Intermediate · 10 min
Density and pressure
Calculate density and explain how contact area affects pressure.
Mass per unit volume
Density is mass divided by volume: ρ = m ÷ V. It tells us how much mass a material has in a given volume. Use compatible units: kilograms and cubic metres give kg/m³. Convert volume carefully because it is three-dimensional. One cubic metre contains 1,000,000 cubic centimetres, not 100. Comparing density can help identify materials, although different materials can have similar densities.
Worked example
A sample has mass 600 kg and volume 0.3 m³. Density = 600 ÷ 0.3 = 2,000 kg/m³
Force spread over an area
Average pressure is perpendicular force divided by area: p = F ÷ A. Its SI unit is the pascal (Pa), equal to one newton per square metre. For the same force, a smaller contact area gives greater average pressure. A force of the same magnitude spread across a larger area gives lower pressure. Convert areas to square metres before calculating in pascals.
Worked example
A perpendicular force of 90 N acts over 0.03 m². Average pressure = 90 ÷ 0.03 = 3,000 Pa
Compare two contact areas
- Calculate the pressure from a 100 N force on 0.02 m² and then on 0.04 m².
- Explain why doubling the area halves the pressure while leaving the force unchanged.