Why Don't Boats Sink?

Date: 10/15/2002 at 11:04:23
From: Sarah
Subject: Why don't boats sink? 

I want to ask you about why ships don't sink.

- Sarah

Date: 10/15/2002 at 11:08:34
From: Doctor Ian
Subject: Re: Why don't boats sink? 

Hi Sarah,

Suppose you have some water sitting in a container.  (The container 
might be a sink, or it might be an ocean.)  Now suppose you insert 
something into the water. Some of the water has to move out of the 
way to make room for it. How much water? The volume of the part of 
the thing that's submerged.  

Now, the water was happy the way it was before. You had to push it out 
of the way; so it pushes back on the thing you inserted into it. How 
hard does it push?  The amount of force is equal to the weight of the 
displaced water. This principle was discovered by Archimedes.

So what does this mean? Suppose I take a 100-lb. bar of iron, and I 
insert it into some water. Gravity is exerting a 100-lb force 
downward, but suppose the bar displaces 30 lbs of water. (I'm just 
making up the numbers here.)  What does that mean? It means that the 
water is exerting a force of 30 lbs. upward on the bar. So if I were 
standing in the water, holding the bar, it would _feel_ as though it 
were only a 70-lb. bar. Does that make sense? 

Of course, 70 lbs. downward is 70 lbs. downward, so the bar would sink 
if I let go of it. But now suppose I hammer the bar into the shape of 
a boat, and I push the boat into the water so that it's _almost_ 
submerged:


    ~~~~~~\       /~~~~~~
           \     /
            \___/

The iron still weighs 70 lbs. But now it's displacing a _lot_ more 
water! If I can make the inside of the boat big enough to displace 
more than 70 lbs. of water, what will happen?  The upward force will 
be greater than the weight of the boat. And what will happen then?  
The boat will get pushed upward:

          \       /
           \     /
    ~~~~~~~~\___/~~~~~~

Of course, if it goes _too_ far upward, we have a problem: the amount 
of displaced water will be less than the weight of the boat, so it 
will start sinking again, and rising, and sinking, until it settles 
into a condition where the amount of water displaced exactly 
compensates for the weight of the boat. And that's what we call 
'floating'. 

I hope this helps.  Write back if you'd like to talk more about 
this, or anything else. 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/