Mass, weight and density

What the syllabus demands

• —Distinguish mass (amount of matter) from weight (gravitational force)
• —Use W = mg with g = 9.8 N/kg (or 10 N/kg)
• —Define density and calculate it for regular solids, irregular solids and liquids
• —Describe the displacement method for the volume of an irregular object
• —Predict floating and sinking by comparing densities

Definitions that earn marks

Clear definitions to practise — check your course mark scheme

Mass

A measure of the quantity of matter in an object; measured in kilograms and unchanged by location.

Weight

The gravitational force acting on an object; W = mg, measured in newtons, and different on different planets.

Density

Mass per unit volume; ρ = m ÷ V.

Gravitational field strength (g)

The force per unit mass acting on an object in a gravitational field; g = 9.8 N/kg near the Earth's surface.

The equations

More equations to practise: the IGCSE formula sheet.

Where the marks die

Common mistakes to check

1. 01

   Saying an astronaut's mass changes on the Moon. Mass is the same everywhere; only weight changes, because g changes.

2. 02

   Mixing density units: 1 g/cm³ = 1000 kg/m³. If the mass is in grams and the volume in cm³, do not convert to kg and m³ separately mid-calculation.

3. 03

   In the displacement method, forgetting that the volume of the object equals the rise in water level — final reading minus initial reading, not the final reading alone.

4. 04

   Explaining floating with 'it is light'. The mark scheme wants a density comparison: the object floats because its density is less than the density of the liquid.

One worked example, done properly