South Pasadena A.P. Physics Name____________________ Period___

6 Work and Energy Practice Test

1 W o r k

The SI unit for work is the joule (J), which equals one

Newton-meter (N-m). For maximum work to be

done, the object must move in the direction of the

force. If the object is moving at an angle to the force,

determine the component of the force in the direction

of motion, using

W = F x displacement cos θ

Remember, if the object does not move, or moves

perpendicular to the direction of the force, no work has

been done.

Problems:

1. Bud, a very large man of mass 130 kg, is pulling on

the rope attached to the crate with a force of 450 N.

He pulls at an angle of 38 as shown. There is a

frictional force of 125 N.

a) If the crate moves a distance of 55 cm, how much

work does Bud do on the crate?

b) If the crate has a mass of 65 kg, what would be

the acceleration of the cart?

2. Fill in the missing information:

Work

(J) Force (N) Distance (m)

a) 45.0 ? 2.0

b) 122 3.0 ?

c) ? 28.0 30.0 cm

d) ?

75.0 kg firefighter

climbs a flight of

stairs.

10.0 m high

3. An appliance salesman pushes a refrigerator 2

meters across the floor by applying a force of

200 N. Find the work that was done.

4. A friend’s car is stuck on the ice. You push

down on the car to provide more friction for the

tires (by way of increasing the normal force),

allowing the car’s tires to propel it forward 5

meters onto less slippery ground. How much

work did you do?

5. You push a crate up a ramp with a force of

10 N. Despite your pushing, however, the crate

slides down the ramp a distance of 4 m. How

much work did you do?

6. How much work is done in lifting an 8 kg box

from the floor to a height of 2 meters above the

floor?

7. Barry and Sidney pull a 30 kg wagon with a

force of 500 N a distance of 20 m. The force

acts at a 30 angle to the horizontal. Calculate

the work done.

8. The work done in lifting an apple one meter

near Earth’s surface is approximately

a) 1 J c) 100 J

b) 0.01 J d) 1000 J

9. A child applies a constant 20 N force along

the handle of a wagon which makes an angle

of 25 with the horizontal. How much work

does the child do in moving the wagon a

horizontal distance of 4.0 m?

a) 5.0 J c) 73 J

b) 34 J d) 80 J

10. A boy pushes his wagon at constant speed

along a level sidewalk. The graph below

represents the relationship between the

horizontal force exerted by the boy and the

distance the wagon moves.

Force vs. Distance

40.0 -

30.0 -

20. 0 -

10.0 - 0.0 | | | | | |

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Distance (m)

What is the total work done by the boy in

pushing the wagon 4.0 m?

a) 5.0 J c) 120 J

b) 7.5 J d) 180 J

11. A box is wheeled to the right with a varying

horizontal force. The graph below represents

the relationship between the applied force and

the distance the box moves.

Force vs. Distance

9.0 N

6.0 N

3.0 N

0 3.0 6.0

Distance (m)

What is the total work done in moving the

box 6 meters?

a) 9.0 J b) 18 J c) 27 J d) 36 J

12. An 80 – kg wooden box is pulled 10 meters

horizontally across a wood floor at a constant

velocity by a 250−N force at an angle of 37

degrees above the horizontal. If the

coefficient of kinetic friction between the

floor and the box is 0.315, find the work done

by friction. (Hint: First draw a FBD and then

add in the force components)

13. Four carts, initially at rest on a flat surface,

are subjected to varying forces as the carts

move to the right a set distance, depicted in

the diagram below.

30

A

F = 20 N

d = 8 m

F = 30N 60 B

d = 12 m

F = 25N

C 30

d = 8 m

D F = 15N

d = 6 m

Rank the four carts from least to greatest

in terms of

I work done by the applied

force on the carts ___ ___ ___ ___

II inertia ___ ___ ___ ___

III normal force applied by

the surface to the carts. ___ ___ ___ ___

10 kg

20 kg

15 kg

12 kg

14. After finishing her physics homework, Sarah

pulls her 50.0 kg body out of the living room

chair and climbs up the 5.0 m high flight of

stairs to her bedroom. How much work does

Sarah do in ascending the stairs?

