27.
(a) The graph shows F as a function of x assuming x
0
is positive. The work is negative as the object
moves from x = 0 to x = x
0
and
positive as it moves from x = x
0
to x = 2x
0
. Since the area of a
triangle is
1
2
(base)(altitude),the
work done from x = 0 to x = x
0
is
−
1
2
(x
0
)(F
0
) and the work done
from x = x
0
to x = 2x
0
is
1
2
(2x
0
−
x
0
)(F
0
) =
1
2
(x
0
)(F
0
). The total
work is the sum,which is zero.
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.
F
0
−F
0
x
0
2x
0
0
(b) The integral for the work is
W =
2x
0
0
F
0
x
x
0
− 1
dx = F
0
x
2
2x
0
− x
2x
0
0
= 0 .