Weight versus mass
Weight is the gravitational force that pulls an object toward the centre of the Earth. It is a vector measured in newtons (N). Mass is the amount of matter in an object, a scalar measured in kilograms (kg). Mass stays the same everywhere, but weight changes with the gravitational field strength g.
Key formula
W = mg
where W = weight (N), m = mass (kg), g = gravitational field strength (about 9.81 N kg⁻¹ on Earth, often taken as 10 N kg⁻¹).
Why weight changes
The value of g is smaller on the Moon (about 1.6 N kg⁻¹) than on Earth, so the same mass weighs less on the Moon. In free fall a body feels "weightless" because there is no supporting reaction force, although gravity still acts.
Worked example
A student has a mass of 50 kg. Find the weight on Earth (g = 10 N kg⁻¹) and on the Moon (g = 1.6 N kg⁻¹).
On Earth: W = mg = 50 × 10 = 500 N.
On the Moon: W = 50 × 1.6 = 80 N. The mass is still 50 kg in both places.
Measuring
A spring balance measures weight (a force). A lever or beam balance compares mass. Because g is nearly constant on Earth, weight is directly proportional to mass here.
Remember
- Weight is a force (N); mass is matter (kg).
- W = mg — weight depends on g.
- Mass is constant everywhere; weight is not.