less B) greater C) the same 49. The diagram below shows a 1.5-kilogram kitten jumping from the top of a 1.80-meter-high refrigerator to a 0.90-meter-high counter. 51. The graph below represents the relationship between the force applied to a spring and spring elongation for four different springs. Which spring has the smallest spring constant? A) A B) B C) C D) D 52. Base your answer to the following question on A 20.-newton weight is attached to a spring, causing it to stretch, as shown in the diagram below. Compared to the kitten's gravitational potential energy on top of the refrigerator, the kitten's gravitational potential energy on top of the counter is A) half as great B) twice as great C) one-fourth as great D) four times as great 50. Three people of equal mass climb a mountain using paths A, B, and C shown in the diagram below. Along which path(s) does a person gain the greatest amount of gravitational potential energy from start to finish? A) A, only B) B, only C) C, only D) The gain is the same along all paths. How much elastic potential energy is stored in the spring? A) 5 J B) 10 J C) 40 J D) 20 J 53. The potential energy stored in a compressed spring is to the change in the spring's length as the kinetic energy of a moving body is to the body's A) speed B) mass C) radius D) acceleration

10 Base your answers to questions 54 through 58 on the diagram below which shows a 20-newton force pulling an object up a hill at a constant rate of 2 meters per second. 54. The magnitude of the momentum of the moving object is A) 0 kg-m/s B) 10 kg-m/s C) 100 kg-m/s D) 600 kg-m/s 55. How much work is done against friction? 56. The work done by the force in pulling the object from A to B is A) 50 J B) 100 J C) 500 J D) 600 J 57. The kinetic energy of the moving object is A) 5 J B) 10 J C) 15 J D) 50 J 58. The work done against gravity in moving the object from point A to point B is approximately A) 100 J B) 200 J C) 500 J D) 600 J Base your answers to questions 59 through 63 on the information and diagram below. A 3.0-kilogram object is placed on a frictionless track at point A and released from rest. (Assume the gravitational potential energy of the system to be zero at point C.) 59. Calculate the kinetic energy of the object at point F. [Show all work, including the equation and substitution with units.] 60. At what height would the mass need to start at to just make it to point F? 61. Calculate the gravitational potential energy of the object at point A. [Show all work, including the equation and substitution with units]

11 62. Calculate the kinetic energy of the object at point B. [Show all work, including the equation and substitution with units.] 63. Which letter represents the farthest point on the track that the object will reach? 64. Base your answer to parts a through d on the information below. A 8.0-kilogram concrete block is dropped from the top of a tall building. The block has fallen a distance of 60 meters and has a speed of 20 meters per second when it hits the ground. a At the instant the block was released, what was its gravitational potential energy with respect to the ground? [Show all calculations, including the equation and substitution with units.] b Calculate the kinetic energy of the block at the point of impact. [Show all calculations, including the equation and substitution with units.] c How much mechanical energy was "lost" by the block as it fell? d Using one or more complete sentences, explain what happened to the mechanical energy that was "lost" by the block.

12 65. Snow White accelerates uniformly from rest to a speed of 8.00 meters per second. Her kinetic energywas determined at 2.00-meter-per-second intervals and recorded in the data table below by Gingy. Plot the data points for kinetic energy of Snow White versus her speed. Base your answers to questions 66 through 68 on the information below. A roller coaster car has a mass of 290. kilograms. Starting from rest, the car acquires joules of kinetic energy as it descends to the bottom of a hill in 5.3 seconds. 66. Calculate the height of the hill. [Neglect friction.] [Show all work, including the equation and substitution with units.]

13 67. Calculate the speed of the roller coaster car at the bottom of the hill. [Show all work, including the equation and substitution with units.] 68. Calculate the magnitude of the average acceleration of the roller coaster car as it descends to the bottom of the hill. [Show all work, including the equation and substitution with units.] Base your answers to questions 69 through 71 on the graph below, which represents the relationship between vertical height and gravitational potential energy for an object near Earth's surface. 69. Using the graph, calculate the mass of the object. [Show all work, including the equation and substitution with units.] 70. What physical quantity does the slope of the graph represent? 71. Using a straightedge, draw a line on the graph above to represent the relationship between gravitational potential energy and vertical height for an object having a greater mass.