(Hint: The number of stairs or the slope of the stairs

is irrelevant. All that is important is the change in

position.)

2 P o w e r

Power is the rate at which work is done.

Power = work

Elapsed time

The SI unit for power is the watt (W), which equals

one joule per second (J/s). One person is more

powerful than another if he or she can do more work in

a given amount of time, or can do the same amount of

work in less time.

15. In the previous question where Sarah (50.0

kg) climbed the 5.0 meter high staircase, she

took 10.0 seconds to go from the bottom to

the top. The next evening, in a rush to catch

her favorite TV show, she runs up the stairs in

3.0 seconds.

a) What values of power does she generate

each night?

b) On which night does Sarah do more

work?

c) On which night does Sarah generate more

power?

16. Rob and Peter move a sofa 3 meters across

the floor by applying a combined force of 200

N horizontally. If it takes them 6 seconds to

move the sofa, what amount of power did

they supply?

17. Kevin then pushes the same sofa 3 meters across

the floor by applying a force of 200 N. Kevin

however takes 12 seconds to push the sofa.

What amount of power did Kevin supply?

Note: P = Work / time but Work = F x d cos , so

P = F x d cos and distance /time = velocity, so

time

Power also equals Force x average velocity

P = F x V

If you use this equation, do you get the same

answers for Questions 16 & 17?

18. Motor A lifts a 5,000 N steel crossbar upward at

a constant rate of 2 m/s. Motor B lifts a 4,000 N

steel support upward at a constant rate of 3 m/s.

a) Which motor is supplying more power?

b) How many kilowatts of power is each motor

supplying?

Motor A =

Motor b =

19. A 70 kg cyclist develops 210 watts of power

while pedaling at a constant velocity of 7 meters

per second east. What average force is exerted

eastward on the bicycle to maintain this constant

speed?

a) 490 N c) 3.0 N

b) 30 N d) 0 N

20. Alien A lifts a 500 Newton child from the floor

to a height of 0.40 meters in 2 seconds. Alien B

lifts a 400 Newton student from the floor to a

height of 0.50 meters in 1 second. Compared to

Alien A, Alien B does

a) the same work but develops more power.

b) the same work but develops less power.

c) more work but develops less power.

d) less work but develops more power.

21. A 110 kg bodybuilder and his 55 kg friend

run up identical flights of stairs. The

bodybuilder reaches the top in 4.0 seconds

while his friend takes 2.0 seconds. Compared

to the power developed by the bodybuilder

while running up the stairs, the power

developed by his friend is

a) the same. c) half as much

b) twice as much. d) four times as

much.

22. Mary holds a 5 kg mirror against the wall 1.5

meters above the ground for 20 seconds while

Bob nails it in place. What is Mary’s power

output during that time period?

a) 2.45 watts c) 66.7 watts

b) 3.68 watts d) none of the above

23. Which of the following are appropriate units

for power? Choose all that apply.

a) J c) kg m2

s s2

b) N m2 d) kg m

2

s s3

24. A box of mass m is pushed up a ramp at

constant velocity v to a maximum height h in

time t by force F. The ramp makes an angle

of with the horizontal as shown in the

diagram below.

h

F

What is the power supplied by the force?

Choose all that apply.

a) m g h c) F h

t t sin

b) m g h d) F v

t sin

25. Fill in the missing information:

Power

(Watts) Work (Joules)

Time

(seconds)

a) 60.0 20.0 ?

b) 240 ? 2.5

c) ? 183 5.5

d) 3.5kilowatts 4.8 x 10-3

?

e) ? 2.0 mega joules 25.0

a)

b)

c)

d)

e)

26. Which requires more power: Lifting a 2.0 kg

object to a height of 2.0 m in a time of 2.0

seconds or lifting a 4.0 kg object to a height of

1.0 meter in a time of 3.0 seconds?

