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20. (a) With energy in Joules and length in meters, we have
Δ
UU
xU
x
d
x
x
=−=
−
′ −
′
z
b
g
b
g
b
g
06
1
2
0
.
Therefore, with
U
(0) = 27 J, we obtain
U
(
x
) (written simply as
U
) by integrating and
rearranging:
Ux
x
=+
−
27 12
3
2
.
(b) We can maximize the above function by working through the
/0
dU dx
=
condition,
or we can treat this as a force equilibrium situation — which is the approach we show.
Fx
eq
=
¡
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 Spring '08
 Any
 Physics, Energy

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