Download work and energy 12

Modified True/False
Indicate whether the sentence or statement is true or false. If false, change the identified word or phrase to make the
sentence or statement true.
____
1. Work is done when the force and the displacement are in the same direction. _________________________
____
2. Work is done when the force and the displacement are perpendicular. _________________________
____
3. More work is done to lift a 2.00-kg object a distance of 1.00 m at a constant velocity than to push a 1.00-kg
block a distance of 1.00 m with a force of 19.6 N. ______________________________
____
4. The maximum work a force can do on an object occurs when the force is parallel to the direction of motion.
_________________________
____
5. Kinetic energy is a vector quantity. _________________________
____
6. To raise a 2.3-kg mass from its resting place on a table, more work is done by lifting it diagonally than lifting
it straight up. ___________________________________
____
7. If you raise an object above your head and then set it on a table, you do the same work as if you only lifted the
object onto the table. ______________________________
____
8. The change in gravitational potential energy can never have a negative value. _________________________
____
9. A car speeds up as it descends a hill, gaining gravitational potential energy. _________________________
____ 10. Another name for an isolated system is a closed system. _________________________
____ 11. A group of three balls at the top of three different frictionless ramps drop the same vertical distance with the
same final speed regardless of the shape of the ramp. _________________________
____ 12. All of the waste energy of a lawn mower is sound. _________________________
____ 13. Hooke’s law is true for all possible values of x for a real spring. _________________________
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
____ 14. A child pulls a 7.4-kg toboggan 4.2 m across level ground with a 15-N force that is 34° above the horizontal.
The work done is
a. 35 J
d. 3.9 × 102 J
b. 52 J
e. 2.1 × 103 J
c. 63 J
____ 15. Which of the following is not a unit of energy?
a. J
d. W⋅s
b.
e.
c. N⋅m
____ 16. A farmhand does 972 J of work pulling an empty hay wagon along level ground with a force of 310 N [23°
below the horizontal]. A frictional force of 280 N opposes the motion. The distance the wagon travels is
a. 0.39 m
d. 32 m
b. 1.7 m
e. 1.8 × 102 m
c. 3.4 m
____ 17. In which situation is work not done?
a. a frozen turkey is carried upstairs
____ 18.
____ 19.
____ 20.
____ 21.
____ 22.
____ 23.
____ 24.
____ 25.
____ 26.
____ 27.
b. a frozen turkey is carried on level ground
c. a frozen turkey is dropped
d. a frozen turkey is carried downstairs
e. a frozen turkey is fired from a cannon
A student in a lab exerts a 25 N force to pull a block a distance of 48 cm. If a total of 11 J of work is done, the
angle between the force and the displacement is
a. 89°
d. 24°
b. 66°
e. none of the above
c. 61°
A person picks a 1.00-kg box of macaroni from off the shelf and lowers it 0.77 m into a shopping cart. The
work done on the macaroni by the person is
a. 0 J
d. 7.5 J
b. 0.77 J
e. –7.5 J
c. –0.77 J
A person picks up a 1.00-kg box of macaroni from off the shelf and lowers it 0.77 m into a shopping cart. The
work done on the macaroni by Earth is
a. 0 J
d. 7.5 J
b. 0.77 J
e. –7.5 J
c. –0.77 J
Which of the following is NOT a unit of energy?
a. J
d. N⋅m
b. W/s
e. kW⋅h
c. kg⋅m2/s2
When an object doubles its speed, the kinetic energy increases by a factor of
a. 1
d. 6
b. 2
e. 8
c. 4
The kinetic energy of a 24-kg dog running at 22 km/h is
a. 4.5 × 102 J
d. 2.6 × 102 J
b. 5.8 × 103 J
e. 73 J
c. 1.2 × 104 J
The gravitational potential energy of a 3.4-g grasshopper 14 mm above the ground is
a. 4.7 × 102 J
d. 4.7 × 10–2 J
b. 4.7 J
e. 4.7 × 10–4 J
c. 0.47 J
A 75-kg parachutist jumps from a plane at a height of 1.2 km. At the instant he leaves the plane, his
gravitational potential energy compared to the plane is
a. 8.8 × 102 J
d. –8.8 × 105 J
3
b. –8.8 × 10 J
e. 0 J
5
c. 8.8 × 10 J
You raise a 1.00-kg object 1.00 m and then lower it 1.00 m. The total work done on the object by gravity is
a. 0 J
d. 19.6 J
b. 9.8 J
e. –19.6 J
c. –9.8 J
A car slows down as it descends a hill. Which of the following is true?
