Mass is the amount of matter and stays the same everywhere. Weight is the gravitational force on that mass, so it changes with the field strength where the object is.
This lesson is part of gravitation. It links to applying Newton’s law of gravitation, which uses the same field strength idea.
What does each quantity mean?
Each of the three quantities has its own unit and its own formula.
| Quantity | Symbol | Unit | Changes with place? |
|---|---|---|---|
| Mass | m | kg | No |
| Weight | W | N | Yes |
| Gravitational field strength | g | N kg⁻¹ | Yes |
The link between them is W = mg. Weight is the mass multiplied by the field strength at that place.
Worked example: one student, three places
A student has a mass of 60 kg. Use g = 9.81 N kg⁻¹ on Earth and 1.62 N kg⁻¹ on the Moon.
- On Earth: W = 60 × 9.81 = 589 N.
- On the Moon: W = 60 × 1.62 = 97.2 N.
- The mass on both is 60 kg, because no matter was added or removed.
The Moon’s weight is about one sixth of Earth’s, because its field strength is about one sixth as large. The student feels lighter there, but carries exactly the same amount of matter.
How does g change with height?
Field strength falls as you move away from the planet’s centre. At a distance r from the centre, g = GM ÷ r², so doubling the distance divides g by four.
At a point twice as far from Earth’s centre as the surface, g = 9.81 ÷ 4 = 2.45 N kg⁻¹. The same 60 kg student would weigh 60 × 2.45 = 147 N there, still with a mass of 60 kg.
The mistake that costs marks
The slip is to say the mass changes on another planet, or to quote a weight in kilograms. Both appear in answers with correct arithmetic.
| Statement | Problem | Correct |
|---|---|---|
| “Mass on the Moon is 10 kg” for a 60 kg student | Mass does not change | Mass is 60 kg |
| “Weight is 60 kg” | A force is measured in N | W = 589 N |
| “g on the Moon is 9.81” | Uses Earth’s value | g = 1.62 N kg⁻¹ |
Write the unit beside every number and most of this confusion goes away. The units and significant figure checker lets you test your own values.
Check yourself
A rock weighs 39.2 N on Earth, where g = 9.81 N kg⁻¹. Find its mass, then its weight on the Moon.
Answer
Mass = W ÷ g = 39.2 ÷ 9.81 = 4.0 kg.
The mass is the same on the Moon, so the Moon weight = 4.0 × 1.62 = 6.5 N.
What to study next
Go on to explaining centripetal force in orbital motion, where gravity keeps a satellite in orbit. Test the whole chapter with the gravitation practice set.
To have a teacher check your units on new questions, see online one-to-one Physics tuition.