27. Atlas and Hercules, two carnival sideshow

strong men, each lift 200.0-kg barbells 2.00 m

off the ground. Atlas lifts his barbells in 1.00 s

and Hercules lifts his in 3.00 s.

a) Which strong man does more work?

b) Calculate which man is more powerful.

m

3 P o t e n t i a l E n e r g y

a n d K i n e t i c E n e r g y

Energy is the ability to do work. The two kinds of

energy we are dealing with in this chapter are the

energy of position or stored energy (potential energy)

and the energy of motion (kinetic energy).

Gravitational potential energy relies upon the vertical

change in height and not upon the path taken.

Potential Energy = m g h

Other forms of stored energy exist, such as when a bow

is pulled back and before it is released, the energy in

the bow is equal to the work done to deform it. This

stored or potential energy is written as Δ PE = F Δd

The unit of potential energy (like work) is Joules.

Kinetic Energy KE = ½ mv2

Kinetic Energy is the energy of motion and varies with

the square of the speed. Kinetic Energy = ½ mass x

(velocity)2 and the SI unit of KE is also Joules, which

is the same unit used for work. When work is done on

an object, energy is transformed from one form to

another. The sum of the changes in potential, kinetic

and heat energy is equal to the work done on the

object.

28. Legend has it that Isaac Newton “discovered”

gravity when an apple fell from a tree and hit

him on the head. If a 0.20 kg apple fell 7.0 m

before hitting Newton, what was its change in

PE during the fall?

29. It is said that Galileo dropped objects off the

Leaning Tower of Pisa to determine whether

heavy or light objects fall faster. If Galileo

had dropped a 5.0 kg cannon ball to the

ground from a height of 12 m, what was the

change in PE of the cannon ball?

30. The diagram below represents a 155 N box on a

ramp. Applied force F causes the box to slide

from point A to point B.

B

5.60 m

1.80 m

A

F

5.30 m

What is the total amount of gravitational

potential energy gained by the box?

a) 28.4 J c) 868 J

b) 279 J d) 2740 J

31. Which situation describes a system with

decreasing gravitational potential energy?

a) a girl stretching a horizontal spring

b) a bicyclist riding up a steep hill

c) a rocket rising vertically from Earth

d) a boy jumping down from a tree limb

32. Which is an SI unit (or base unit) for energy?

a) kg m2 c) kg m

s2

s

b) kg m2 d) kg m

s s2

33. A car travels at constant speed v up a hill from

point A to point B as shown in the diagram

below:

B

A Horizontal

As the car travels from A to B, its gravitational

potential energy

a) increases and its kinetic energy decreases

b) increases and its kinetic energy remains the same

c) remains the same and its kinetic energy decreases

d) remains the same and its kinetic energy remains

the same

155 N

box

34. An object is thrown vertically upward.

Which pair of graphs best represents the

object’s kinetic energy (left graph) and

gravitational potential energy (right graph) as

functions of its displacement while it rises?

a) KE PE

Displacement Displacement

b) KE PE

Displacement Displacement

c) KE

Displacement Displacement

d) KE

Displacement Displacement

35. While riding a chairlift, a 55 kg snowboarder

is raised a vertical distance of 370 m. What is

the total change in the snowboarder’s

gravitational potential energy?

a) 5.4 x 101 J c) 2.0 x 10

4 J

b) 5.4 x 102 J d) 2.0 x 10

5 J

36. Fill in the missing information:

Potential

Energy (J) Mass (kg)

Height

(m)

a) 50.0 75.0 ?

b) 280 ? 1.8

c) ? 17.3 5.5

d) 3.5 kilojoules 4.8 x 10-3

?

a )

b )

c )

d )

37. A greyhound at a race track, can run at a

speed of 16.0 m/s. What is the Kinetic

Energy of a 20.0 kg greyhound as it crosses

the finish line?

38. A 7.0 kg bowling ball is moving at 2.0 m/s.

What is its Kinetic Energy?

39. An 1800 kg truck has a kinetic energy of

95,000 Joules. What is the truck’s velocity?

40. A car with 54,000 joules of kinetic energy

is moving at 35 m/s? What is the car’s mass?

41. An oxygen molecule of mass 5.31 x 10-26

kg,

has a kinetic energy of 6.21 x 10-21

Joules.

