1 k. 1 m. m A. AP Physics Multiple Choice Practice Work-Energy

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1 AP Physics Multiple Choice Practice Wor-Energy 1. A ass attached to a horizontal assless spring with spring constant, is set into siple haronic otion. Its axiu displaceent fro its equilibriu position is A. What is the asses speed as it passes through its equilibriu position? ( A)0 ( B) A ( C) A ( D) 1 A ( E) 1 A. A force F at an angle θ above the horizontal is used to pull a heavy suitcase of weight g a distance d along a level floor at constant velocity. The coefficient of friction between the floor and the suitcase is µ. The wor done by the frictional force is: (A) Fd cos θ (B) gh Fd cos θ (C) µ Fd cos θ (D) -µgd (E) -µ gd cos θ 3. If the unit for force is F, the unit for velocity V, and the unit for tie T, then the unit for energy is: (A) FVT (B) F/T (C) FV/T (D) F/T (E) FV /T 4. A force of 10 N stretches a spring that has a spring constant of 0 N/. The potential energy stored in the spring is: (A).5 J (B) 5.0 J (C) 10 J (D) 40 J (E) 00 J 5. A g ball is attached to a 0.80 string and whirled in a horizontal circle at a constant speed of 6 /s. The wor done on the ball during each revolution is: (A) 450 J (B) 90 J (C) 7 J (D) 16 J (E) zero 6. A pendulu bob of ass on a cord of length L is pulled sideways until the cord aes an angle θ with the vertical as shown in the figure to the right. The change in potential energy of the bob during the displaceent is: (A) gl (1 cos θ) (B) gl (1 sin θ) (C) gl sin θ (D) gl cos θ (E) gl (1 sin θ) 7. A force F directed at an angle θ above the horizontal is used to pull a crate a distance D across a level floor. The wor done by the force F is (A) FD (B) FD cos θ (C) FD sin θ (D) g sin θ (E) gd cos θ 8. A copressed spring has 16 J of potential energy. What is the axiu speed it can ipart to a g object? (A).8 /s (B) 4.0 /s (C) 5.6 /s (D) 8.0 /s (E) 16 /s 9. A softball player catches a ball of ass, which is oving towards her with horizontal speed V. While bringing the ball to rest, her hand oved bac a distance d. Assuing constant deceleration, the horizontal force exerted on the ball by the hand is (A) V /(d) (B) V /d (C) Vd (D) V/d (E) V/d 10. A 3 g bloc with initial speed 4 /s slides across a rough horizontal floor before coing to rest. The frictional force acting on the bloc is 3 N. How far does the bloc slide before coing to rest? (A) 1.0 (B).0 (C) 4.0 (D) 8.0 (E) A construction laborer holds a 0 g sheet of wallboard 3 above the floor for 4 seconds. During these 4 seconds how uch power was expended on the wallboard? (A) 400 W (B) 340 W (C) 7 W (D) 15 W (E) none of these

2 1. A pendulu is pulled to one side and released. It swings freely to the opposite side and stops. Which of the following ight best represent graphs of inetic energy (E ), potential energy (E p ) and total echanical energy (E T ) Probles 13 and 14 refer to the following situation: A car of ass slides across a patch of ice at a speed v with its braes loced. It the hits dry paveent and sids to a stop in a distance d. The coefficient of inetic friction between the tires and the dry road isµ. 13. If the car has a ass of, it would have sidded a distance of (A) 0.5 d (B) d (C) 1.41 d (D) d (E) 4 d 14. If the car has a speed of v, it would have sidded a distance of (A) 0.5 d (B) d (C) 1.41 d (D) d (E) 4 d 15. A ball is thrown vertically upwards with a velocity v and an initial inetic energy E. When half way to the top of its flight, it has a velocity and inetic energy respectively of (A) v E, (B) v E, (C) v E, 4 (D) v E, (E) v E,

