1. The SI standard of time is based on:
A. the daily rotation of the earth
B. the frequency of light emitted by Kr86
C. the yearly revolution of the earth about the sun
D. a precision pendulum clock
E. none of these
ANS: E
2. A nanosecond is:
A. 109 s
B. 10−9 s
C. 10−10 s
D. 10−10 s
E. 10−12
ANS: B
3. The SI standard of length is based on:
A. the distance from the north pole to the equator along a meridian passing through Paris
B. wavelength of light emitted by Hg198
C. wavelength of light emitted by Kr86
D. a precision meter stick in Paris
E. the speed of light
ANS: E
4. In 1866, the U. S. Congress defined the U. S. yard as exactly 3600/3937 international meter. This was done primarily because:
A. length can be measured more accurately in meters than in yards
B. the meter is more stable than the yard
C. this definition relates the common U. S. length units to a more widely used system
D. there are more wavelengths in a yard than in a meter
E. the members of this Congress were exceptionally intelligent
ANS: C
5. Which of the following is closest to a yard in length?
A. 0.01m
B. 0.1m
C. 1m
D. 100m
E. 1000m
ANS: C
1 6. There is no SI base unit for area because:
A. an area has no thickness; hence no physical standard can be built
B. we live in a three (not a two) dimensional world
C. it is impossible to express square feet in terms of meters
D. area can be expressed in terms of square meters
E. area is not an important physical quantity
ANS: D
7. The SI base unit for mass is:
A. gram
B. pound
C. kilogram
D. ounce
E. kilopound
ANS: C
8. A gram is:
A. 10−6 kg
B. 10−3 kg
C. 1 kg
D. 103 kg
E. 106 kg
ANS: B
9. Which of the following weighs about a pound?
A. 0.05 kg
B. 0.5 kg
C. 5 kg
D. 50 kg
E. 500 kg
ANS: D
10. (5.0 × 104) × (3.0 × 106) =
A. 1.5 × 109
B. 1.5 × 1010
C. 1.5 × 1011
D. 1.5 × 1012
E. 1.5 × 1013
ANS: C
11. (5.0 × 104) × (3.0 × 10−6) =
A. 1.5 × 10−3
B. 1.5 × 10−1
C. 1.5 × 101
D. 1.5 × 103
E. 1.5 × 105
ANS: B
2
12. 5.0 × 105 + 3.0 × 106 =
A. 8.0 × 105
B. 8.0 × 106
C. 5.3 × 105
D. 3.5 × 105
E. 3.5 × 106
ANS: E
13. (7.0 × 106)/(2.0 × 10−6) =
A. 3.5 × 10−12
B. 3.5 × 10−6
C. 3.5
D. 3.5 × 106
E. 3.5 × 1012
ANS: E
14. The number of significant figures in 0.00150 is:
A. 2
B. 3
C. 4
D. 5
E. 6
ANS: B
15. The number of significant figures in 15.0 is:
A. 1
B. 2
C. 3
D. 4
E. 5
ANS: C
16. 3.2 × 2.7 =
A. 9
B. 8
C. 8.6
D. 8.64
E. 8.640
ANS: C
3 17. 1.513 + 27.3 =
A. 29
B. 28.8
C. 28.9
D. 28.81
E. 28.813 ( )
ANS: B
18. 1 mi is equivalent to 1609 m so 55 mph is:
A. 15 m/s
B. 25 m/s
C. 66 m/s
D. 88 m/s
E. 1500 m/s
ANS: B
19. A sphere with a radius of 1.7 cm has a volume of:
A. 2.1 × 10−5 m3
B. 9.1 × 10−4 m3
C. 3.6 × 10−3 m3
D. 0.11 m3
E. 21 m3
ANS: A
20. A sphere with a radius of 1.7 cm has a surface area of:
A. 2.1 × 10−5 m2
B. 9.1 × 10−4 m2
C. 3.6 × 10−3 m2
D. 0.11 m2
E. 36 m2
ANS: C
21. A right circular cylinder with a radius of 2.3 cm and a height of 1.4 m has a volume of:
A. 0.20 m3
B. 0.14 m3
C. 9.3 × 10−3 m3
D. 2.3 × 10−3 m3
E. 7.4 × 10−4 m3
ANS: D
22. A right circular cylinder with a radius of 2.3 cm and a height of 1.4 cm has a total surface area of:
A. 1.7 × 10−3 m2
B. 3.2 × 10−3 m2
C. 2.0 × 10−3 m3
D. 5.3 × 10−3 m2
E. 7.4 × 10−3 m2
ANS: D
4
23. A cubic box with an edge of exactly 1 cm has a volume of:
A. 10−9 m3
B. 10−6 m3
C. 10−3 m3
D. 103 m3
E. 106 m3
ANS: B
24. A square with an edge of exactly 1 cm has an area of:
A. 10−6 m2
B. 10−4 m2
C. 102 m2
D. 104 m2
E. 106 m2
ANS: B
25. 1 m is equivalent to 3.281 ft. A cube with an edge of 1.5 ft has a volume of:
A. 1.2 × 102 m3
B. 9.6 × 10−2 m3
C. 10.5 m3
D. 9.5 × 10−2 m3
E. 0.21 m3
ANS: B
26. During a short interval of time the speed v in m/s of an automobile is given by v = at2 + bt3, where the time t is in seconds. The units of a and b are respectively:
A. m • s2; m• s4
B. s3/m; s4/m
C. m/s2; m/s3
D. m/s3; m/s4
E. m/s4; m/s5
ANS: D
27. Suppose A = BC, where A has the dimension L/M and C has the dimension L/T. Then B has the dimension:
A. T/M
B. L2/TM
C. TM/L2
D. L2T/M
E. M/L2T
ANS: A
5 28. Suppose A = BnCm, where A has dimensions LT, B has dimensions L2T−1, and C has dimensions LT2. Then the exponents n and m have the values:
A. 2/3; 1/3
B. 2; 3
C. 4/5; −1/5
D. 1/5; 3/5
E. 1/2; 1/2
ANS: D
6
A. xi = 4m, xf = 6m
B. xi = −4m, xf = −8m
C. xi = −4m, xf = 2m
D. xi = 4m, xf = −2m
E. xi = −4m, xf = 4m
ANS: E
2. A particle moves along the x axis from xi to xf . Of the following values of the initial and final coordinates, which results in a negative displacement?
A. xi = 4m, xf = 6m
B. xi = −4m, xf = −8m
C. xi = −4m, xf = 2m
D. xi = −4m, xf = −2m
E. xi = −4m, xf = 4m
ANS: B
3. The average speed of a moving object during a given interval of time is always:
A. the magnitude of its average velocity over the interval
B. the distance covered during the time interval divided by the time interval
C. one-half its speed at the end of the interval
D. its acceleration multiplied by the time interval
E. one-half its acceleration multiplied by the time interval.
ANS: B
4. Two automobiles are 150 kilometers apart and traveling toward each other. One automobile is moving at 60km/h and the other is moving at 40km/h mph. In how many hours will they meet?
A. 2.5
B. 2.0
C. 1.75
D. 1.5
E. 1.25
ANS: D
5. A car travels 40 kilometers at an average speed of 80km/h and then travels 40 kilometers at an average speed of 40km/h. The average speed of the car for this 80-km trip is:
A. 40km/h
B. 45km/h
C. 48km/h
D. 53km/h
E. 80km/h
ANS: D
7 6. A car starts from Hither, goes 50 km in a straight line to Yon, immediately turns around, and returns to Hither. The time for this round trip is 2 hours. The magnitude of the average velocity of the car for this round trip is:
A. 0
B. 50 km/hr
C. 100 km/hr
D. 200 km/hr
E. cannot be calculated without knowing the acceleration
ANS: A
7. A car starts from Hither, goes 50 km in a straight line to Yon, immediately turns around, and returns to Hither. The time for this round trip is 2 hours. The average speed of the car for this round trip is:
A. 0
B. 50 km/h
C. 100 km/h
D. 200 km/h
E. cannot be calculated without knowing the acceleration
ANS: B
8. The coordinate of a particle in meters is given by x(t) = 16t − 3.0t3, where the time t is in seconds. The particle is momentarily at rest at t =
A. 0.75 s
B. 1.3 s
C. 5.3 s
D. 7.3 s
E. 9.3 s
ANS: B
9. A drag racing car starts from rest at t = 0 and moves along a straight line with velocity given by v = bt2, where b is a constant. The expression for the distance traveled by this car from its position at t = 0 is:
A. bt3
B. bt3/3
C. 4bt2
D. 3bt2
E. bt3/2
ANS: B
10. A ball rolls up a slop
E. At the end of three seconds its velocity is 20 cm/s; at the end of eight seconds its velocity is 0. What is the average acceleration from the third to the eighth second?
A. 2.5 cm/s2
B. 4.0 cm/s2
C. 5.0 cm/s2
D. 6.0 cm/s2
E. 6.67 cm/s2
ANS: B
8
11. The coordinate of an object is given as a function of time by x = 7t − 3t2, where x is in meters and t is in seconds. Its average velocity over the interval from t = 0 to t = 4 s is:
A. 5m/s
B. −5m/s
C. 11m/s
D. −11m/s
E. −14.5m/s
ANS: B
12. The velocity of an object is given as a function of time by v = 4t − 3t2, where v is in m/s and t is in seconds. Its average velocity over the interval from t = 0 to t = 2s:
A. is 0
B. is −2m/s
C. is 2m/s
D. is −4m/s
E. cannot be calculated unless the initial position is given
ANS: A
13. The coordinate of an object is given as a function of time by x = 4t2 −3t3, where x is in meters and t is in seconds. Its average acceleration over the interval from t = 0 to t = 2 s is:
A. −4m/s2
B. 4m/s2
C. −10m/s2
D. 10m/s2
E. −13m/s2
ANS: C
14. Each of four particles move along an x axis. Their coordinates (in meters) as functions of time (in seconds) are given by particle 1: x(t) = 3.5 − 2.7t3 particle 2: x(t) = 3.5 +2.7t3 particle 3: x(t) = 3.5 +2.7t2 particle 4: x(t) = 3.5 − 3.4t − 2.7t2 Which of these particles have constant acceleration?
A. All four
B. Only 1 and 2
C. Only 2 and 3
D. Only 3 and 4
E. None of them
ANS: D
9 15. Each of four particles move along an x axis. Their coordinates (in meters) as functions of time (in seconds) are given by particle 1: x(t) = 3.5 − 2.7t3 particle 2: x(t) = 3.5 +2.7t3 particle 3: x(t) = 3.5 +2.7t2 particle 4: x(t) = 3.5 − 3.4t − 2.7t2 Which of these particles is speeding up for t > 0?
A. All four
B. Only 1
C. Only 2 and 3
D. Only 2, 3, and 4
E. None of them
ANS: A
16. An object starts from rest at the origin and moves along the x axis with a constant acceleration of 4m/s2. Its average velocity as it goes from x = 2m to x = 8m is:
A. 1m/s
B. 2m/s
C. 3m/s
D. 5m/s
E. 6m/s
ANS: E
17. Of the following situations, which one is impossible?
A. A body having velocity east and acceleration east
B. A body having velocity east and acceleration west
C. A body having zero velocity and non-zero acceleration
D. A body having constant acceleration and variable velocity
E. A body having constant velocity and variable acceleration
ANS: E
18. Throughout a time interval, while the speed of a particle increases as it moves along the x axis, its velocity and acceleration might be:
A. positive and negative, respectively
B. negative and positive, respectively
C. negative and negative, respectively
D. negative and zero, respectively
E. positive and zero, respectively
ANS: C
19. A particle moves on the x axis. When its acceleration is positive and increasing:
A. its velocity must be positive
B. its velocity must be negative
C. it must be slowing down
D. it must be speeding up
E. none of the above must be true
ANS: E
10
20. The position y of a particle moving along the y axis depends on the time t according to the equation y = at − bt2. The dimensions of the quantities a and b are respectively:
A. L2/T, L3/T2
B. L/T2, L2/T
C. L/T, L/T2
D. L3/T, T2/L
E. none of these
ANS: C
21. A particle moves along the x axis according to the equation x = 6t2, where x is in meters and t is in seconds. Therefore:
A. the acceleration of the particle is 6 m/s2
B. t cannot be negative
C. the particle follows a parabolic path
D. each second the velocity of the particle changes by 9.8 m/s
E. none of the above
ANS: E
22. Over a short interval near time t = 0 the coordinate of an automobile in meters is given by x(t) = 27t − 4.0t3, where t is in seconds. At the end of 1.0 s the acceleration of the auto is:
A. 27 m/s2
B. 4.0 m/s2
C. −4.0 m/s2
D. −12 m/s2
E. −24 m/s2
ANS: E
23. Over a short interval, starting at time t = 0, the coordinate of an automobile in meters is given by x(t) = 27t − 4.0t3, where t is in seconds. The magnitudes of the initial (at t = 0) velocity and acceleration of the auto respectively are:
A. 0; 12 m/s2
B. 0; 24 m/s2
C. 27 m/s; 0
D. 27 m/s; 12 m/s2
E. 27 m/s; 24 m/s2
ANS: C
24. At time t = 0 a car has a velocity of 16 m/s. It slows down with an acceleration given by −0.50t, in m/s2 for t in seconds. It stops at t =
A. 64 s
B. 32 s
C. 16 s
D. 8.0 s
E. 4.0 s
ANS: D
11 25. At time t = 0 a car has a velocity of 16 m/s. It slows down with an acceleration given by −0.50t, in m/s2 for t in seconds. At the end of 4.0 s it has traveled:
A. 0
B. 12 m
C. 14 m
D. 25 m
E. 59 m
ANS: E
26. At time t = 0 a car has a velocity of 16 m/s. It slows down with an acceleration given by −0.50t, in m/s2 for t in seconds. By the time it stops it has traveled:
A. 15 m
B. 31 m
C. 62 m
D. 85 m
E. 100 m
ANS: D
27. Starting at time t = 0, an object moves along a straight line with velocity in m/s given by v(t) = 98 − 2t2, where t is in seconds. When it momentarily stops its acceleration is:
A. 0
B. −4.0 m/s2
C. −9.8 m/s2
D. −28 m/s2
E. 49 m/s2
ANS: D
28. Starting at time t = 0, an object moves along a straight lin
E. Its coordinate in meters is given by x(t) = 75t − 1.0t3, where t is in seconds. When it momentarily stops its acceleration is:
A. 0
B. −73 m/s2
C. −30 m/s2
D. −9.8 m/s2
E. 9.2 × 103 m/s2
ANS: C
29. A car, initially at rest, travels 20 m in 4 s along a straight line with constant acceleration. The acceleration of the car is:
A. 0.4m/s2
B. 1.3m/s2
C. 2.5m/s2
D. 4.9m/s2
E. 9.8m/s2
ANS: C
12
30. A racing car traveling with constant acceleration increases its speed from 10m/s to 50m/s over a distance of 60 m. How long does this take?
A. 2.0 s
B. 4.0 s
C. 5.0 s
D. 8.0 s
E. The time cannot be calculated since the speed is not constant
ANS: B
31. A car starts from rest and goes down a slope with a constant acceleration of 5 m/s2. After 5 s the car reaches the bottom of the hill. Its speed at the bottom of the hill, in meters per second, is:
A. 1
B. 12.5
C. 25
D. 50
E. 160
ANS: C
32. A car moving with an initial velocity of 25 m/s north has a constant acceleration of 3 m/s2 south. After 6 seconds its velocity will be:
A. 7 m/s north
B. 7 m/s south
C. 43 m/s north
D. 20 m/s north
E. 20 m/s south
ANS: A
33. An object with an initial velocity of 12 m/s west experiences a constant acceleration of 4 m/s2 west for 3 seconds. During this time the object travels a distance of:
A. 12 m
B. 24 m
C. 36 m
D. 54 m
E. 144 m
ANS: D
34. How far does a car travel in 6 s if its initial velocity is 2 m/s and its acceleration is 2 m/s2 in the forward direction?
A. 12 m
B. 14 m
C. 24 m
D. 36 m
E. 48 m
ANS: E
13 35. At a stop light, a truck traveling at 15 m/s passes a car as it starts from rest. The truck travels at constant velocity and the car accelerates at 3 m/s2. How much time does the car take to catch up to the truck?
A. 5 s
B. 10 s
C. 15 s
D. 20 s
E. 25 s
ANS: B
36. A ball is in free fall. Its acceleration is:
A. downward during both ascent and descent
B. downward during ascent and upward during descent
C. upward during ascent and downward during descent
D. upward during both ascent and descent
E. downward at all times except at the very top, when it is zero
ANS: A
37. A ball is in free fall. Upward is taken to be the positive direction. The displacement of the ball during a short time interval is:
A. positive during both ascent and descent
B. negative during both ascent and descent
C. negative during ascent and positive during descent
D. positive during ascent and negative during descent
E. none of the above
ANS: D
38. A baseball is thrown vertically into the air. The acceleration of the ball at its highest point is:
A. zero
B. g, down
C. g, up
D. 2g, down
E. 2g, up
ANS: B
39. Which one of the following statements is correct for an object released from rest?
A. The average velocity during the first second of time is 4.9m/s
B. During each second the object falls 9.8m
C. The acceleration changes by 9.8m/s2 every second
D. The object falls 9.8m during the first second of time
E. The acceleration of the object is proportional to its weight
ANS: A
14
40. A freely falling body has a constant acceleration of 9.8 m/s2. This means that:
A. the body falls 9.8 m during each second
B. the body falls 9.8 m during the first second only
C. the speed of the body increases by 9.8 m/s during each second
D. the acceleration of the body increases by 9.8 m/s2 during each second
E. the acceleration of the body decreases by 9.8 m/s2 during each second
ANS: C
41. An object is shot vertically upwar
D. While it is rising:
A. its velocity and acceleration are both upward
B. its velocity is upward and its acceleration is downward
C. its velocity and acceleration are both downward
D. its velocity is downward and its acceleration is upward
E. its velocity and acceleration are both decreasing
ANS: B
42. An object is thrown straight up from ground level with a speed of 50 m/s. If g = 10 m/s2 its distance above ground level 1.0 s later is:
A. 40 m
B. 45 m
C. 50 m
D. 55 m
E. 60 m
ANS: B
43. An object is thrown straight up from ground level with a speed of 50 m/s. If g = 10 m/s2 its distance above ground level 6.0 s later is:
A. 0.00 m
B. 270 m
C. 330 m
D. 480 m
E. none of these
ANS: E
44. At a location where g = 9.80 m/s2, an object is thrown vertically down with an initial speed of 1.00 m/s. After 5.00 s the object will have traveled:
A. 125 m
B. 127.5 m
C. 245 m
D. 250 m
E. 255 m
ANS: B
15 45. An object is thrown vertically upward at 35 m/s. Taking g = 10 m/s2, the velocity of the object 5 s later is:
A. 7.0 m/s up
B. 15 m/s down
C. 15 m/s up
D. 85 m/s down
E. 85 m/s up
ANS: B
46. A feather, initially at rest, is released in a vacuum 12 m above the surface of the earth. Which of the following statements is correct?
