On 12/14/2009 11:11 AM, Terry Blanton wrote:
Hmmm, suppose you have an accordion device that you drop into the ocean with a rock. The device pressurizes air as it sinks and locks into place, then you drop the ballast and it floats to the top. You use the pressurized air to do work. Is possible?
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If so, is it OU?
Well, hrmmmmph ... that seems to be harder to answer than I expected, after a page of scribbles failed to get me anywhere.
Work done on the accordion by the water, in squishing the air in it, is proportional to the log of the ratio of the pressure at the surface to the pressure at the bottom. (But that's just half the problem, of course.)
Work done on the (rock+accordion) by (gravity-buoyancy) is related to depth of the ocean and not a lot else; density of the water enters in there somewhere but seems to get messy. Simplest approach is probably to assume neutral buoyancy for the system at the surface; buoyancy decreases as it sinks, of course, as the accordion is squished.
If it's not OU then those two quantities of work had better be provably equal and right now it looks like trying to prove apples equal oranges.
To make it more interesting, you can replace the rock with a bag of sand, and let it slide down a slope underwater, and then the sand can be left behind little by little as it sinks, so that the accordion+sandbag are neutrally buoyant all the way down. Then the net work done by (gravity-buoyancy) on the system must be zero, but the accordion has still gained energy. Erk? Where'd it come from?
Anyhow gotta go do some day-job work, sad to say, this puzzle is more interesting...