14 Base your answers to questions 72 through 74 on the information and diagram below. A kilogram empty cart moving with a speed of 6.0 meters per second is about to collide with a stationary loaded cart having a total mass of kilograms, as shown. After the collision, the carts lock and move together. [Assume friction is negligible.] 77. Base your answer to the following question on the information and diagram below. A 160.-newton box sits on a 10.-meter-long frictionless plane inclined at an angle of 30. to the horizontal as shown. Force (F) applied to a rope attached to the box causes the box to move with a constant speed up the incline. 72. Calculate the speed of the combined carts after the collision. 73. Calculate the kinetic energy of the combined carts after the collision. 74. How does the kinetic energy of the combined carts after the collision compare to the kinetic energy of the carts before the collision? Base your answers to questions 75 and 76 on the information below. A 50.-kilogram child running at 6.0 meters per second jumps onto a stationary 10.-kilogram sled. The sled is on a level frictionless surface. 75. a Calculate the speed of the sled with the child after she jumps onto the sled. [Show all work, including the equation and substitution with units.] b Calculate the kinetic energy of the sled with the child after she jumps onto the sled.[show all work, including the equation and substitution with units.] Calculate the amount of work done in moving the box from the bottom to the top of the inclined plane. [Show all work, including the equation and substitution with units.] 76. After a short time, the moving sled with the child aboard reaches a rough level surface that exerts a constant frictional force of 54 newtons on the sled. How much work must be done by friction to bring the sled with the child to a stop?

15 Answer Key Regents Practice:Momentum, Impulse, Work, Energy, Power, and Conservation Laws 1. D 2. A 3. D 4. D 5. B 36. C 37. A 38. D 39. D 40. D 61. DPE = mgdh DPE = (3.0 kg)(9.81 m/s 2 )(3.0 m) DPE = 88 J or 88.3 kg m 2 /s C 7. C 41. C 42. C A 43. C 9. D 44. A 10. C 45. C 11. D 12. C 13. A 14. A 15. C 16. B 17. C 46. D 47. C 48. C 49. A 50. D 51. D 52. A 62. ET = PE + KE + Q KE = mgdh KE = (3.0 kg)((.81 m/s 2 )(3.0 m 1.0 m) KE = 59 J or 58.9 J B 53. A 19. C 20. B 21. D 22. C 23. B 24. D 25. A 26. D 27. A 28. D 29. A 30. A 31. B 32. C 33. D 34. A 54. B J 56. D 57. B 58. C 59. ET = PE + KE + Q KE = mg h KE = (3.0 kg)((.81 m/s 2 )(3.0 m 1.0 m) KE = 59 J or 58.9 J 60. B 63. G 64. A) PE = 4720 J ; B) KE = 1600 J; C) The difference for what the student calculated in part a and b; D)The energy was lost due to air friction. or The energy was converted to heat energy. or The energy was lost due to friction. or Work was one on the air by the block. or The energy was lost due to work done against friction Examples: weight of object or weight mg force Fg 35. B

16 Answer Key Regents Practice:Momentum, Impulse, Work, Energy, Power, and Conservation Laws v f = 1.0 m/s 73. KE = 3.0 x 10 3 J 74. The KE of the combined carts after the collision is less than the KE of the carts before the collision. 75. a Pbefore = Pafter or mbeforevbefore = mafter vafter (50. kg)(6.0 m/s) = (60. kg) v after J vafter = (50. kg) (6.0 m/s) / (60. kg) vafter = 5.0 m/s b KE = mv 2 KE = (60. kg)(5.0 m/s) 2 KE = 750 J 77. w = Fd sin w = (160. N)(10. m)(sin 30. ) w = 800 J

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