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13.62. Set Up:
Steel has density
The maximum buoyant force is
Solve:
The volume of steel in the barge is
The mass of the barge is
and
The volume of this mass of coal is
The volume of the barge is
this mass of coal easily fits into the barge.
13.63. Set Up:
The density of lead is
The buoyant force when the wood sinks is
where
is the volume of the wood plus the volume of the lead.
Solve:
Using
and
gives
then gives
Reflect:
The volume of the lead is only 3.9% of the volume of the wood. If the contribution of the volume of the
lead to
is neglected, the calculation is simplified:
and
The result
of this calculation is in error by about 9%.
13.64. Set Up:
where
V
is the volume of the airship. The lift is
Solve: (a)
so
(b)
Hydrogen is explosive, helium is not.
13.65. Set Up:
Seawater has density
is the submerged volume:
where
is the volume of the life preserver and
is the volume of the person.
Solve:
gives
r
lp
5
1
1.03
3
10
3
kg
/
m
3
21
0.0400 m
3
1
3
0.80
43
0.0765 m
3
42
2
75.0 kg
0.0400 m
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 Spring '07
 Shoberg
 Force, Mass

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