You might ask why a ship floats when it is made from steel with a density 6-7 times that of water. The reason is that the steel is shaped
in such a way that it displaces more water than the volume it occupies. Consider for example a ship with mass 100,000 kg. The
area of the bottom cross section of the ship is 20 m
. We ask
how deep will the ship sink into the water. The answer is that the
ship sinks until the buoyant force equals the force of gravity. The
buoyant force is given by
where d is the distance of the bottom of the hull below the surface
of the water. We determine d from
Putting in numbers we get
