1. AP Physics Semester Review 26 is torque
32, 45-52, 58, 59 deal with momentum
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2. 1. The position of a particle moving along the x axis is given
by , where t is in seconds. What is the average velocity during the time interval t = 1.0 s to
t = 3.0 s?
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3. 2. A bullet is fired through a board, 50
2. A bullet is fired through a board, 50.0 cm thick, with its line of motion perpendicular to the face of the board. If it enters with a speed of and emerges with a speed of , what is the bullet's acceleration as it passes through the board?
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4. 3. The position of a particle moving along the x axis is given by x = 6.0t t3, where x is in meters and t in seconds. What is the position of the particle when it achieves its maximum speed in the positive x direction?
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5. 4. A particle moving along the x axis has a position given by
x = (54t - 2t3)m, where t is in seconds. How far is the particle from the origin (x = 0) when the particle is not moving?
The particle is not moving at the instand the velocity equals zero.
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6. 5. An object is thrown vertically and has an upward velocity of v when it reaches one fourth of its maximum height above its launch point. What is the initial (launch) speed of the object?
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7. 6. A ball thrown vertically from ground level is caught 3
6. A ball thrown vertically from ground level is caught 3.0 seconds later by a person on a balcony which is 30 meters above the ground. Determine the initial speed of the ball.
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8. 7. Vx is the velocity of a particle moving along the x axis as shown
7. Vx is the velocity of a particle moving along the x axis as shown. If x = 2.0 m at t = 1.0 s, what is the position of the particle at t = 6.0 s?
∆x is the area under the line. The area between t = 1 sec and t = 3 sec cancels out. So we’ll find the area from t = 3 sec to t = 6 sec.
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9. 8. An object is thrown vertically upward such that it has a speed of when it reaches two thirds of its maximum height above the launch point. Determine this maximum height.
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10. 9. Object A is thrown downward at t = 0 with an initial speed of from a height of 60m above the ground. At the same instant, a object B is propelled vertically upward from ground level with a speed of At what height above the ground will the two objects pass each other?
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11. 10. A car travels north at 30 for one half hour
10. A car travels north at for one half hour. It then travels south at for 15 minutes. The total distance the car has traveled and its displacement are:
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12. 11. A particle starts from the origin at t = 0 with a velocity of 8
11. A particle starts from the origin at t = 0 with a velocity of 8.0i and moves in the xy plane with a constant acceleration of (-2.0i + 4.0j) At the instant the particle achieves its maximum positive x coordinate, how far is it from the origin?
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13. 12. A rock is projected from the edge of the top of a 100-ft tall building at some unknown angle above the horizontal. The rock strikes the ground a horizontal distance of 160 ft from the base of the building 5.0 seconds after being projected. Assume that the ground is level and that the side of the building is vertical. Determine the speed with which the rock was projected.
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14. 13. A football is thrown upward at a 30° angle to the horizontal
13. A football is thrown upward at a 30° angle to the horizontal. To throw a 40.0-meter pass, what must be the initial speed of the ball?
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15. 14. The horizontal surface on which the objects slide is frictionless
14. The horizontal surface on which the objects slide is frictionless. If M = 2.0 Kg and the Tension in string 1 is 18 Newtons, Determine F.
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16. 15. A particle starts from the origin at t = 0 with a velocity of
and moves in the xy plane with a constant acceleration of At the instant the x coordinate of the particle is 32 meters, what is the magnitude of the y coordinate?
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17. 16. The surface of an inclined plane is frictionless
16. The surface of an inclined plane is frictionless. If F = 30N, what is the magnitude of the force exerted on the 3kg block by the 2kg block
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19. First, find the acceleration of the system!
17. If P = 5.0 N, what is the magnitude of the force exerted on block 1 by block 2? 3 2 1 P
5 Kg
3 Kg
2 Kg
First, find the acceleration of the system!
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20. For every action Force there is an equal and opposite reaction Force!
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21. 18. If a = (20i + 2.7j), and b is as shown, what is the magnitude of the Resultant of the two vectors? y b
30° 20 x
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22. 19. The graph below shows the force on an object of mass m as a function of time. For the time interval t = 0 to t = 3 seconds, the total change in the momentum of the object is
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23. 20. The position of a particle moving along the x axis is given by , where x is in meters and t is in seconds. What is the average acceleration between 2 sec < t < 4 sec ?
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24. 21. If M = 5.0 Kg, what is the Tension in the string between the two objects of equal mass? All surfaces are frictionless.
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26. 22. If the tension T = 15 N and the acceleration , what is the mass m of the suspended object? All surfaces are frictionless! a T T m m
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27. 23. If the Tension in string 1 is 40N and the Tension in string 2 is 25N, what is mass m of the object?