How fast is it moving?

42. If the kinetic energy of an arrow is doubled,

by what factor has its velocity increased?

43. If the velocity of the arrow is doubled, by

what factor does its kinetic energy increase?

4 W o r k - E n e r g y

T h e o r e m

Work done on an object = change in its K.E.

F x d = change in Kinetic Energy

44. How much work must be done to stop a

1000 kg car traveling at 31 m/s?

45. When the brakes of a motorcycle traveling

at 60 km/hr become locked, how much

farther will the motorcycle skid than if it

were traveling at 20 km/hr?

46. How much work is required to stop an

electron (m= 9.11 x 10-31

kg), which is moving

with a speed of 1.90 x 106 m/s?

47. A car does 7.0 x 104 J of work in traveling 2.8

km (2,800 m) at constant speed. What was the

average retarding force (from all sources)

acting on the car?

48. Given the following sets of velocity and net

force vectors for a given object, state whether

you expect the kinetic energy of the object to

increase, decrease or remain the same.

V Fnet Answers

(1) ________________

(2) ________________

(3) ________________

(4) ________________

49. A chef pushes a 10 kg pastry cart from rest a

distance of 5 meters with a constant horizontal

force of 10 N. Assuming a frictionless surface,

determine the cart’s change in kinetic energy

and its final velocity.

50. A pitcher throws a baseball of 143 grams toward

the catcher at 45 m/s. If the catcher’s hand

moves back a distance of 6 cm in stopping the

ball, determine the average force exerted on the

catcher’s hand.

51. In the following diagrams, a force F acts on a

cart in motion on a frictionless surface to change

its velocity. The initial velocity of the cart and

final velocity of each cart are shown. You do

not know how far or in which direction the cart

travelled. Rank the energy required to change

each cart’s velocity from greatest to least.

a) 2 kg Cart V0 = 5 m/s V = 2 m/s

b) 3 kg Cart V0 = 3 m/s V = − 3 m/s

c) 5 kg Cart V0 = 5 m/s V = 6 m/s

d) 4 kg Cart V0 = −1 m/s V = 2 m/s

____ > ____ > ____ > ____

52. Given the force vs. displacement graph below

for a net force applied horizontally to an object

of mass 5.0 kg initially at rest on a frictionless

surface, determine the object’s final speed.

Fmax ─

45 ─

40 ─

35 ─

Fnet

─

25 ─

20 ─

15 ─

10 ─

5 ─

0 | | | | | |

0 4 8 12 16 20 24

Displacement (meters)

5 C o n s e r v a t i o n o f

E n e r g y

According to the law of conservation of energy, energy

cannot be created or destroyed, but remains constant in

a system, when no forces are acting other than gravity.

Δ KE = ΔPE or

Total Mechanical Energy = P.E. + K.E.

KE I + PE I = KE f + PE f

Example: What is the total mechanical energy of an

F/A─18 Hornet Fighter Jet with a mass of 20,000

kilograms flying at an altitude of 10,000 m above the

surface of the Earth with a velocity of 250 m/s.

The ET = GPE + KE m g h + ½ mv2

Answer is 2.59 x 109 Joules

For a bowling ball, the equation simplifies to mgh

= ½ mv2, so then Velocity at bottom = √2gh

53. A 7.5 kg bowling ball is brought back to

a height of 1.2 meters and released.

How much kinetic energy will it have at

the lowest point in its swing?

54. What will be the velocity of the bowling

ball above at the lowest point?

55. When the bowling ball above is released, how

much kinetic energy will it have when it is

0.60 meters above its lowest point?

cont.

56. How much kinetic energy will the bowling

ball have when it swings to the highest point

on the other side of its swing?

57. How much potential energy will the bowling

ball have when it swings to the highest point

on the other side of its swing?

58. If you turn on the radio in your car with the

engine off, will more gasoline be burned

later when the car engine is turned on, as a

result of having turned on the radio?

a) YES b) NO

59. A lawyer knocks her folder of mass m off her

desk of height y. What is the speed of the

folder upon striking the floor?

a) √2 g h c) m g y

b) 2 g y d) m y

60. A 65 kg pole vaulter wishes to vault to a

height of 5.5 meters.

