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Chapter 15: Problem 9
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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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?
Lakes on Saturn's moon Titan are filled with liquid hydrocarbons-largely methane but also some ethane. Suppose scientists want to send a probe to explore Titan's largest lake (which is about the size of Earth's Lake Ontario). The probe is to be a cylinder \(56.3 \mathrm{~cm}\) in diameter, with a mass of \(135 \mathrm{~kg}\), and it's supposed to float with the long dimension vertical, half submerged and half above the lake surface. If the liquid in the lake has density \(482 \mathrm{~kg} / \mathrm{m}^{3}\), what should be the probe's length?
Why is it easier to float in the ocean than in fresh water?
Barometric pressure in the eye of a hurricane is \(0.94\) atm (714.4 mm of mercury). How does the level of the ocean surface under the eye compare with the level under a distant fair-weather region where the pressure is \(1.0\) atm?
An 8.3-g jewel has apparent weight \(56 \mathrm{mN}\) when submerged in water. Could the jewel be a sapphire (density \(3.98 \mathrm{~g} / \mathrm{cm}^{3}\) )?
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