Mass and weight
Mass is the amount of matter in an object, measured in kilograms (kg). It is a scalar and stays the same everywhere. Weight is the gravitational force acting on that mass; it is a vector measured in newtons (N) and changes with the strength of the gravitational field.
Key idea
W = m × g, where g is the gravitational field strength. On Earth g ≈ 10 N/kg (more precisely 9.8 N/kg). So a 1 kg mass weighs about 10 N on Earth.
Why they differ
An astronaut carrying a 60 kg toolkit has the same mass on the Moon, but its weight is far less because the Moon's g is only about 1.6 N/kg. Mass is measured with a balance by comparison; weight is measured with a calibrated spring balance (newtonmeter), which really measures force.
Worked example
Find the weight on Earth of a 5.0 kg bag (g = 10 N/kg). W = m × g = 5.0 × 10 = 50 N. On the Moon (g = 1.6 N/kg) the same bag weighs 5.0 × 1.6 = 8.0 N, yet its mass is still 5.0 kg.
Gravitational field strength
Gravitational field strength g is the force per unit mass, g = W ÷ m, in N/kg. Its value is the same number as the acceleration of free fall, so on Earth objects fall with an acceleration of about 10 m/s².
Remember
- Mass (kg) is constant; weight (N) depends on g.
- W = mg; use g ≈ 10 N/kg on Earth.
- Weight is a force, so it is measured in newtons.