a. the gravitational potential energy decreases
b. the kinetic energy increases
c. heat is produced by friction
____ 28.
____ 29.
____ 30.
____ 31.
____ 32.
____ 33.
d. two of A, B, and C are correct
e. all of A, B, and C are correct
A student has 474 J of gravitational energy while standing on a stool 0.84 m above the ground. The mass of
the student is
d. 40 kg (to two significant digits)
a. 5.8 × 102 kg
b. 48 kg
e. 60 kg (to two significant digits)
c. 58 kg
To maximize the gravitational potential energy of an object, you should
a. raise it as quickly as possible
d. get it as high as possible
b. maximize the total distance travelled
e. lower it in the vertical direction
c. avoid acceleration during lifting
As a student lifts a 4.5-kg book bag 120 cm into the air, the amount of work that the force of gravity does on
the bag is
a. 5.4 J
d. –5.4 J
b. 53 J
e. –53 J
c. 540 J
A 102-g sparrow flying at 12.3 m/s wishes to have equal kinetic and gravitational potential energies. The
height that will accomplish this is
a. 0.315 m
d. 1.13 m
b. 0.628 m
e. 7.72 m
c. 0.787 m
A cyclist reaches the bottom of a hill with a speed of 18 m/s. Neglecting air resistance and other friction, to
what maximum height can they coast up the hill without pedalling?
a. 17 m
d. 20 m
b. 18 m
e. 21 m
c. 19 m
A 1.30-kg pendulum bob is pulled to the side, raising it 19.0 cm above its rest position. After it is released, the
maximum speed will be
a. 0.616 m/s
d. 6.16 m/s
b. 1.93 m/s
e. 37.2 m/s
c. 3.72 m/s
____ 34. In the picture of a roller coaster track shown below, the point where the roller coaster car would be travelling
the fastest, under negligible friction is
a. A
d. D
b. B
e. E
c. C
____ 35. In the picture of a roller coaster track shown below, the point where the roller coaster car would be travelling
the slowest under negligible friction is
____ 36.
____ 37.
____ 38.
____ 39.
____ 40.
____ 41.
____ 42.
____ 43.
____ 44.
____ 45.
a. A
d. D
b. B
e. E
c. C
A 19.1-kg curling stone travels 28.8 m against a frictional force of 8.22 N. The thermal energy produced is
a. 184 J
d. 237 J
b. 237 N
e. not enough information
c. 362 J
Rubbing your hands together can quickly produce 45 J of thermal energy. If it is done with an average
frictional force of 8.4 N, the distance your hands have slid past each other is
a. 49 m
d. 3.7 m
b. 5.4 m
e. 1.2 m
c. 4.5 m
A student exerts a force of 12 N to compress a spring 2.54 cm. The force constant for the spring is
a. 0.30 N/m
d. 31 N/m
b. 4.7 N/m
e. 4.7 × 102 N/m
c. 15 N/m
A spring with a force constant of 2.1 × 104 N/m compresses 3.5 cm when stepped on by a boxer. The mass of
the boxer is
a. 65 kg
d. 82 kg
b. 73 kg
e. 740 kg
c. 75 kg
The work done to compress a spring with a force constant of 290.0 N/m a total of 12.3 mm is
a. 0.0219 J
d. 23.6 J
b. 1.78 J
e. 3.57 × 103 J
c. 3.57 J
A 0.25-kg apple is gently hung from a spring that stretches 4.6 cm. The force constant of the spring is
a. 0.054 N/m
d. 53 N/m
b. 6.1 N/m
e. 180 N/m
c. 18 N/m
A horizontal spring, with a force constant of 39 N/m, is compressed 12.4 cm, and placed between a wall and a
0.17-kg box resting on a smooth floor. If the spring is released, the maximum speed of the box is
a. 1.9 m/s
d. 5.3 m/s
b. 2.7 m/s
e. 28 m/s
c. 3.5 m/s
A spring with force constant 87 N/m is set into simple harmonic motion when a 350-g mass is attached to it.
