Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 8/23/84; site ucbcad.UUCP Path: utzoo!watmath!clyde!burl!ulysses!allegra!mit-eddie!genrad!decvax!ucbvax!ucbcad!moore From: moore@ucbcad.UUCP Newsgroups: net.physics Subject: Re: Re: Floating a battleship in a gallon of water Message-ID: <18@ucbcad.UUCP> Date: Wed, 12-Dec-84 20:00:33 EST Article-I.D.: ucbcad.18 Posted: Wed Dec 12 20:00:33 1984 Date-Received: Fri, 14-Dec-84 05:47:27 EST References: <27@daisy.UUCP> <1296@hao.UUCP> Distribution: net Organization: UC Berkeley CAD Group, Berkeley, CA Lines: 58 > ******Arrgh. Here we go. The principle of Archimedes would, for the purposes > of this discussion, best be stated: "When an object is freely suspended in > a liquid, the object will be buoyed up by a force equal to the weight of the > displaced liquid." Therefore, if you have a 100,000 ton ship, you are going > to need 100,000 tons of water for it to displace; otherwise, a force of some > other description will be found to be responsible for supporting the ship. > > How is it that the water can hold up a ship which weighs > > more than the water? -dbell- > The layer of water has to be thin enough that small scale molecular interaction > between the water and the container transfers the force represented by the > weight of the ship directly to the walls of the container. Then the water is > between a rock and a hard place, and has no choice but to support the ship. > Howard Hull > {ucbvax!hplabs | allegra!nbires | harpo!seismo } !hao!hull RESOLVED : You can float a 100,000 ton ship in an arbitrarily small amount of water. PROOF : A gedanken experiment. Take your battleship and float it in the ocean (We agree that is possible). Now replace the replace the water more than an inch away from the hull with a wall instead. The remaining water is unaffected, since the wall will keep it in place as well as the replaced water did. The battleship is still floating (how would even `know' that the water not touching it has been removed?). So now the ship is floating on a inch thick layer of water. We can of course change the inch to an arbitrarily small thickness (at least until we start getting to thicknesses on the order of inter-molecular spacing), thus we can float the ship on an arbitrarily small amount of water. EXPLAINATION : I think part of the trouble is a instinctual belief in 'conservation of force'. We feel since there is be 100,000 tons of force holding up the ship, there must me 100,000 tons of something around applying the force. This just ain't so. As another author so nicely pointed out, the important concept is leverage; which allows a small force (the weight of the remaining water) to be translated into a large force (the 100,000 tons of the battleship). As to the Archimedes' principle, you place to much weight (excuse me) on the word displaced. Imagine our battleship floating in the ocean once again, and suppose we wish to figure out the forces applied to it by the surrounding water. One could do the proper vector intergals over the surface of the ship, but there is a much neater method. Imagine replacing the ship with a volume of water shaped like the portion of the ship below the water-line. Since this would result in just a flat expanse of water, this replacement shouldn't cause any re-arraignment of the water. Thus the net force on the replacement volume of water (and thus on the battleship it replaced) should be exactly equal to the volume's weight. Notice this argument does not require the replacement volume of water to actually exist, it only uses it as an imaginary artifice. EXPERIMENT : Get two nesting pots and try it. Peter Moore moore@Berkeley, ...!ucbvax!moore