p08_023.pdf

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23. (a) As the string reaches its lowest point, its original potential energy
U
=
mgL
(measured relative to
the lowest point) is converted into kinetic energy. Thus,
mgL
=
1
mv
2
=⇒
v
=
2
2gL
.
With
L
= 1.20 m we obtain
v
= 4.85 m/s.
2
(b) In this case, the total mechanical energy is shared between kinetic
1
mv
b
and potential
mgy
b
. We
2
note that
y
b
= 2r where
r
=
L
−
d
= 0.450 m. Energy conservation leads to
mgL
=
which yields
v
b
=
1
2
mv
b
+
mgy
b
2
2gL
−
2g(2r) = 2.42 m/s
.

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