A. The maximum velocity of the feather is 9.8 m/s
B. The acceleration of the feather decreases until terminal velocity is reached
C. The acceleration of the feather remains constant during the fall
D. The acceleration of the feather increases during the fall
E. The acceleration of the feather is zero
ANS: C
47. An object is released from rest. How far does it fall during the second second of its fall?
A. 4.9m
B. 9.8m
C. 15m
D. 20m
E. 25m
ANS: C
48. A heavy ball falls freely, starting from rest. Between the third and fourth second of time it travels a distance of:
A. 4.9 m
B. 9.8 m
C. 29.4 m
D. 34.3 m
E. 39.8 m
ANS: D
49. As a rocket is accelerating vertically upward at 9.8 m/s2 near Earth’s surface, it releases a projectil
E. Immediately after release the acceleration (in m/s2) of the projectile is:
A. 9.8 down
B. 0
C. 9.8 up
D. 19.6 up
E. none of the above
ANS: A
16
50. A stone is released from a balloon that is descending at a constant speed of 10 m/s. Neglecting air resistance, after 20 s the speed of the stone is:
A. 2160 m/s
B. 1760 m/s
C. 206 m/s
D. 196 m/s
E. 186 m/s
ANS: C
51. An object dropped from the window of a tall building hits the ground in 12.0 s. If its acceleration is 9.80 m/s2, the height of the window above the ground is:
A. 29.4 m
B. 58.8 m
C. 118 m
D. 353 m
E. 706 m
ANS: E
52. Neglecting the effect of air resistance a stone dropped off a 175-m high building lands on the ground in:
A. 3 s
B. 4 s
C. 6 s
D. 18 s
E. 36 s
ANS: C
53. A stone is thrown vertically upward with an initial speed of 19.5 m/s. It will rise to a maximum height of:
A. 4.9 m
B. 9.8 m
C. 19.4 m
D. 38.8 m
E. none of these
ANS: C
54. A baseball is hit straight up and is caught by the catcher 2.0 s later. The maximum height of the ball during this interval is:
A. 4.9 m
B. 7.4 m
C. 9.8 m
D. 12.6 m
E. 19.6 m
ANS: A
17 55. An object is thrown straight down with an initial speed of 4 m/s from a window which is 8 m above the groun
D. The time it takes the object to reach the ground is:
A. 0.80 s
B. 0.93 s
C. 1.3 s
D. 1.7 s
E. 2.0 s
ANS: B
56. A stone is released from rest from the edge of a building roof 190 m above the groun
D. Neglecting air resistance, the speed of the stone, just before striking the ground, is:
A. 43 m/s
B. 61 m/s
C. 120 m/s
D. 190 m/s
E. 1400 m/s
ANS: B
57. An object is thrown vertically upward with a certain initial velocity in a world where the acceleration due to gravity is 19.6 m/s2. The height to which it rises is that to which the object would rise if thrown upward with the same initial velocity on the Earth. Neglect friction.
A. half
B. √2 times
C. twice
D. four times
E. cannot be calculated from the given data
ANS: A
58. A projectile is shot vertically upward with a given initial velocity. It reaches a maximum height of 100 m. If, on a second shot, the initial velocity is doubled then the projectile will reach a maximum height of:
A. 70.7 m
B. 141.4 m
C. 200 m
D. 241 m
E. 400 m
ANS: E
59. One object is thrown vertically upward with an initial velocity of 100 m/s and another object with an initial velocity of 10 m/s. The maximum height reached by the first object will be that of the other.
A. 10 times
B. 100 times
C. 1000 times
D. 10, 000 times
E. none of these
ANS: B
18
60. The area under a velocity-time graph represents:
A. acceleration
B. change in acceleration
C. speed
D. change in velocity
E. displacement
ANS: E
61. Displacement can be obtained from:
A. the slope of an acceleration-time graph
B. the slope of a velocity-time graph
C. the area under an acceleration-time graph
D. the area under a velocity-time graph
E. the slope of an acceleration-time graph
ANS: D
62. An object has a constant acceleration of 3 m/s2. The coordinate versus time graph for this object has a slope:
A. that increases with time
B. that is constant
C. that decreases with time
D. of 3 m/s
E. of 3 m/s2
ANS: A
63. The coordinate-time graph of an object is a straight line with a positive slop
E. The object has:
A. constant displacement
B. steadily increasing acceleration
C. steadily decreasing acceleration
D. constant velocity
E. steadily increasing velocity
ANS: D
19
A. During the interval from 1.0 s to 3.0 s
B. At t = 3.5 s
C. At t = 4.0 s
D. At t = 5.0 s
E. At no other time less than or equal to 5 s
ANS: E
A. displacement can be specified by a magnitude and a direction
B. operating with displacements according to the rules for manipulating vectors leads to results in agreement with experiments
C. a displacement is obviously not a scalar
D. displacement can be specified by three numbers
E. displacement is associated with motion
ANS: B
3. A vector of magnitude 3 CANNOT be added to a vector of magnitude 4 so that the magnitude of the resultant is:
A. zero
B. 1
C. 3
D. 5
E. 7
ANS: A
4. A vector of magnitude 20 is added to a vector of magnitude 25. The magnitude of this sum might be:
A. zero
B. 3
C. 12
D. 47
E. 50
ANS: C
27 5. A vector S of magnitude 6 and another vector T have a sum of magnitude 12. The vector T:
A. must have a magnitude of at least 6 but no more than 18
B. may have a magnitude of 20
C. cannot have a magnitude greater than 12
D. must be perpendicular to S
E. must be perpendicular to the vector sum
ANS: A
6. The vector − A is:
A. greater than A in magnitude
B. less than A in magnitude
C. in the same direction as A
D. in the direction opposite to A
E. perpendicular to A
ANS: D
8. If | A + B |2 = A2 + B2, then:
A. A and B must be parallel and in the same direction
B. A and B must be parallel and in opposite directions
C. either A or B must be zero
D. the angle between Aand B must be 60◦
E. none of the above is true
ANS: E
28
9. If | A + B | = A + B and neither A nor B vanish, then:
A. A and B are parallel and in the same direction
B. A and B are parallel and in opposite directions
C. the angle between A and B is 45◦
D. the angle between A and B is 60◦
E. A is perpendicular to B
ANS: A
10. If | A − B | = A + B and neither A nor B vanish, then:
A. A and B are parallel and in the same direction
B. A and B are parallel and in opposite directions
C. the angle between A and B is 45◦
D. the angle between A and B is 60◦
E. A is perpendicular to B
ANS: B
12. Vectors A and B lie in the xy plan
E. We can deduce that A = B if:
A. A2 x + A2 y = B2 x + B2 y
B. Ax + Ay = Bx + By
C. Ax = Bx and Ay = By
D. Ay/Ax = By/Bx
E. Ax = Ay and Bx = By
ANS: C
29 13. A vector has a magnitude of 12. When its tail is at the origin it lies between the positive x axis and the negative y axis and makes an angle of 30◦ with the x axis. Its y component is:
A. 6/√3
B. −6√3
C. 6
D. −6
E. 12
ANS: D
14. If the x component of a vector A, in the xy plane, is half as large as the magnitude of the vector, the tangent of the angle between the vector and the x axis is:
A. √3
B. 1/2
C. √3/2
D. 3/2
E. 3
ANS: D
15. If A = (6m)ˆi − (8 m)ˆj then 4 A has magnitude:
A. 10m
B. 20m
C. 30m
D. 40m
E. 50m
ANS: D
16. A vector has a component of 10m in the +x direction, a component of 10m in the +y direction, and a component of 5m in the +z direction. The magnitude of this vector is:
A. zero
B. 15m
C. 20m
D. 25m
E. 225m
ANS: B
17. Let V = (2.00 m)ˆi + (6.00 m)ˆj − (3.00 m) ˆk. The magnitude of V is:
A. 5.00m
B. 5.57m
C. 7.00m
D. 7.42m
E. 8.54m
ANS: C
30
18. A vector in the xy plane has a magnitude of 25m and an x component of 12m. The angle it makes with the positive x axis is:
A. 26◦
B. 29◦
C. 61◦
D. 64◦
E. 241◦
ANS: C
19. The angle between A = (25 m)ˆi + (45 m)ˆj and the positive x axis is:
A. 29◦
B. 61◦
C. 151◦
D. 209◦
E. 241◦
ANS: B
20. The angle between A = (−25 m)ˆi + (45 m)ˆj and the positive x axis is:
A. 29◦
B. 61◦
C. 119◦
D. 151◦
E. 209◦
ANS: C
21. Let A = (2m)ˆi +(6 m)ˆj −(3 m)ˆk and B = (4m)ˆi +(2 m)ˆj+(1m)ˆk. The vector sum S = A + B is:
A. (6 m)ˆi + (8 m)ˆj − (2 m)ˆk
B. (−2m)ˆi + (4 m)ˆj − (4 m) ˆk
C. (2 m)ˆi − (4 m)ˆj + (4 m)ˆk
D. (8 m)ˆi + (12 m)ˆj − (3 m) ˆk
E. none of these
ANS: A
22. Let A = (2m)ˆi + (6 m)ˆj − (3 m)ˆk and B = (4m)ˆi + (2mˆj + (1 m) ˆk. The vector difference D = A − B is:
A. (6 m)ˆi + (8 m)ˆj − (2 m)ˆk
B. (−2m)ˆi + (4 m)ˆj − (4 m) ˆk
C. (2 m)ˆi − (4 m)ˆj + (4 m)ˆk
D. (8 m)ˆi + (12 m)ˆj − (3 m) ˆk
E. none of these
ANS: B
31 23. If A = (2m)ˆi − (3 m)ˆj and B = (1m)ˆi − (2 m)ˆj, then A − 2 B =
A. (1 m)ˆj
B. (−1m)ˆj
C. (4 m)ˆi − (7 m)ˆj
D. (4 m)ˆi + (1 m)ˆj
E. (−4m)ˆi + (7 m)ˆj
ANS: A
25. A certain vector in the xy plane has an x component of 4m and a y component of 10m. It is then rotated in the xy plane so its x component is double
D. Its new y component is about:
A. 20m
B. 7.2m
C. 5.0m
D. 4.5m
E. 2.2m
ANS: B
26. Vectors A and B each have magnitude L. When drawn with their tails at the same point, the angle between them is 30◦. The value of A • B is:
A. zero
B. L2
C. √3L2/2
D. 2L2
E. none of these
ANS: C
32
27. Let A = (2m)ˆi + (6 m)ˆj − (3 m)ˆk and B = (4m)ˆi + (2 m)ˆj + (1 m)ˆk. Then A • B =
A. (8 m)ˆi + (12 m)ˆj − (3 m) ˆk
B. (12 m)ˆi − (14 m)ˆj − (20 m) ˆk
C. 23m2
D. 17m2
E. none of these
ANS: D
28. Two vectors have magnitudes of 10m and 15 m. The angle between them when they are drawn with their tails at the same point is 65◦. The component of the longer vector along the line of the shorter is:
A. 0
B. 4.2m
C. 6.3m
D. 9.1m
E. 14m
ANS: C
29. Let S = (1m)ˆi + (2 m)ˆj + (2 m) ˆk and T = (3m)ˆi + (4 m) ˆk. The angle between these two vectors is given by:
A. cos−1(14/15)
B. cos−1(11/225)
C. cos−1(104/225)
D. cos−1(11/15)
E. cannot be found since S and T do not lie in the same plane
ANS: D
30. Two vectors lie with their tails at the same point. When the angle between them is increased by 20◦ their scalar product has the same magnitude but changes from positive to negativ
E. The original angle between them was:
A. 0
B. 60◦
C. 70◦
D. 80◦
E. 90◦
ANS: D
31. If the magnitude of the sum of two vectors is less than the magnitude of either vector, then:
A. the scalar product of the vectors must be negative
B. the scalar product of the vectors must be positive
C. the vectors must be parallel and in opposite directions
D. the vectors must be parallel and in the same direction
E. none of the above
ANS: A
33 32. If the magnitude of the sum of two vectors is greater than the magnitude of either vector, then:
A. the scalar product of the vectors must be negative
B. the scalar product of the vectors must be positive
C. the vectors must be parallel and in opposite directions
D. the vectors must be parallel and in the same direction
E. none of the above
ANS: E
33. Vectors A and B each have magnitude L. When drawn with their tails at the same point, the angle between them is 60◦. The magnitude of the vector product A × B is:
A. L2/2
B. L2
C. √3L2/2
D. 2L2
E. none of these
ANS: C
34. Two vectors lie with their tails at the same point. When the angle between them is increased by 20◦ the magnitude of their vector product doubles. The original angle between them was about:
A. 0
B. 18◦
C. 25◦
D. 45◦
E. 90◦
ANS: B
35. Two vectors have magnitudes of 10m and 15 m. The angle between them when they are drawn with their tails at the same point is 65◦. The component of the longer vector along the line perpendicular to the shorter vector, in the plane of the vectors, is:
A. 0
B. 4.2m
C. 6.3m
D. 9.1m
E. 14m
ANS: E
36. The two vectors (3 m)ˆi − (2 m)ˆj and (2 m)ˆi +(3 m)ˆj − (2 m) ˆk define a plan
E. It is the plane of the triangle with both tails at one vertex and each head at one of the other vertices. Which of the following vectors is perpendicular to the plane?
A. (4 m)ˆi + (6 m)ˆj + (13 m) ˆk
B. (−4m)ˆi + (6 m)ˆj + (13 m) ˆk
C. (4 m)ˆi − (6 m)ˆj + (13 m) ˆk
D. (4 m)ˆi + (6mˆj − (13 m) ˆk
E. (4 m)ˆi + (6 m)ˆj
ANS: A
34
37. Let R = S × T and θ = 90◦, where θ is the angle between S and T when they are drawn with their tails at the same point. Which of the following is NOT true?
A. | R | = | S ||T| sin θ
B. − R = T × S
C. R • S = 0
D. R • T = 0
E. S • T = 0
ANS: E
38. The value of ˆi • (ˆj × ˆk) is:
A. zero
B. +1
C. −1
D. 3
E. √3
ANS: B
39. The value of ˆk • (ˆk × ˆi) is:
A. zero
B. +1
C. −1
D. 3
E. √3
ANS: A
35
A. rate of change of position with time
B. position divided by time
C. rate of change of acceleration with time
D. a speeding up or slowing down
E. change of position
ANS: A
2. Acceleration is defined as:
A. rate of change of position with time
B. speed divided by time
C. rate of change of velocity with time
D. a speeding up or slowing down
E. change of velocity
ANS: C
3. Which of the following is a scalar quantity?
A. Speed
B. Velocity
C. Displacement
D. Acceleration
E. None of these
ANS: A
4. Which of the following is a vector quantity?
A. Mass
B. Density
C. Speed
D. Temperature
E. None of these
ANS: E
5. Which of the following is NOT an example of accelerated motion?
A. Vertical component of projectile motion
B. Circular motion at constant speed
C. A swinging pendulum
D. Earth’s motion about sun
E. Horizontal component of projectile motion
ANS: E
36
6. A particle goes from x = −2m, y = 3m, z = 1m to x = 3m, y = −1m, z = 4 m. Its displacement is:
A. (1 m)ˆi + (2 m)ˆj + (5 m)ˆk
B. (5 m)ˆi − (4 m)ˆj + (3 m)ˆk
C. −(5 m)ˆi + (4 m)ˆj − (3 m) ˆk
D. −(1 m)ˆi − (2 m)ˆj − (5 m) ˆk
E. −(5 m)ˆi − (2 m)ˆj + (3 m) ˆk
ANS: B
7. A jet plane in straight horizontal flight passes over your hea
D. When it is directly above you, the sound seems to come from a point behind the plane in a direction 30◦ from the vertical. The speed of the plane is:
A. the same as the speed of sound
B. half the speed of sound
C. three-fifths the speed of sound
D. 0.866 times the speed of sound
E. twice the speed of sound
ANS: B
8. A plane traveling north at 200m/s turns and then travels south at 200m/s. The change in its velocity is:
A. zero
B. 200m/s north
C. 200m/s south
D. 400m/s north
E. 400m/s south
ANS: E
9. Two bodies are falling with negligible air resistance, side by side, above a horizontal plan
E. If one of the bodies is given an additional horizontal acceleration during its descent, it:
A. strikes the plane at the same time as the other body
B. strikes the plane earlier than the other body
C. has the vertical component of its velocity altered
D. has the vertical component of its acceleration altered
E. follows a straight line path along the resultant acceleration vector
ANS: A
10. The velocity of a projectile equals its initial velocity added to:
A. a constant horizontal velocity
B. a constant vertical velocity
C. a constantly increasing horizontal velocity
D. a constantly increasing downward velocity
E. a constant velocity directed at the target
ANS: D
37 11. A stone thrown from the top of a tall building follows a path that is:
A. circular
B. made of two straight line segments
C. hyperbolic
D. parabolic
E. a straight line
ANS: D
12. Identical guns fire identical bullets horizontally at the same speed from the same height above level planes, one on the Earth and one on the Moon. Which of the following three statements is/are true? I. The horizontal distance traveled by the bullet is greater for the Moon. II. The flight time is less for the bullet on the Earth. III. The velocity of the bullets at impact are the sam
E.
