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(b) When its speed is
v
= 4 m/s, its mechanical energy is
1
2
2
5
mv
U
+
bg
. This must equal
the energy at the origin:
1
2
5
1
2
0
22
mv
U
mv
U
+=
+
o
so that the speed at the origin is
vv
m
UU
o
=+
−
2
2
50
ch
.
Thus, with
U
(5) = 246 J,
U
(0) = 0 and
m
= 20 kg, we obtain
v
o
= 6.4 m/s.
(c) Our original formula for
U
is changed to
Ux
x
x
=− +
+
8
3
2
2
5
3
3
in this case. Therefore,
U
(2) = 11 J. But we still have
v
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 Spring '08
 Any
 Physics, Energy

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