js2j@mhuxt.UUCP (sonntag) (04/12/85)
Having received mail redescribing the membrane-cup PMM, I sat down to analyze it and discover why it wouldn't work. My first step was to modify it slightly to make it slightly easier to analyze. I've replaced the cup and the membrane with a cylinder, closed at one end, and a massive piston: A (inverted) B (rightside up) ---------------- | | | | | | | | | | | air | | | | | |+-------------+| |+-------------+| || heavy piston|| || heavy piston|| water |+-------------+| |+-------------+| | air | | | | | | | ----------------- Well, I failed miserably at showing why it wouldn't work. All I was able to show was that the bouyancy is greater for the inverted configuration than for the non-inverted configuration. And if that's true, I really can't figure out why one couldn't hook a lot of these to a vertical loop of chain and have a PMM. (I mean, nothing is moving near the speed of light here, so I *should* be able to figure out why it doesn't work!) Maybe someone can point out my mistake? A: Force pushing piston down: F=p*A+M*g, where: p=pressure of air 1.) Force pushing piston up: F=g*d*A*D A=area of piston M=mass of piston Solving for p, p=g*(d*D - M/A) g=gravitational acc. d=depth of piston surf. D=density of water 2.) B: Same steps give p=g*(d*D + M/A) for the non-inverted cells. We'll need to know the volume of that air: 3.) V' = V * p /p' where: V= volume of air in piston o o (V is initial volume, V' is o current volume.) Since we're concerned only with the *difference* in bouyancy between inverted and non-inverted cells at the same depth, we can, in the following calculations, ignore the mass of the system the the volume of everything but the air, since these things remain constant. 4.) Delta bouyancy is = D * (V[a] - V[b]). Making the appropriate substitutions, we find that delta bouyancy, dB ((:-)), is: D*V *p dB = o o 2*M -------- ------------ g * A (d*D)^2 - (M/A)^2 I *know* it can't work, but I just can't figure out why. Help! -- Jeff Sonntag ihnp4!mhuxt!js2j "Pulled a muscle in my ear!"-Penfold
matt@oddjob.UUCP (Matt Crawford) (04/14/85)
Would one of you debaters please take a cup covered with a flexible membrane down to the bottom of a swimming pool and turn it over a few times? Report the results to the rest of the newsgroup. _____________________________________________________ Matt University crawford@anl-mcs.arpa Crawford of Chicago ihnp4!oddjob!matt