Work and Energy

x

Work and Energy 06

A 500-kg elevator is pulled upward with a constant

force of 5500 N for a distance of 50.0 m. What is the

net work done on the elevator?

Ref: Sec. 6.1

Work and Energy 06

01

(A) 2.75 × 105 J

(B) -2.45 × 105 J

(C) 3.00 × 104 J

(D) -5.20 × 105 J

Work and Energy 06

x θcosFW Work

Matthew pulls his little sister Sarah in a sled on an icy

surface (assume no friction), with a force of 60.0 N at an

angle of 37.0° upward from the horizontal. If he pulls her

a distance of 12.0 m, what is the work done by Matthew?

Ref: Sec. 6.1

Work and Energy 06

02

(A) 185 J

(B) 433 J

(C) 575 J

(D) 720 J

Work and Energy 06

x θcosFW Work

A force moves an object in the

direction of the force. The graph

shows the force versus the object's

position. Find the work done when

the object moves from 0 to 6.0 m.

Ref: Sec. 6.2

Work and Energy 06

03

(A) 20 J

(B) 40 J

(C) 60 J

(D) 80 J

Work and Energy 06

Work is the product of force times distance

Work

A horizontal force of 200 N is applied to move a 55-kg

cart (initially at rest) across a 10 m level surface. What

is the final kinetic energy of the cart?

Ref: Sec. 6.3

Work and Energy 06

04

(A) 1.0 × 103 J

(B) 2.0 × 103 J

(C) 2.7 × 103 J

(D) 4.0 × 103 J

Work and Energy 06

FxW

Work

KEΔWnet Work/Energy Theorem

If it takes 50 m to stop a car initially moving at 25 m/s,

what distance is required to stop a car moving at 50 m/s

under the same condition?

Ref: Sec. 6.3

Work and Energy 06

05

(A) 50 m

(B) 100 m

(C) 200 m

(D) 400 m

Work and Energy 06

FxW

Work

2mv

KE2

Kinetic Energy

KEΔWnet

Work/Energy Theorem

A spring-driven dart gun propels a 10-g dart. It is cocked by

exerting a constant force of 20 N over a distance of 5.0 cm.

With what speed will the dart leave the gun, assuming the

spring has negligible mass?

Ref: Sec. 6.3

Work and Energy 06

06

(A) 10 m/s

(B) 14 m/s

(C) 17 m/s

(D) 20 m/s

Work and Energy 06

FxW

Work

2mv

KE2

Kinetic Energy

KEΔWnet

Work/Energy Theorem

A 100-N force has a horizontal component of 80 N and a

vertical component of 60 N. The force is applied to a box

which rests on a level frictionless floor. The cart starts

from rest, and moves 2.0 m horizontally along the floor.

What is the cart's final kinetic energy?

Ref: Sec. 6.3

Work and Energy 06

07

(A) 200 J

(B) 160 J

(C) 120 J

(D) zero

Work and Energy 06

x θcosFW Work

A 15.0-kg object is moved from a height of 7.00 m above a

floor to a height of 15.0 m above the floor. What is the

change in gravitational potential energy?

Ref: Sec. 6.4-6.5

Work and Energy 06

08

(A) 1030 J

(B) 1176 J

(C) 1910 J

(D) 2205

Work and Energy 06

yΔmgPEΔ g Gravitational Potential Energy

A 400-N box is pushed up an inclined plane. The plane is 4.0 m

long and rises 2.0 m. If the plane is frictionless, how much work

was done by the push?

Ref: Sec. 6.4-6.5

Work and Energy 06

09

(A) 1600 J

(B) 800 J

(C) 400 J

(D) 100 J

Work and Energy 06

yΔmgPEΔW g Gravitational Potential Energy

A spring is characterized by a spring constant of 60 N/m.

How much potential energy does it store, when stretched

by 1.0 cm?