The period is
a. 0.40 s
d. 25 s
b. 3.1 s
e. 99 s
c. 13 s
A spring-powered SHM oscillator vibrates with a period of 0.29 s. If the force constant of the spring is 180
N/m, the mass used is
a. 0.38 kg
d. 2.4 kg
b. 0.77 kg
e. 2.6 kg
c. 1.3 kg
A spring-powered SHM oscillator vibrates with a frequency of 9.2 Hz. If the mass used is 45 g, the force
constant of the spring is
a. 0.38 N/m
d. 1.6 × 104 N/m
b. 2.6 N/m
e. none of the above
c. 5.2 N/m
____ 46. During an experiment carried out by an astronaut on the Moon (g = 1.6 N/kg), a 1.4-kg mass is dropped onto
a spring with a force constant of 49 N/m. The maximum compression in the spring is
a. 0.28 m
d. 4.8 m
b. 0.48 m
e. not enough information
c. 3.6 m
____ 47. As the mass of a SHM oscillator increases
a. the period of vibration increases
b. a larger spring constant would be required to prevent a change in the period
c. the frequency is inversely proportional to the mass
d. two of A, B, and C
e. all of A, B, and C
____ 48. If the period of vibration of a SHM oscillator increases
a. the mass might have decreased
b. the spring constant might have decreased
c. the frequency also increases
d. two of A, B, and C
e. all of A, B, and C
____ 49. If the mass of a car is doubled and its speed is cut in half, then the kinetic energy changes by a factor of
a. 0.25
d. 2
b. 0.5
e. 4
c. 1
____ 50. A rocket triples its height but looses half its mass in fuel. The gravitational potential energy of the rocket has
changed by a factor of
a. 0.33
d. 1.5
b. 0.5
e. 3
c. 1
____ 51. A bird flying at a height of 12 m doubles its speed as it descends to a height of 6.0 m. The kinetic energy has
changed by a factor of
a. 0.25
d. 2
b. 0.5
e. 4
c. 1
____ 52. A bird flying at a height of 12 m doubles its speed as it descends to a height of 6.0 m. The gravitational
potential energy has changed by a factor of
a. 0.25
d. 2
b. 0.5
e. 4
c. 1
____ 53. A person running in a race has to pick up a mass equal to her own mass. Assuming she can still do the same
amount of work, her speed will be changed by a factor of
a. 0.25
d. 1
b. 0.50
e. 2
c. 0.71
____ 54. A person runs at a constant speed up a slope that is angled at 12° to the horizontal. At one point, he is 3.2 m
vertically above the bottom of the hill. To double the gravitational energy compared to the bottom of the hill,
the runner must run an additional
a. 0.66 m up the slope
d. 6.4 m up the slope
b. 1.6 m up the slope
e. 15 m up the slope
c. 3.2 m up the slope
____ 55. A crane exerts a force of 4.8 × 105 N to lift a steel beam 15 m into the air in 18 s. If the time taken was 36 s,
the energy required would change by a factor of
a. 4
b. 2
c. 1
d. 0.5
e. 0.25
____ 56. A race is set up with five balls placed at the top of the five ramps shown below and released at the same
instant. Each ramp drops the same vertical height. The ramp that will allow the ball to arrive at the bottom
first is
a. A
d. D
b. B
e. E
c. C
____ 57. A race is set up with five balls placed at the top of the five ramps shown below and released at the same
instant. Each ramp drops the same vertical height. That ramp that will allow the ball to arrive at the bottom
last is
a. A
d. D
b. B
e. E
c. C
____ 58. You want to ride a bicycle to the house shown below. Neglecting friction, at which point should you start in
order to use the least amount of work to get there?
a. A
d. D
b. B
e. E
c. C
____ 59. You want to ride a bicycle to the house shown below. Neglecting friction, at which point should you start in
order to use the most amount of work to get there?
a. A
d. D
b. B
e. E
c. C
Completion
Complete each sentence or statement.
