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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
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