Ref: Sec. 6.4-6.5

Work and Energy 06

10

(A) 3.0 × 10-3 J

(B) 0.30 J

(C) 60 J

(D) 600 J

Work and Energy 06

2kx

PE2

s

Spring Potential Energy

A spring with a spring constant of 15 N/m is initially

compressed by 3.0 cm. How much work is required to

compress the spring an additional 4.0 cm?

Ref: Sec. 6.4-6.5

Work and Energy 06

11

(A) 0.0068 J

(B) 0.012 J

(C) 0.024 J

(D) 0.030 J

Work and Energy 06

2kx

PE2

s

Spring Potential Energy

A skier, of mass 40 kg, pushes off the top of a hill with an

initial speed of 4.0 m/s. Neglecting friction, how fast will

she be moving after dropping 10 m in elevation?

Ref: Sec. 6.6-6.7

Work and Energy 06

12

(A) 7.3 m/s

(B) 15 m/s

(C) 49 m/s

(D) 196 m/s

Work and Energy 06

0PEΔKEΔ g Conservation of Energy

A 1.0-kg ball falls to the floor. When it is 0.70 m above

the floor, its potential energy exactly equals its kinetic

energy. How fast is it moving?

Ref: Sec. 6.6-6.7

Work and Energy 06

13

(A) 3.7 m/s

(B) 6.9 m/s

(C) 14 m/s

(D) 45 m/s

Work and Energy 06

KEPEg Energy

mgyPEg

Potential Energy

2mv

KE2

Kinetic Energy

A roller coaster starts with a speed of 5.0 m/s at a point 45 m

above the bottom of a dip as shown in the diagram. Neglect

friction, what will be the speed of the roller coaster at the top

of the next slope, which is 30 m above the bottom of the dip?

Ref: Sec. 6.6-6.7

Work and Energy 06

14

(A) 12 m/s

(B) 14 m/s

(C) 16 m/s

(D) 18 m/s

Work and Energy 06

0PEΔKEΔ g Cons. of Energy

mghPE

Potential Energy2

mvKE

2

Kinetic Energy

A pendulum of length 50 cm is pulled 30 cm away from the

vertical axis and released from rest. What will be its speed

at the bottom of its swing?

Ref: Sec. 6.6-6.7

Work and Energy 06

15

(A) 0.50 m/s

(B) 0.79 m/s

(C) 1.2 m/s

(D) 1.4 m/s

Work and Energy 06

0PEΔKEΔ g Cons. of Energy

mghPE

Potential Energy

2mv

KE2

Kinetic Energy

A 1500-kg car moving at 25 m/s hits an initially uncompressed

horizontal spring with spring constant of 2.0 × 106 N/m. What

is the maximum compression of the spring? (Neglect the mass

of the spring.)

Ref: Sec. 6.6-6.7

Work and Energy 06

16

(A) 0.17 m

(B) 0.34 m

(C) 0.51 m

(D) 0.68 m

Work and Energy 06

0PEΔKEΔ g Cons. of Energy

mghPE

Potential Energy

2mv

KE2

Kinetic Energy

The kinetic friction force between a 60.0-kg object and a

horizontal surface is 50.0 N. If the initial speed of the object

is 25.0 m/s, what distance will it slide before coming to a stop?

Ref: Sec. 6.8-6.9

Work and Energy 06

17

(A) 15.0 m

(B) 30.0 m

(C) 375 m

(D) 750 m

Work and Energy 06

KEΔWf Work/Energy Theorem

2mv

KE2

Kinetic EnergyWork/Friction

dfW kf

A force of 10 N is applied horizontally to a 2.0-kg mass on a

level surface. The coefficient of kinetic friction between the

mass and the surface is 0.20. If the mass is moved a distance

of 10 m, what is the change in its kinetic energy?

Ref: Sec. 6.8-6.9

Work and Energy 06

18

(A) 20 J

(B) 39 J

(C) 46 J

(D) 61 J

Work and Energy 06

netWKEΔ Work/Energy Theorem

FxW

WorkNμf kk

Friction

A 1500-kg car accelerates from 0 to 25 m/s in 7.0 s.

What is the average power delivered by the engine?