60. No work is done when the angle between the force and the displacement is ____________________.
61. The amount of kinetic energy is proportional to the __________________ of the velocity.
62. To indicate a downward vertical displacement we place a _________________________ in front of the
numerical value.
63. Gravitational potential energy is due to ____________________ above Earth’s surface.
64. The law of conservation of energy applies to a(n) ____________________ system.
65. Friction causes kinetic energy to transform into ____________________ energy.
66. Thermal energy occurs when the ____________________ inside an object begin to speed up.
67. ____________________ law states that the magnitude of the force exerted by an ideal spring is directly
proportional to the distance the spring moves from equilibrium.
68. A spring with a force constant of 34 N/m is ____________________ to stretch than a spring with a force
constant of 42 N/m.
Matching
Match the type of energy to the correct description.
a. electromagnetic
f. nuclear potential
b. electrical
g. sound
c. electric potential
h. elastic potential
d. gravitational potential
i. thermal
e. chemical potential
____
____
____
____
____
____
____
____
____
69.
70.
71.
72.
73.
74.
75.
76.
77.
includes radio waves and microwaves
electrons flowing in a wire
energy that causes static cling
stored in raised objects
stored in sugar molecules
released in a nuclear reactor
a longitudinal wave
propels an arrow from a bow
easily produced by friction
Short Answer
78. How much work is done when a pen is pushed 26 cm across a level desk with a horizontal force of 0.27 N?
79. Give an example of a common type of employment (or “work”) that does not involve a significant amount of
the physical definition of work.
80. Why are speed limits reduced near most schools?
81. How much work is done to speed up a 2200-kg car from 12 m/s to 24 m/s?
82. Give two examples of how the high kinetic energy of motor vehicles has changed our society.
83. How can a small object with small mass have a higher kinetic energy than a large object with large mass?
84. How much gravitational potential energy is possessed by a 1.9-kg bird nest located 15 m above the ground?
85. How high up a tree must a 32-kg monkey crawl to have 1.0 kJ of energy?
86. How is natural gravitational potential energy used to create electric energy?
87. A wrecking ball is commonly used to destroy old buildings. The energy comes from a motor pulling a large
pendulum back, which then allows it to swing against a wall. Why not just use the motor to do the same work
on the wall?
88. A battery-powered toy travelling at 2.2 m/s drives off a diving board at a height of 1.2 m above the water.
What is the impact speed of the toy?
89. A cannon ball is fired with a speed of 88 m/s from the top of a cliff. It strikes the plain below with a speed of
91 m/s. If we neglect air friction, how high is the cliff?
90. A small spring with a force constant of 83 N/m is held vertically and then stretched 18 cm. A 1.8-kg mass is
attached to it and then released. Calculate the acceleration of the mass at the moment of release.
91. Will a spring-operated bathroom scale (that gives a reading in kilograms) give the correct mass reading on the
Moon?
92. When a car travels down a highway, only about 25% of the chemical potential energy from the gasoline is
converted to kinetic energy. Name two other forms of energy that are produced.
93. A 12-kg block sliding across a smooth table at 1.9 m/s hits a spring bumper with a force constant of 490 N/m.
What is the maximum compression of the spring?
