Mass and weight

Two ideas that people mix up

'I weigh $50$ kilograms' mixes two ideas. Physics keeps them apart.

• Mass ($m$) is how much matter an object has, in kilograms. It is the same everywhere, and it measures the object's inertia.
• Weight ($W$) is the force with which gravity pulls the object, in newtons. It depends on where the object is.

The link between them

On the Earth a $1\ \text{kg}$ bag weighs $9.8\ \text{N}$. Weight points towards the centre of the Earth.

You should find that the line for the Moon is far less steep: about $6$ times less. A $62.5\ \text{kg}$ mass weighs $100\ \text{N}$ there.

Watch out. A bathroom scale measures a force but shows kilograms, using the Earth's $g$. On the Moon it would show a wrong 'mass'. A beam balance, which compares two masses, would still be right.

A worked example

A $48\ \text{kg}$ girl: find her mass and weight on the Earth, the Moon and Mars ($g = 9.8\ \text{m/s}^2$, $1.6\ \text{m/s}^2$ and $3.7\ \text{m/s}^2$).

1. Mass. $48\ \text{kg}$ everywhere.
2. Weight. Earth $48\ \text{kg} \times 9.8\ \text{m/s}^2 = 470.4\ \text{N}$; Moon $76.8\ \text{N}$; Mars $177.6\ \text{N}$.
3. So only the weight changes from world to world.

Practise with new numbers

Try it in Python

The program works out the girl's weight on three worlds.

Remember these

• Mass: matter, in kg, the same everywhere. Weight: a force, in N, $W = mg$.
• $1\ \text{kg}$ weighs $9.8\ \text{N}$ on the Earth and $1.6\ \text{N}$ on the Moon.
• A spring balance measures weight; a beam balance compares masses.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. What is the weight of a $5\ \text{kg}$ bag on the Earth?

2. An astronaut's mass is $70\ \text{kg}$ on the Earth. What is it on the Moon?

3. Something weighs $196\ \text{N}$ on the Earth. What is its mass?

4. Which is the right unit for weight: kg or N?