(1 hp = 746 W)

Ref: Sec. 6.10

Work and Energy 06

19

(A) 60 hp

(B) 70 hp

(C) 80 hp

(D) 90 hp

Work and Energy 06

KEΔWnet Work/Energy Theorem

tW

P

Power Kinetic Energy

2mv

KE2

A 500-kg elevator is pulled upward with a constant

force of 5500 N for a distance of 50.0 m. What is the

net work done on the elevator?

01

Work and Energy 06

mg

F

xmgFWnet

m 05m/s 9.8 kg 500N 5500W 2net

J 000,03Wnet

xFW netnet Work

Matthew pulls his little sister Sarah in a sled on an icy

surface (assume no friction), with a force of 60.0 N at an

angle of 37.0° upward from the horizontal. If he pulls her

a distance of 12.0 m, what is the work done by Matthew?

02

Work and Energy 06

x

F

m 12 37 cos N 60W

J 755W

x θcosFW Work

A force moves an object in the

direction of the force. The graph

shows the force versus the object's

position. Find the work done when

the object moves from 0 to 6.0 m.

03

Work and Energy 06

20 J 40 J 20 J

80 JWork is equal to the area under under the curve

Work is the product of force times distance.

Work

A horizontal force of 200 N is applied to move a 55-kg

cart (initially at rest) across a 10 m level surface. What

is the final kinetic energy of the cart?

04

Work and Energy 06

KEFx

m 10N 200KE J 000,2

FxW

Work

KEΔWnet Work/Energy Theorem

If it takes 50 m to stop a car initially moving at 25 m/s,

what distance is required to stop a car moving at 50 m/s

under the same condition?

05

Work and Energy 06

0

2mv

Fx2

constantx

vmF2 2

2

22

1

21

x

v

x

v

21

22

12 v

vxx

2

2 m/s 25m/s 50

m50x

m 200x2

FxW

Work

2mv

KE2

Kinetic EnergyKEΔWnet

Work/Energy Theorem

A spring-driven dart gun propels a 10-g dart. It is cocked by

exerting a constant force of 20 N over a distance of 5.0 cm.

With what speed will the dart leave the gun, assuming the

spring has negligible mass?

06

Work and Energy 06

0

2mv

Fx2

mFx2

v

kg 0.010m 0.05 N 20 2 m/s .141

FxW

Work KEΔWnet

Work/Energy Theorem

2mv

KE2

Kinetic Energy

A 100-N force has a horizontal component of 80 N and a

vertical component of 60 N. The force is applied to a box

which rests on a level frictionless floor. The cart starts

from rest, and moves 2.0 m horizontally along the floor.

What is the cart's final kinetic energy?

07

Work and Energy 06

x

F

60

80

8060

θtan

8060

tanθ 1 o9.36

m 2.0 36.9 cos N 100W

m 2.0 36.9 cos N 100W

J 160W

x θcosFW Work

A 15.0-kg object is moved from a height of 7.00 m above a

floor to a height of 15.0 m above the floor. What is the

change in gravitational potential energy?

08

Work and Energy 06

m 7m 15 m/s 9.8 kg 15PEΔ 2g

J 1761PEΔ g

15 m

7 m

yΔmgPEΔ g Gravitational Potential Energy

A 400-N box is pushed up an inclined plane. The plane is 4.0 m

long and rises 2.0 m. If the plane is frictionless, how much work

was done by the push?

09

Work and Energy 06

yΔmgW

m 2.0 N 400W

J 800W

gPEΔW Gravitational Potential Energy

A spring is characterized by a spring constant of 60 N/m.

How much potential energy does it store, when stretched

by 1.0 cm?

10

Work and Energy 06

2

m 0.01 N/m 60PE

2

s

J 003.0PEs

2kx

PE2

s

Spring Potential Energy

A spring with a spring constant of 15 N/m is initially

compressed by 3.0 cm. How much work is required to

compress the spring an additional 4.0 cm?