60° 1 2 2 m
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28. 24. A roller-coaster car has a mass of 500kg when fully loaded with passengers. The car passes over a hill of radius 20 m. At the top of the hill, the car has a speed of What is the force of the track on the car at the top of the hill?
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29. 25. A uniform ladder, 15 ft long and weighing 60 lbs
25. A uniform ladder, 15 ft long and weighing 60 lbs., is leaning against a frictionless wall at an angle of 53° above the horizontal. A 120 lb boy climbs 6.0 ft up the ladder. What is the magnitude of the friction force exerted on the ladder by the floor?
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31. 26. A uniform, horizontal meter stick, supported at the 50 cm mark, has a mass of 500 grams hanging at the 20 cm mark and a 300 gram mass hanging at the 60 cm mark. Determine the position on the meter stick at which one would hang a third mass of 600 grams to keep the meter stick balanced.
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32. 27. The three blocks are released from rest
27. The three blocks are released from rest. Determine the acceleration of the system if no friction is present.
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33. 28. A person weighing 600N rides in an elevator that has a downward acceleration of What is the magnitude of the force of the elevator floor on the person?
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34. 29. A 0.20-kg object attached to the end of a string swings in a vertical circle of radius = 80 cm. At the top of the circle the speed of the object is What is the magnitude of the tension in the string at this position?
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35. 30. A roller-coaster car has a mass of 500 kg when fully loaded with passengers. At the bottom of a circular dip of radius 40 m (as shown in the figure) the car has a speed of What is the magnitude of the force of the track on the car at the bottom of the dip?
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36. 31. Daniel’s apparent weight at the top of an inverted loop of radius 30 m while riding a roller coaster is 3W. What is Daniel’s apparent weight at the bottom of the loop?
At the top!
At the bottom!
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37. 32. As shown in the top view above, a disc of mass m is moving horizontally to the right with speed v on a table with negligible friction when it collides with a second disc of mass 2m. The second disc is moving horizontally to the right with speed v/2 at the moment of impact. The two discs stick together upon impact. The speed of the composite body immediately after the collision is
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38. 33. A 0.30-kg mass attached to the end of a string swings in a vertical circle (R = 1.4 m), as shown. At an instant when q = 30°, the speed of the mass is 6.0. What is the magnitude of the resultant force on the mass at this instant?
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39. The driver and car crash into the outer wall!
34. A race car traveling at enters an unbanked turn of 400 m radius. The coefficient of friction between the tires and the track is 1.1. The track has both an inner and an outer wall. Which statement is correct?
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The driver and car crash into the outer wall! 39

40. 35. A force acting on an object moving along the x axis is given by where x is in meters. If the force is applied at an angle of 37° with respect to the horizontal, how much work is done by this force as the object moves from x = -1 m to x = +2 m?
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41. 36. A particle of mass m moves along a straight path with a speed v defined by the function , where b and c are constants and t is time. What is the magnitude F of the net force on the particle at time t = t1 ?
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42. 37. A 0.50-kg particle moves under the influence of a single conservative force. At point A where the particle has a speed of 10 , the potential energy associated with the conservative force is +40 J. As the particle moves from A to B, the force does +25 Joules of work on the particle. What is the value of the potential energy at point B?
If the KE increases by +25J, then the U must decrease by the same amount.
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43. 38. To stretch a certain nonlinear spring by an amount x requires a force F given by , where F is in newtons and x is in meters. What is the change in potential energy when the spring is stretched 2 meters from its equilibrium position?
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44. 39. A skier weighing 550N comes down a frictionless ski run that is circular (R = 30 m) at the bottom, as shown. If her speed is at point A, what is her speed at the bottom of the hill (point B)?
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45. 40. A block (mass = 4.0 kg) sliding on a horizontal frictionless surface is attached to one end of a horizontal spring ( k =100 ) which has its other end fixed. If the maximum distance the block slides from the equilibrium position is equal to 20 cm, what is the speed of the block at an instant when it is a distance of 16 cm from the equilibrium position?
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46. 41. A 1.2-kg mass is projected down a rough circular track (radius = 2.0 m) as shown. The speed of the mass at point A is , and at point B, it is How much work is done on the mass between A and B by the force of friction?
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47. 42. A 25-kg block on a horizontal surface is attached to a light spring ( k = ). The block is pulled 10 cm to the right from its equilibrium position and released from rest. When the block has moved 5.0 cm toward its equilibrium position, its kinetic energy is 12 J. How much work is done by the frictional force on the block as it moves the 5.0 cm?
