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

A) the same inertia and a smaller magnitude ofmomentum

B) the same inertia and the same magnitude ofmomentum

C) greater inertia and a smaller magnitude ofmomentum

D) greater inertia and the same magnitude ofmomentum

1. Cart A has a mass of 2 kilograms and a speed of 3meters per second. Cart B has a mass of 3 kilogramsand a speed of 2 meters per second. Compared to theinertia and magnitude of momentum of cart A, cart B has

A) 4.5 × 104 kg•m/s, eastB) 4.5 × 104 kg•m/s, westC) 4.5 × 106 kg•m, eastD) 4.5 × 106 kg•m, west

2. What is the momentum of a 1.5 × 103-kilogram car asit travels at 30. meters per second due east for 60.seconds?

A) N-m/s2 B) kg-m/s2

C) N-m/s D) kg-m/s

3. Which is a unit of momentum?

A) 2.2 N B) 2.9 N C) 17 N D) 56 N

4. A 0.149-kilogram baseball, initially moving at 15meters per second, is brought to rest in 0.040 secondby a baseball glove on a catcher's hand. Themagnitude of the average force exerted on the ball bythe glove is

A) 50. N•s B) 2.0 N•sC) 6.0 N•s D) 12 N•s

5. In the diagram below, a 60.-kilogram rollerskaterexerts a 10.-newton force on a 30.-kilogramrollerskater for 0.20 second.

What is the magnitude of the impulse applied to the30.-kilogram rollerskater?

A) 7.0 × 101 N B) 8.2 × 102 NC) 1.7 × 103 N D) 2.0 × 103 N

6. During a collision, an 84-kilogram driver of a carmoving at 24 meters per second is brought to rest byan inflating air bag in 1.2 seconds. The magnitude ofthe force exerted on the driver by the air bag isapproximately

A) 20 kg m/s B) 30 kg m/sC) 60 kg m/s D) 80 kg m/s

7. The velocity-time graph below represents the motionof a 3-kilogram cart along a straight line. The cartstarts at t = 0 and initially moves north.

What is the magnitude of the change in momentum ofthe cart between t = 0 and t = 3 seconds?

Base your answers to questions 8 through 11 on the diagram below which represents two objects atrest on a frictionless horizontal surface with a spring compressed between them. When thecompressed spring is released, the two objects are pushed apart.

A) 25 J B) 20. J C) 10. J D) 5.0 J

8. What kinetic energy does the 2.0-kilogram object have after gaining a velocity of 5.0 meters persecond?

A) 20. kg-m/s B) 10. kg-m/s C) 5.0 kg-m/s D) 0 kg-m/s

9. What is the total momentum of the two-object system after the expansion of the spring?

A) 1.0 m/s B) 2.0 m/s C) 5.0 m/s D) 10. m/s

10. What is the velocity of the 2.0-kilogram object after being acted on by 10. Newton-seconds ofimpulse?

A) 0 N-s B) –5.0 N-s C) –10. N-s D) –20. N-s

11. If the 1.0-kilogram object receives an impulse of +20.-newton-seconds, what impulse does the2.0-kilogram object receive?

A) conservation of heatB) conservation of energyC) conservation of momentumD) conservation of mass

12. A rocket engine acquires motion by ejecting hotgases in the opposite direction. This is an example ofthe law of

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, andthen collides elastically with block B, which is at rest. Block A stops moving, and block B movesto the right after the collision.

A) B) C) D)

What is the total change in momentum of blocks A and B ?

A) 0.50 m/s left B) 0.50 m/s rightC) 5.5 m/s left D) 5.5 m/s right

14. The diagram below shows an 8.0-kilogram cartmoving to the right at 4.0 meters per second about tomake a head-on collision with a 4.0-kilogram cartmoving to the left at 6.0 meters per second.

After the collision , the 4.0-kilogram cart moves tothe right at 3.0 meters per second. What is thevelocity of the 8.0-kilogram cart after the collision?

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 0.20second. [Assume friction-less conditions.]

A) 0 m/s2 B) 10. m/s2 C) 25 m/s2 D) 50. m/s2

15. What is the average acceleration of cart B during the 0.20-second interaction?

A) 5.0 N-sec B) 10. N-sec C) 50. N-sec D) 100 N-sec

16. What is the magnitude of the impulse applied by the spring on cart A?

A) one-half as great B) twice as greatC) the same D) four times as great

17. Compared to the magnitude of the impulse acting on cart A, the magnitude of the impulse acting oncart B is

A) one-half as great B) twice as greatC) 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 greatC) 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 thecarts after the spring is released is

A)B)C)D)

20. In the diagram below, scaled vectors represent themomentum of each of two masses, A and B, slidingtoward each other on a frictionless, horizontalsurface.