3 16. A football is iced off the ground a distance of 50 yards downfield. Neglecting air resistance, which of the following stateents would be INCORRECT when the football reaches the highest point? (A) all of the balls original inetic energy has been changed into potential energy (B) the balls horizontal velocity is the sae as when it left the icers foot (C) the ball will have been in the air one-half of its total flight tie (D) the ball has an acceleration of g (E) the vertical coponent of the velocity is equal to zero 17. A ass is attached to a spring with a spring constant. If the ass is set into otion by a displaceent d fro its equilibriu position, what would be the speed, v, of the ass when it returns to equilibriu position? (A) v d (B) v d (C) v d (D) v gd g (E) v d 18. If M represents units of ass, L represents units of length, and T represents units of tie, the diensions of power would be: (A) ML T (B) ML T (C) ML 3 T (D) ML T (E) ML T 19. An autoobile engine delivers 4000 watts of power to a car s driving wheels. If the car aintains a constant speed of 30 /s, what is the agnitude of the retarding force acting on the car? (A) 800 N (B) 960 N (C) 1950 N (D) 70,000 N (E) 1,560,000 N 0. A fan blows the air and gives it inetic energy. An hour after the fan has been turned off, what has happened to the inetic energy of the air? (A) it disappears (B) it turns into potential energy (C) it turns into theral energy (D) it turns into sound energy (E) it turns into electrical energy 1. A box of old textboos is on the iddle shelf in the booroo 1.3 fro the floor. If the janitor relocates the box to a shelf that is.6 fro the floor, how uch wor does he do on the box? The box has a ass of 10 g. (A) 13 J (B) 6 J (C) 5 J (D) 130 J (E) 60 J. A ass, M, is at rest on a frictionless surface, connected to an ideal horizontal spring that is unstretched. A person extends the spring 30 c fro equilibriu and holds it by applying a 10 N force. The spring is brought bac to equilibriu and the ass connected to it is now doubled to M. If the spring is extended bac 30 c fro equilibriu, what is the necessary force applied by the person to hold the ass stationary there? (A) 0 N (B) 14.1 N (C) 10 N (D) 7.07 N (E) 5 N 3. A deliveryan oves 10 cartons fro the sidewal, along a 10-eter rap to a loading doc, which is 1.5 eters above the sidewal. If each carton has a ass of 5 g, what is the total wor done by the deliveryan on the cartons to ove the to the loading doc? (A) 500 J (B) 3750 J (C) J (D) 5000 J (E) J 4. A roc is dropped fro the top of a tall tower. Half a second later another roc, twice as assive as the first, is dropped. Ignoring air resistance, (A) the distance between the rocs increases while both are falling. (B) the acceleration is greater for the ore assive roc. (C) the speed of both rocs is constant while they fall. (D) they strie the ground ore than half a second apart. (E) they strie the ground with the sae inetic energy. 5. A 60.0-g ball of clay is tossed vertically in the air with an initial speed of 4.60 /s. Ignoring air resistance, what is the change in its potential energy when it reaches its highest point? (A) 0 J (B) 45 J (C) 80 J (D) 635 J (E) 700 J

4 6. Which of the following is true for a syste consisting of a ass oscillating on the end of an ideal spring? (A) The inetic and potential energies are equal to each other at all ties. (B) The inetic and potential energies are both constant. (C) The axiu potential energy is achieved when the ass passes through its equilibriu position. (D) The axiu inetic energy and axiu potential energy are equal, but occur at different ties. (E) The axiu inetic energy occurs at axiu displaceent of the ass fro its equilibriu position 7. Fro the top of a high cliff, a ball is thrown horizontally with initial speed v o. Which of the following graphs best represents the ball's inetic energy K as a function of tie t? 8. A person pushes a box across a horizontal surface at a constant speed of 0.5 eter per second. The box has a ass of 40 ilogras, and the coefficient of sliding friction is 0.5. The power supplied to the box by the person is (A) 0. W (B) 5 W (C) 50 W (D) 100 W (E) 00 W 9. A horizontal force F is used to pull a 5-ilogra bloc across a floor at a constant speed of 3 eters per second. The frictional force between the bloc and the floor is 10 newtons. The wor done by the force F in 1 inute is ost nearly (A) 0 J (B) 30 J (C) 600 J (D) 1,350 J (E) 1,800 J Questions 30-31: A bloc oscillates without friction on the end of a spring as shown. The iniu and axiu lengths of the spring as it oscillates are, respectively, x in and x ax. The graphs below can represent quantities associated with the oscillation as functions of the length x of the spring. 30. Which graph can represent the total echanical energy of the bloc-spring syste as a function of x? (A) A (B) B (C) C (D) D (E) E 31. Which graph can represent the inetic energy of the bloc as a function of x? (A) A (B) B (C) C (D) D (E) E

