Homework 6
−
Solution
CHANG
1 (a) Work done by a constant force on the body is
W
F
F
cos
s
where
is the
angle between the force and the displacement. Here the applied force
F
50 N makes an
angle
30
∘
with the upward displacement
s
1
.5m
.Sowehave
W
F
F
cos
s
50
cos30
∘
1.5
65.0 J
Since the vertical component of
F
is upward, in the same direction of the displacement, the
work is indeed positive.
(b) The weight of the collar is
w
mg
pointing downward, and the displacement is
upward, so using the definition of work we have
W
g
−
mgs
. We can also directly use the
formula and get the same result: Take the starting point
A
as the reference with
y
upward to
measure the vertical positions, and we have:
W
g
mg
y
A
−
y
B
mg
0
−
s
−
mgs
−
2
9.8
1.5
−
29.4 J
Note that gravity does negative work here because the weight (downward) is in the
opposite direction of the displacement (upward).
(c) The work done by the spring is
W
s
1/2
k
x
A
2
−
x
B
2
. From geometry, the deformations
in the spring
x
A
and
x
B
at the initial and final points
A
and
B
can be found to be
x
A
l
A
−
l
0
2
−
1.6
0.4 m
x
B
l
B
−
l
0
2
2
1.5
2
−
1.6
0.9 m
Hence the work by the spring is:
W
s
1
2
k
x
A
2
−
x
B
2
1
2
24
0.4
2
−
0.9
2
−
7.8 J
CHANG
2 (a) The applied pushing force
F
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 Spring '08
 TSChang
 Physics, Force, Work, Cos

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