A. III only
B. I and II only
C. I and III only
D. II and III only
E. I, II, III
ANS: B
14. A bullet shot horizontally from a gun:
A. strikes the ground much later than one dropped vertically from the same point at the same instant
B. never strikes the ground
C. strikes the ground at approximately the same time as one dropped vertically from the same point at the same instant
D. travels in a straight line
E. strikes the ground much sooner than one dropped from the same point at the same instant
ANS: C
17. An object is shot from the back of a railroad flatcar moving at 40km/h on a straight horizontal roa
D. The launcher is aimed upward, perpendicular to the bed of the flatcar. The object falls:
A. in front of the flatcar
B. behind the flatcar
C. on the flatcar
D. either behind or in front of the flatcar, depending on the initial speed of the object
E. to the side of the flatcar
ANS: C
19. A stone is thrown outward from the top of a 59.4-m high cliff with an upward velocity component of 19.5m/s. How long is stone in the air?
A. 4.00 s
B. 5.00 s
C. 6.00 s
D. 7.00 s
E. 8.00 s
ANS: C
20. A large cannon is fired from ground level over level ground at an angle of 30◦ above the horizontal. The muzzle speed is 980m/s. Neglecting air resistance, the projectile will travel what horizontal distance before striking the ground?
A. 4.3km
B. 8.5km
C. 43km
D. 85km
E. 170km
ANS: D
40
21. A boy on the edge of a vertical cliff 20m high throws a stone horizontally outward with a speed of 20m/s. It strikes the ground at what horizontal distance from the foot of the cliff? Use g = 10m/s2.
A. 10m
B. 40m
C. 50m
D. 50√5m
E. none of these
ANS: B
25. A projectile is fired from ground level over level ground with an initial velocity that has a vertical component of 20m/s and a horizontal component of 30m/s. Using g = 10m/s2, the distance from launching to landing points is:
A. 40m
B. 60m
C. 80m
D. 120m
E. 180m
ANS: D
28. An airplane makes a gradual 90◦ turn while flying at a constant speed of 200m/s. The process takes 20.0 seconds to complet
E. For this turn the magnitude of the average acceleration of the plane is:
A. zero
B. 40m/s2
C. 20m/s2
D. 14m/s2
E. 10m/s2
ANS: D
29. An airplane is flying north at 500 km/h. It makes a gradual 180◦ turn at constant speed, changing its direction of travel from north through east to south. The process takes 40 s. The average acceleration of the plane for this turn (in km/h•s) is:
A. 12.5km/h • s, north
B. 12.5km/h • s, east
C. 12.5km/h • s, south
D. 25km/h • s, north
E. 25km/h • s, south
ANS: E
30. An object is moving on a circular path of radius π meters at a constant speed of 4.0m/s. The time required for one revolution is:
A. 2/π2 s
B. π2/2 s
C. π/2 s
D. π2/4
E. 2/π s
ANS: B
31. A particle moves at constant speed in a circular path. The instantaneous velocity and instantaneous acceleration vectors are:
A. both tangent to the circular path
B. both perpendicular to the circular path
C. perpendicular to each other
D. opposite to each other
E. none of the above
ANS: C
32. A stone is tied to a string and whirled at constant speed in a horizontal circl
E. The speed is then doubled without changing the length of the string. Afterward the magnitude of the acceleration of the stone is:
A. the same
B. twice as great
C. four times as great
D. half as great
E. one-fourth as great
ANS: C
44
33. Two objects are traveling around different circular orbits with constant spee
D. They both have the same acceleration but object A is traveling twice as fast as object
B. The orbit radius for object A is the orbit radius for object
B.
A. one-fourth
B. one-half
C. the same as
D. twice
E. four times
ANS: E
34. A stone is tied to a 0.50-m string and whirled at a constant speed of 4.0m/s in a vertical circl
E. Its acceleration at the top of the circle is:
A. 9.8m/s2, up
B. 9.8m/s2, down
C. 8.0m/s2, down
D. 32m/s2, up
E. 32m/s2, down
ANS: E
35. A stone is tied to a 0.50-m string and whirled at a constant speed of 4.0m/s in a vertical circl
E. Its acceleration at the bottom of the circle is:
A. 9.8m/s2, up
B. 9.8m/s2, down
C. 8.0m/s2, up
D. 32m/s2, up
E. 32m/s2, down
ANS: D
36. A car rounds a 20-m radius curve at 10m/s. The magnitude of its acceleration is:
A. 0
B. 0.20m/s2
C. 5.0m/s2
D. 40m/s2
E. 400m/s2
ANS: C
37. For a biological sample in a 1.0-m radius centrifuge to have a centripetal acceleration of 25g its speed must be:
A. 11m/s
B. 16m/s
C. 50m/s
D. 122m/s
E. 245m/s
ANS: B
45 38. A girl jogs around a horizontal circle with a constant spee
D. She travels one fourth of a revolution, a distance of 25m along the circumference of the circle, in 5.0 s. The magnitude of her acceleration is:
A. 0.31m/s2
B. 1.3m/s2
C. 1.6m/s2
D. 3.9m/s2
E. 6.3m/s2
ANS: C
39. A stone is tied to the end of a string and is swung with constant speed around a horizontal circle with a radius of 1.5m. If it makes two complete revolutions each second, the magnitude of its acceleration is:
A. 0.24m/s2
B. 2.4m/s2
C. 24m/s2
D. 240m/s2
E. 2400m/s2
ANS: D
40. A Ferris wheel with a radius of 8.0m makes 1 revolution every 10 s. When a passenger is at the top, essentially a diameter above the ground, he releases a ball. How far from the point on the ground directly under the release point does the ball land?
A. 0
B. 1.0m
C. 8.0m
D. 9.1m
E. 16m
ANS: D
41. A boat is able to move through still water at 20m/s. It makes a round trip to a town 3.0 km upstream. If the river flows at 5m/s, the time required for this round trip is:
A. 120 s
B. 150 s
C. 200 s
D. 300 s
E. 320 s
ANS: E
46
42. A boat is traveling upstream at 14km/h with respect to a river that is flowing at 6 km/h (with respect to the ground). A man runs directly across the boat, from one side to the other, at 6km/h (with respect to the boat). The speed of the man with respect to the ground is:
A. 10km/h
B. 14km/h
C. 18.5km/h
D. 21km/h
E. 26km/h
ANS: A
43. A ferry boat is sailing at 12km/h 30◦ W of N with respect to a river that is flowing at 6.0km/h
E. As observed from the shore, the ferry boat is sailing:
A. 30◦ E of N
B. due N
C. 30◦ W of N
D. 45◦ E of N
E. none of these
ANS: B
46. A motor boat can travel at 10 km/h in still water. A river flows at 5 km/h west. A boater wishes to cross from the south bank to a point directly opposite on the north bank. At what angle must the boat be headed?
A. 27◦ E of N
B. 30◦ E of N
C. 45◦ E of N
D. 60◦ E of N
E. depends on the width of the river
ANS: B
47. Two projectiles are in flight at the same tim
E. The acceleration of one relative to the other:
A. is always 9.8m/s2
B. can be as large as 19.8m/s2
C. can be horizontal
D. is zero
E. none of these
ANS: D
A. any reference frame that is not accelerating
B. a frame attached to a particle on which there are no forces
C. any reference frame that is at rest
D. a reference frame attached to the center of the universe
E. a reference frame attached to Earth
ANS: B
2. An object moving at constant velocity in an inertial frame must:
A. have a net force on it
B. eventually stop due to gravity
C. not have any force of gravity on it
D. have zero net force on it
E. have no frictional force on it
ANS: D
3. In SI units a force is numerically equal to the , when the force is applied to it.
A. velocity of the standard kilogram
B. speed of the standard kilogram
C. velocity of any object
D. acceleration of the standard kilogram
E. acceleration of any object
ANS: D
4. Which of the following quantities is NOT a vector?
A. Mass
B. Displacement
C. Weight
D. Acceleration
E. Force
ANS: A
5. A newton is the force:
A. of gravity on a 1 kg body
B. of gravity on a 1 g body
C. that gives a 1 g body an acceleration of 1 cm/s2
D. that gives a 1 kg body an acceleration of 1m/s2
E. that gives a 1 kg body an acceleration of 9.8m/s2
ANS: D
49 6. The unit of force called the newton is:
A. 9.8kg • m/s2
B. 1 kg • m/s2
C. defined by means of Newton’s third law
D. 1 kg of mass
E. 1 kg of force
ANS: B
7. A force of 1N is:
A. 1 kg/s
B. 1 kg • m/s
C. 1 kg • m/s2
D. 1 kg • m2/s
E. 1 kg • m2/s2
ANS: C
8. The standard 1-kg mass is attached to a compressed spring and the spring is release
D. If the mass initially has an acceleration of 5.6m/s2, the force of the spring has a magnitude of:
A. 2.8N
B. 5.6N
C. 11.2N
D. 0
E. an undetermined amount
ANS: B
9. Acceleration is always in the direction:
A. of the displacement
B. of the initial velocity
C. of the final velocity
D. of the net force
E. opposite to the frictional force
ANS: D
10. The term “mass” refers to the same physical concept as:
A. weight
B. inertia
C. force
D. acceleration
C. volume
ANS: B
50
11. The inertia of a body tends to cause the body to:
A. speed up
B. slow down
C. resist any change in its motion
D. fall toward Earth
E. decelerate due to friction
ANS: C
13. When a certain force is applied to the standard kilogram its acceleration is 5.0m/s2. When the same force is applied to another object its acceleration is one-fifth as much. The mass of the object is:
A. 0.2kg
B. 0.5kg
C. 1.0kg
D. 5.0kg
E. 10 kg
ANS: D
14. Mass differs from weight in that:
A. all objects have weight but some lack mass
B. weight is a force and mass is not
C. the mass of an object is always more than its weight
D. mass can be expressed only in the metric system
E. there is no difference
ANS: B
51 15. The mass of a body:
A. is slightly different at different places on Earth
B. is a vector
C. is independent of the free-fall acceleration
D. is the same for all bodies of the same volume
E. can be measured most accurately on a spring scale
ANS: C
16. The mass and weight of a body:
A. differ by a factor of 9.8
B. are identical
C. are the same physical quantities expressed in different units
D. are both a direct measure of the inertia of the body
E. have the same ratio as that of any other body placed at that location
ANS: E
17. An object placed on an equal-arm balance requires 12 kg to balance it. When placed on a spring scale, the scale reads 12 kg. Everything (balance, scale, set of weights and object) is now transported to the Moon where the free-fall acceleration is one-sixth that on Earth. The new readings of the balance and spring scale (respectively) are:
A. 12 kg, 12 kg
B. 2kg, 2kg
C. 12 kg, 2 kg
D. 2 kg, 12 kg
E. 12 kg, 72 kg
ANS: C
18. Two objects, one having three times the mass of the other, are dropped from the same height in a vacuum. At the end of their fall, their velocities are equal because:
A. anything falling in vacuum has constant velocity
B. all objects reach the same terminal velocity
C. the acceleration of the larger object is three times greater than that of the smaller object
D. the force of gravity is the same for both objects
E. none of the above
ANS: E
19. A feather and a lead ball are dropped from rest in vacuum on the Moon. The acceleration of the feather is:
A. more than that of the lead ball
B. the same as that of the lead ball
C. less than that of the lead ball
D. 9.8m/s2
E. zero since it floats in a vacuum
ANS: B
24. Equal forces F act on isolated bodies A and
B. The mass of B is three times that of
A. The magnitude of the acceleration of A is:
A. three times that of B
B. 1/3 that of B
C. the same as B
D. nine times that of B
E. 1/9 that of B
ANS: A
25. A car travels east at constant velocity. The net force on the car is:
A. east
B. west
C. up
D. down
E. zero
ANS: E
26. A constant force of 8.0 N is exerted for 4.0 s on a 16-kg object initially at rest. The change in speed of this object will be:
A. 0.5m/s
B. 2m/s
C. 4m/s
D. 8m/s
E. 32m/s
ANS: B
54
27. A 6-kg object is moving south. A net force of 12N north on it results in the object having an acceleration of:
A. 2m/s2, north
B. 2m/s2, south
C. 6m/s2, north
D. 18m/s2, north
E. 18m/s2, south
ANS: A
28. A 9000-N automobile is pushed along a level road by four students who apply a total forward force of 500 N. Neglecting friction, the acceleration of the automobile is:
A. 0.055m/s2
B. 0.54m/s2
C. 1.8m/s2
D. 9.8m/s2
E. 18m/s2
ANS: B
29. An object rests on a horizontal frictionless surfac
E. A horizontal force of magnitude F is applie
D. This force produces an acceleration:
A. only if F is larger than the weight of the object
B. only while the object suddenly changes from rest to motion
C. always
D. only if the inertia of the object decreases
E. only if F is increasing
ANS: C
30. A 25-kg crate is pushed across a frictionless horizontal floor with a force of 20 N, directed 20◦ below the horizontal. The acceleration of the crate is:
A. 0.27m/s2
B. 0.75m/s2
C. 0.80m/s2
D. 170m/s2
E. 470m/s2
ANS: B
31. A ball with a weight of 1.5N is thrown at an angle of 30◦ above the horizontal with an initial speed of 12m/s. At its highest point, the net force on the ball is:
A. 9.8N, 30◦ below horizontal
B. zero
C. 9.8N, up
D. 9.8N, down
E. 1.5N, down
ANS: E
55 32. Two forces are applied to a 5.0-kg crate; one is 6.0N to the north and the other is 8.0N to the west. The magnitude of the acceleration of the crate is:
A. 0.50m/s2
B. 2.0m/s2
C. 2.8m/s2
D. 10m/s2
E. 50m/s2
ANS: B
33. A 400-N steel ball is suspended by a light rope from the ceiling. The tension in the rope is:
A. 400N
B. 800N
C. zero
D. 200N
E. 560N
ANS: A
34. A heavy steel ball B is suspended by a cord from a block of wood W. The entire system is dropped through the air. Neglecting air resistance, the tension in the cord is:
A. zero
B. the difference in the masses of B and W
C. the difference in the weights of B and W
D. the weight of B
E. none of these
ANS: A
36. A 1000-kg elevator is rising and its speed is increasing at 3m/s2. The tension force of the cable on the elevator is:
A. 6800N
B. 1000N
C. 3000N
D. 9800N
E. 12800N
ANS: E
∗37. A 5-kg block is suspended by a rope from the ceiling of an elevator as the elevator accelerates downward at 3.0m/s2. The tension force of the rope on the block is:
A. 15 N, up
B. 34 N, up
C. 34 N, down
D. 64 N, up
E. 64 N, down
ANS: B
38. A crane operator lowers a 16, 000-N steel ball with a downward acceleration of 3m/s2. The tension force of the cable is:
A. 4900N
B. 11, 000N
C. 16, 000N
D. 21, 000N
E. 48, 000N
ANS: B
40. A car moves horizontally with a constant acceleration of 3m/s2. A ball is suspended by a string from the ceiling of the car. The ball does not swing, being at rest with respect to the car. What angle does the string make with the vertical?