94. Why does a car suspension included shock absorbers?
95. Should car bumpers act as an ideal spring?
96. How is speed related to braking distance?
Problem
97. A toy gun fires a 9.41-g projectile disc by using a compressed spring (k = 1.72 × 103 N/m) and a 13.1 cm long
barrel. As the disc travels through the barrel, it experiences a constant frictional force of 0.13 N. If the spring
is compressed 14 mm, what is the speed of the disc as it leaves the gun?
98. A 23-kg block slides 18 m on level ground before coming to rest. If 430 J of work are done by friction,
calculate the coefficient of friction between the block and the ground.
99. A driver carelessly ignores the reduced speed limit of 40.0 km/h in a school zone and continues at 65 km/h.
Assuming a good reaction time of 0.80 s, how many more metres will it take him to stop than if he had
reduced his speed? Assume a constant emergency braking acceleration of –7.8 m/s2.
100. A robin of mass 110 g speeds up from 12.3 m/s to 15.4 m/s in level flight. Calculate how much work is done
by the robin.
101. A total of 490 J of work is done on a pin when a 5.0-kg sledgehammer strikes it (bringing the sledgehammer
to rest). Calculate the initial speed of the sledgehammer.
102. As you travel faster, more work is required to increase your speed by 15 m/s.
(a) Use an example to compare two different speed increases of 15 m/s to demonstrate this.
(b) How does this affect someone who is trying to set a new speed record for a land vehicle?
103. A ball starts from rest and rolls 5.8 m down a short ramp so that it drops 1.8 m vertically. Calculate the
acceleration of the ball.
104. A child swings on a swing so that her centre of mass is located 2.4 m from the point where the rope is
attached to the tree. If she swings so that her maximum amplitude causes the rope to make an angle of 47°
with the vertical, calculate the child’s maximum speed during the swing.
105. A 1.2-kg block is dropped from 48 cm above a spring in equilibrium. The force constant for the spring is 124
N/m. Calculate the maximum compression in the spring.
106. A 1.00-kg mass and a 2.00-kg mass are set gently on a platform mounted on an ideal spring of force constant
40.0 N/m. The 2.00-kg mass is suddenly removed. How high above its starting position does the 1.00-kg mass
reach?
107. An 87-g box is attached to a spring with a force constant of 82 N/m. The spring is compressed 11 cm and the
system is released.
(a) What is the speed of the box when the spring is stretched by 7.0 cm?
(b) What is the maximum speed of the box?
108. A spring is suspended from a ceiling and a 256-g mass is attached to it and pulled down to stretch the spring
by 18.2 cm. The mass is released and travels through the equilibrium position with a speed of 0.746 m/s.
Calculate the force constant of the spring.
109. Two boxes each of mass 12 kg are raised 1.8 m to a shelf. The first one is lifted and the second is pushed up a
smooth ramp. If the applied force on the second box is 48 N, calculate the angle between the ramp and the
ground.
110. Two boxes are connected over a pulley and held at rest as shown below. Box A has a mass of 15 kg and box
B has a mass of 12 kg. If the bottom of box A is originally 85 cm above the floor, with what speed will it
contact the floor when the system is released? Use conservation of energy and assume that friction is
negligible.
Essay
111. Use your understanding of frictional forces, work, and kinetic energy to explain why it is common to have a
reduced speed near an area with small children. Word your explanation so that it can be understood by
someone who has never taken high school physics.
MODIFIED TRUE/FALSE
1. T
2. F, parallel
3. F, The same amount of work is done
4. T
5. F, scalar
6. F, the same amount of work is done
7. T
8. F, can have
9. F, losing
10. T
11. T
12. F, some
13. F, ideal
MULTIPLE CHOICE
14.
21.
28.
35.
42.
49.
56.
