Density and pressure
Physics · Key Stage 3 · The School
Density is mass per volume
DENSITY is how much mass is packed into a given volume: density equals mass divided by volume, usually in grams per cubic centimetre. It is a property of the MATERIAL, not the object — a small iron nail and a large iron gate have the same density. That is why density identifies a material while mass alone cannot.
Floating
An object floats if its density is less than the fluid's. Steel is far denser than water, yet a steel ship floats because its shape encloses a great deal of air, making the AVERAGE density of the whole ship lower than water. Punch a hole and water replaces the air, the average density rises past water's, and it sinks.
Pressure
PRESSURE is force divided by area, in newtons per square metre. The same force over a smaller area gives more pressure, which is why a drawing pin has a sharp point and a flat head, and why snowshoes stop you sinking. In fluids, pressure increases with depth because more fluid is above you pressing down.
An iron nail: mass 8 g, volume 1 cm³, so density = 8 ÷ 1 = 8 g/cm³. Water is 1 g/cm³, so the nail sinks. A steel ship: 40,000,000 kg, but its hull encloses 80,000 m³ of mostly air, so its average density is 40,000,000 ÷ 80,000 = 500 kg/m³ — half that of water, so it floats. The material is the same. The shape changed the volume, and volume is half of density.