A. 17◦
B. 35◦
C. 52◦
D. 73◦
E. Cannot be found without knowing the length of the string
ANS: A
41. A man weighing 700 Nb is in an elevator that is accelerating upward at 4m/s2. The force exerted on him by the elevator floor is:
A. 71N
B. 290N
C. 410N
D. 700N
E. 990N
ANS: E
42. You stand on a spring scale on the floor of an elevator. Of the following, the scale shows the highest reading when the elevator:
A. moves upward with increasing speed
B. moves upward with decreasing speed
C. remains stationary
D. moves downward with increasing speed
E. moves downward at constant speed
ANS: A
43. You stand on a spring scale on the floor of an elevator. Of the following, the scale shows the highest reading when the elevator:
A. moves downward with increasing speed
B. moves downward with decreasing speed
C. remains stationary
D. moves upward with decreasing speed
E. moves upward at constant speed
ANS: B
44. When a 25-kg crate is pushed across a frictionless horizontal floor with a force of 200 N, directed 20◦ below the horizontal, the magnitude of the normal force of the floor on the crate is:
A. 25N
B. 68N
C. 180N
D. 250N
E. 310N
ANS: E
58
45. A block slides down a frictionless plane that makes an angle of 30◦ with the horizontal. The acceleration of the block is:
A. 980 cm/s2
B. 566 cm/s2
C. 849 cm/s2
D. zero
E. 490 cm/s2
ANS: E
46. A 25-N crate slides down a frictionless incline that is 25◦ above the horizontal. The magnitude of the normal force of the incline on the crate is:
A. 11N
B. 23N
C. 25N
D. 100N
E. 220N
ANS: B
47. A 25-N crate is held at rest on a frictionless incline by a force that is parallel to the inclin
E. If the incline is 25◦ above the horizontal the magnitude of the applied force is:
A. 4.1N
B. 4.6N
C. 8.9N
D. 11N
E. 23N
ANS: D
48. A 25-N crate is held at rest on a frictionless incline by a force that is parallel to the inclin
E. If the incline is 25◦ above the horizontal the magnitude of the normal force of the incline on the crate is:
A. 4.1N
B. 4.6N
C. 8.9N
D. 11N
E. 23N
ANS: E
49. A 32-N force, parallel to the incline, is required to push a certain crate at constant velocity up a frictionless incline that is 30◦ above the horizontal. The mass of the crate is:
A. 3.3kg
B. 3.8kg
C. 5.7kg
D. 6.5kg
E. 160 kg
ANS: D
59 50. A sled is on an icy (frictionless) slope that is 30◦ above the horizontal. When a 40-N force, parallel to the incline and directed up the incline, is applied to the sled, the acceleration of the sled is 2.0m/s2, down the inclin
E. The mass of the sled is:
A. 3.8kg
B. 4.1kg
C. 5.8kg
D. 6.2kg
E. 10 kg
ANS: E
51. When a 40-N force, parallel to the incline and directed up the incline, is applied to a crate on a frictionless incline that is 30◦ above the horizontal, the acceleration of the crate is 2.0m/s2, up the inclin
E. The mass of the crate is:
A. 3.8kg
B. 4.1kg
C. 5.8kg
D. 6.2kg
E. 10 kg
ANS: C
52. The “reaction” force does not cancel the “action” force because:
A. the action force is greater than the reaction force
B. they are on different bodies
C. they are in the same direction
D. the reaction force exists only after the action force is removed
E. the reaction force is greater than the action force
ANS: B
53. A book rests on a table, exerting a downward force on the tabl
E. The reaction to this force is:
A. the force of Earth on the book
B. the force of the table on the book
C. the force of Earth on the table
D. the force of the book on Earth
E. the inertia of the book
ANS: B
54. A lead block is suspended from your hand by a string. The reaction to the force of gravity on the block is the force exerted by:
A. the string on the block
B. the block on the string
C. the string on the hand
D. the hand on the string
E. the block on Earth
ANS: E
60
55. A 5-kg concrete block is lowered with a downward acceleration of 2.8m/s2 by means of a rop
E. The force of the block on the rope is:
A. 14 N, up
B. 14 N, down
C. 35 N, up
D. 35 N, down
E. 49 N, up
ANS: D
56. A 90-kg man stands in an elevator that is moving up at a constant speed of 5.0m/s. The force exerted by him on the floor is about:
A. zero
B. 90N
C. 880N
D. 450N
E. 49N
ANS: C
57. A 90-kg man stands in an elevator that has a downward acceleration of 1.4m/s2. The force exerted by him on the floor is about:
A. zero
B. 90N
C. 760N
D. 880N
E. 1010N
ANS: C
58. A 5-kg concrete block is lowered with a downward acceleration of 2.8m/s2 by means of a rop
E. The force of the block on Earth is:
A. 14 N, up
B. 14 N, down
C. 35 N, up
D. 35 N, down
E. 49 N, up
ANS: E
69. A short 10-g string is used to pull a 50-g toy across a frictionless horizontal surfac
E. If a 3.0 × 10−2-N force is applied horizontally to the free end, the force of the string on the toy, at the other end, is:
A. 0.15N
B. 6.0 × 10−3 N
C. 2.5 × 10−2 N
D. 3.0 × 10−2 N
E. 3.5 × 10−2 N
ANS: C
65
E. Which of the following will increase the magnitude of the frictional force on it?
A. Putting a second brick on top
B. Decreasing the surface area of contact
C. Increasing the surface area of contact
D. Decreasing the mass of the brick
E. None of the above
ANS: A
2. The coefficient of kinetic friction:
A. is in the direction of the frictional force
B. is in the direction of the normal force
C. is the ratio of force to area
D. can have units of newtons
E. is none of the above
ANS: E
3. When the brakes of an automobile are applied, the road exerts the greatest retarding force:
A. while the wheels are sliding
B. just before the wheels start to slide
C. when the automobile is going fastest
D. when the acceleration is least
E. at the instant when the speed begins to change
ANS: B
4. A forward horizontal force of 12N is used to pull a 240-N crate at constant velocity across a horizontal floor. The coefficient of friction is:
A. 0.5
B. 0.05
C. 2
D. 0.2
E. 20
ANS: B
5. The speed of a 4.0-N hockey puck, sliding across a level ice surface, decreases at the rate of 0.61m/s2. The coefficient of kinetic friction between the puck and ice is:
A. 0.062
B. 0.41
C. 0.62
D. 1.2
E. 9.8
ANS: A
8. A 40-N crate rests on a rough horizontal floor. A 12-N horizontal force is then applied to it. If the coefficients of friction are μs = 0.5 and μk = 0.4, the magnitude of the frictional force on the crate is:
A. 8N
B. 12N
C. 16N
D. 20N
E. 40N
ANS: B
67 9. A 24-N horizontal force is applied to a 40-N block initially at rest on a rough horizontal surfac
E. If the coefficients of friction are μs = 0.5 and μk = 0.4, the magnitude of the frictional force on the block is:
A. 8N
B. 12N
C. 16N
D. 20N
E. 400N
ANS: C
10. A horizontal shove of at least 200N is required to start moving a 800-N crate initially at rest on a horizontal floor. The coefficient of static friction is:
A. 0.25
B. 0.125
C. 0.50
D. 4.00
E. none of these
ANS: A
11. A force F (larger than the largest possible force of static friction) is applied to the left to an object moving to the right on a horizontal surfac
E. Then:
A. the object must be moving at constant speed
B. F and the friction force act in opposite directions
C. the object must be slowing down
D. the object must be speeding up
E. the object must come to rest and remain at rest
ANS: C
12. A bureau rests on a rough horizontal surface (μs = 0.50, μk = 0.40). A constant horizontal force, just sufficient to start the bureau in motion, is then applie
D. The acceleration of the bureau is:
A. 0
B. 0.98m/s2
C. 3.3m/s2
D. 4.5m/s2
E. 8.9m/s2
ANS: B
13. A car is traveling at 15m/s on a horizontal roa
D. The brakes are applied and the car skids to a stop in 4.0 s. The coefficient of kinetic friction between the tires and road is:
A. 0.38
B. 0.69
C. 0.76
D. 0.92
E. 1.11
ANS: A
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19. A 12-kg crate rests on a horizontal surface and a boy pulls on it with a force that is 30◦ below the horizontal. If the coefficient of static friction is 0.40, the minimum magnitude force he needs to start the crate moving is:
A. 44N
B. 47N
C. 54N
D. 56N
E. 71N
ANS: E
20. A crate resting on a rough horizontal floor is to be moved horizontally. The coefficient of static friction is 0.40. To start the crate moving with the weakest possible applied force, in what direction should the force be applied?
A. Horizontal
B. 24◦ below the horizontal
C. 22◦ above the horizontal
D. 24◦ above the horizontal
E. 66◦ below the horizontal
ANS: C
21. A 50-N force is applied to a crate on a horizontal rough floor, causing it to move horizontally. If the coefficient of kinetic friction is 0.50, in what direction should the force be applied to obtain the greatest acceleration?
A. Horizontal
B. 60◦ above the horizontal
C. 30◦ above the horizontal
D. 27◦ above the horizontal
E. 30◦ below the horizontal
ANS: D
71 22. A professor holds an eraser against a vertical chalkboard by pushing horizontally on it. He pushes with a force that is much greater than is required to hold the eraser. The force of friction exerted by the board on the eraser increases if he:
A. pushes with slightly greater force
B. pushes with slightly less force
C. stops pushing
D. pushes so his force is slightly downward but has the same magnitude
E. pushes so his force is slightly upward but has the same magnitude
ANS: D
23. A horizontal force of 12N pushes a 0.5-kg book against a vertical wall. The book is initially at rest. If the coefficients of friction are μs = 0.6 and μk = 0.8 which of the following is true?
A. The magnitude of the frictional force is 4.9N
B. The magnitude of the frictional force is 7.2N
C. The normal force is 4.9N
D. The book will start moving and accelerate
E. If started moving downward, the book will decelerate
ANS: A
24. A horizontal force of 5.0N pushes a 0.50-kg book against a vertical wall. The book is initially at rest. If the coefficients of friction are μs = 0.6 and μk = 0.80, the magnitude of the frictional force is:
A. 0
B. 4.9N
C. 3.0N
D. 5.0N
E. 4.0N
ANS: E
25. A horizontal force of 12N pushes a 0.50-kg book against a vertical wall. The book is initially at rest. If μs = 0.6 and μk = 0.80, the acceleration of the book in m/s2 is:
A. 0
B. 9.4m/s2
C. 9.8m/s2
D. 14.4m/s2
E. 19.2m/s2
ANS: A
26. A horizontal force of 5.0N pushes a 0.50-kg block against a vertical wall. The block is initially at rest. If μs = 0.60 and μk = 0.80, the acceleration of the block in m/s2 is:
A. 0
B. 1.8
C. 6.0
D. 8.0
E. 9.8
ANS: B
29. A box rests on a rough board 10 meters long. When one end of the board is slowly raised to a height of 6 meters above the other end, the box begins to slid
E. The coefficient of static friction is:
A. 0.8
B. 0.25
C. 0.4
D. 0.6
E. 0.75
ANS: E
73 30. A block is placed on a rough wooden plan
E. It is found that when the plane is tilted 30◦ to the horizontal, the block will slide down at constant spee
D. The coefficient of kinetic friction of the block with the plane is:
A. 0.500
B. 0.577
C. 1.73
D. 0.866
E. 4.90
ANS: B
31. A crate is sliding down an incline that is 35◦ above the horizontal. If the coefficient of kinetic friction is 0.40, the acceleration of the crate is:
A. 0
B. 2.4m/s2
C. 5.8m/s2
D. 8.8m/s2
E. 10.3m/s2
ANS: B
32. A 5.0-kg crate is resting on a horizontal plank. The coefficient of static friction is 0.50 and the coefficient of kinetic friction is 0.40. After one end of the plank is raised so the plank makes an angle of 25◦ with the horizontal, the force of friction is:
A. 0
B. 18N
C. 21N
D. 22N
E. 44N
ANS: C
33. A 5.0-kg crate is resting on a horizontal plank. The coefficient of static friction is 0.50 and the coefficient of kinetic friction is 0.40. After one end of the plank is raised so the plank makes an angle of 30◦ with the horizontal, the force of friction is:
A. 0
B. 18N
C. 21N
D. 22N
E. 44N
ANS: B
74
34. A 5.0-kg crate is on an incline that makes an angle of 30◦ with the horizontal. If the coefficient of static friction is 0.50, the minimum force that can be applied parallel to the plane to hold the crate at rest is:
A. 0
B. 3.3N
C. 30N
D. 46N
E. 55N
ANS: B
43. A 1000-kg airplane moves in straight flight at constant spee
D. The force of air friction is 1800 N. The net force on the plane is:
A. zero
B. 11800N
C. 1800N
D. 9800N
E. none of these
ANS: A
44. Why do raindrops fall with constant speed during the later stages of their descent?
A. The gravitational force is the same for all drops
B. Air resistance just balances the force of gravity
C. The drops all fall from the same height
D. The force of gravity is negligible for objects as small as raindrops
E. Gravity cannot increase the speed of a falling object to more than 9.8m/s
ANS: B
45. A ball is thrown downward from the edge of a cliff with an initial speed that is three times the terminal spee
D. Initially its acceleration is
A. upward and greater than g
B. upward and less than g
C. downward and greater than g
D. downward and less than g
E. downward and equal to g
ANS: A
78
46. A ball is thrown upward into the air with a speed that is greater than terminal spee
D. On the way up it slows down and, after its speed equals the terminal speed but before it gets to the top of its trajectory:
A. its speed is constant
B. it continues to slow down
C. it speeds up
D. its motion becomes jerky
E. none of the above
ANS: B
47. A ball is thrown upward into the air with a speed that is greater than terminal spee
D. It lands at the place where it was thrown. During its flight the force of air resistance is the greatest:
A. just after it is thrown
B. halfway up
C. at the top of its trajectory
D. halfway down
E. just before it lands.
ANS: A
48. Uniform circular motion is the direct consequence of:
A. Newton’s third law
B. a force that is always tangent to the path
C. an acceleration tangent to the path
D. a force of constant magnitude that is always directed away from the same fixed point
E. a force of constant magnitude that is always directed toward the same fixed point
ANS: E
49. An object moving in a circle at constant speed:
A. must have only one force acting on it
B. is not accelerating
C. is held to its path by centrifugal force
D. has an acceleration of constant magnitude
E. has an acceleration that is tangent to the circle
ANS: D
50. An object of mass m and another object of mass 2m are each forced to move along a circle of radius 1.0m at a constant speed of 1.0m/s. The magnitudes of their accelerations are:
A. equal
B. in the ratio of √2 : 1
C. in the ratio of 2 : 1
D. in the ratio of 4 : 1
E. zero
ANS: A
79 51. The magnitude of the force required to cause a 0.04-kg object to move at 0.6m/s in a circle of radius 1.0m is:
A. 2.4 × 10−2 N
B. 1.4 × 10−2 N
C. 1.4π × 10−2 N
D. 2.4π2 × 10−2 N
E. 3.13N
ANS: B
52. A 0.2-kg stone is attached to a string and swung in a circle of radius 0.6m on a horizontal and frictionless surfac
E. If the stone makes 150 revolutions per minute, the tension force of the string on the stone is:
A. 0.03N
B. 0.2N
C. 0.9N
D. 1.96N
E. 30N
ANS: E
54. An object moves around a circl
E. If the radius is doubled keeping the speed the same then the magnitude of the centripetal force must be:
A. twice as great
B. half as great
C. four times as great
D. one-fourth as great
E. the same
ANS: B
80
55. An object moves in a circl
E. If the mass is tripled, the speed halved, and the radius unchanged, then the magnitude of the centripetal force must be multiplied by a factor of:
A. 3/2
B. 3/4
C. 9/4
D. 6
E. 12
ANS: B
56. If a satellite moves above Earth’s atmosphere in a circular orbit with constant speed, then:
A. its acceleration and velocity are always in the same direction
B. the net force on it is zero
C. its velocity is constant
D. it will fall back to Earth when its fuel is used up
E. its acceleration is toward the Earth
ANS: E
57. A 800-N passenger in a car presses against the car door with a 200N force when the car makes a left turn at 13m/s. The (faulty) door will pop open under a force of 800 N. Of the following, the least speed for which the passenger is thrown out of the car is:
A. 14m/s
B. 19m/s
C. 20m/s
D. 26m/s
E. 54m/s
ANS: D
58. If a certain car, going with speed v1, rounds a level curve with a radius R1, it is just on the verge of skidding. If its speed is now doubled, the radius of the tightest curve on the same road that it can round without skidding is:
A. 2R1
B. 4R1
C. R1/2
D. R1/4
E. R1
ANS: B
59. An automobile moves on a level horizontal road in a circle of radius 30 m. The coefficient of friction between tires and road is 0.50. The maximum speed with which this car can round this curve is:
A. 3.0m/s
B. 4.9m/s
C. 9.8m/s
D. 12m/s
E. 13m/s
ANS: D
81 60. The driver of a 1000-kg car tries to turn through a circle of radius 100m on an unbanked curve at a speed of 10m/s. The actual frictional force between the tires and slippery road has a magnitude of 900 N. The car:
A. slides into the inside of the curve
B. makes the turn
C. slows down due to the frictional force
D. makes the turn only if it goes faster
E. slides off to the outside of the curve
ANS: E
61. A car rounds a 75-m radius curve at a constant speed of 18m/s. A ball is suspended by a string from the ceiling the car and moves with the car. The angle between the string and the vertical is:
A. 0
B. 1.4◦
C. 24◦
D. 90◦
E. cannot be found without knowing the mass of the ball
ANS: C
64. A person riding a Ferris wheel is strapped into her seat by a seat belt. The wheel is spun so that the centripetal acceleration is g. Select the correct combination of forces that act on her when she is at the top. In the table Fg = force of gravity, down; Fb = seat belt force, down; and Fs = seat force, up. Fg Fb Fs
A. 0 mg 0
B. mg 0 0
C. 0 0 mg
D. mg mg 0
E. mg 0 mg
ANS: B
65. One end of a 1.0-m long string is fixed, the other end is attached to a 2.0-kg ston
E. The stone swings in a vertical circle, passing the bottom point at 4.0m/s. The tension force of the string at this point is about:
A. 0
B. 12N
C. 20N
D. 32N
E. 52N
ANS: E
83 66. One end of a 1.0-m string is fixed, the other end is attached to a 2.0-kg ston
E. The stone swings in a vertical circle, passing the top point at 4.0m/s. The tension force of the string (in newtons) at this point is about:
A. 0
B. 12
C. 20
D. 32
E. 52
ANS: B
67. A coin is placed on a horizontal phonograph turntabl
E. Let N be the magnitude of the normal force exerted by the turntable on the coin, f be the magnitude of the frictional force exerted by the turntable on the coin, and fs, max be the maximum possible force of static friction. The speed of the turntable is increased in small steps. If the coin does not slide, then
A. N increases, f increases, and fs, max stays the same
B. N increases, f increases, and fs, max increases
C. f increases and both N and fs, max stay the same
D. N, f, and fs, max all stay the same
E. N, f, and fs, max all increase
ANS: C
69. A block is suspended by a rope from the ceiling of a car. When the car rounds a 45-m radius horizontal curve at 22m/s (about 50 mph), what angle does the rope make with the vertical?
