CHAPTER
6
WORK AND ENERGY
CONCEPTUAL QUESTIONS
____________________________________________________________________________________________
1.
REASONING AND SOLUTION
The work done by
F
1
in moving the box through a
displacement
s
is
. The work done by
F
2
is
From
the drawing, we see that
; therefore, the force
F
1
does more work.
1
1
1
(
cos 0
)
W
F
s
F
=
°
=
s
.
s
2
2
(
cos
)
W
F
θ
=
1
2
cos
F
F
θ
>
____________________________________________________________________________________________
2.
REASONING AND SOLUTION
The force
P
acts along the displacement; therefore, it
does positive work. Both the normal force
F
N
and the weight
m
g
are perpendicular to the
displacement; therefore, they do zero work. The kinetic frictional force
f
k
acts opposite to
the direction of the displacement; therefore, it does negative work.
____________________________________________________________________________________________
3.
REASONING AND SOLUTION
Work can be positive or negative. Work is positive when
the force has a component in the same direction as the direction of the displacement, or
equivalently, when the angle
θ
between the force
F
and the displacement
s
is less than 90°.
The work is negative when the force has a component in the direction
opposite
to the
displacement; that is, when
θ
is greater than 90°.
Since the force does positive work on a particle that has a displacement pointing in the +
x
direction, the force must have an
x
component that points in the +
x
direction. Furthermore,
since the same force does negative work on a particle that has a displacement pointing in the
+
y
direction, the force has a
y
component that points in the
negative
y
direction.
When the
x
and
y
components of this force are sketched
head to tail, as in the figure at the right, we see that the
force must point in the fourth quadrant.
F
x
F
y
F
____________________________________________________________________________________________
4.
SSM
REASONING AND SOLUTION
The sailboat moves at constant velocity, and,
therefore, has zero acceleration. From Newton's second law, we know that the net external
force on the sailboat must be zero.
a. There is no work done on the sailboat by a zero net external force.
b. Work is done by the individual forces that act on the boat; namely the wind that propels
the boat forward and the water that resists the motion of the boat. Since the wind propels the
boat forward, it does positive work on the boat. Since the force of the water is a resistive
force, it acts opposite to the displacement of the boat, and, therefore, it does negative work.
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Chapter 6
Conceptual Questions
277
Since the total work done on the boat is zero, each force must do an equal amount of work
with one quantity being positive, and the other being negative.
Note:
The answer to part (a) could have been deduced from the workenergy theorem as
well. Since the velocity of the boat is constant, the kinetic energy of the boat does not
change and the total work done on the boat is zero.
____________________________________________________________________________________________
5.
REASONING AND SOLUTION
The speed of the ball decreases; therefore, the ball is
subjected to an external resistive force. A resistive force always points opposite to the
direction of the displacement of the ball. Therefore, the external force does negative work.
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 Spring '08
 holland
 Energy, Force, Potential Energy, Work

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