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371
Chapter 6
Work and Energy
Conceptual Problems
*1
•
Determine the Concept
A force does work on an object when its point of application
moves through some distance
and there is a component of the force along the line of
motion.
(
a
) False. The
net
force acting on an object is the vector sum of all the forces acting on
the object and is responsible for displacing the object. Any or all of the forces
contributing to the net force may do work.
(
b
) True. The object could be at rest in one reference frame and moving in another. If we
consider only the frame in which the object is at rest, then, because it must undergo a
displacement in order for work to be done on it, we would conclude that the statement is
true.
(
c
) True. A force that is always perpendicular to the velocity of a particle changes neither
it’s kinetic nor potential energy and, hence, does no work on the particle.
2
•
Determine the Concept
If we ignore the work that you do in initiating the horizontal
motion of the box and the work that you do in bringing it to rest when you reach the
second table, then neither the kinetic nor the potential energy of the system changed as
you moved the box across the room. Neither did any forces acting on the box produce
displacements. Hence, we must conclude that the minimum work you did on the box is
zero.
3
•
False. While it is true that the person’s kinetic energy is not changing due to the fact that
she is moving at a constant speed, her gravitational potential energy is continuously
changing and so we must conclude that the force exerted by the seat on which she is
sitting is doing work on her.
*4
•
Determine the Concept
The kinetic energy of any object is proportional to the square of
its speed. Because
,
2
2
1
mv
K
=
replacing
v
by 2
v
yields
()
.
4
4
2
2
2
1
2
2
1
K
mv
v
m
K'
=
=
=
Thus doubling the speed of a car quadruples its kinetic
energy.
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View Full DocumentChapter 6
372
5
•
Determine the Concept
No.
The work done on any object by any force
F
r
is defined as
r
F
r
r
d
dW
⋅
=
. The direction of
net
F
r
is toward the center of the circle in which the object
is traveling and
r
r
d
is tangent to the circle. No work is done by the net force because
net
F
r
and
r
r
d
are perpendicular so the dot product is zero.
6
•
Determine the Concept
The kinetic energy of any object is proportional to the square of
its speed and is always positive. Because
,
2
2
1
mv
K
=
replacing
v
by 3
v
yields
()
.
9
9
3
2
2
1
2
2
1
K
mv
v
m
K'
=
=
=
Hence tripling the speed of an object increases its
kinetic energy by a factor of 9 and
correct.
is
)
(
d
*7
•
Determine the Concept
The work required to stretch or compress a spring a distance
x
is
given by
2
2
1
kx
W
=
where
k
is the spring’s stiffness constant. Because
W
∝
x
2
, doubling
the distance the spring is stretched will require four times as much work.
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 Spring '10
 Mikael

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