(a) Calculate the minimum amount of kinetic

energy the vaulter needs to reach this

height if air friction is neglected and all

the vaulting energy is derived from

kinetic energy.

(b) Calculate the speed the vaulted must

attain to have the necessary kinetic

energy.

61. The work done in accelerating an object along

a frictionless horizontal surface is equal to the

change in the object’s

a) momentum

b) velocity

c) potential energy

d) kinetic energy

62. A car initially traveling at 30 m/s slows

uniformly as it skids to a stop after the brakes

are applied. Sketch a graph showing the

relationship between the kinetic energy of the

car as it is being brought to a stop and the

work done by friction in stopping the car.

KE

Work Done

By Friction

63. A 2 kg block sliding down a ramp from a

height of 3 meters above the ground reaches

the ground with a kinetic energy of 50 J. The

total work done by friction on the block as it

slides down the ramp is approximately

a) 6 J c) 18 J

b) 9 J d) 44 J

64. Four objects travel down an inclined plane

from the same height without slipping.

Which will reach the bottom of the incline

first?

a) a baseball rolling down the incline.

b) an unopened soda can, rolling down the

incline.

c) a physics book sliding down the incline

(without friction).

d) an empty soup can, rolling down the

incline.

65. As a box is pushed 30 meters across a

horizontal floor by a constant horizontal force

of 25 N, the kinetic energy of the box

increases by 300 J. How much total internal

energy (heat energy) is produced during the

process?

a) 150 J c) 450 J

b) 250 J d) 750 J

66. Mass m1, sits on a frictionless surface and is

attached by a light string across a frictionless

pulley to mass m2, as shown in the diagram

below.

What happens to the gravitational potential

energy and kinetic energy of m1 and m2 when

m2 is released from rest?

_____________________________________

_____________________________________

_____________________________________

_____________________________________

67. Andy the Adventurous Adventurer, while

running from evil bad guys in the Amazonian

Rainforest, trips, falls, and slides down a

frictionless mudslide of height 20 meters as

depicted below:

20 m

Mudslide

15 m

?

Once he reaches the bottom of the mudslide, he

has the misfortune to fly horizontally off a 15 m

cliff. How far from the base of the cliff does

Andy land?

6 E f f i c i e n c y

Efficiency is the ratio of the work output to the work

input and has no units and is usually expressed as a

percentage.

Efficiency = work output x 100

work input or

AMA x 100

IMA

68. A bicycle rider is doing 35 joules of work for a

return of 32 joules of work output by the

bicycle. What is the efficiency of the bicycle?

7 M a c h i n e s

Machines are devices that help do work by

changing the magnitude or direction of the applied

force.

Work In = Work Out

or

F x d = F x d

Examples of machines include:

A lever A pulley An inclined plane

FORMULAS for MACHINES

Work in = Work out

Actual Mechanical Advantage = F out/F in or

Ideal Mechanical Advantage =

distance in / distance out

69. If a force of 25 Newton is applied in order

to lift a 45 Newton weight a distance of

125 cm, then what distance must the applied

force be moved, using a lever?

70. What is the mechanical advantage of this

machine?

m1

m2

Cliff

71. A lever is used to lift a 25 kg lead

mass a distance of 40 cm. If the distance

that the input force is moved is 80 cm, what

is the amount of force used to lift the mass?

72. What is the mechanical advantage of this

machine?

73. A crate of bananas weighing 3000 N is

shipped from South America to New York,

where it is unloaded by a dockworker, who

lifts the crate by pulling on the rope of a

pulley system with a force of 200 N. What is

the actual mechanical advantage of the pulley

system?

74. If the worker above lifted the crate of

bananas a distance of 10 m,

what distance of rope did he pull?

8 M i s c e l l a n e o u s

75. If the dials on an electric meter read 23810

for the initial reading and then read 23890

for the final reading 3 days later, what is the

cost for the energy if the Edison company

charges $.15 per kilowatt - hour?