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48. 43. As an object moves from point A to point B only two forces act on it: one force is nonconservative and does -30 Joules of work, the other force is conservative and does +50 Joules of work. Between A and B,
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49. 44. A 2-kg object moving with a speed of 6
44. A 2-kg object moving with a speed of 6.0 collides perpendicularly with a wall and emerges with a speed of in the opposite direction. If the object is in contact with the wall for 2.0 msec, what is the magnitude of the average force on the object by the wall?
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50. 45. A 1. 0-kg playground ball is moving with a velocity of 6
45. A 1.0-kg playground ball is moving with a velocity of 6.0 directed 30° below the horizontal just before it strikes a horizontal surface. The ball leaves this surface 0.50 s later with a velocity of directed 60° above the horizontal. What is the magnitude of the average resultant force on the ball?
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52. 46. The only force acting on a 2
46. The only force acting on a 2.0-kg object moving along the x axis is shown If the velocity vx = at t = 0, what is the velocity at t = 4.0 seconds?
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53. 47. The speed of a 2. 0-kg object changes from 30 to 40 during a 5
47. The speed of a 2.0-kg object changes from to during a 5.0-second time interval. During this same time interval, the velocity of the object changes its direction by 90¯. What is the magnitude of the average total force acting on the object during this time interval?
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54. 48. A 2. 0-kg object moving 5. 0 collides with and sticks to an 8
48. A 2.0-kg object moving collides with and sticks to an 8.0-kg object initially at rest. Determine the kinetic energy lost by the system as a result of this collision.
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55. 49. A 2-kg block is attached to the end of a 3
49. A 2-kg block is attached to the end of a 3.0-m string to form a pendulum. The pendulum is released from rest when the string is horizontal. At the lowest point of its swing when it is moving horizontally, the block is hit by a 25-gram bullet moving horizontally in the opposite direction. The bullet remains embedded in the block and causes the block to come to rest at the low point of its swing. What was the magnitude of the bullet's velocity just before hitting the block?
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57. 50. A 3.0-kg mass sliding on a frictionless surface has a velocity of east when it undergoes a one-dimensional inelastic collision with a 2.0-kg mass that has an initial velocity of west. After the collision the 3.0-kg mass has a velocity of east. How much kinetic energy does the two-mass system lose during the collision?
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59. 51. A 80-kg man who is ice skating south collides with a 40-kg boy who is ice skating east. Immediately after the collision, the man and boy are observed to be moving together with a velocity of , in a direction 37¯ south of east. What was the magnitude of the boy's velocity before the collision?
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60. 52. A 6-kg object, initially at rest, "explodes" into three objects of equal mass. Two of these are determined to have velocities of equal magnitudes (4.0 ) with directions that differ by 90¯. How much kinetic energy was released in the explosion?
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62. 53. A particle moves in the xy plane with a constant acceleration given by At t = 0 its position and velocity are 10i m and , respectively. What is the distance from the origin to the particle at
t = 2.0 s?
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63. 54. A ball is thrown horizontally from the top of a building 80 meters high. The ball strikes the ground at a point 100 meters horizontally away from and below the point of release. What is the speed of the ball just before it strikes the ground?
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64. A 5-kg mass starts from rest under the influence of variable force F as a function of distance x as shown on the graph below. 30
F(N) 20 10
x (m) 2 4 6 8 10 12
-10
55. During which time interval(s) will the velocity of the mass be constant?
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When the acceleration = 0 and the Force = 0. Between x = 6 m and x = 8 m. 64

65. 56. During which time interval will the most Work be done?30
F(N) 20 10
x (m) 2 4 6 8 10 12
-10
The areas between x = 0 and x 4 m, between x = 4 m and x = 6 m, and between x = 8m and x = 12 m are all the same. So the same work is done in all three areas.
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66. 57. What is the velocity of the object at x = 12 m?30
F(N) 20 10
x (m) 2 4 6 8 10 12
-10
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67. Double the mass = half the velocity!
An object of mass m, initially at rest, slides down from a height of 1.25 meters on a frictionless ramp, collides and sticks to an identicle particle 2 of mass m at rest as shown. Then particle 1 and 2 together collide elastically with particle 3 of mass 2m which is also initially at rest.
58. The speed of particle 1 after the collision with particle 2 would be?
Double the mass = half the velocity!
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68. 59. The speed of particle 1 and 2 together after the elastic collision with particle 3 would be?
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69. 60. The same force F is applied horizontally to bodies 1, 2, 3 and 4, of masses m, 2m, 3m and 4m, initially at rest and on a frictionless surface, until each body has traveled distance 2d. The correct listing of the magnitudes of the velocities of the bodies, v1, v2, v3, and v4 is
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73. 61. A constant force F is applied to a body of mass m that initially is headed east at velocity vo until its velocity becomes -2vo. The total time of travel is 3t. The total distance the body travels in that time is
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