Float Your Boat: Newsletter Challenge (December 2012)

This month's Challenge Question: Specs & Techs from GlobalSpec:

Make a model boat of aluminum foil, and float it in a half-full bathtub. If you sink the boat (topple it), it will end up at the bottom of the bathtub. Will the pressure at the bottom of the bathtub decrease, increase, or remain the same?

And the answer is:

When the boat is floating it displaces a weight of water equal to its weight - this is the Archimedes' law. When the boat is at the bottom of the bathtub it displaces a volume of water equal to its own volume. The density of the metal foil (the material the boat is made of) is larger than the density of water (1.0), otherwise it would not sink.

The relationship between the weight (W) of water displaced when the boat is floating and the volume of water displaced (V) when the boat is at the bottom of the bathtub is precisely the density of the boat, or in equation form:

or