Which scaled vector best represents the momentumof the system after the masses collide?

A) B)

C) D)

21. The diagram below represents two masses beforeand after they collide. Before the collision, mass mA is moving to the right with speed v, and mass mB isat rest. Upon collision, the two masses stick together.

Which expression represents the speed, v ', of themasses after the collision? [Assume no outsideforces are acting on mA or mB.]

A) less B) greaterC) the same

22. As shown in the diagrams below, a lump of claytravels horizontally to the right toward a block at reston a frictionless surface. Upon collision, the clayand the block stick together and move to the right.

Compared to the total momentum of the clay and theblock before the collision, the momentum of theclay-block system after the collision is

A) 2.7 × 103 kg B) 2.0 × 103 kgC) 1.5 × 103 kg D) 1.1 × 103 kg

23. Satellite A has a mass of 1.5 × 103 kilograms and istraveling east at 8.0 × 103 meters per second.Satellite B is traveling west at 6.0 × 103 meters persecond. The satellites collide head-on and come torest. What is the mass of satellite B?

A) lifting the object from the floor to the ceilingB) pushing the object along a horizontal floor

against a frictional forceC) decreasing the speed of the object until it comes

to restD) holding the object stationary above the

ground

24. Which action would require no work to be done onan object?

25. Base your answer to the following question on A boxis pushed to the right with a varying horizontal force.The graph below represents the relationship betweenthe applied force and the distance the box moves.

A) 9.0 J B) 18 J C) 6.0 J D) 36 J

What is the total work done in moving the box from3.0 to 6.0 meters?

A) W would remain the same and the magnitude ofF would decrease.

B) W would remain the same and the magnitude ofF would increase.

C) W would increase and the magnitude of F would decrease.

D) W would increase and the magnitude of F would increase.

26. The diagram below shows a 50.-kilogram crate on africtionless plane at angle to the horizontal. Thecrate is pushed at constant speed up the incline frompoint A to point B by force F.

If angle were increased, what would be the effecton the magnitude of force F and the total work W done on the crate as it is moved from A to B?

A) 100. J B) 200. JC) 150. J D) 40.0 J

27. In the diagram below, a 20.0-newton force is used topush a 2.00-kilogram cart a distance of 5.00 meters.

The work done on the cart is

A) 80 J B) 120 JC) 240 J D) 480 J

28. A horizontal force of 40 Newtons pushes a blockalong a level table at a constant speed of 2 metersper second. How much work is done on the block in6 seconds?

A) 1.0 J B) 0.0 J C) 3.0 J D) 7.0 J

29. A block weighing 15 Newtons is pulled to the top ofan incline that is 0.20 meter above the ground, asshown below.

If 4.0 joules of work are needed to pull the block thefull length of the incline, how much work is doneagainst friction?

A) 40. J B) 360 JC) 400. J D) 760 J

30. In the diagram below, 400. joules of work is doneraising a 72-newton weight a vertical distance of 5.0meters.

How much work is done to overcome friction as theweight is raised?

A) 18 J B) 24 J C) 30. J D) 42 J

31. A student pulls a block 3.0 meters along a horizontalsurface at constant velocity. The diagram belowshows the components of the force exerted on theblock by the student.

How much work is done against friction?

A) 5.0 J B) 34 J C) 73 J D) 80. J

32. As shown in the diagram below, a child applies aconstant 20.-newton force along the handle of awagon which makes a 25° angle with the horizontal.

How much work does the child do in moving thewagon a horizontal distance of 4.0 meters?

A) impulse B) momentumC) speed D) power

33. The graph below represents the relationship betweenthe work done by a student running up a flight ofstairs and the time of ascent.

What does the slope of this graph represent?

A) joule/second B) joule/voltC) joule/ohm D) joule/coulomb

34. Which unit is equivalent to a watt, the SI unit ofpower?

A) B)

C) D)

35. A student running up a flight of stairs increases herspeed at a constant rate. Which graph best representsthe relationship between work and time for thestudent's run up the stairs?

A) 24 J B) 6.0 J C) 12 J D) 33 J

36. In the diagram below, it takes a force of 40. Newtonsto pull back the string of a bow 0.60 meter.

As the arrow, leaves the bow, its kinetic energy is

A)B)C)D)

37. Which energy transformation occurs in an operatingelectric motor?

A) 4.91 J B) 50.0 JC) 250. J D) 491 J

38. The diagram below shows a moving, 5.00-kilogramcart at the foot of a hill 10.0 meters high. For the cartto reach the top of the hill, what is the minimumkinetic energy of the cart in the position shown?[Neglect energy loss due to friction.]

A) The kinetic energy decrease is more than thepotential energy increase.

B) The kinetic energy increase is more than thepotential energy decrease.