5 Questions 3-33 A ball swings freely bac and forth in an arc fro point I to point IV, as shown. Point II is the lowest point in the path, III is located 0.5 eter above II, and IV is I eter above II. Air resistance is negligible. 3. If the potential energy is zero at point II, where will the inetic and potential energies of the ball be equal? (A) At point II (B) At soe point between II and III (C) At point III (D) At soe point between III and IV (E) At point IV 33. The speed of the ball at point II is ost nearly (A) 3.0 /s (B) 4.5 /s (C) 9.8 /s (D) 14 /s (E) 0 /s 34. An ideal spring obeys Hooe's law, F = -x. A ass of 0.50 ilogra hung vertically fro this spring stretches the spring eter. The value of the force constant for the spring is ost nearly (A) 0.33 N/ (B) 0.66 N/ (C) 6.6 N/ (D) 33 N/ (E) 66 N/ 35. The figure shows a rough seicircular trac whose ends are at a vertical height h. A bloc placed at point P at one end of the trac is released fro rest and slides past the botto of the trac. Which of the following is true of the height to which the bloc rises on the other side of the trac? (A) It is equal to h/( ) (B) It is equal to h/4 (C) It is equal to h/ (D) It is equal to h (E) It is between zero and h; the exact height depends on how uch energy is lost to friction. 36. A weight lifter lifts a ass at constant speed to a height h in tie t. What is the average power output of the weight lifter? (A) g (B) h (C) gh (D) ght (E) gh /t 37. A bloc of ass slides on a horizontal frictionless table with an initial speed v o. It then copresses a spring of force constant and is brought to rest. How uch is the spring copressed fro its natural length? v (A) 0 g (B) v 0 (C) v 0 (D) (E) g Questions v 0 v 0 A plane 5 eters in length is inclined at an angle of 37, as shown. A bloc of weight 0 newtons is placed at the top of the plane and allowed to slide down. 38. The ass of the bloc is ost nearly (A) 1.0 g (B) 1. g (C) 1.6 g (D).0 g (E).5 g 39. The agnitude of the noral force exerted on the bloc by the plane is ost nearly (A) 10 N (B) 1 N (C) 16 N (D) 0 N (E) 33 N 40. The wor done on the bloc by the gravitational force during the 5-eter slide down the plane is ost nearly (A) 0 J (B) 60 J (C) 80 J (D) 100 J (E) 130 J

6 41. A student weighing 700 N clibs at constant speed to the top of an 8 vertical rope in 10 s. The average power expended by the student to overcoe gravity is ost nearly (A) 1.1 W (B) 87.5 W (C) 560 W (D) 875 W (E) 5,600 W 4. The graph shown represents the potential energy U as a function of displaceent x for an object on the end of a spring oving bac and forth with aplitude x. Which of the following graphs represents the inetic energy K of the object as a function of displaceent x? 43. A child pushes horizontally on a box of ass which oves with constant speed v across a horizontal floor. The coefficient of friction between the box and the floor is. At what rate does the child do wor on the box? (A) gv (B) gv (C) g/v (D) g/v (E) v 44. A bloc of ass 3.0 g is hung fro a spring, causing it to stretch 1 c at equilibriu, as shown. The 3.0 g bloc is then replaced by a 4.0 g bloc, and the new bloc is released fro the position shown, at which the spring is unstretched. How far will the 4.0 g bloc fall before its direction is reversed? (A) 9 c (B) 18 c (C) 4 c (D) 3 c (E) 48 c 45. What is the inetic energy of a satellite of ass that orbits the Earth, of ass M, in a circular orbit of radius R? (A) Zero (B) 1 GM R (C) 1 4 GM R 1 GM (D) R (E) GM R

7 Questions A roc of ass is thrown horizontally off a building fro a height h, as shown above. The speed of the roc as it leaves the thrower s hand at the edge of the building is v How uch tie does it tae the roc to travel fro the edge of the building to the ground? (A) hv o (B) h v 0 (C) hv g 0 (D) h g (E) h g 47. What is the inetic energy of the roc just before it hits the ground? (A) gh (B) ½ v 0 (C) ½ v 0 - gh (D) ½ v 0 +gh (E) gh-½ v 0 A sphere of ass 1, which is attached to a spring, is displaced downward fro its equilibriu position as shown above left and released fro rest. A sphere of ass, which is suspended fro a string of length L, is displaced to the right as shown above right and released fro rest so that it swings as a siple pendulu with sall aplitude. Assue that both spheres undergo siple haronic otion 48. Which of the following is true for both spheres? (A) The axiu inetic energy is attained as the sphere passes through its equilibriu position. (B) The axiu inetic energy is attained as the sphere reaches its point of release. (C) The iniu gravitational potential energy is attained as the sphere passes through its equilibriu position. (D) The axiu gravitational potential energy is attained when the sphere reaches its point of release. (E) The axiu total energy is attained only as the sphere passes through its equilibriu position.