A. 0
B. 25◦
C. 48◦
D. 65◦
E. 90◦
ANS: C
84
70. Circular freeway entrance and exit ramps are commonly banked to handle a car moving at 13m/s. To design a similar ramp for 26m/s one should:
A. increase radius by factor of 2
B. decrease radius by factor of 2
C. increase radius by factor of 4
D. decrease radius by factor of 4
E. increase radius by factor of √2
ANS: C
71. At what angle should the roadway on a curve with a 50m radius be banked to allow cars to negotiate the curve at 12m/s even if the roadway is icy (and the frictional force is zero)?
A. 0
B. 16◦
C. 18◦
D. 35◦
E. 73◦
ANS: B
85
A. erg
B. ft•lb
C. watt
D. newton•meter
E. joule
ANS: C
2. Which of the following groups does NOT contain a scalar quantity?
A. velocity, force, power
B. displacement, acceleration, force
C. acceleration, speed, work
D. energy, work, distance
E. pressure, weight, time
ANS: B
5. An object moves in a circle at constant spee
D. The work done by the centripetal force is zero because:
A. the displacement for each revolution is zero
B. the average force for each revolution is zero
C. there is no friction
D. the magnitude of the acceleration is zero
E. the centripetal force is perpendicular to the velocity
ANS: E
6. An object of mass 1 g is whirled in a horizontal circle of radius 0.5m at a constant speed of 2m/s. The work done on the object during one revolution is:
A. 0
B. 1 J
C. 2 J
D. 4 J
E. 16 J
ANS: A
7. The work done by gravity during the descent of a projectile:
A. is positive
B. is negative
C. is zero
D. depends for its sign on the direction of the y axis
E. depends for its sign on the direction of both the x and y axes
ANS: A
8. A baseball is hit high into the upper bleachers of left fiel
D. Over its entire flight the work done by gravity and the work done by air resistance, respectively, are:
A. positive; positive
B. positive; negative
C. negative; positive
D. negative; negative
E. unknown since vital information is lacking
ANS: D
9. A line drive to the shortstop is caught at the same height as it was originally hit. Over its entire flight the work done by gravity and the work done by air resistance, respectively, are:
A. zero; positive
B. zero; negative
C. positive; negative
D. negative; positive
E. negative; negative
ANS: B
87 10. A 2-kg object is moving at 3m/s. A 4-N force is applied in the direction of motion and then removed after the object has traveled an additional 5m. The work done by this force is:
A. 12 J
B. 15 J
C. 18 J
D. 20 J
E. 38 J
ANS: D
11. A sledge (including load) weighs 5000 N. It is pulled on level snow by a dog team exerting a horizontal force on it. The coefficient of kinetic friction between sledge and snow is 0.05. How much work is done by the dog team pulling the sledge 1000m at constant speed?
A. 2.5 × 104 J
B. 2.5 × 105 J
C. 5.0 × 105 J
D. 2.5 × 106 J
E. 5.0 × 106 J
ANS: B
12. Camping equipment weighing 6000N is pulled across a frozen lake by means of a horizontal rop
E. The coefficient of kinetic friction is 0.05. The work done by the campers in pulling the equipment 1000m at constant velocity is:
A. 3.1 × 104 J
B. 1.5 × 105 J
C. 3.0 × 105 J
D. 2.9 × 106 J
E. 6.0 × 106 J
ANS: C
13. Camping equipment weighing 6000N is pulled across a frozen lake by means of a horizontal rop
E. The coefficient of kinetic friction is 0.05. How much work is done by the campers in pulling the equipment 1000m if its speed is increasing at the constant rate of 0.20m/s2?
A. −1.2 × 106 J
B. 1.8 × 105 J
C. 3.0 × 105 J
D. 4.2 × 105 J
E. 1.2 × 106 J
ANS: D
14. A 1-kg block is lifted vertically 1m by a boy. The work done by the boy is about:
A. 1 ft • lb
B. 1 J
C. 10 J
D. 0.1J
E. zero
ANS: C
88
15. A 0.50-kg object moves in a horizontal circular track with a radius of 2.5m. An external force of 3.0N, always tangent to the track, causes the object to speed up as it goes aroun
D. The work done by the external force as the mass makes one revolution is:
A. 24 J
B. 47 J
C. 59 J
D. 94 J
E. 120 J
ANS: B
17. A man pushes an 80-N crate a distance of 5.0m upward along a frictionless slope that makes an angle of 30◦ with the horizontal. His force is parallel to the slop
E. If the speed of the crate decreases at a rate of 1.5m/s2, then the work done by the man is:
A. −200 J
B. 61 J
C. 140 J
D. 200 J
E. 260 J
ANS: C
18. A man pushes an 80-N crate a distance of 5.0m upward along a frictionless slope that makes an angle of 30◦ with the horizontal. The force he exerts is parallel to the slop
E. If the speed of the crate is constant, then the work done by the man is:
A. −200 J
B. 61 J
C. 140 J
D. 200 J
E. 260 J
ANS: D
89 19. An 80-N crate slides with constant speed a distance of 5.0m downward along a rough slope that makes an angle of 30◦ with the horizontal. The work done by the force of gravity is:
A. −400 J
B. −200 J
C. −69 J
D. 200 J
E. 400 J
ANS: D
20. A man pulls a sled along a rough horizontal surface by applying a constant force F at an angle θ above the horizontal. In pulling the sled a horizontal distance d, the work done by the man is:
A. Fd
B. Fdcos θ
C. Fdsin θ
D. Fd/ cos θ
E. Fd/ sin θ
ANS: B
21. A man wishes to pull a crate 15m across a rough floor by exerting a force of 100 N. The coefficient of kinetic friction is 0.25. For the man to do the least work, the angle between the force and the horizontal should be:
A. 0
B. 14◦
C. 43◦
D. 66◦
E. 76◦
ANS: A
22. A particle moves 5m in the positive x direction while being acted upon by a constant force F = (4N)ˆi + (2 N)ˆj − (4 N)ˆk . The work done on the particle by this force is:
A. 20 J
B. 10 J
C. −20 J
D. 30 J
E. is impossible to calculate without knowing other forces
ANS: A
26. When a certain rubber band is stretched a distance x, it exerts a restoring force of magnitude F = Ax, where A is a constant. The work done by a person in stretching this rubber band from x = 0 to x = L, beginning and ending at rest, is:
A. AL2
B. A + 2L
C. A + 2L2
D. A/L
E. AL2/2
ANS: E
27. When a certain rubber band is stretched a distance x, it exerts a restoring force of magnitude F = ax+bx2, where a and b are constants. The work done in stretching this rubber band from x = 0 to x = L is:
A. aL2 + bLx3
B. aL + 2bL2
C. a + 2bL
D. bL
E. aL2/2 +bL3/3
ANS: E
28. An ideal spring is hung vertically from the ceiling. When a 2.0-kg mass hangs at rest from it the spring is extended 6.0 cm from its relaxed length. A downward external force is now applied to the mass to extend the spring an additional 10 cm. While the spring is being extended by the force, the work done by the spring is:
A. −3.6J
B. −3.3J
C. −3.4 × 10−5 J
D. 3.3J
E. 3.6J
ANS: A
29. An ideal spring is hung vertically from the ceiling. When a 2.0-kg block hangs at rest from it the spring is extended 6.0 cm from its relaxed length. A upward external force is then applied to the block to move it upward a distance of 16 cm. While the block is moving upward the work done by the spring is:
A. −1.0J
B. −0.52 J
C. −0.26 J
D. 0.52 J
E. 1.0J
ANS: A
92
30. Which of the following bodies has the largest kinetic energy?
A. Mass 3M and speed V
B. Mass 3M and speed 2V
C. Mass 2M and speed 3V
D. Mass M and speed 4V
E. All four of the above have the same kinetic energy
ANS: C
31. Two trailers, X with mass 500 kg and Y with mass 2000 kg, are being pulled at the same spee
D. The ratio of the kinetic energy of Y to that of X is:
A. 1:1
B. 2:1
C. 4:1
D. 9:1
E. 1500:1
ANS: C
32. A 8000-N car is traveling at 12m/s along a horizontal road when the brakes are applie
D. The car skids to a stop in 4.0 s. How much kinetic energy does the car lose in this time?
A. 4.8 × 104 J
B. 5.9 × 104 J
C. 1.2 × 105 J
D. 5.8 × 105 J
E. 4.8 × 106 J
ANS: B
33. The velocity of a particle moving along the x axis changes from vi to vf . For which values of vi and vf is the total work done on the particle positive?
A. vi = 5m/s, vf = 2m/s
B. vi = 5m/s, vf = −2m/s
C. vi = −5m/s, vf = −2m/s
D. vi = −5m/s, vf = 2m/s
E. vi = 2m/s, vf = −5m/s
ANS: E
34. An object is constrained by a cord to move in a circular path of radius 0.5m on a horizontal frictionless surfac
E. The cord will break if its tension exceeds 16 N. The maximum kinetic energy the object can have is:
A. 4 J
B. 8 J
C. 16 J
D. 32 J
E. 64 J
ANS: A
93 35. The weight of an object on the moon is one-sixth of its weight on Earth. The ratio of the kinetic energy of a body on Earth moving with speed V to that of the same body moving with speed V on the moon is:
A. 6:1
B. 36:1
C. 1:1
D. 1:6
E. 1:36
ANS: C
36. Which of the following is the correct combination of dimensions for energy?
A. MLT
B. LT2/m
C. ML2/T2
D. M2L3T
E. ML/T2
ANS: C
37. The amount of work required to stop a moving object is equal to:
A. the velocity of the object
B. the kinetic energy of the object
C. the mass of the object times its acceleration
D. the mass of the object times its velocity
E. the square of the velocity of the object
ANS: B
38. A 5.0-kg cart is moving horizontally at 6.0m/s. In order to change its speed to 10.0m/s, the net work done on the cart must be:
A. 40 J
B. 90 J
C. 160 J
D. 400 J
E. 550 J
ANS: C
40. An 8-N block slides down an inclin
E. It has an initial speed of 7m/s. The work done by the resultant force on this block is:
A. 3 J
B. 6 J
C. 56 J
D. impossible to calculate without more information
E. none of these
ANS: D
41. A 4-kg cart starts up an incline with a speed of 3m/s and comes to rest 2m up the inclin
E. The total work done on the car is:
A. 6 J
B. 8 J
C. 12 J
D. 18 J
E. impossible to calculate without more information
ANS: D
42. Two objects with masses of m1 and m2 have the same kinetic energy and are both moving to the right. The same constant force F is applied to the left to both masses. If m1 = 4m2, the ratio of the stopping distance of m1 to that of m2 is:
A. 1:4
B. 4:1
C. 1:2
D. 2:1
E. 1:1
ANS: E
95 43. A Boston Red Sox baseball player catches a ball of mass m that is moving toward him with speed v. While bringing the ball to rest, his hand moves back a distance
D. Assuming constant deceleration, the horizontal force exerted on the ball by his hand is:
A. mv/d
B. mvd
C. mv2/d
D. 2mv/d
E. mv2/(2d)
ANS: E
44. A 0.50-kg object moves on a horizontal circular track with a radius of 2.5m. An external force of 3.0N, always tangent to the track, causes the object to speed up as it goes aroun
D. If it starts from rest its speed at the end of one revolution is:
A. 9.8m/s
B. 14m/s
C. 15m/s
D. 19m/s
E. 21m/s
ANS: B
45. A 0.50-kg object moves on a horizontal frictionless circular track with a radius of 2.5m. An external force of 3.0N, always tangent to the track, causes the object to speed up as it goes aroun
D. If it starts from rest, then at the end of one revolution the radial component of the force of the track on it is:
A. 19N
B. 38N
C. 47N
D. 75N
E. 96N
ANS: B
46. A 2-kg block is attached to a horizonal ideal spring with a spring constant of 200N/m. When the spring has its equilibrium length the block is given a speed of 5m/s. What is the maximum elongation of the spring?
A. 0
B. 0.05m
C. 5m
D. 10m
E. 100m
ANS: C
96
47. At time t = 0 a particle starts moving along the x axis. If its kinetic energy increases uniformly with t the net force acting on it must be:
A. constant
B. proportional to t
C. inversely proportional to t
D. proportional to √t
E. proportional to 1/√t
ANS: E
48. At time t = 0 a 2-kg particle has a velocity of (4m/s)ˆi − (3m/s)ˆj. At t = 3 s its velocity is (2m/s)ˆi + (3m/s)ˆj. During this time the work done on it was:
A. 4 J
B. −4J
C. −12 J
D. −40 J
E. (4 J)ˆi + (36 J)ˆj
ANS: C
49. A particle starts from rest at time t = 0 and moves along the x axis. If the net force on it is proportional to t, its kinetic energy is proportional to:
A. t
B. t2
C. t4
D. 1/t2
E. none of the above
ANS: C
50. A 1.5-kg crate falls from a height of 2.0m onto an industrial spring scale with a spring constant of 1.5 × 105 N/m. At its greatest compression the reading on the scale is:
A. 15N
B. 30N
C. 1.5 × 103 N
D. 2.1 × 103 N
E. 3.0 × 103 N
ANS: E
51. A particle moving along the x axis is acted upon by a single force F = F0e−kx, where F0 and k are constants. The particle is released from rest at x = 0. It will attain a maximum kinetic energy of:
A. F0/k
B. F0/ek
C. kF0
D. 1/2(kF0)2
E. kekF0
ANS: A
97 52. The mechanical advantage of any machine is:
A. the efficiency of the machine
B. the work done by the machine
C. the ratio of the work done by the machine to the work expended on it
D. the ratio of the force exerted by the machine to the force applied to it
E. the ratio of the force applied to the machine to the force exerted by it
ANS: D
53. In raising an object to a given height by means of an inclined plane, as compared with raising the object vertically, there is a reduction in:
A. work required
B. distance pushed
C. friction
D. force required
E. value of the acceleration due to gravity
ANS: D
54. A watt is:
A. kg • m/s3
B. kg • m2/s
C. kg • m2/s3
D. kg • m/s
E. kg • m2/s2
ANS: C
55. Power has the dimensions of:
A. ML2/T2
B. MT/L2
C. ML/T2
D. ML2/T3
E. none of these
ANS: D
56. Which of the following five units represents a quantity that is NOT the same as the other four?
A. joule
B. erg
C. watt
D. foot•pound
E. newton•meter
ANS: C
98
57. Which of the following five quantities is NOT an expression for energy? Here m is a mass, g is the acceleration due to gravity, h and d are distances, F is a force, v is a speed, a is an acceleration, P is power, and t is tim
E.
A. mgh
B. Fd
C. 1/2mv2
D. ma
E. Pt
ANS: D
58. A watt•second is a unit of:
A. force
B. power
C. displacement
D. speed
E. energy
ANS: E
59. A watt per hour is a unit of:
A. energy
B. power
C. force
D. acceleration
E. none of these
ANS: E
60. A kilowatt•hour is a unit of:
A. power
B. energy/time
C. work
D. power/time
E. force/distance
ANS: C
99 62. A woman lifts a barbell 2.0m in 5.0 s. If she lifts it the same distance in 10 s, the work done by her is:
A. four times as great
B. two times as great
C. the same
D. half as great
E. one-fourth as great
ANS: C
100
64. A person holds an 80-N weight 2m above the floor for 30 seconds. The power required to do this is:
A. 80W
B. 40W
C. 20W
D. 10W
E. none of these
ANS: E
65. A 50-N force is the only force on a 2-kg object that starts from rest. When the force has been acting for 2 s the rate at which it is doing work is:
A. 75W
B. 100W
C. 1000W
D. 2500W
E. 5000W
ANS: D
66. A 50-N force is the only force a 2-kg crate that starts from rest. At the instant the object has gone 2m the rate at which the force is doing work is:
A. 2.5W
B. 25W
C. 75W
D. 100W
E. 500W
ANS: E
67. A particle starts from rest and is acted on by a net force that does work at a rate that is proportional to the time t. The speed of the particle is proportional to:
A. √t
B. t
C. t2
D. 1/√t
E. 1/t
ANS: A
A. is its work zero when the particle moves exactly once around any closed path
B. is its work always equal to the change in the kinetic energy of the particle
C. does it obey Newton’s second law
D. does it obey Newton’s third law
E. is it not a frictional force
ANS: A
2. A nonconservative force:
A. violates Newton’s second law
B. violates Newton’s third law
C. cannot do any work
D. must be perpendicular to the velocity of the particle on which it acts
E. none of the above
ANS: E
3. The sum of the kinetic and potential energies of a system of objects is conserved:
A. only when no external force acts on the objects
B. only when the objects move along closed paths
C. only when the work done by the resultant external force is zero
D. always
E. none of the above
ANS: E
4. A force on a particle is conservative if:
A. its work equals the change in the kinetic energy of the particle
B. it obeys Newton’s second law
C. it obeys Newton’s third law
D. its work depends on the end points of every motion, not on the path between
E. it is not a frictional force
ANS: D
5. Two particles interact by conservative forces. In addition, an external force acts on each particl
E. They complete round trips, ending at the points where they starte
D. Which of the following must have the same values at the beginning and end of this trip?
A. the total kinetic energy of the two-particle system
B. the potential energy of the two-particle system
C. the mechanical energy of the two-particle system
D. the total linear momentum of the two-particle system
E. none of the above
ANS: B
102
6. Two objects interact with each other and with no other objects. Initially object A has a speed of 5m/s and object B has a speed of 10m/s. In the course of their motion they return to their initial positions. Then A has a speed of 4m/s and B has a speed of 7m/s. We can conclude:
A. the potential energy changed from the beginning to the end of the trip
B. mechanical energy was increased by nonconservative forces
C. mechanical energy was decreased by nonconservative forces
D. mechanical energy was increased by conservative forces
E. mechanical energy was decreased by conservative forces
ANS: C
7. A good example of kinetic energy is provided by:
A. a wound clock spring
B. the raised weights of a grandfather’s clock
C. a tornado
D. a gallon of gasoline
E. an automobile storage battery
ANS: C
8. No kinetic energy is possessed by:
A. a shooting star
B. a rotating propeller on a moving airplane
C. a pendulum at the bottom of its swing
D. an elevator standing at the fifth floor
E. a cyclone
ANS: D
9. The wound spring of a clock possesses:
A. kinetic but no potential energy
B. potential but no kinetic energy
C. both potential and kinetic energy in equal amounts
D. neither potential nor kinetic energy
E. both potential and kinetic energy, but more kinetic energy than potential energy
ANS: B
10. A body at rest in a system is capable of doing work if:
A. the potential energy of the system is positive
B. the potential energy of the system is negative
C. it is free to move in such a way as to decrease its kinetic energy
D. it is free to move in such a way as to decrease the potential energy of the system
E. it is free to move in such a way as to increase the potential energy of the system
ANS: D
11. Which one of the following five quantities CANNOT be used as a unit of potential energy?
A. watt•second
B. gram•cm/s2
C. joule
D. kg•m2/s2
E. ft•lb
ANS: B
12. Suppose that the fundamental dimensions are taken to be: force (F), velocity (V) and time (T). The dimensions of potential energy are then:
A. F/T
B. FVT
C. FV/T
D. F/T2
E. FV2/T2
ANS: B
16. A 6.0-kg block is released from rest 80m above the groun
D. When it has fallen 60m its kinetic energy is approximately:
A. 4800 J
B. 3500 J
C. 1200 J
D. 120 J
E. 60 J
ANS: B
105 17. A 2-kg block is thrown upward from a point 20m above Earth’s surfac
E. At what height above Earth’s surface will the gravitational potential energy of the Earth-block system have increased by 500 J?
