Section 1 of 5Mass and Weight
These two quantities are linked, but they are not the same thing.
Mass
- Mass is the amount of matter in an object, measured in kilograms, and it is the same everywhere.
Weight
- Weight is the force of gravity on an object, measured in newtons, and it depends on the local gravitational field.
Scalar and vector
- Mass has size only, while weight is a vector because it always acts towards the centre of the planet.
Measuring
- A balance compares masses, while a newtonmeter or spring balance measures weight directly.
Section 2 of 5The Equation W = mg
The Equation W = mg
Equation
- Weight = mass × gravitational field strength, written W = mg.
Units
- W is in newtons (N), m in kilograms (kg) and g in newtons per kilogram (N/kg).
Earth
- Near the surface of the Earth g is about 10 N/kg, so each kilogram has a weight of about 10 N.
Proportional
- For a given place weight is directly proportional to mass, giving a straight-line graph through the origin.
| Place | Approximate g in N/kg | Weight of a 60 kg person |
|---|---|---|
| Earth | 10 | 600 N |
| Moon | 1.6 | 96 N |
| Deep space far from any mass | about 0 | about 0 N |
Section 3 of 5Weight Changes, Mass Does Not
Travelling to the Moon shows the difference clearly.
1
A person has a mass of 60 kg on Earth, where the gravitational field strength is 10 N/kg.
2
Their weight on Earth is 60 × 10 = 600 N, which is the pull of the Earth on them.
3
On the Moon the gravitational field strength is smaller, about 1.6 N/kg, because the Moon has far less mass.
4
Their weight there is 60 × 1.6 = 96 N, which is about one sixth of the weight on Earth.
5
Their mass is still 60 kg, because the amount of matter in their body has not changed at all.
Section 4 of 5Worked Example
Question
- An astronaut has a mass of 60 kg.
- Calculate her weight (a) on Earth where g = 10 N/kg and (b) on the Moon where g = 1.6 N/kg.
- Use W = mg for each place.
- (a) Earth: W = 60 × 10 = 600 N.
- (b) Moon: W = 60 × 1.6 = 96 N.
- Commentthe mass is 60 kg in both places, and only the weight changes.
Answer 600 N on Earth and 96 N on the Moon
Section 5 of 5Exam Checklist & Tips
2.6.2 – Key Points for the Exam
- Mass The amount of matter in an object, in kg.
- Weight The force of gravity on an object, in newtons.
- Gravitational field strength The force per kilogram on a mass in a gravitational field, in N/kg.
- Free fall Motion under the influence of gravity alone.
Common Mistakes
- Quoting weight in kilograms; weight is a force and its unit is the newton.
- Saying mass is smaller on the Moon; only the weight is smaller.
- Forgetting to convert grams to kilograms before using W = mg.
- Writing g as 10 m/s without recognising that N/kg and m/s² are equivalent units.