Density: floating & sinking

Drop an ice cube into your drink: it floats on top. A stone by the lake sinks right away, and a drop of oil settles on the water. Whether something floats or sinks is no accident, it is a question of density. And you can calculate it yourself.

What is density?

Density tells you how much mass fits into a certain volume: density = mass divided by volume. It is often measured in g/cm³. A cube of water with 1 cm edges weighs 1 g, so water has a density of 1.0 g/cm³. A steel cube of the same size weighs almost 8 g, its material is packed more tightly. The formula can also be rearranged: if you know density and volume, the mass equals density times volume. If you know density and mass, the volume equals mass divided by density.

The 1.0 decides

Just compare with water: if an object's density is less than 1.0 g/cm³, it floats. If it is greater, it sinks. Wood at 0.6 g/cm³ floats, a stone at 2.5 g/cm³ sinks. Oil has about 0.9 g/cm³, which is why it settles on top of the water.

Why does a steel ship float?

Steel has a density of almost 8 g/cm³ and really ought to sink. The trick is the shape: the hull is hollow inside and encloses a great deal of air. Counting steel and air together, the average density of the whole ship is less than 1.0 g/cm³, and that is why it floats. If the ship springs a leak and fills with water, that advantage is lost.