A. 5m
B. 25m
C. 46m
D. 70m
E. 270m
ANS: C
18. An elevator is rising at constant spee
D. Consider the following statements: I. the upward cable force is constant II. the kinetic energy of the elevator is constant III. the gravitational potential energy of the Earth-elevator system is constant IV. the acceleration of the elevator is zero V. the mechanical energy of the Earth-elevator system is constant
A. all five are true
B. only II and V are true
C. only IV and V are true
D. only I, II, and III are true
E. only I, II, and IV are true
ANS: E
19. A projectile of mass 0.50 kg is fired with an initial speed of 10m/s at an angle of 60◦ above the horizontal. The potential energy of the projectile-Earth system (relative potential energy when the projectile is at ground level) is:
A. 25 J
B. 18.75 J
C. 12.5J
D. 6.25 J
E. none of these
ANS: B
24. A particle moves along the x axis under the influence of a stationary object. The net force on the particle is given by F = (8N/m3)x3. If the potential energy is taken to be zero for x = 0 then the potential energy is given by:
A. (2 J/m4)x4
B. (−2J/m4)x4
C. (24 J/m2x2
D. (−24 J/m2)x2
E. 5 J − (2 J/m4)x4
ANS: B
25. A 0.20-kg particle moves along the x axis under the influence of a stationary object. The potential energy is given by U(x) = (8.0J/m2)x2 + (2.0J/m4)x4 , where x is in coordinate of the particl
E. If the particle has a speed of 5.0m/s when it is at x = 1.0m, its speed when it is at the origin is:
A. 0
B. 2.5m/s
C. 5.7m/s
D. 7.9m/s
E. 11m/s
ANS: E
27. A force of 10N holds an ideal spring with a 20-N/m spring constant in compression. The potential energy stored in the spring is:
A. 0.5J
B. 2.5J
C. 5 J
D. 10 J
E. 200 J
ANS: B
28. An ideal spring is used to fire a 15.0-g pellet horizontally. The spring has a spring constant of 20N/m and is initially compressed by 7.0 cm. The kinetic energy of the pellet as it leaves the spring is:
A. zero
B. 2.5 × 10−2 J
C. 4.9 × 10−2 J
D. 9.8 × 10−2 J
E. 1.4J
ANS: C
29. A 0.50-kg block attached to an ideal spring with a spring constant of 80N/m oscillates on a horizontal frictionless surfac
E. The total mechanical energy is 0.12 J. The greatest extension of the spring from its equilibrium length is:
A. 1.5 × 10−3 m
B. 3.0 × 10−3 m
C. 0.039m
D. 0.054m
E. 18m
ANS: D
30. A 0.50-kg block attached to an ideal spring with a spring constant of 80N/m oscillates on a horizontal frictionless surfac
E. The total mechanical energy is 0.12 J. The greatest speed of the block is:
A. 0.15m/s
B. 0.24m/s
C. 0.49m/s
D. 0.69m/s
E. 1.46m/s
ANS: D
31. A 0.50-kg block attached to an ideal spring with a spring constant of 80N/m oscillates on a horizontal frictionless surfac
E. When the spring is 4.0 cm longer than its equilibrium length, the speed of the block is 0.50m/s. The greatest speed of the block is:
A. 0.23m/s
B. 0.32m/s
C. 0.55m/s
D. 0.71m/s
E. 0.93m/s
ANS: D
109 32. A 0.5-kg block slides along a horizontal frictionless surface at 2m/s. It is brought to rest by compressing a very long spring of spring constant 800N/m. The maximum spring compression is:
A. 0
B. 3 cm
C. 5 cm
D. 80 cm
E. 80m
ANS: C
33. A block of mass m is initially moving to the right on a horizontal frictionless surface at a speed v. It then compresses a spring of spring constant k. At the instant when the kinetic energy of the block is equal to the potential energy of the spring, the spring is compressed a distance of:
A. v m/2k
B. (1/2)mv2
C. (1/4)mv2
D. mv2/4k
E. (1/4) mv/k
ANS: A
34. A 700-N man jumps out of a window into a fire net 10m below. The net stretches 2m before bringing the man to rest and tossing him back into the air. The maximum potential energy of the net, compared to its unstretched potential energy, is:
A. 300 J
B. 710 J
C. 850 J
D. 7000 J
E. 8400 J
ANS: E
44. The potential energy of a particle moving along the x axis is given by U(x) = (8.0J/m2)x2 + (2.0J/m4)x4 . If the total mechanical energy is 9.0 J, the limits of motion are:
A. −0.96 m; +0.96m
B. −2.2m; +2.2m
C. −1.6m; +1.6m
D. −0.96 m; +2.2m
E. −0.96 m; +1.6m
ANS: A
113 45. The potential energy of a 0.20-kg particle moving along the x axis is given by U(x) = (8.0J/m2)x2 + (2.0J/m4)x4 . When the particle is at x = 1.0m it is traveling in the positive x direction with a speed of 5.0m/s. It next stops momentarily to turn around at x =
A. 0
B. −1.1m
C. 1.1m
D. −2.3m
E. 2.3m
ANS: C
46. Given a potential energy function U(x), the corresponding force F is in the positive x direction if:
A. U is positive
B. U is negative
C. U is an increasing function of x
D. U is a decreasing function of x
E. it is impossible to obtain the direction of F from U
ANS: D
52. The potential energy of a body of mass m is given by U = −mgx + 1 2kx2. The corresponding force is:
A. −mgx2/2 + kx3/6
B. mgx2/2 − kx3/6
C. −mg + kx/2
D. −mg + kx
E. mg − kx
ANS: E
53. The potential energy of a 0.20-kg particle moving along the x axis is given by U(x) = (8.0J/m2)x2 + (2.0J/m4)x4 . When the particle is at x = 1.0m the magnitude of its acceleration is:
A. 0
B. −8m/s2
C. 8m/s2
D. −40m/s2
E. 40m/s2
ANS: D
117 55. The thermal energy of a system consisting of a thrown ball, Earth, and the air is most closely associated with:
A. the gravitational interaction of Earth and the ball
B. the kinetic energy of the ball as a whole
C. motions of the individual particles within the ball
D. motions of individual particles within the ball and the air
E. the kinetic energy of Earth as a whole
ANS: D
57. Objects A and B interact with each other via both conservative and nonconservative forces. Let KA and KB be the kinetic energies, U be the potential energy, and Eint be the thermal energy. If no external agent does work on the objects then:
A. KA + U is conserved
B. KA + U + Eint is conserved
C. KA + KB + Eint is conserved
D. KA + KB + U is conserved
E. KA + KB + U + Eint is conserved
ANS: E
58. A block slides across a rough horizontal table top. The work done by friction changes:
A. only the kinetic energy
B. only the potential energy
C. only the internal energy
D. only the kinetic and potential energies
E. only the kinetic and internal energies
ANS: E
59. A 25-g ball is released from rest 80m above the surface of Earth. During the fall the total internal energy of the ball and air increases by 15 J. Just before it hits the surface its speed is
A. 19m/s
B. 36m/s
C. 40m/s
D. 45m/s
E. 53m/s
ANS: A
60. A 5-kg projectile is fired over level ground with a velocity of 200m/s at an angle of 25◦ above the horizontal. Just before it hits the ground its speed is 150m/s. Over the entire trip the change in the internal energy of the projectile and air is:
A. +19, 000 J
B. −19, 000 J
C. +44, 000 J
D. −44, 000 J
E. 0
ANS: C
61. A 0.75-kg block slides on a rough horizontal table top. Just before it hits a horizontal ideal spring its speed is 3.5m/s. It compresses the spring 5.7 cm before coming to rest. If the spring constant is 1200N/m, the internal energy of the block and the table top must have:
A. not changed
B. decreased by 1.9J
C. decreased by 2.6J
D. increased by 1.9J
E. increased by 2.6J
ANS: C
119
A. the center of mass of an object must lie within the object
B. all the mass of an object is actually concentrated at its center of mass
C. the center of mass of an object cannot move if there is zero net force on the object
D. the center of mass of a cylinder must lie on its axis
E. none of the above
ANS: E
3. The center of mass of a uniform disk of radius R is located:
A. on the rim
B. a distance R/2 from the center
C. a distance R/3 from the center
D. a distance 2R/3 from the center
E. at the center
ANS: E
4. The center of mass of the system consisting of Earth, the Sun, and the planet Mars is:
A. closer to Earth than to either of the other bodies
B. closer to the Sun than to either of the other bodies
C. closer to Mars than to either of the other bodies
D. at the geometric center of the triangle formed by the three bodies
E. at the center of the line joining Earth and Mars
ANS: B
120
5. The center of mass of Earth’s atmosphere is:
A. a little less than halfway between Earth’s surface and the outer boundary of the atmosphere
B. near the surface of Earth
C. near the outer boundary of the atmosphere
D. near the center of Earth
E. none of the above
ANS: D
8. Block A, with a mass of 4 kg, is moving with a speed of 2.0m/s while block B, with a mass of 8 kg, is moving in the opposite direction with a speed of 3m/s. The center of mass of the two block-system is moving with a velocity of:
A. 1.3m/s in the same direction as A
B. 1.3m/s in the same direction as B
C. 2.7m/s in the same direction as A
D. 1.0m/s in the same direction as B
E. 5.0m/s in the same direction as A
ANS: B
9. At the same instant that a 0.50-kg ball is dropped from 25m above Earth, a second ball, with a mass of 0.25 kg, is thrown straight upward from Earth’s surface with an initial speed of 15m/s. They move along nearby lines and pass each other without colliding. At the end of 2.0 s the height above Earth’s surface of the center of mass of the two-ball system is:
A. 2.9m
B. 4.0m
C. 5.0m
D. 7.1m
E. 10.4m
ANS: D
10. At the same instant that a 0.50-kg ball is dropped from 25m above Earth, a second ball, with a mass of 0.25 kg, is thrown straight upward from Earth’s surface with an initial speed of 15m/s. They move along nearby lines and pass without colliding. At the end of 2.0 s the velocity of the center of mass of the two-ball system is:
A. 11m/s, down
B. 11m/s, up
C. 15m/s, down
D. 15m/s, up
E. 20m/s, down
ANS: C
11. At the same instant that a 0.50-kg ball is dropped from 25m above Earth, a second ball, with a mass of 0.25 kg, is thrown straight upward from Earth’s surface with an initial speed of 15m/s. They move along nearby lines and pass without colliding. At the end of 2.0 s the magnitude of the acceleration of the center of mass of the two-ball system is:
A. 0.25g
B. 0.50g
C. 0.75g
D. g
E. g/0.75
ANS: D
122
12. A light rope passes over a light frictionless pulley attached to the ceiling. An object with a large mass is tied to one end and an object with a smaller mass is tied to the other en
D. Starting from rest the heavier object moves downward and the lighter object moves upward with the same magnitude acceleration. Which of the following statements is true for the system consisting of the two masses?
A. The center of mass remains at rest.
B. The net external force is zero.
C. The velocity of the center of mass is a constant.
D. The acceleration of the center of mass is g, downwar
D.
E. None of the above statements are tru
E.
ANS: E
13. Two 4.0-kg blocks are tied together with a compressed spring between them. They are thrown from the ground with an initial velocity of 35m/s, 45◦ above the horizontal. At the highest point of the trajectory they become untied and spring apart. About how far below the highest point is the center of mass of the two-block system 2.0 s later, before either fragment has hit the ground?
A. 12m
B. 20m
C. 31m
D. Can’t tell because the velocities of the fragments are not given.
E. Can’t tell because the coordinates of the highest point are not given.
ANS: B
14. The center of mass of a system of particles has a constant velocity if:
A. the forces exerted by the particles on each other sum to zero
B. the external forces acting on particles of the system sum to zero
C. the velocity of the center of mass is initially zero
D. the particles are distributed symmetrically around the center of mass
E. the center of mass is at the geometric center of the system
ANS: B
15. The center of mass of a system of particles remains at the same place if:
A. it is initially at rest and the external forces sum to zero
B. it is initially at rest and the internal forces sum to zero
C. the sum of the external forces is less than the maximum force of static friction
D. no friction acts internally
E. none of the above
ANS: A
16. A man sits in the back of a canoe in still water. He then moves to the front of the canoe and sits ther
E. Afterwards the canoe:
A. is forward of its original position and moving forward
B. is forward of its original position and moving backward
C. is rearward of its original position and moving forward
D. is rearward of its original position and moving backward
E. is rearward of its original position and not moving
ANS: E
123 17. A 640-N hunter gets a rope around a 3200-N polar bear. They are stationary, 20m apart, on frictionless level ic
E. When the hunter pulls the polar bear to him, the polar bear will move:
A. 1.0m
B. 3.3m
C. 10m
D. 12m
E. 17m
ANS: B
18. Two boys, with masses of 40 kg and 60 kg, respectively, stand on a horizontal frictionless surface holding the ends of a light 10-m long ro
