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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>
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Organization: UC Berkeley CAD Group, Berkeley, CA
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> ******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