11

Work and Energy 06

2kx

ΔPEΔ2

s

2

kx

2

kxPEΔ

21

22

s

22s m 0.03m 0.07

2 N/m 15

PEΔ

21

22 xx

2k

J 03.0

2kx

PE2

s

Spring Potential Energy

A skier, of mass 40 kg, pushes off the top of a hill with an

initial speed of 4.0 m/s. Neglecting friction, how fast will

she be moving after dropping 10 m in elevation?

12

Work and Energy 06

0PEΔKEΔ g Conservation of Energy

00mgy2

mv

2

mv 2i

2f

gy2vv 2if

m 10 m/s 9.8 2m/s 4.0v 22f m/s 14.6

A 1.0-kg ball falls to the floor. When it is 0.70 m above

the floor, its potential energy exactly equals its kinetic

energy. How fast is it moving?

13

Work and Energy 06

2mv

mgy2

gy2v

m 0.70 m/s 9.8 2v 2 m/s 3.7

yv

KEPEg Energy

mgyPEg

Potential Energy

2mv

KE2

Kinetic Energy

A roller coaster starts with a speed of 5.0 m/s at

a point 45 m above the bottom of a dip as shown

in the diagram. Neglect friction, what will be

the speed of the roller coaster at the top of the

next slope, which is 30 m above the bottom of

the dip?

14

Work and Energy 06

21212 yyg2vv

0mgymgy2

mv

2

mv12

21

22

y2

y1

m 30m 45 m/s 9.8 2m/s 5 22

m/s 9.17v2

0PEΔKEΔ g Cons. of Energy

mghPE

Potential Energy

2mv

KE2

Kinetic Energy

A pendulum of length 50 cm is pulled 30 cm away from the

vertical axis and released from rest. What will be its speed

at the bottom of its swing?

15

Work and Energy 06

0mgy002

mv2

gy2v

L

yx

v

H

HLy

22 xLH

22 m 3.0m 5.0H m 40.0

m 40.0m 50.0y m 10.0

m 0.10 9.8m/s 2v 2

m/s 1.4v

0PEΔKEΔ g Cons. of Energy mghPE

Potential Energy

2mv

KE2

Kinetic Energy

A 1500-kg car moving at 25 m/s hits an initially uncompressed

horizontal spring with spring constant of 2.0 × 106 N/m. What

is the maximum compression of the spring? (Neglect the mass

of the spring.)

16

Work and Energy 06

002

kx2

mv0

22

kmv

x2

N/m 10x 2.0

m/s 25 kg 15006

2

m 68.0x

0PEΔKEΔ g Cons. of Energy

mghPE

Potential Energy

2mv

KE2

Kinetic Energy

The kinetic friction force between a 60.0-kg object and a

horizontal surface is 50.0 N. If the initial speed of the object

is 25.0 m/s, what distance will it slide before coming to a stop?

17

Work and Energy 06

2mv

0df2

k

k

2

f2mv

d N 50 2

m/s 25 kg 60 2

m 375d

KEΔWf Work/Energy Theorem

2mv

KE2

Kinetic EnergyWork/Friction

dfW kf

A force of 10 N is applied horizontally to a 2.0-kg mass on a

level surface. The coefficient of kinetic friction between the

mass and the surface is 0.20. If the mass is moved a distance

of 10 m, what is the change in its kinetic energy?

18

Work and Energy 06

fF WWKEΔ

Ffk

x

xfFxKEΔ kmgμf kk

mgxμFxKEΔ k

10m m/s 9.8 kg 2 0.20m 10N 10KEΔ 2

J 8.06KEΔ

netWKEΔ Work/Energy Theorem

FxW

Work

Nμf kk Friction

A 1500-kg car accelerates from 0 to 25 m/s in 7.0 s.

What is the average power delivered by the engine?

(1 hp = 746 W)

19

Work and Energy 06

tKE

P

t2mv

P2

s 7.0 2

m/s 25 kg 1500 2

hp 8.89P

KEΔWnet Work/Energy Theorem

tW

P

Power

Kinetic Energy

2mv

KE2