8 Questions An object of ass is initially at rest and free to ove without friction in any direction in the xy-plane. A constant net force of agnitude F directed in the +x direction acts on the object for 1 s. Iediately thereafter a constant net force of the sae agnitude F directed in the +y direction acts on the object for 1 s. After this, no forces act on the object. 49. Which of the following vectors could represent the velocity of the object at the end of 3 s, assuing the scales on the x and y axes are equal? 50. Which of the following graphs best represents the inetic energy K of the object as a function of tie?

9 51. A constant force of 900 N pushes a 100 g ass up the inclined plane shown at a unifor speed of 4 /s. The power developed by the 900 N force is ost nearly (A) 400 W (B) 800 W (C) 900 W (D) 1000W (E) 3600 W 5. An object of ass is lifted at constant velocity a vertical distance H in tie T. The power supplied by the lifting force is (A) ght (B) gh/t (C) g/ht (D) gt/h (E) zero 53. A syste consists of two objects having asses l and ( l < ). The objects are connected by a assless string, hung over a pulley as shown, and then released. When the object of ass has descended a distance h, the potential energy of the syste has decreased by (A) ( - l )gh (B) gh (C) ( 1 + )gh (D) ½( l + )gh (E) The following graphs, all drawn to the sae scale, represent the net force F as a function of displaceent x for an object that oves along a straight line. Which graph represents the force that will cause the greatest change in the inetic energy of the object fro x = 0 to x = x 1?

10 55. Fro the top of a 70-eter-high building, a l-ilogra ball is thrown directly downward with an initial speed of 10 eters per second. If the ball reaches the ground with a speed of 30 eters per second, the energy lost to friction is ost nearly (A) 0J (B) 100 J (C) 300 J ( D) 400 J (E) 700 J 56. A pendulu consists of a ball of ass suspended at the end of a assless cord of length L as shown. The pendulu is drawn aside through an angle of 60 with the vertical and released. At the low point of its swing, the speed of the pendulu ball is (A) gl (B) gl (C) ½gL (D) gl (E) gl 57. A roc is lifted for a certain tie by a force F that is greater in agnitude than the roc's weight W. The change in inetic energy of the roc during this tie is equal to the (A) wor done by the net force (F - W) (B) wor done by F alone (C) wor done by W alone (D) difference in the oentu of the roc before and after this tie (E) difference in the potential energy of the roc before and after this tie. 58. A ball is thrown upward. At a height of 10 eters above the ground, the ball has a potential energy of 50 joules (with the potential energy equal to zero at ground level) and is oving upward with a inetic energy of 50 joules. Air friction is negligible. The axiu height reached by the ball is ost nearly (A) 10 (B) 0 (C) 30 (D) 40 (E) A bloc on a horizontal frictionless plane is attached to a spring, as shown. The bloc oscillates along the x-axis with aplitude A. Which of the following stateents about energy is correct? (A) The potential energy of the spring is at a iniu at x = 0. (B) The potential energy of the spring is at a iniu at x = A. (C) The inetic energy of the bloc is at a iniu at x =0. (D) The inetic energy of the bloc is at a axiu at x = A. (E) The inetic energy of the bloc is always equal to the potential energy of the spring. 60. During a certain tie interval, a constant force delivers an average power of 4 watts to an object. If the object has an average speed of eters per second and the force acts in the direction of otion of the object, the agnitude of the force is (A) 16 N (B) 8 N (C) 6 N (D) 4N (E) N 61. A spring-loaded gun can fire a projectile to a height h if it is fired straight up. If the sae gun is pointed at an angle of 45 fro the vertical, what axiu height can now be reached by the projectile? (A) h/4 (B) h (C) h/ (D) h (E) h 6. A force F is exerted by a broo handle on the head of the broo, which has a ass. The handle is at an angle to the horizontal, as shown. The wor done by the force on the head of the broo as it oves a distance d across a horizontal floor is (A) Fd sin (B) Fd cos (C) F cos (D) F tan (E) Fd sin

