Solutions to Homework #4
Chapter 7
10.
Picture the Problem
: The mop head is being pushed
downward into the floor.
Strategy:
Use equation 73 keeping in mind the angle
between the force and the direction of motion.
Solution:
1. (a)
Use equation 73:
(
29
(
29
o
cos
50.0 N
0.50 m cos55
14 J
W
Fd
θ
=
=
=
2. (b)
If the angle is increased to 65°, a smaller component of the force will be along the direction
of motion and therefore the work done by the janitor will decrease.
Insight:
Only the component of the force along the direction of the motion does any work.
The
vertical component of the force increases the normal force.
22.
Picture the Problem
: The car slows down as it rolls horizontally a distance of 30.0 m through the
sand.
Strategy:
The kinetic energy of the car is reduced by the amount of work done by friction.
The
work done is the force times the distance, so once we know the work done and the distance, we can
find the force.
Solution:
1. (a)
The net work done on the car must have been negative since the kinetic energy
decreased.
2. (b)
The work done by
friction equals the average
force of friction times the
distance the car traveled.
Apply equations 71 and 77,
including a minus sign to
indicate the force and distance
are in opposite directions:
(
29
(
29
(
29
(
29
2
2
1
f
i
2
2
2
1
1
f
i
2
2
2
2
2
2
1
2
so that
1300 kg 15
18 m /s
2100 N
2.1 kN
30.0 m
m v
v
W
Fd
K
mv
mv
F
d
F

= 
= ∆
=

= 

= 
=
=
Insight:
Kinetic friction always does negative work because the force is always opposite to the
direction of motion.
The actual force exerted on the car would be −2100 N if the distance traveled
is taken to be +30.0 m.
28.
Picture the Problem
: The work done by the force is
the area under the force versus position graph.
Strategy:
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 Fall '08
 Ashkenkai
 Physics, Energy, Force, Potential Energy, Work

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