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37. (a) We assume the center of mass is closer to the right end of the rod, so the distance from the left
end to the center of mass is
`
=0
.
60 m. Four forces act on the rod: the upward force of the left
rope
T
L
, the upward force of the right rope
T
R
, the downward force of gravity
mg
,andtheupward
buoyant force
F
b
. The force of gravity (e±ectively) acts at the center of mass, and the buoyant
force acts at the geometric center of the rod (which has length
L
.
80 m). Computing torques
about the left end of the rod, we ²nd
T
R
L
+
F
b
µ
L
2
¶
−
mg`
=0 =
⇒
T
R
=
mg`
−
F
b
L/
2
L
.
Now, the buoyant force is equal to the weight of the displaced water (where the volume of displace
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 Fall '08
 SPRUNGER
 Physics, Center Of Mass, Force, Mass

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