Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site petsd.UUCP Path: utzoo!watmath!clyde!cbosgd!ihnp4!houxm!vax135!petsd!cjh From: cjh@petsd.UUCP (Chris Henrich) Newsgroups: net.physics Subject: Re: Re: Floating a battleship in a gallon of water Message-ID: <396@petsd.UUCP> Date: Tue, 11-Dec-84 20:12:10 EST Article-I.D.: petsd.396 Posted: Tue Dec 11 20:12:10 1984 Date-Received: Wed, 12-Dec-84 06:22:18 EST Organization: Perkin-Elmer DSG, Tinton Falls, N.J. Lines: 101 [] > > How is it that the water can hold up a ship which weighs > > more than the water? -dbell- > As I stated earlier, it probably can't. However if you are willing to > warp your definition of which water molecules are "holding up the ship" > and if you will also allow me a little poetic license, lookie here: > > || > /||\ > 50,000 tons of water here ------------------ 50,000 tons of water here > |~~~~~~~~~~~~~~~~~~~~~~~~~| 100,000 tons |~~~~~~~~~~~~~~~~~~~~~~~~~| > |~~~~~~~~~~~~~~~~~~~~~~~~~\ /~~~~~~~~~~~~~~~~~~~~~~~~~| > |~~~~~~~~~~~~~~~~~~~~~~/\~~\ /~~/\~~~~~~~~~~~~~~~~~~~~~~| > ----------------------/ \~~\ SHIP /~~/ \--------------------- > \~~\ /~~/ > \~~\ /~~/ > \~~\ /~~/ > \~~\ /~~/ > \~~\--/~~/ > \~~~~~~/<-- 8 pounds of water in trough. > \~~~~/ > \--/ > Howard Hull Where do we start? Let me first observe that the trough is not hanging in midair; it must be pushing up with a force of 100,000 tons to keep the ship stationary against gravity. First reductio ad absurdum: if it is impossible for 8 pounds of water to hold up 100,000 tons of battleship, then it is infinitely more impossible for *ZERO* pounds of water to hold up 100,000 tons of battleship, yet that is just what would happen if the gallon of water were removed and the battleship settled down in the nice dry trough. Second reductio ad absurdum: Let's take that picture and redraw it slightly. || /||\ 50,000 tons of water here ------------------ 50,000 tons of water here |~~~~~~~~~~~~~~~~~~~~~~~|~| 100,000 tons |~|~~~~~~~~~~~~~~~~~~~~~~~| |~~~~~~~~~~~~~~~~~~~~~~~|~\ /~|~~~~~~~~~~~~~~~~~~~~~~~| |~~~~~~~~~~~~~~~~~~~~~~/\~~\ /~~/\~~~~~~~~~~~~~~~~~~~~~~| ----------------------/ \~~\ SHIP /~~/ \--------------------- \~~\ /~~/ \~~\ /~~/ \~~\ /~~/ \~~\ /~~/ \~~\--/~~/ \~~~~~~/<-- 8 pounds of water in trough. \~~~~/ \--/ All I did was to put a thin barrier between the gallon of water in the trough and the 2 X 50,000 tons on either side. If you think that the water on the side is holding up the battleship, then you have to infer that 100,000 tons of force is somehow being transmitted across that thin barrier. Actually, the relative magnitudes of 8 pounds versus 100,000 tons are irrelevant to floating the battleship, because the support provided by the water is not a matter of balancing the water against the ship; it is a matter of the variation of pressure in the water at different depths. This pressure is proportional to the depth; in fact, the force on an area A at depth D is the weight of a column of water, of that depth, over a *horizontal* area A. The subtle thing about pressure is that the same pressure is exerted on the area A, no moatter how A is oriented. Now let's look at the picture again: || /||\ 50,000 tons of water here ------------------ 50,000 tons of water here |~~~~~~~~~~~~~~~~~~~~~~~~~|XX100,000 tonsXX|~~~~~~~~~~~~~~~~~~~~~~~~~| |~~~~~~~~~~~~~~~~~~~~~~~~~\XXXXXXXXXXXXXXXX/~~~~~~~~~~~~~~~~~~~~~~~~~| |~~~~~~~~~~~~~~~~~~~~~~/\~~\XXXXXXXXXXXXXX/~~/\~~~~~~~~~~~~~~~~~~~~~~| ----------------------/ \~~\XXXXSHIPXXXX/~~/ \--------------------- \~~\XXXXXXXXXX/~~/ \~~\XXXXXXXX/~~/ \~~\XXXXXX/~~/ \~~\XXXX/~~/ \~~\--/~~/ \~~~~~~/<-- 8 pounds of water in trough. \~~~~/ \--/ This time, I shaded in the volume of the ship that is below the water level. It can be shown that, because the magnitude of the pressure in the water increases with depth, the net upward force exerted by that pressure on the ship is equal to the volume shaded in times the density of water. This is Archimedes' law. The usual expression of it, involving "displacement," is meant to be a concise way of referring to that volume. One over-interprets the words if one insists on seeing all the water that was supposedly displaced. Regards, Chris -- Full-Name: Christopher J. Henrich UUCP: ..!(cornell | ariel | ukc | houxz)!vax135!petsd!cjh US Mail: MS 313; Perkin-Elmer; 106 Apple St; Tinton Falls, NJ 07724 Phone: (201) 870-5853