B
B
C
A
A
B
B
15. E
22. C
29. D
36. D
43. A
50. D
57. C
16. C
23. A
30. E
37. B
44. A
51. E
58. A
17. B
24. E
31. E
38. E
45. E
52. B
59. C
18. D
25. E
32. A
39. C
46. E
53. C
19. E
26. A
33. B
40. A
47. E
54. E
20.D
27. D
34. C
41. D
48. B
55. C
COMPLETION
60. 90°
61. square
62. negative sign
66. molecules, atoms, particles 67. Hooke’s
63. elevation, position
68. easier
64. isolated
65. thermal
MATCHING
69. A
75. G
70. B
76. H
71. C
77. I
72. D
73. E
74.F
SHORT ANSWER
78. The work done is 7.0 × 10–2 J
79. Some possibilities: teacher, clergy, office worker, driver, or nuclear plant operator
80. The kinetic energy is proportional to the square of the speed of a vehicle. The brakes can only supply a
constant friction force to stop the vehicle. Near schools where children may be on the street, the speed limit is
reduced to reduce stopping time of vehicles.
81. The work done to speed up the car is 4.8 × 105 J.
82. Possible answers
- motor vehicle deaths or injuries
- treatment of deaths/injuries
- emergency response (ambulances, tow trucks, Jaws of Life, etc.)
- repair shops
- junk yards
- safety legislation (time of Parliament)
- employment for safety devices (seat belts, airbags, energy-absorbing frames)
83. The smaller object could have a much larger velocity.
84. The nest has a gravitational potential energy of 2.8 × 102 J.
85. The monkey would need to climb 3.2 m up the tree.
86. Hydroelectric generating stations convert the gravitational energy of water as it falls down rivers and converts
it into electrical energy.
87. The motor does a small amount of work over a large distance, storing it as gravitational energy in the
wrecking ball. The wrecking ball does the same work in a very short distance with a force large enough to
damage the wall.
88. The impact speed of the toy is 5.3 m/s.
89. The cliff is 27 m high.
90. The acceleration of the mass is 1.5 m/s2 [down].
91. No, the spring scale is calibrated with the assumption that the gravitational field strength is 9.8 N/kg. On the
moon, the value is less than 9.8 N/kg, so the scale reading will be too small.
92. thermal, sound, electrical, electromagnetic, gravitational potential energy if going uphill
93. The kinetic energy of the block will become elastic energy in the spring. The maximum compression in the
spring is 0.30 m.
94. The shock absorbers are required to dampen the SHM of the springs when a car hits a bump.
95. No they should not. If a car bumper acts as an ideal spring, after bringing the car to rest, it would accelerate it
back to its original speed in the opposite direction, which would be very dangerous.
96. The kinetic energy of a vehicle is proportional to the square of the velocity. Doubling your speed would
quadruple your energy. The stopping distance depends on the work done by the constant force of your brakes.
Quadrupling the energy would quadruple your stopping distance.
PROBLEM
97. The speed of the disc is 1.8 m/s.
98. The coefficient of friction is 0.11.
99. It would take 19 m more to stop.
100. The robin must do 4.7 J of work to increase its speed.
101. The initial speed of the sledgehammer was 14 m/s.
102. (a) We can see that much more work is required to increase the speed by 15 m/s at faster speeds.
(b) This would make it more difficult to go very fast in a vehicle because a more powerful engine would be
required to supply all of the work necessary.
103. The acceleration of the ball is 3.0 m/s2.
104. The child’s maximum speed is 3.9 m/s
105. The spring would compress 41 cm.
106. The 1.00-kg mass reaches a maximum height of 1.10 m above its start position.
107. ANS:
(a) The speed at a stretch of 7.0 cm is 2.6 m/s.
(b) The maximum speed is 3.4 m/s.
108. The spring constant is 31.9 N/m
109. The ramp makes an angle of 24°° with the ground.
110. The impact speed of box A will be 1.4 m/s.
ESSAY
111. Some points in the essay may be as follows:
- frictional force is constant and is what stops the car
- amount of distance to stop a vehicle depends on the size of the braking force (friction)
- when an car is travelling faster, the amount of energy it has increases as the square of the velocity
- the kinetic energy of the vehicle is “taken away” by the frictional force, so doubling the speed will
quadruple the stopping distance
- little children are prone to run out into the street without regard for vehicles
- a slower speed greatly reduces the stopping time and the likelihood of tragedy