11 Question A spring has a force constant of 100 N/ and an unstretched length of One end is attached to a post that is free to rotate in the center of a sooth table, as shown in the top view. The other end is attached to a 1 g disc oving in unifor circular otion on the table, which stretches the spring by Friction is negligible. 63. What is the centripetal force on the disc? (A) 0.3 N (B) 3N (C) 10 N (D) 300 N (E) 1,000 N 64. What is the wor done on the disc by the spring during one full circle? (A) 0 J (B) 94 J (C) 186 J (D) 314 J (E) 68 J 65. A frictionless pendulu of length 3 swings with an aplitude of 10. At its axiu displaceent, the potential energy of the pendulu is 10 J. What is the inetic energy of the pendulu when its potential energy is 5 J? (A) 3.3 J (B) 5 J (C) 6.7 J (D) 10 J (E) 15 J 66. A descending elevator of ass 1,000 g is uniforly decelerated to rest over a distance of 8 by a cable in which the tension is 11,000 N. The speed v i of the elevator at the beginning of the 8 descent is ost nearly (A) 4 /s (B) 10 /s (C) 13 /s (D) 16 /s (E) 1 /s 67. An ideal assless spring is fixed to the wall at one end, as shown. A bloc of ass M attached to the other end of the spring oscillates with aplitude A on a frictionless, horizontal surface. The axiu speed of the bloc is v. The force constant of the spring is (A) Mg A (B) Mgv A (C) Mv A (D) Mv A (E) Mv A 68. A 1000 W electric otor lifts a 100 g safe at constant velocity. The vertical distance through which the otor can raise the safe in 10 s is ost nearly (A) 1 (B) 3 (C) 10 (D) 3 (E) A deliveryan oves 10 cartons fro the sidewal, along a 10-eter rap to a loading doc, which is 1.5 eters above the sidewal. If each carton has a ass of 5 g, what is the total wor done by the deliveryan on the cartons to ove the to the loading doc? (A) 500 J ( B) 3750 J (C) J (D) 5000 J (D) J 70. A 60.0-g ball of clay is tossed vertically in the air with an initial speed of 4.60 /s. Ignoring air resistance, what is the change in its potential energy when it reaches its highest point? (A) 0 J (B) 45 J (C) 80 J (D) 635 J (E) 700

12 71. A 500-g car is oving at 8 /s. The driver sees a barrier ahead. If the car taes 95 eters to coe to rest, what is the agnitude of the iniu average net force necessary to stop? (A) 47.5 N (B) 1400 N (C) 060 N (D) N (E) N 7. A person pushes a bloc of ass M = 6.0 g with a constant speed of 5.0 /s straight up a flat surface inclined 30.0 above the horizontal. The coefficient of inetic friction between the bloc and the surface is μ = What is the net force acting on the bloc? (A) 0N (B) 1N (C) 30N (D) 51N (E) 76N 73. A bloc of ass M on a horizontal surface is connected to the end of a assless spring of spring constant. The bloc is pulled a distance x fro equilibriu and when released fro rest, the bloc oves toward equilibriu. What coefficient of inetic friction between the surface and the bloc would allow the bloc to return to equilibriu and stop? ( A) x Mg ( B) x Mg ( C) x Mg ( D) Mg x ( E) 4Mgx 74. An object is dropped fro rest fro a certain height. Air resistance is negligible. After falling a distance d, the object s inetic energy is proportional to which of the following? (A) 1 / d (B) 1 / d (C) d (D) d (E) d 75. An object is projected vertically upward fro ground level. It rises to a axiu height H. If air resistance is negligible, which of the following ust be true for the object when it is at a height H/? (A) Its speed is half of its initial speed. (B) Its inetic energy is half of its initial inetic energy. (C) Its potential energy is half of its initial potential energy. (D) Its total echanical energy is half of its initial value. (E) Its total echanical energy is half of its value at the highest point. 76. A particle P oves around the circle of radius R under the influence of a radial force of agnitude F as shown. What is the wor done by the radial force as the particle oves fro position 1 to position halfway around the circle? (A) Zero (B) RF (C) RF (D) πrf (E) πrf