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Chapter 15: Problem 12
A barge filled with steel beams overturns in a lake, spilling its cargo. Does the water level in the lake rise, fall, or remain the same?
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At a hearing on a proposed wind farm, a wind-energy advocate says an installation of 800 turbines, with blade diameter \(95 \mathrm{m}\) could displace a \(1-\) GW nuclear power plant. You're asked if that's really possible. How do you answer, given an average wind speed of \(12 \mathrm{m} / \mathrm{s}\) and a turbine power output that averages \(30 \%\) of the theoretical maximum?
Archimedes purportedly used his principle to verify that the king's crown was pure gold by weighing the crown submerged in water. Suppose the crown's actual weight was \(25.0 \mathrm{N}\). What would be its apparent weight if it were made of (a) pure gold and (b) \(75 \%\) gold and \(25 \%\) silver, by volume? The densities of gold, silver, and water are \(19.3 \mathrm{g} / \mathrm{cm}^{3}, 10.5 \mathrm{g} / \mathrm{cm}^{3},\) and \(1.00 \mathrm{g} / \mathrm{cm}^{3},\) respectively.
A steel drum has volume \(0.23 \mathrm{m}^{3}\) and mass \(16 \mathrm{kg} .\) Will it float in water when filled with (a) water or (b) gasoline (density \(\left.860 \mathrm{kg} / \mathrm{m}^{3}\right) ?\)
A plumber comes to your ancient apartment building where you have a part-time job as caretaker. He's checking the hot-water heating system, and notes that the water pressure in the basement is 18 psi. He asks, "How high is the building?" "Three stories, each about 11 feet," you reply. "OK, about 33 feet," he says, pausing to do some calculations in his head. "The pressure is fine," he declares. On what basis did he come to that conclusion?
Water pressure at the bottom of the ocean arises from the weight of the overlying water. Does this mean that the water exerts pressure only in the downward direction? Explain.
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