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From: fons@mcvax.UUCP (Fons Kuijk)
Newsgroups: net.physics
Subject: Re: Floating a battleship in a gallon of water
Message-ID: <6235@mcvax.UUCP>
Date: Tue, 11-Dec-84 20:12:47 EST
Article-I.D.: mcvax.6235
Posted: Tue Dec 11 20:12:47 1984
Date-Received: Thu, 13-Dec-84 02:21:03 EST
References: <27@daisy.UUCP>
Reply-To: fons@mcvax.UUCP (Fons Kuijk)
Distribution: net
Organization: CWI, Amsterdam
Lines: 95
Summary: 

In article <27@daisy.UUCP> dbell@daisy.UUCP (David I. Bell) writes:
>
>                                                |          ||          |
>      A COUNTER-INTUITIVE FACT                  |         /||\         |
>                                                |  ------------------  |
>Something that I have found amusing             |  |                |  |
>is the fact that a ship can float in a          \  \                /  /
>container of water which only contains           \~~\              /~~/
>a VERY small amount of water.                     \~~\    SHIP    /~~/
>                                                   \~~\          /~~/
>For example, if a container is shaped so            \~~\        /~~/
>that it is 1/10 inch away from the ship on           \~~\      /~~/
>all sides (and the bottom), then the water            \~~\    /~~/
>filling that small gap will hold it up.  =====>        \~~\--/~~/
>                                                        \~~~~~~/
>The counter-intuitive fact is that the weight of         \~~~~/
>the water can be *much* less than the ship's weight.      \--/
>
>How is it that the water can hold up a ship which weighs
>more than the water?                                             -dbell-


Remember this from long ago?

   |                      |       | |
   \                      /       | |
    \~~~~~~~~~~~~~~~~~~~~/        |~|
     \~~~~~~~~~~~~~~~~~~/         |~|
      \~~~~~~~~~~~~~~~~/          |~|
       \~~~~~~~~~~~~~~/           |~|
        \~~~~~~~~~~~~/            |~|
         \~~~~~~~~~~/             |~|
          \~~~~~~~~/              |~|
           \~~~~~~/               |~|
            \~~~~/                |~|
             \~~/                 |~|
             |~~|_________________|~|
             |~~~~~~~~~~~~~~~~~~~~~~|
             ------------------------


What is the difference compared to

   |          ||          |
   |         /||\         |
   |  ------------------  |
   |  |                |  |       | |
   \  \                /  /       | |
    \~~\              /~~/        |~|
     \~~\    SHIP    /~~/         |~|
      \~~\          /~~/          |~|
       \~~\        /~~/           |~|
        \~~\      /~~/            |~|
         \~~\    /~~/             |~|
          \~~\--/~~/              |~|
           \~~~~~~/               |~|
            \~~~~/                |~|
             \~~/                 |~|
             |~~|_________________|~|
             |~~~~~~~~~~~~~~~~~~~~~~|
             ------------------------

It is all a matter of balancing forces.

------------------------------------------------------------
|> The counter-intuitive fact is that
|> the weight of the water can be *much* less than the ship's weight.
|******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.
------------------------------------------------------------

You are not serious about really having to displace 100,000 ton of water?
You might as well start with a container containing a small amount of
water in it. By inserting the ship, the water will rise. This will cause an
upward force due to pressure on the ships surface.
Now in this system during insertion, not only the surface of the ship below
water level will increase, but also the pressure wil rise due to rising of
the water.
It is no surprise that the total upward force (being the total sum of local
pressure*surface area) equals the weigth of the water that would occupy the
same volume that the part of the ship below water level occupies.

The system behaves much like a hydrolic lever, which to some people already
is thought to be counter intuitive. But apart from that, due to the v-shape
of the ship and the container, the system does not behave linear, which makes
it amusing indeed.

---
No joke                                        Fons Kuijk
No graphics                                    ...mcvax!fons
No maxim [for insiders:-)]