Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Francesca on 06/08/2008 13:32:33

Francesca asked the Naked Scientists:
Hi there! thanks for the company!
I was discussing with a friend about objects floating... he says that if you have 2 boxes with the same volume and filled with the same amount of sand, but one with a square bottom and one rectangular, the one with the square bottom will sink more than the rectangular one.
Is it true and, if so, why is that?
Thanks, love your podcast! (http://www.thenakedscientists.com/HTML/podcasts/)
What do you think?

What do you mean by the same amount of sand ?, if you mean the same weight the greater the area of the box the less it will sink it being irrelevant whether it is square, rectangular or round.
This assumes the density of the box material contributes nothing to the buoyancy and merely contains the sand

According to Archimedes' principle (http://en.wikipedia.org/wiki/Buoyancy) both your boxes will displace the same volume of water when they float.
When floating, the box which had the smallest horizontal crosssection in the plane of the water surface
would have the the highest point (or surface) above the surface of the water.

There are two points to make.
1. (As said above) both objects will displace the same amount of water (their weights). If they are the same average density, there will be the same volume above the surface.
2. The attitude of any object when floating will end up with the least gravitational potential  it will be 'as low as possible'. So a pole wouldn't float upright, however dense it was; it would always lay on its side in the water. For an object with arbitrary mass distribution, the attitude could be 'anything'.