Mass and weight
Mass as the quantity of matter, weight as the force of gravity on a mass, and gravitational field strength.
Review these first
Learning objectives
What you need to be able to do
Teacher-mapped phrasing — check against the official Cambridge syllabus for exact wording.
- 1.3.1Distinguish between mass and weight, and state that weight is a gravitational force.
- 1.3.2Recall and use W = mg and understand g as gravitational field strength.
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Mass and weight
Mass and weight are mixed up constantly in everyday speech, and separating them properly is worth several marks in every paper.
Mass
Mass is the amount of matter in an object, measured in kilograms. It does not depend on location — take an object to the Moon and its mass is unchanged, because it is still made of the same amount of stuff.
Weight
Weight is the force of gravity acting on that mass: W = mg, measured in newtons. Because it is a force, weight is a vector, and it depends on where you are.
Gravitational field strength
g, gravitational field strength, is the weight per unit mass at a location, in N/kg. On Earth, g ≈ 9.8 N/kg (often taken as 10 N/kg). On the Moon, g is only about 1.6 N/kg, because the Moon has far less mass than the Earth.
A 70 kg astronaut has the same mass on the Moon as on Earth, but weighs roughly six times less there, because g is roughly six times smaller.
How to measure each
Mass is measured with a balance, comparing against known masses. Weight is measured with a newtonmeter (spring balance), which measures the force stretching a spring.
Think of it like this
Mass is how much "stuff" is in your backpack — it does not change no matter where you carry it. Weight is how hard gravity pulls on that backpack, which is why the same backpack would feel lighter on the Moon.
Worked examples
Method, step by step
An object has a mass of 8.0 kg. Calculate its weight on Earth (g = 9.8 N/kg) and on the Moon (g = 1.6 N/kg).
- 1W = mg
- 2On Earth: W = 8.0 × 9.8
- 3On the Moon: W = 8.0 × 1.6
Earth: 78.4 N. Moon: 12.8 N. Mass is 8.0 kg in both cases.
Common misconceptions
- Saying an astronaut is "weightless" because they have no mass in space. Their mass is unchanged; their weight is very small (or effectively zero in free fall) because they are far from a large gravitational source.
- Using "weight" and "mass" interchangeably, and their units (kg for weight) as a result — weight is always in newtons.
- Assuming g is a universal constant. It depends on the mass of the nearby planet or moon, so it is different everywhere.
In the exam
- A question that gives a mass in kg and asks for a "weight" wants an answer in newtons, using W = mg — check units before submitting.
- If asked to explain why an astronaut weighs less on the Moon, the answer must reference gravitational field strength, not simply "there is less gravity" without saying why that changes weight but not mass.