(Hint: Find the # of kW•hrs used by the

difference and multiply by the cost per kW•hr)

76. If you leave on a 100-watt light bulb in a

lamp for a time period of 10 hours, how

many kilowatt - hours of energy is being

consumed?(Hint: Convert watts to

kilowatts and multiply by the # of hours.)

77. How much will it cost to operate that 100

watt bulb for the 10 hours? (Hint: Multiply

your answer to # 36 by cost/kW-Hr)

78. Which light bulb use will cost more?

Operating a 60-watt bulb for 5.0 hours or

operating a 100-watt bulb for a time period of

2.5 hours?

(Hint: Calculate the kilowatt-hours for each

bulb and then multiply by $.15 per kilowatt –

hour)

79. Is a hand-held generator easier or harder to

crank when a light bulb is screwed into it?

a) easier b) harder

80. If two identical cars are speeding along and

then they both apply their brakes, for the car

traveling at twice the speed, how much

more distance will be required to come to a

stop, compared to the car that is traveling at

half the speed?

a) both cars require the same braking

distance

b) faster car will require twice the braking

distance

c) faster car will require four times the

braking distance.

d) faster care will require nine times the

braking distance.

9 Lab Related Questions

81. Considering a small cart with a mass in it

that is being pulled up a ramp with a force

that is parallel to the ramp. The ramp has an

angle θ. If you vary the angle of the ramp to

various angles and measure the force each

time, would you need the cosine of θ in your

calculations?

___________________________________

82. If you collect data for the pulling force and

the distance for a cart pulled up a ramp at

varying angles, how would you expect the

calculated values for the work to compare

for each different angle or elevation?

a) The calculated values for work should

each get measurably larger as the angle

increases.

b) The calculated values for work should

each get measurably smaller as the angle

increases.

c) The calculated values for work should

stay approximately constant (at least to 2

significant figures) as the angle

increases.

83. For the same lab in the previous question,

would you expect the calculated work to be

approximately the same or to be different

for two different trials of a 25 angle of

incline and a 45 angle of incline?

Explain why or why not?

___________________________________

___________________________________

___________________________________

___________________________________

84. In a laboratory experiment, a student

tries to duplicate the demonstration

shown in class, using the steel ball

pendulum and the razor blade.

If the distance that the steel ball fell is

89.5 cm and it landed 69.7 cm

horizontally from the point it was cut by

the razor blade, then how many cm

above the lowest point was the steel ball

brought and released?

_____________________________

floor

ANSWERS to Chapter 6 Practice

Test (Work and Energy)

1. a) Force in direction of motion

= 450 N cos 38 = 354.6 N

Work = F x d = 354.6 N x 0.55 m = 195 J

or 2.0 x 102 Joules

b) Net Force = Pulling Force – Friction Force

= 354.6 N – 125 N = 230 N

a = Fn/m = 230 N / 65 kg = 3.5 m/s2

2.

Work (J) Force (N) Distance (m)

45.0 22.5 N 2.0

122 3.00 40.7 m

8.40 J 28.0 30.0 cm

7,350 J 75.0 kg

firefighter

climbs a flight of

stairs 10.0 m high

3. Work = F x d cos

= (200 N) (2 m)cos 0 = 400 J

4. The downward force is perpendicular to the

direction of the motion so the angle theta is

90 and cos 90 = zero so no work was

done.

5. The direction of the force is opposite to the

direction of the motion of the crate’s

displacement, so angle theta is 180, so

Work = (10N)(4 m) cos 180

= −40 Joules

6. Work = mg x d cos

= (8 kg)(9.8 m/s2)(2 m) cos 0 = 157 J

7. Work = (500 N)(20 m)(cos 30)

= 8,660 J

8. (a) Since an apple has a weight of about 1

Newton (you should remember this) the

work done is (1 N)(1 m) cos0 = 1 J

9. (c) Work = (20N) (4 m) (cos 25) =73 J

10. (c) Work = Area (rectangle) =l w

= (4m) (30 N) = 120 J

11. (c) Work done = Area rectangle + Area triangle

= l w + ½ b h

= (6 N) (3 m) + ½ (6 N)(3 m) = 27 J

250 N

12. 37

10 m

FN Fapp

FBD Ff

W = mg

Replace the Fapp with Fy =Fsin and Fx = Fcos

Since velocity is constant, acceleration is zero

and

Fnet = Fapp cos − Ff = ma

250 N cos 37 − Ff = 0

Ff = 200 N

Work done by friction = Ff x d cos (180)

