7
CHAPTER OUTLINE
7.1
Systems and Environments
7.2
Work Done by a Constant
Force
7.3
The Scalar Product of Two
Vectors
7.4
Work Done by a Varying
Force
7.5
Kinetic Energy and the
WorkKinetic Energy
Theorem
7.6
The NonIsolated
System—Conservation of
7.7
Situations Involving Kinetic
Energy
Friction
7.8
Power
7.9
Energy and the Automobile
Energy and Energy Transfer
ANSWERS TO QUESTIONS
Q7.1
The force is perpendicular to every increment of displacement.
Therefore,
F
r
⋅
=
∆
0
.
Q7.2
(a)
Positive work is done by the chicken on the dirt.
(b)
No work is done, although it may seem like there is.
(c)
Positive work is done on the bucket.
(d)
Negative work is done on the bucket.
(e)
Negative work is done on the person’s torso.
Q7.3
Yes. Force times distance over which the toe is in contact with
the ball. No, he is no longer applying a force. Yes, both air
friction and gravity do work.
Q7.4
Force of tension on a ball rotating on the end of a string. Normal force and gravitational force on an
object at rest or moving across a level floor.
Q7.5
(a)
Tension
(b)
Air resistance
(c)
Positive in increasing velocity on the downswing.
Negative in decreasing velocity on the upswing.
Q7.6
No. The vectors might be in the third and fourth quadrants, but if the angle between them is less
than 90
°
their dot product is positive.
Q7.7
The scalar product of two vectors is positive if the angle between them is between 0 and 90°. The
scalar product is negative when 90
180
°<
<
°
θ
.
Q7.8
If the coils of the spring are initially in contact with one another, as the load increases from zero, the
graph would be an upwardly curved arc. After the load increases sufficiently, the graph will be
linear, described by Hooke’s Law. This linear region will be quite large compared to the first region.
The graph will then be a downward curved arc as the coiled spring becomes a completely straight
wire. As the load increases with a straight wire, the graph will become a straight line again, with a
significantly smaller slope. Eventually, the wire would break.
Q7.9
′ =
k
k
2
. To stretch the smaller piece one meter, each coil would have to stretch twice as much as one
coil in the original long spring, since there would be half as many coils. Assuming that the spring is
ideal, twice the stretch requires twice the force.
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Energy and Energy Transfer
Q7.10
Kinetic energy is always positive. Mass and squared speed are both positive. A moving object can
always do positive work in striking another object and causing it to move along the same direction
of motion.
Q7.11
Work is only done in accelerating the ball from rest. The work is done over the effective length of the
pitcher’s arm—the distance his hand moves through windup and until release.
Q7.12
Kinetic energy is proportional to mass. The first bullet has twice as much kinetic energy.
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 Spring '08
 Shannon
 Energy, Force, Friction, Kinetic Energy, Work, Cos

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