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Learn0625Papers 2, 4 · ExtendedMotion, forces and energyMass, weight and density
Motion, forces and energy · Subtopic 3 of 10

Mass, Weight and Density

Mass is how much matter something contains, in kilograms, and it's the same everywhere. Weight is the gravitational force on that mass, W=mgW=mg, in newtons, and it changes from planet to planet. Density is mass per unit volume; objects less dense than a liquid float in it.

Cambridge 5054 Paper 1Cambridge 5054 Paper 2Cambridge 0625 Papers 2, 4Cambridge 0625 Papers 1, 3Edexcel 4PH1 Paper 1PEdexcel 4PH1 Paper 2P≈ 30 minRevision 5 · updated 2026-10-27
Section 1 of 14

Learning objectives

  • Distinguish mass from weight, and use W=mgW=mg.
  • Explain why weight changes on the Moon but mass doesn't.
  • Calculate density using ρ=mV\rho=\dfrac mV, with correct units.
  • Describe how to measure density, and predict whether objects float.
Pause and think

An astronaut has a mass of 6060 kg. On the Moon, what is her mass? Would she feel lighter?

Section 2 of 14

Core idea

Start hereWhy does a ship float but a nail sink?

A steel ship weighs thousands of tonnes yet floats; a tiny steel nail sinks. What matters isn't how heavy something is but how much mass is packed into each bit of space: its density.

The big idea

ρ=mV\rho=\frac mV: mass per unit volume. Objects less dense than a liquid float in it.

1. The idea

Same size, different mass: density
corkwateriron0.24 g/cm³1.0 g/cm³7.9 g/cm³each block is 1 cm³
Cork floats on water (less dense); iron sinks (more dense).
ρ=mV\rho=\frac mV
where
ρ\rho
density (kg/m³ or g/cm³; 1 g/cm³ = 1000 kg/m³).
mm
mass.
VV
volume.
Edge caseThe ship The ship's hull encloses lots of air, so its average density is less than water.

2. Measuring

  • Regular solid: measure sides, calculate volume, weigh.
  • Irregular solid: displacement of water.
  • Liquid: weigh the cylinder with and without the liquid.
Displacement: the rise in water level is the stone's volume
50 cm³74 cm³beforeafter
The stone pushes aside its own volume of water.
Worked exampleA stone

60 g stone raises water from 50 to 74 cm³.

Goal
Density; float or sink?
Strategy
Displacement gives volume.
  1. V=74−50=24 cm3V=74-50=24\text{ cm}^3
    Water displaced.
  2. ρ=6024=2.5 g/cm3\rho=\frac{60}{24}=2.5\text{ g/cm}^3
    Divide.
Answer2.52.5 g/cm³: sinks (water is 1 g/cm³).
✓ CheckTypical rock density ✓.
Worked exampleAir in a room

Room 5×4×35\times4\times3 m; ρair=1.2\rho_{\text{air}}=1.2 kg/m³.

Goal
Mass of air.
Strategy
m=ρVm=\rho V.
  1. V=60 m3V=60\text{ m}^3
    Multiply dimensions.
  2. m=1.2×60=72 kgm=1.2\times60=72\text{ kg}
    Rearranged formula.
Answer7272 kg: about a person's mass!
✓ CheckUnits: kg/m³ × m³ = kg ✓.
Common misconceptionMixed units Don't divide grams by m³: convert first.
Pause and think

Ice: 0.92 g/cm³. Does it float on water?

Summary

  • ρ=m/V\rho=m/V.
  • Displacement for irregular volumes.
  • Less dense floats.
Key words
Density
Mass per unit volume.
HistoryArchimedes and the crown. The story goes that King Hiero asked Archimedes whether his crown was pure gold. Getting into a bath, Archimedes realised the water displaced would give the crown's volume, so he could compare its density with gold's. He supposedly ran through the streets shouting "Eureka!"
Fun factA spoonful of neutron star. Neutron stars are so dense that a teaspoon of their material would have a mass of about a billion tonnes. Osmium, the densest element on Earth, is just 22.622.6 g/cm³.
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