What is density?
Density is the mass per unit volume of a substance. It tells us how tightly matter is packed. A dense material such as lead has a lot of mass in a small volume, while a low-density material such as cork has little mass for its size.
Key idea
ρ = m ÷ V, where ρ is density (kg/m3 or g/cm3), m is mass and V is volume. Water has a density of 1000 kg/m3 = 1.0 g/cm3.
Measuring density
For a regular solid, find the mass with a balance and the volume from its dimensions (e.g. length × width × height). For an irregular solid, use the displacement method: lower it into water in a measuring cylinder and read the rise in level, which equals its volume. For a liquid, measure the mass of a known volume in a measuring cylinder.
Worked example
A metal block has mass 240 g and volume 30 cm3. ρ = m ÷ V = 240 ÷ 30 = 8.0 g/cm3. This is close to the density of iron.
Floating and sinking
An object floats on a liquid if its density is less than the liquid's density, and sinks if it is greater. Ice (about 920 kg/m3) floats on water (1000 kg/m3) for this reason.
Remember
- ρ = m ÷ V; rearrange to m = ρV or V = m ÷ ρ.
- 1 g/cm3 = 1000 kg/m3.
- Less dense than the liquid → floats.