C) The kinetic energy decrease is equal to thepotential energy increase.

D) The kinetic energy increase is equal to thepotential energy decrease.

39. As the pendulum swings fromposition A to position B as shown in the diagramabove, what is the relationship of kinetic energy topotential energy? [Neglect friction.]

A) mgh1 B) Mg(h1-h2)C) Mg(h2-h3) D) Mg(h1-h3)E) 0 J

40. A cart of mass M on a frictionless track starts fromrest at the top of a hill having height h1, as shown inthe diagram below.

What is the kinetic energy of the cart when itreaches the flat, having height h3?

A) Gravitational potential energy at ti is convertedto internal energy at tf.

B) Elastic potential energy at ti is converted tokinetic energy at tf.

C) Both elastic potential energy and kineticenergy at ti are converted to internal energyat tf.

D) Both kinetic energy and internal energy at ti areconverted to elastic potential energy at tf.

41. A wound spring provides the energy to propel a toycar across a level floor. At time ti,the car ismoving-at speed vi across the floor and the spring isunwinding, as shown below. At time tf, the springhas fully unwound and the car has coasted to a stop.

Which statement best describes the transformationof energy that occurs between the ti and tf?

A) accelerating on a flat horizontal surfaceB) sliding up a frictionless inclineC) falling freelyD) being lifted at constant velocity

42. The graph below represents the kinetic energy,gravitational potential energy, and total mechanicalenergy of a moving block.

Which best describes the motion of the block?

A) 1 B) 2 C) 3 D) 4

43. The wrecking crane shown below is moving towarda brick wall which is to be torn down.

At what point in the swing of the wrecking ballshould the ball make contact with the wall to make acollision with the greatest kinetic energy?

A) generator B) motorC) transformer D) mass spectrometer

44. Which device transforms mechanical energy intoelectrical energy?

A) 10. m/s B) 14 m.sC) 20. m/s D) 25 m/s

45. During an emergency stop, a 1.5 × 103-kilogram carlost a total of 3.0 × 105 joules of kinetic energy.What was the speed of the car at the moment thebrakes were applied?

A) unchanged B) halvedC) doubled D) quadrupled

46. If the velocity of a moving object is doubled, theobject's kinetic energy is

A) The kinetic energy increases and thegravitational potential energy remains the same.

B) The kinetic energy increases and thegravitational potential energy decreases.

C) The kinetic energy decreases and thegravitational potential energy remains thesame.

D) The kinetic energy decreases and thegravitational potential energy increases.

47. A shopping cart slows as it moves along a levelfloor. Which statement describes the energies of thecart?

A) less B) greaterC) the same

48. Two students of equal weight go from the first floorto the second floor. The first student uses an elevatorand the second student walks up a flight of stairs.Compared to the gravitational potential energygained by the first student, the gravitational potentialenergy gained by the second student is

A) half as great B) twice as greatC) one-fourth as great D) four times as great

49. The diagram below shows a 1.5-kilogram kittenjumping from the top of a 1.80-meter-highrefrigerator to a 0.90-meter-high counter.

Compared to the kitten's gravitational potentialenergy on top of the refrigerator, the kitten'sgravitational potential energy on top of the counter is

A) A, onlyB) B , onlyC) C, onlyD) The gain is the same along all paths.

50. Three people of equal mass climb a mountain usingpaths A, B, and C shown in the diagram below.

Along which path(s) does a person gain the greatestamount of gravitational potential energy from startto finish?

A) A B) B C) C D) D

51. The graph below represents the relationship betweenthe force applied to a spring and spring elongationfor four different springs.

Which spring has the smallest spring constant?

52. Base your answer to the following question on A20.-newton weight is attached to a spring, causing itto stretch, as shown in the diagram below.

A) 5 J B) 10 J C) 40 J D) 20 J

How much elastic potential energy is stored in thespring?

A) speed B) massC) radius D) acceleration

53. The potential energy stored in a compressed springis to the change in the spring's length as the kineticenergy of a moving body is to the body's

Base your answers to questions 54 through 58 on the diagram below which shows a 20-newton forcepulling an object up a hill at a constant rate of 2 meters per second.

A) 0 kg-m/s B) 10 kg-m/s C) 100 kg-m/s D) 600 kg-m/s

54. The magnitude of the momentum of the moving object is

55. How much work is done against friction?

A) 50 J B) 100 J C) 500 J D) 600 J

56. The work done by the force in pulling the object from A to B is

A) 5 J B) 10 J C) 15 J D) 50 J

57. The kinetic energy of the moving object is

A) 100 J B) 200 J C) 500 J D) 600 J

58. The work done against gravity in moving the object from point A to point B is approximately

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. (Assumethe 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 andsubstitution 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 theequation and substitution with units]

62. Calculate the kinetic energy of the object at point B. [Show all work, including the equation andsubstitution 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 adistance 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 theground? [Show all calculations, including the equation and substitution with units.]

bCalculate the kinetic energy of the block at the point of impact. [Show all calculations, including theequation and substitution with units.]

cHow much mechanical energy was "lost" by the block as it fell?

dUsing one or more complete sentences, explain what happened to the mechanical energy that was"lost" by the block.