= (200 N) (10 m) cos (180)

= − 2000 J

13. I D, A, C, B

II A, D, C, B

III A, D, C, B

14. Weight = 50.0 kg x 9.8 m/s2 = 490 N

Work(Sarah) = 490 N x 5.0 m = 2,450 J

80 kg

15. a) 1st night = 250 W; 2nd

night = 817 W

b) Sarah does the same work both nights

c) More power generated 2nd

night

16. P = W/t = (200 N) (3 m) = 100 Watts

6 seconds

17. P = W/t = (200 N) (3 m) = 50 Watts

12 seconds

Kevin did the same amount of work but supplied

half the power because it took him twice as long

to do the same job.

18. Motor B supplies more power than Motor A

PA = F x v = (5,000 N)(2 m/s) = 10,000 W

PB = F x v = (4,000 N)(3 m/s) = 12,000 W

19. (b) 30 N F = P/v = 210 W/ 7 m/s = 30 N

20. a) same work but more power

21. a) the same

22. d) none of the above because there is no work

done due to no displacement of the mirror so

there is no power.

23. a) J/s

24. c) & d) are both correct

25. Power (Watts)

Work (Joules) Time

(seconds)

60.0 20.0 a) .33 s

240 b) 600 J 2.5

c) 33 W 183 5.5

3.5 kilowatts 4.8 x 10-3

d) 1.4 x 10-6

s

e) 80,000 W 2.0 mega joules 25.0

26. Lifting 2.0 kg mass (20 Watts):

(Other mass requires 13 W)

27. a) Both do the same amount of work

b) Atlas is more powerful (4,000 Watts)

28. PE =0.20 kg x 9.8 m/s2x 7.0 m =13.7 J

29. PE =5.0 kg x 9.8 m/s2x 12 m =588 J

30. b) PE =155 N x 1.8 m =279 J

31. d)

32. a) is equivalent to N-m aka Joule

33. b)

34. b) shows the object’s KE decreasing as it

slows down on its way upward, while its

GPE increases as its height increases.

35. d) PE =m g h

= (55 kg)(9.8 m/s2) (370 m) =2x10

5 J

36.

Potential Energy

(J) Mass (kg) Height (m)

50.0 75.0 a) 0.0680 m

280 b) 15.9 kg 1.80

c) 932 J 17.3 5.50

3.5 kilojoules 4.8 x 10-3

d) 74,405 m

37. KE = ½ x 20.0 kg x (16.0 m/s)2 = 2,560 J

38. KE = ½ x 7.0 kg x (2.0 m/s)2 = 14 J

39. v = (2 x 95,000 J/1800 kg)1/2

= 10.3 m/s

40. mass = (2 x 54,000 J)/ (35 m/s)2 = 88 kg

41. v = (2 x 6.21 x 10−21

J/5.31 x 10 –26

kg)1/2

= 484 m/s

42. KE = ½ mv2 → 2 KE = ½ mv

2

v = √2 =1.41 1.41 x greater

43. KE = ½ mv2 → KE = ½ m2v

2

2v

2 = 4x greater

44. Work = F x d = ΔKE

= ½ x 1000 kg x (31 m/s)2 = 480,500 J

45. F x d = ΔKE (60/20)2 = 3

2 x further

= 9x further

46. Work = F x d = ΔKE

= ½ x 9.11 x 10 -31

x (1.90 x 10 6 m/s)

2

= 1.64 x 10 -18

J

47. W = F x d so F = 7.0 x 10 4 J/ 2,800 m

= 25 N

48. (1) decrease

(2) remain the same

(v & F are perpendicular)