D. The boys pull themselves together along the ro
D. When they meet the 60-kg boy will have moved what distance?
A. 4m
B. 5m
C. 6m
D. 10m
E. need to know the forces they exert
ANS: A
19. The center of mass of a system of particles obeys an equation similar to Newton’s second law F = macom, where:
A. F is the net internal force and m is the total mass of the system
B. F is the net internal force and m is the mass acting on the system
C. F is the net external force and m is the total mass of the system
D. F is the force of gravity and m is the mass of Earth
E. F is the force of gravity and m is the total mass of the system
ANS: C
21. A 2.0-kg block is attached to one end of a spring with a spring constant of 100N/m and a 4.0-kg block is attached to the other en
D. The blocks are placed on a horizontal frictionless surface and set into motion. At one instant the 2.0-kg block is observed to be traveling to the right with a speed of 0.50m/s and the 4.0-kg block is observed to be traveling to the left with a speed of 0.30m/s. Since the only forces on the blocks are the force of gravity, the normal force of the surface, and the force of the spring, we conclude that:
A. the spring is compressed at the time of the observation
B. the spring is not compressed at the time of observation
C. the motion was started with the masses at rest
D. the motion was started with at least one of masses moving
E. the motion was started by compressing the spring
ANS: D
22. A 2.0-kg mass is attached to one end of a spring with a spring constant of 100N/m and a 4.0-kg mass is attached to the other en
D. The masses are placed on a horizontal frictionless surface and the spring is compressed 10 cm. The spring is then released with the masses at rest and the masses oscillat
E. When the spring has its equilibrium length for the first time the 2.0-kg mass has a speed of 0.36m/s. The mechanical energy that has been lost to the instant is:
A. zero
B. 0.31 J
C. 0.61 J
D. 0.81 J
E. 1.2J
ANS: B
23. Momentum may be expressed in:
A. kg/m
B. gram•s
C. N•s
D. kg/(m•s)
E. N/s
ANS: C
24. The momentum of an object at a given instant is independent of its:
A. inertia
B. mass
C. speed
D. velocity
E. acceleration
ANS: E
125 25. Two bodies, A and B, have equal kinetic energies. The mass of A is nine times that of
B. The ratio of the momentum of A to that of B is:
A. 1:9
B. 1:3
C. 1:1
D. 3:1
E. 9:1
ANS: D
26. Two objects, P and Q, have the same momentum. Q has more kinetic energy than P if it:
A. weighs more than P
B. is moving faster than P
C. weighs the same as P
D. is moving slower than P
E. is moving at the same speed as P
ANS: B
28. A 1.0-kg ball moving at 2.0m/s perpendicular to a wall rebounds from the wall at 1.5m/s. The change in the momentum of the ball is:
A. zero
B. 0.5N • s away from wall
C. 0.5N • s toward wall
D. 3.5N • s away from wall
E. 3.5N • s toward wall
ANS: D
126
29. If the total momentum of a system is changing:
A. particles of the system must be exerting forces on each other
B. the system must be under the influence of gravity
C. the center of mass must have constant velocity
D. a net external force must be acting on the system
E. none of the above
ANS: D
30. When you step on the accelerator to increase the speed of your car, the force that accelerates the car is:
A. the force of your foot on the accelerator
B. the force of friction of the road on the tires
C. the force of the engine on the drive shaft
D. the normal force of the road on the tires
E. none of the above
ANS: B
31. A 2.5-kg stone is released from rest and falls toward Earth. After 4.0 s, the magnitude of its momentum is:
A. 98 kg • m/s
B. 78 kg • m/s
C. 39 kg • m/s
D. 24 kg • m/s
E. zero
ANS: A
32. A 64-kg woman stands on frictionless level ice with a 0.10-kg stone at her feet. She kicks the stone with her foot so that she acquires a velocity of 0.0017m/s in the forward direction. The velocity acquired by the stone is:
A. 1.1m/s forward
B. 1.1m/s backward
C. 0.0017m/s forward
D. 0.0017m/s backward
E. none of these
ANS: B
33. A man is marooned at rest on level frictionless ic
E. In desperation, he hurls his shoe to the right at 15m/s. If the man weighs 720N and the shoe weighs 4.0N, the man moves to the left with a speed of:
A. 0
B. 2.1 × 10−2 m/s
C. 8.3 × 10−2 m/s
D. 15m/s
E. 2.7 × 103 m/s
ANS: C
127 34. Two spacemen are floating together with zero speed in a gravity-free region of spac
E. The mass of spaceman A is 120 kg and that of spaceman B is 90 kg. Spaceman A pushes B away from him with B attaining a final speed of 0.5m/s. The final recoil speed of A is:
A. zero
B. 0.38m/s
C. 0.5m/s
D. 0.67m/s
E. 1.0m/s
ANS: B
35. A projectile in flight explodes into several fragments. The total momentum of the fragments immediately after this explosion:
A. is the same as the momentum of the projectile immediately before the explosion
B. has been changed into kinetic energy of the fragments
C. is less than the momentum of the projectile immediately before the explosion
D. is more than the momentum of the projectile immediately before the explosion
E. has been changed into radiant energy
ANS: A
36. A rifle of mass M is initially at rest but free to recoil. It fires a bullet of mass m and velocity v (relative to the ground). After firing, the velocity of the rifle (relative to the ground) is:
A. −mv
B. −Mv/m
C. −mv/M
D. −v
E. mv/M
ANS: C
37. Bullets from two revolvers are fired with the same velocity. The bullet from gun #1 is twice as heavy as the bullet from gun #2. Gun #1 weighs three times as much as gun #2. The ratio of the momentum imparted to gun #1 to that imparted to gun #2 is:
A. 2:3
B. 3:2
C. 2:1
D. 3:1
E. 6:1
ANS: C
39. Force:
A. equals the negative integral (with respect to distance) of the potential energy function
B. is the ability to do work
C. is the rate of change of doing work
D. equals the time rate of change of momentum
E. has dimensions of momentum multiplied by time
ANS: D
40. Cart A, with a mass of 0.20 kg, travels on a horizontal air track at 3.0m/s and hits cart B, which has a mass of 0.40 kg and is initially traveling away from A at 2.0m/s. After the collision the center of mass of the two cart system has a speed of:
A. zero
B. 0.33m/s
C. 2.3m/s
D. 2.5m/s
E. 5.0m/s
ANS: B
42. A cart loaded with sand slides forward along a horizontal frictionless track. As the cart moves, sand trickles out at a constant rate through a hole in the back of the cart. The acceleration of the cart is:
A. constant and in the forward direction
B. constant and in the backward direction
C. variable and in the forward direction
D. variable and in the backward direction
E. zero
ANS: E
43. The thrust of a rocket is:
A. a gravitational force acting on the rocket
B. the force of the exiting fuel gases on the rocket
C. any force that is external to the rocket-fuel system
D. a force that arises from the reduction in mass of the rocket-fuel system
E. none of the above
ANS: B
: 44. At one instant of time a rocket is traveling in outer space at 2500m/s and is exhausting fuel at a rate of 100 kg/s. If the speed of the fuel as it leaves the rocket is 1500m/s, relative to the rocket, the thrust is:
A. 0
B. 1.0 × 105 N
C. 1.5 × 105 N
D. 2.9 × 105 N
E. 2.5 × 105 N
ANS: C
45. A rocket exhausts fuel with a velocity of 1500m/s, relative to the rocket. It starts from rest in outer space with fuel comprising 80 per cent of the total mass. When all the fuel has been exhausted its speed is:
A. 3600m/s
B. 2400m/s
C. 1200m/s
D. 880m/s
E. 400m/s
ANS: B
47. The physical quantity “impulse” has the same dimensions as that of:
A. force
B. power
C. energy
D. momentum
E. work
ANS: D
48. The law of conservation of momentum applies to a system of colliding objects only if:
A. there is no change in kinetic energy of the system
B. the coefficient of restitution is one
C. the coefficient of restitution is zero
D. the net external impulse is zero
E. the collisions are all elastic
ANS: D
49. Sphere X, of mass 2 kg, is moving to the right at 10m/s. Sphere Y, of mass 4 kg, is moving to the left at 10m/s. The two spheres collide head-on. The magnitude of the impulse of X on Y is:
A. twice the magnitude of the impulse of Y on X
B. half the magnitude of the impulse of Y on X
C. one-fourth the magnitude of the impulse of Y on X
D. four times the magnitude of the impulse of Y on X
E. the same as the magnitude of the impulse of Y on X
ANS: E
50. Two bodies of unequal mass, placed at rest on a frictionless surface, are acted on by equal horizontal forces for equal times. Just after these forces are removed, the body of greater mass will have:
A. the greater speed
B. the greater acceleration
C. the smaller momentum
D. the greater momentum
E. the same momentum as the other body
ANS: E
51. A 0.2-kg rubber ball is dropped from the window of a building. It strikes the sidewalk below at 30m/s and rebounds up at 20m/s. The impulse on the ball during the collision is:
A. 10N • s upward
B. 10N • s downward
C. 2.0N • s upward
D. 2.0N • s downward
E. 9.8N • s upward
ANS: A
52. A 10-kg block of ice is at rest on a frictionless horizontal surfac
E. A 1.0-N force is applied in an easterly direction for 1.0 s. During this time interval, the block:
A. acquires a speed of 1m/s
B. moves 10 cm
C. acquires a momentum of 1.0kg • m/s
D. acquires a kinetic energy of 0.1J
E. none of the above
ANS: C
54. What magnitude impulse will give a 2.0-kg object a momentum change of magnitude + 50 kg • m/s?
A. +25N • s
B. −25N • s
C. +50N • s
D. −50N • s
E. +100N • s
ANS: C
55. A student’s life was saved in an automobile accident because an airbag expanded in front of his hea
D. If the car had not been equipped with an airbag, the windshield would have stopped the motion of his head in a much shorter tim
E. Compared to the windshield, the airbag:
A. causes a much smaller change in momentum
B. exerts a much smaller impulse
C. causes a much smaller change in kinetic energy
D. exerts a much smaller force
E. does much more work
ANS: D
57. A golf ball of mass m is hit by a golf club so that the ball leaves the tee with speed v. The club is in contact with the ball for time T. The magnitude of the average force on the club on the ball during the time T is:
A. mvT
B. mv/T
C. (1/2)mv2T
D. mv2/(2T)
E. mT2/(2v)
ANS: B
58. A 640-N acrobat falls 5.0m from rest into a net. The net tosses him back up with the same speed he had just before he hit the net. The magnitude of the average upward force exerted on him by the net during this collision is:
A. 32N
B. 64N
C. 320N
D. 640N
E. impossible to determine from given data
ANS: E
59. Whenever an object strikes a stationary object of equal mass:
A. the two objects cannot stick together
B. the collision must be elastic
C. the first object must stop
D. momentum is not necessarily conserved
E. none of the above
ANS: E
60. For a two-body collision involving objects with different masses, a frame of reference which has the same velocity relative to the laboratory as does the center of mass of the two objects is:
A. a frame for which the momentum of the incident object is zero
B. a frame for which the momentum of the target object is zero
C. a frame for which the average momentum of the two objects is zero
D. a frame for which the total momentum of the two objects is zero
E. none of the above
ANS: D
61. An inelastic collision is one in which:
A. momentum is not conserved but kinetic energy is conserved
B. total mass is not conserved but momentum is conserved
C. neither kinetic energy nor momentum is conserved
D. momentum is conserved but kinetic energy is not conserved
E. the total impulse is equal to the change in kinetic energy
ANS: D
62. A 4.0-N puck is traveling at 3.0m/s. It strikes a 8.0-N puck, which is stationary. The two pucks stick together. Their common final speed is:
A. 1.0m/s
B. 1.5m/s
C. 2.0m/s
D. 2.3m/s
E. 3.0m/s
ANS: A
63. A 3.00-g bullet traveling horizontally at 400m/s hits a 3.00-kg wooden block, which is initially at rest on a smooth horizontal tabl
E. The bullet buries itself in the block without passing through. The speed of the block after the collision is:
A. 1.33m/s
B. 0.40m/s
C. 12.0m/s
D. 40.0m/s
E. 160m/s
ANS: B
64. A 2-kg cart, traveling on a horizontal air track with a speed of 3m/s, collides with a stationary 4-kg cart. The carts stick together. The impulse exerted by one cart on the other has a magnitude of:
A. 0
B. 4N • s
C. 6N • s
D. 9N • s
E. 12N • s
ANS: B
65. A 3-g bullet is fired horizontally into a 10-kg block of wood suspended by a rope from the ceiling. The block swings in an arc, rising 3mm above its lowest position. The velocity of the bullet was:
A. unknown since the heat generated in the collision was not given
B. 8.0 × 102 m/s
C. 24.0m/s
D. 8.00m/s
E. 2.4 × 104 m/s
ANS: B
66. A 3.0-kg and a 2.0-kg cart approach each other on a horizontal air track. They collide and stick together. After the collision their total kinetic energy is 40 J. The speed of their center of mass is:
A. zero
B. 2.8m/s
C. 4.0m/s
D. 5.2m/s
E. 6.3m/s
ANS: C
67. Blocks A and B are moving toward each other. A has a mass of 2.0 kg and a velocity of 50m/s, while B has a mass of 4.0 kg and a velocity of −25m/s. They suffer a completely inelastic collision. The kinetic energy lost during the collision is:
A. 0
B. 1250 J
C. 3750 J
D. 5000 J
E. 5600 J
ANS: C
68. For a completely inelastic two-body collision the kinetic energy retained by the objects is the same as:
A. the total kinetic energy before the collision
B. the difference in the kinetic energies of the objects before the collision
C. 1 2Mv2 com, where M is the total mass and vcom is the velocity of the center of mass
D. the kinetic energy of the more massive body before the collision
E. the kinetic energy of the less massive body before the collision
ANS: C
69. A 75-kg man is riding in a 30-kg cart at 2.0m/s. He jumps off in such a way as to land on the ground with no horizontal velocity. The resulting change in speed of the cart is:
A. zero
B. 2.0m/s
C. 3.0m/s
D. 5.0m/s
E. 7.0m/s
ANS: D
70. An elastic collision is one in which:
A. momentum is not conserved but kinetic energy is conserved
B. total mass is not conserved but momentum is conserved
C. kinetic energy and momentum are both conserved
D. momentum is conserved but kinetic energy is not conserved
E. the total impulse is equal to the change in kinetic energy
ANS: C
71. Object A strikes the stationary object B head-on in an elastic collision. The mass of A is fixed, you may choose the mass of B appropriately. Then:
A. for B to have the greatest recoil speed, choose mB = mA
B. for B to have the greatest recoil momentum, choose mB mA
C. for B to have the greatest recoil kinetic energy, choose mB mA
D. for B to have the least recoil speed, choose mB = mA
E. for B to have the greatest recoil kinetic energy, choose mB = mA
ANS: E
72. Block A, with a mass of 2.0 kg, moves along the x axis with a velocity of 5.0m/s in the positive x direction. It suffers an elastic collision with block B, initially at rest, and the blocks leave the collision along the x axis. If B is much more massive than A, the speed of A after the collision is:
A. 0
B. +5.0m/s
C. −5.0m/s
D. +10m/s
E. −10m/s
ANS: C
73. A very massive object traveling at 10m/s strikes a very light object, initially at rest, and the light object moves off in the direction of travel of the heavy object. If the collision is elastic, the speed of the lighter object is:
A. 5.0m/s
B. 10m/s
C. 15m/s
D. 20m/s
E. Can’t tell from the information given.
ANS: D
74. Sphere A has mass m and is moving with velocity v. It makes a head-on elastic collision with a stationary sphere B of mass 2m. After the collision their speeds (vA and vB) are:
A. 0, v/2
B. −v/3, 2v/3
C. −v, v
D. −2v/3, v/3
E. none of these
ANS: B
75. Blocks A and B are moving toward each other along the x axis. A has a mass of 2.0 kg and a velocity of 50m/s, while B has a mass of 4.0 kg and a velocity of −25m/s. They suffer an elastic collision and move off along the x axis. The kinetic energy transferred from A to B during the collision is:
A. 0
B. 2500 J
C. 5000 J
D. 7500 J
E. 10000 J
ANS: A
76. When a particle suffers a head-on elastic collision with another particle, initially at rest, the greatest fraction of kinetic energy is transferred if:
A. the incident particle is initially traveling very fast
B. the incident particle is traveling very slowly
C. the incident particle is much more massive than the target particle
D. the incident particle is much less massive than the target particle
E. the incident and target particle have the same mass
ANS: E
77. Two objects, X and Y, are held at rest on a horizontal frictionless surface and a spring is compressed between them. The mass of X is 2/5 times the mass of Y. Immediately after the spring is released, X has a kinetic energy of 50 J and Y has a kinetic energy of:
A. 20 J
B. 8 J
C. 310 J
D. 125 J
E. 50 J
ANS: D
79. Two identical carts travel at 1m/s in opposite directions on a common horizontal surfac
E. They collide head-on and are reported to rebound, each with a speed of 2m/s. Then:
A. momentum was not conserved; therefore, the report must be false
B. if some other form of energy were changed to kinetic during the collision, the report could be true
C. if the collision were elastic, the report could be true
D. if friction were present, the report could be true
E. if the duration of the collision were long enough, the report could be true
ANS: B
80. A block moves at 5.0m/s in the positive x direction and hits an identical block, initially at rest. A small amount of gunpowder had been placed on one of the blocks. The explosion does not harm the blocks but it doubles their total kinetic energy. After the explosion the blocks move along the x axis and the incident block has a speed in of:
A. 1.8m/s
B. 5.0m/s
C. 6.8m/s
D. 7.1m/s
E. 11.8m/s
ANS: A
A. 25◦
B. 37◦
C. 45◦
D. 57◦
E. 90◦
ANS: D
2. One revolution is the same as:
A. 1 rad
B. 57 rad
C. π/2 rad
D. π rad
E. 2π rad
ANS: E
3. One revolution per minute is about:
A. 0.0524 rad/s
B. 0.105 rad/s
C. 0.95 rad/s
D. 1.57 rad/s
E. 6.28 rad/s
ANS: B
4. If a wheel turns with constant angular speed then:
A. each point on its rim moves with constant velocity
B. each point on its rim moves with constant acceleration
C. the wheel turns through equal angles in equal times
D. the angle through which the wheel turns in each second increases as time goes on
E. the angle through which the wheel turns in each second decreases as time goes on
ANS: C
5. If a wheel is turning at 3.0 rad/s, the time it takes to complete one revolution is about:
A. 0.33 s
B. 0.67 s
C. 1.0 s
D. 1.3 s
E. 2.1 s
ANS: E
6. If wheel turning at a constant rate completes 100 revolutions in 10 s its angular speed is:
A. 0.31 rad/s
B. 0.63 rad/s
C. 10 rad/s
D. 31 rad/s
E. 63 rad/s
ANS: E
7. The angular speed of the second hand of a watch is:
A. (π/1800) rad/s
B. (π/60)m/s
C. (π/30)m/s
D. (2π)m/s
E. (60)m/s
ANS: C
8. The angular speed of the minute hand of a watch is:
A. (60/π)m/s
B. (1800/π)m/s
C. (π)m/s
D. (π/1800)m/s
E. (π/60)m/s
ANS: D
9. A flywheel is initially rotating at 20 rad/s and has a constant angular acceleration. After 9.0 s it has rotated through 450 ra
D. Its angular acceleration is:
A. 3.3 rad/s
B. 4.4 rad/s
C. 5.6 rad/s
D. 6.7 rad/s
E. 11 rad/s
ANS: D
10. Ten seconds after an electric fan is turned on, the fan rotates at 300 rev/min. Its average angular acceleration is:
A. 3.14 rad/s2
B. 30 rad/s2
C. 30 rev/s2
D. 50 rev/min2
E. 1800 rev/s2
ANS: A
11. A wheel rotates with a constant angular acceleration of π rad/s2. During a certain time interval its angular displacement is π ra
D. At the end of the interval its angular velocity is 2π rad/s. Its angular velocity at the beginning of the interval is:
A. zero
B. 1 rad/s
C. π rad/s
D. π√2 rad/s
E. 2π rad/s
ANS: D
12. A flywheel rotating at 12 rev/s is brought to rest in 6 s. The magnitude of the average angular acceleration in rad/s2 of the wheel during this process is:
A. 1/π
B. 2
C. 4
D. 4π
E. 72
ANS: D
13. A phonograph turntable, initially rotating at 0.75 rev/s, slows down and stops in 30 s. The magnitude of its average angular acceleration in rad/s2 for this process is:
A. 1.5
B. 1.5π
C. π/40
D. π/20
E. 0.75
ANS: D
14. The angular velocity of a rotating wheel increases by 2 rev/s every minut
E. The angular acceleration in rad/s2 of this wheel is:
A. 4π2
B. 2π
C. 1/30
D. π/15
E. 4π
ANS: D
15. A wheel initially has an angular velocity of 18 rad/s. It has a constant angular acceleration of 2.0 rad/s2 and is slowing at first. What time elapses before its angular velocity is 18 rad/s in the direction opposite to its initial angular velocity?