65. Snow White accelerates uniformly from rest to a speed of 8.00 meters per second. Her kineticenergywas determined at 2.00-meter-per-second intervals and recorded in the data table below byGingy.

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 3.13 ×105 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 andsubstitution with units.]

67. Calculate the speed of the roller coaster car at the bottom of the hill. [Show all work, including theequation and substitution with units.]

68. Calculate the magnitude of the average acceleration of the roller coaster car as it descends to thebottom 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 relationshipbetween 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 andsubstitution 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 betweengravitational potential energy and vertical height for an object having a greater mass.

Base your answers to questions 72 through 74 on theinformation and diagram below.

A 1000.-kilogram empty cart moving with aspeed of 6.0 meters per second is about to collidewith a stationary loaded cart having a total massof 5000. kilograms, as shown. After the collision,the carts lock and move together. [Assumefriction is negligible.]

72. Calculate the speed of the combined carts after thecollision.

73. Calculate the kinetic energy of the combined cartsafter the collision.

74. How does the kinetic energy of the combined cartsafter the collision compare to the kinetic energy ofthe carts before the collision?

Base your answers to questions 75 and 76 on theinformation below.

A 50.-kilogram child running at 6.0 meters persecond 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 aftershe jumps onto the sled. [Show all work, includingthe equation and substitution with units.]b Calculate the kinetic energy of the sled with thechild after she jumps onto the sled.[Show all work,including the equation and substitution with units.]

76. After a short time, the moving sled with the childaboard reaches a rough level surface that exerts aconstant frictional force of 54 newtons on the sled.How much work must be done by friction to bringthe sled with the child to a stop?

77. Base your answer to the following question on theinformation and diagram below.

A 160.-newton box sits on a 10.-meter-longfrictionless plane inclined at an angle of 30.° tothe horizontal as shown. Force (F) applied to arope attached to the box causes the box to movewith a constant speed up the incline.

Calculate the amount of work done in moving thebox from the bottom to the top of the inclined plane.[Show all work, including the equation andsubstitution with units.]

Answer KeyRegents Practice:Momentum, Impulse, Work, Energy, Power, and Conservation Laws

1. D2. A3. D4. D5. B6. C7. C8. A9. D10. C11. D12. C13. A14. A15. C16. B17. C18. B19. C20. B21. D22. C23. B24. D25. A26. D27. A28. D29. A30. A31. B32. C33. D34. A35. B

36. C37. A38. D39. D40. D41. C42. C43. C44. A45. C46. D47. C48. C49. A50. D51. D52. A53. A54. B55. 109.5 J56. D57. B58. C59. ET = PE + KE + Q

KE= mg hKE= (3.0 kg)((.81 m/s2

)(3.0 m – 1.0 m)KE = 59 J or 58.9 J

60. B

61. DPE = mgDhDPE = (3.0 kg)(9.81m/s2)(3.0 m)DPE = 88 J or 88.3kg•m2/s2

62. ET = PE + KE + QKE = mgDhKE = (3.0 kg)((.81 m/s2

)(3.0 m – 1.0 m)KE = 59 J or 58.9 J

63. G64. A) PE = 4720 J ;

B) KE = 1600 J; C)The difference forwhat the studentcalculated in part aand b; D)The energywas lost due to airfriction. or Theenergy wasconverted to heatenergy. or Theenergy was lost dueto friction. or Workwas one on the airby the block. or Theenergy was lost dueto work done againstfriction.

65.

66.

67.

68.

69.

70. Examples: – weightof object or weight –mg – force – Fg

Answer KeyRegents Practice:Momentum, Impulse, Work, Energy, Power, and Conservation Laws

71.

72. v f = 1.0 m/s73. KE = 3.0 x 103 J74. The KE of the

combined carts afterthe collision is lessthan the KE of thecarts before thecollision.

75. a Pbefore = Pafter or

mbeforevbefore = maftervafter

(50. kg)(6.0 m/s) =(60. kg) vafter

vafter = (50. kg) (6.0m/s) / (60. kg)

vafter = 5.0 m/s

b KE = mv2

KE = (60. kg)(5.0m/s)2

KE = 750 J76. 750 J77. w = Fd sin

w = (160. N)(10.m)(sin 30.°)w = 800 J