CHAPTER
6
Work and Energy
1* ·
True or false: (
a
) Only the net force acting on an object can do work. (
b
) No work is done on a particle that
remains at rest. (
c
) A force that is always perpendicular to the velocity of a particle never does work on the particle.
(
a
) False
(
b
) True
(
c
) True
2
·
A heavy box is to be moved from the top of one table to the top of another table of the same height on the other
side of the room. Is work required to do this?
No; there is no change in potential or kinetic energy.
3
·
To get out of bed in the morning, do you have to do work?
Yes, if
your center of mass is higher when standing than when lying in bed. Otherwise, no.
4
·
By what factor does the kinetic energy of a car change when its speed is doubled?
Note that
K v
2
;
K
′
= 4
K
.
5* ·
An object moves in a circle at constant speed. Does the force that accounts for its acceleration do work on it?
Explain.
No;
dW
=
F
d
r
and here
F
is perpendicular to
d
r
.
6
·
An object initially has kinetic energy
K
. The object then moves in the opposite direction with three times its
initial speed. What is the kinetic energy now? (
a
)
K
(
b
) 3
K
(
c
) 3
K
(
d
) 9
K
(
e
) 9
K
.
(
d
)
K v
2
.
7
·
A 15g bullet has a speed of 1.2 km/s. (
a
) What is its kinetic energy in joules? (
b
) What is its kinetic energy if its
speed is halved? (
c
) What is its kinetic energy if its speed is doubled?
(
a
)
K
1/2
mv
2
(
b
)
K
is reduced by a factor of 4
(
c
)
K
is increased by a factor of 4
K
1/2
(0.015)(1.2
×
10
3
)
2
J = 10.8 kJ
K
= (10.8 kJ)/4 = 2.7 kJ
K
= 4(10.8 kJ) = 43.2 kJ
8
·
Find the kinetic energy in joules of (
a
) a 0.145kg baseball moving with a speed of 45 m/s and (
b
) a 60kg
jogger running at a steady pace of 9 min/mi.
(
a
)
K
1/2
2
(
b
)
K
1/2
2
; (1/9)mi/min=0.179km/min=2.98m/s
K
1/2
(0.145)(45)
2
J = 147 J
K
1/2
(60 kg))(2.98 m/s)
2
= 267 J
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View Full DocumentChapter 6
Work and Energy
9* ·
A 6kg box is raised from rest a distance of 3 m by a vertical force of 80 N.
Find (
a
) the work done by the
force, (
b
) the work done by gravity, and (
c
) the final kinetic energy of the box.
(
a
)
W
=
Fy
(
b
)
W
g
= 
mgy
(
c
)
K
W + W
g
W
= 3
×
80 J = 240 J
W
g
= (6)(9.81)(3) J = 177 J
K
= 63 J
10 ·
A constant force of 80 N acts on a box of mass 5.0 kg that is moving in the direction of the applied force with a
speed of 20 m/s. Three seconds later the box is moving with a speed of 68 m/s. Determine the work done by this
force.
W
=
K
f

K
i
1/2
m
(
v
f
2

v
i
2
)
W
1/2
(5)[(68)
2
 (20)
2
] J = 10.56 kJ
11 ··
You run a race with your girlfriend. At first you each have the same kinetic energy, but you find that she is beating
you. When you increase your speed by 25%, you are running at the same speed she is. If your mass is
85 kg, what is her mass?
1/2
m
1
v
2
1/2
m
2
(1.25
v
)
2
m
1
= 85 kg; solve for
m
2
= (85/1.56) kg = 54.4 kg
12 ·
How does the work required to stretch a spring 2 cm from its natural length compare with that required to stretch
it 1 cm from its natural length?
W
1/2
kx
2
;
W
x
2
; therefore work is increased by factor of 4.
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 Spring '08
 staff
 Energy, Force, Potential Energy, Work, Sal

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