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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