(3) increase

(4) decrease

49. ΔKE = (10 N)(5 m) = 50 J

KE = ½ mv2 so vf = 3.2 m/s

50. Work = F x d = ΔKE so F = mv2/2d

= 2415 N

51. C > B > A > D

52. Work total = 100 J + 500 J + 250 J = 850 J

v = 2(850 J0/5 kg = 18.4 m/s or 18 m/s

53. PE I = KE f = 7.5 kg x 9.8 m/s2 x 1.2 m

= 88 J

54. v = √(2gh) = √(2 (9.8 m/s2) 1.2 m)

= 4.849 or 4.8 m/s

55. (K.E. – mgh)

= 88 J – (7.5 kg x 9.8 m/s2 x 0.6 m)

= 88 J – 44 J = 44 J

56. 0 J

57. 88 J

58. YES NO

59. a) √2 g h

60. (a) KE = GPE = (65 kg)(9.8 m/s2)(5.5 m)

= 3500 J

(b) 3500 J = ½ mv2 v =10 m/s

Notice the finished practice test has a

different order of the questions from 61

forward (only for periods 1, 3 & 5)

61. d) due to the work−energy theorem

62.

KE

Work Done

By Friction

63. GPE = KE + Wfriction

Wfriction = GPE – KE

= (2 kg)(9.8 m/s2)(3 m) – 50 J = 9 J

64. c) (the physics book is the only object that

is not rolling. When something rolls, there

is an additional type of energy called

rotational energy) The ball in cup lab is an

example of this if solved using energy

considerations.

65. c) Work done on box = (25 N)(30 m) = 750 J

If the kinetic energy of the box only

increases by 300 J instead of 750 J, then the

other 450 J of energy must have gone

somewhere. It must have been transformed

into heat energy (or internal energy)

66. The gravitational potential energy of m1

remains the same while its kinetic energy

increases. The gravitational potential

energy of m2 decreases while its kinetic

energy increases. Total Energy is

Conserved.

67. He lands 34.6 m away from the base of the

cliff.

v at the bottom of mudslide = 19.8 m/s

time in air = 1.75 s

horizontal distance = v time in air

=34.6 m

68. Efficiency = 32 J / 35J x 100 = 91.4 %

69. F x d = F x d d = (45 N x 125 cm)/ 25 N

= 225 cm

70. M.A. = 225 cm / 125 cm = 1.8

71. F = (25 kg x 10 m/s2 x 40 cm)/ 80 cm

=125 N

72. M.A. = 80 cm/ 40 cm = 2

73. A.M.A. = 3,000 N/200 N = 15

74. d = (3,000 N x 10 m) / 200 N =150 m

75. 80 kilowatt-hr x $.15 /kilowatt-hr = $12

76. 100 watt x 1 kilowatt/1,000 watts x 10 hrs.

= 1 kilowatt-hr

77. 1 kilowatt-hr x $.15 /kilowatt-hr =15 ¢

78. 60 watt bulb

60 W x 1 kW/1,000 W x 10 hrs. x $.15/kwatt-hr

vs.

100 W x 1 kW/1,000 W x 2.5 hrs. x $.15/kwatt-

hr

79. harder because work is being done

80. c)

81. Cosine was not used and was not needed

since the angle between the applied force

and the displacement of the cart was always

zero degrees. You would not need cos

since theta is 0 and cos0 = 1

82. c) You would expect that the calculated

values for work would be the same for any

angle, since the elevation for each trial was

identical and therefore according to

conservation of energy, the amount of work

to bring an object to a certain height is the

same regardless of the path that is taken.

83. They should give the same amount of work

because for the smaller 25 angle the force

will be smaller but the distance will be

proportionately longer while for the larger

45 angle, the force will be larger but the

distance will be proportionately shorter.

84. Work backwards and you get 13.6 cm

first: time in air = 0.427 s

second: velocity = d/t or 69.7 cm/ 0.427s =

163 cm/s or 1.63 m/s

third: v = 2gh or h = v2/2g = 0.136 m or

13.6 cm