A. 3.0 s
B. 6.0 s
C. 9.0 s
D. 18 s
E. 36 s
ANS: D
16. A wheel initially has an angular velocity of 36 rad/s but after 6.0 s its angular velocity is 24 rad/s. If its angular acceleration is constant its value is:
A. 2.0 rad/s2
B. −2.0 rad/s2
C. 3.0 rad/s2
D. −3.0 rad/s2
E. 6.0 rad/s2
ANS: B
17. A wheel initially has an angular velocity of −36 rad/s but after 6.0 s its angular velocity is −24 rad/s. If its angular acceleration is constant the value is:
A. 2.0 rad/s2
B. −2.0 rad/s2
C. 3.0 rad/s2
D. −3.0 rad/s2
E. −6.0 rad/s2
ANS: A
18. A wheel initially has an angular velocity of 18 rad/s but it is slowing at a rate of 2.0 rad/s2. By the time it stops it will have turned through:
A. 81 rad
B. 160 rad
C. 245 rad
D. 330 rad
E. 410 rad
ANS: A
19. A wheel starts from rest and has an angular acceleration of 4.0 rad/s2. When it has made 10 rev its angular velocity is:
A. 16 rad/s
B. 22 rad/s
C. 32 rad/s
D. 250 rad/s
E. 500 rad/s
ANS: B
20. A wheel starts from rest and has an angular acceleration of 4.0 rad/s2. The time it takes to make 10 rev is:
A. 0.50 s
B. 0.71 s
C. 2.2 s
D. 2.8 s
E. 5.6 s
ANS: E
21. A wheel starts from rest and has an angular acceleration that is given by α(t) = (6 rad/s4)t2. The angle through which it turns in time t is given by:
A. [(1/8)t4] rad
B. [(1/4)t4] rad
C. [(1/2)t4] rad
D. (t4) rad
E. 12 rad
ANS: C
22. A wheel starts from rest and has an angular acceleration that is given by α(t) = (6.0 rad/s4)t2. The time it takes to make 10 rev is:
A. 2.8 s
B. 3.3 s
C. 4.0 s
D. 4.7 s
E. 5.3 s
ANS: B
23. A wheel starts from rest and has an angular acceleration that is given by α(t) = (6.0 rad/s4)t2. After it has turned through 10 rev its angular velocity is:
A. 63 rad/s
B. 75 rad/s
C. 89 rad/s
D. 130 rad/s
E. 210 rad/s
ANS: B
24. A wheel is spinning at 27 rad/s but is slowing with an angular acceleration that has a magnitude given by (3.0 rad/s4)t2. It stops in a time of:
A. 1.7 s
B. 2.6 s
C. 3.0 s
D. 4.4 s
E. 7.3 s
ANS: C
25. If the angular velocity vector of a spinning body points out of the page then, when viewed from above the page, the body is spinning:
A. clockwise about an axis that is perpendicular to the page
B. counterclockwise about an axis that is perpendicular to the page
C. about an axis that is parallel to the page
D. about an axis that is changing orientation
E. about an axis that is getting longer
ANS: B
26. The angular velocity vector of a spinning body points out of the pag
E. If the angular acceleration vector points into the page then:
A. the body is slowing down
B. the body is speeding up
C. the body is starting to turn in the opposite direction
D. the axis of rotation is changing orientation
E. none of the above
ANS: A
27. A child, riding on a large merry-go-round, travels a distance of 3000m in a circle of diameter 40 m. The total angle through which she revolves is:
A. 50 rad
B. 75 rad
C. 150 rad
D. 314 rad
E. none of these
ANS: C
30. A wheel of diameter 3.0 cm has a 4.0-m cord wrapped around its periphery. Starting from rest, the wheel is given a constant angular acceleration of 2.0 rad/s2. The cord will unwind in:
A. 0.82 s
B. 2.0 s
C. 8.0 s
D. 16 s
E. 130 s
ANS: D
31. A particle moves in a circular path of radius 0.10m with a constant angular speed of 5 rev/s. The acceleration of the particle is:
A. 0.10π m/s2
B. 0.50m/s2
C. 500π m/s2
D. 1000π2 m/s2
E. 10π2 m/s2
ANS: E
32. A car travels north at constant velocity. It goes over a piece of mud, which sticks to the tir
E. The initial acceleration of the mud, as it leaves the ground, is:
A. vertically upward
B. horizontally to the north
C. horizontally to the south
D. zero
E. upward and forward at 45◦ to the horizontal
ANS: A
146
33. Wrapping paper is being from a 5.0-cm radius tube, free to rotate on its axis. If it is pulled at the constant rate of 10 cm/s and does not slip on the tube, the angular velocity of the tube is:
A. 2.0 rad/s
B. 5.0 rad/s
C. 10 rad/s
D. 25 rad/s
E. 50 rad/s
ANS: A
34. String is wrapped around the periphery of a 5.0-cm radius cylinder, free to rotate on its axis. The string is pulled straight out at a constant rate of 10 cm/s and does not slip on the cylinder. As each small segment of string leaves the cylinder, its acceleration changes by:
A. 0
B. 0.010m/s2
C. 0.020m/s2
D. 0.10m/s2
E. 0.20m/s2
ANS: E
35. A flywheel of diameter 1.2m has a constant angular acceleration of 5.0 rad/s2. The tangential acceleration of a point on its rim is:
A. 5.0 rad/s2
B. 3.0m/s2
C. 5.0m/s2
D. 6.0m/s2
E. 12m/s2
ANS: B
36. For a wheel spinning with constant angular acceleration on an axis through its center, the ratio of the speed of a point on the rim to the speed of a point halfway between the center and the rim is:
A. 1
B. 2
C. 1/2
D. 4
E. 1/4
ANS: B
37. For a wheel spinning on an axis through its center, the ratio of the tangential acceleration of a point on the rim to the tangential acceleration of a point halfway between the center and the rim is:
A. 1
B. 2
C. 1/2
D. 4
E. 1/4
ANS: B
147 38. For a wheel spinning on an axis through its center, the ratio of the radial acceleration of a point on the rim to the radial acceleration of a point halfway between the center and the rim is:
A. 1
B. 2
C. 1/2
D. 4
E. 1/4
ANS: B
39. Two wheels are identical but wheel B is spinning with twice the angular speed of wheel
A. The ratio of the magnitude of the radial acceleration of a point on the rim of B to the magnitude of the radial acceleration of a point on the rim of A is:
A. 1
B. 2
C. 1/2
D. 4
E. 1/4
ANS: D
40. A wheel starts from rest and spins with a constant angular acceleration. As time goes on the acceleration vector for a point on the rim:
A. decreases in magnitude and becomes more nearly tangent to the rim
B. decreases in magnitude and becomes more early radial
C. increases in magnitude and becomes more nearly tangent to the rim
D. increases in magnitude and becomes more nearly radial
E. increases in magnitude but retains the same angle with the tangent to the rim
ANS: D
41. The magnitude of the acceleration of a point on a spinning wheel is increased by a factor of 4 if:
A. the magnitudes of the angular velocity and the angular acceleration are each multiplied by a factor of 4
B. the magnitude of the angular velocity is multiplied by a factor of 4 and the angular acceleration is not changed
C. the magnitudes of the angular velocity and the angular acceleration are each multiplied by a factor of 2
D. the magnitude of the angular velocity is multiplied by a factor of 2 and the angular acceleration is not changed
E. the magnitude of the angular velocity is multiplied by a factor of 2 and the magnitude of the angular acceleration is multiplied by a factor of 4
ANS: E
46. The rotational inertia of a wheel about its axle does not depend upon its:
A. diameter
B. mass
C. distribution of mass
D. speed of rotation
E. material composition
ANS: D
150
47. Consider four objects, each having the same mass and the same radius: 1. a solid sphere 2. a hollow sphere 3. a flat disk in the x, y plane 4. a hoop in the x, y plane The order of increasing rotational inertia about an axis through the center of mass and parallel to the z axis is:
A. 1, 2, 3, 4
B. 4, 3, 2, 1
C. 1, 3, 2, 4
D. 4, 2, 3, 1
E. 3, 1, 2, 4
ANS: C
49. Two uniform circular disks having the same mass and the same thickness are made from different materials. The disk with the smaller rotational inertia is:
A. the one made from the more dense material
B. the one made from the less dense material
C. neither – both rotational inertias are the same
D. the disk with the larger angular velocity
E. the disk with the larger torque
ANS: A
50. A uniform solid cylinder made of lead has the same mass and the same length as a uniform solid cylinder made of woo
D. The rotational inertia of the lead cylinder compared to the wooden one is:
A. greater
B. less
C. same
D. unknown unless the radii are given
E. unknown unless both the masses and the radii are given
ANS: B
51. To increase the rotational inertia of a solid disk about its axis without changing its mass:
A. drill holes near the rim and put the material near the axis
B. drill holes near the axis and put the material near the rim
C. drill holes at points on a circle near the rim and put the material at points between the holes
D. drill holes at points on a circle near the axis and put the material at points between the holes
E. do none of the above (the rotational inertia cannot be changed without changing the mass)
ANS: B
52. The rotational inertia of a disk about its axis is 0.70 kg •m2. When a 2.0-kg weight is added to its rim, 0.40m from the axis, the rotational inertia becomes:
A. 0.38 kg • m2
B. 0.54 kg • m2
C. 0.70 kg • m2
D. 0.86 kg • m2
E. 1.0kg • m2
ANS: E
53. When a thin uniform stick of mass M and length L is pivoted about its midpoint, its rotational inertia is ML2/12. When pivoted about a parallel axis through one end, its rotational inertia is:
A. ML2/12
B. ML2/6
C. ML2/3
D. 7ML2/12
E. 13ML2/12
ANS: C
54. The rotational inertia of a solid uniform sphere about a diameter is (2/5)MR2, where M is its mass and R is its radius. If the sphere is pivoted about an axis that is tangent to its surface, its rotational inertia is:
A. MR2
B. (2/5)MR2
C. (3/5)MR2
D. (5/2)MR2
E. (7/5)MR2
ANS: E
152
55. A solid uniform sphere of radius R and mass M has a rotational inertia about a diameter that is given by (2/5)MR2. A light string of length 3R is attached to the surface and used to suspend the sphere from the ceiling. Its rotational inertia about the point of attachment at the ceiling is:
A. (2/5)MR2
B. 9MR2
C. 16MR2
D. (47/5)MR2
E. (82/5)MR2
ANS: E
56. A force with a given magnitude is to be applied to a wheel. The torque can be maximized by:
A. applying the force near the axle, radially outward from the axle
B. applying the force near the rim, radially outward from the axle
C. applying the force near the axle, parallel to a tangent to the wheel
D. applying the force at the rim, tangent to the rim
E. applying the force at the rim, at 45◦ to the tangent
ANS: D
59. τ = Iα for an object rotating about a fixed axis, where τ is the net torque acting on it, I is its rotational inertia, and α is its angular acceleration. This expression:
A. is the definition of torque
B. is the definition of rotational inertia
C. is the definition of angular acceleration
D. follows directly from Newton’s second law
E. depends on a principle of physics that is unrelated to Newton’s second law
ANS: D
62. A disk is free to rotate on a fixed axis. A force of given magnitude F, in the plane of the disk, is to be applie
D. Of the following alternatives the greatest angular acceleration is obtained if the force is:
A. applied tangentially halfway between the axis and the rim
B. applied tangentially at the rim
C. applied radially halfway between the axis and the rim
D. applied radially at the rim
E. applied at the rim but neither radially nor tangentially
ANS: B
63. A cylinder is 0.10m in radius and 0.20m in length. Its rotational inertia, about the cylinder axis on which it is mounted, is 0.020 kg •m2. A string is wound around the cylinder and pulled with a force of 1.0N. The angular acceleration of the cylinder is:
A. 2.5 rad/s2
B. 5.0 rad/s2
C. 10 rad/s2
D. 15 rad/s2
E. 20 rad/s2
ANS: B
64. A disk with a rotational inertia of 2.0kg • m2 and a radius of 0.40m rotates on a frictionless fixed axis perpendicular to the disk faces and through its center. A force of 5.0N is applied tangentially to the rim. The angular acceleration of the disk is:
A. 0.40 rad/s2
B. 0.60 rad/s2
C. 1.0 rad/s2
D. 2.5 rad/s2
E. 10 rad/s2
ANS: C
65. A disk with a rotational inertia of 5.0kg • m2 and a radius of 0.25m rotates on a frictionless fixed axis perpendicular to the disk and through its center. A force of 8.0N is applied along the rotation axis. The angular acceleration of the disk is:
A. 0
B. 0.40 rad/s2
C. 0.60 rad/s2
D. 1.0 rad/s2
E. 2.5 rad/s2
ANS: A
66. A disk with a rotational inertia of 5.0kg•m2 and a radius of 0.25m rotates on a frictionless fixed axis perpendicular to the disk and through its center. A force of 8.0N is applied tangentially to the rim. If the disk starts at rest, then after it has turned through half a revolution its angular velocity is:
A. 0.57 rad/s
B. 0.64 rad/s
C. 0.80 rad/s
D. 1.6 rad/s
E. 3.2 rad/s
ANS: D
67. A thin circular hoop of mass 1.0 kg and radius 2.0m is rotating about an axis through its center and perpendicular to its plan
E. It is slowing down at the rate of 7.0 rad/s2. The net torque acting on it is:
A. 7.0N • m
B. 14.0N • m
C. 28.0N • m
D. 44.0N • m
E. none of these
ANS: C
156
68. A certain wheel has a rotational inertia of 12 kg • m2. As it turns through 5.0 rev its angular velocity increases from 5.0 rad/s to 6.0 rad/s. If the net torque is constant its value is:
A. 0.016N • m
B. 0.18N • m
C. 0.57N • m
D. 2.1N • m
E. 3.6N • m
ANS: D
70. A 8.0-cm radius disk with a rotational inertia of 0.12 kg • m2 is free to rotate on a horizontal axis. A string is fastened to the surface of the disk and a 10-kg mass hangs from the other en
D. The mass is raised by using a crank to apply a 9.0-N•m torque to the disk. The acceleration of the mass is:
A. 0.50m/s2
B. 1.7m/s2
C. 6.2m/s2
D. 12m/s2
E. 20m/s2
ANS: A
157 71. A 0.70-kg disk with a rotational inertia given by MR2/2 is free to rotate on a fixed horizontal axis suspended from the ceiling. A string is wrapped around the disk and a 2.0-kg mass hangs from the free en
D. If the string does not slip, then as the mass falls and the cylinder rotates, the suspension holding the cylinder pulls up on the cylinder with a force of:
A. 6.9N
B. 9.8N
C. 16N
D. 26N
E. 29N
ANS: B
74. A block is attached to each end of a rope that passes over a pulley suspended from the ceiling. The blocks do not have the same mass. If the rope does not slip on the pulley, then at any instant after the blocks start moving, the rope:
A. pulls on both blocks, but exerts a greater force on the heavier block
B. pulls on both blocks, but exerts a greater force on the lighter block
C. pulls on both blocks and exerts the same magnitude force on both
D. does not pull on either block
E. pulls only on the lighter block
ANS: A
75. A pulley with a radius of 3.0 cm and a rotational inertia of 4.5×10−3 kg •m2 is suspended from the ceiling. A rope passes over it with a 2.0-kg block attached to one end and a 4.0-kg block attached to the other. The rope does not slip on the pulley. When the speed of the heavier block is 2.0m/s the kinetic energy of the pulley is:
A. 0.15 J
B. 0.30 J
C. 1.0J
D. 10 J
E. 20 J
ANS: D
159 76. A pulley with a radius of 3.0 cm and a rotational inertia of 4.5×10−3 kg •m2 is suspended from the ceiling. A rope passes over it with a 2.0-kg block attached to one end and a 4.0-kg block attached to the other. The rope does not slip on the pulley. At any instant after the blocks start moving, the object with the greatest kinetic energy is:
A. the heavier block
B. the lighter block
C. the pulley
D. either block (the two blocks have the same kinetic energy)
E. none (all three objects have the same kinetic energy)
ANS: C
77. A disk with a rotational inertia of 5.0kg • m2 and a radius of 0.25m rotates on a fixed axis perpendicular to the disk and through its center. A force of 2.0N is applied tangentially to the rim. As the disk turns through half a revolution the work done by the force is:
A. 1.6J
B. 2.5J
C. 6.3J
D. 10 J
E. 40 J
ANS: A
78. A circular saw is powered by a motor. When the saw is used to cut wood, the wood exerts a torque of 0.80N • m on the saw blad
E. If the blade rotates with a constant angular velocity of 20 rad/s the work done on the blade by the motor in 1.0 min is:
A. 0
B. 480 J
C. 960 J
D. 1400 J
E. 1800 J
ANS: C
79. A disk has a rotational inertia of 6.0kg • m2 and a constant angular acceleration of 2.0 rad/s2. If it starts from rest the work done during the first 5.0 s by the net torque acting on it is:
A. 0
B. 30 J
C. 60 J
D. 300 J
E. 600 J
ANS: D
80. A disk starts from rest and rotates around a fixed axis, subject to a constant net torqu
E. The work done by the torque during the second 5 s is as the work done during the first 5 s.
A. the same
B. twice as much
C. half as much
D. four times as much
E. one-fourth as much
ANS: D
160
81. A disk starts from rest and rotates about a fixed axis, subject to a constant net torqu
E. The work done by the torque during the second revolution is as the work done during the first revolution.
A. the same
B. twice as much
C. half as much
D. four times as much
E. one-fourth as much
ANS: A
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