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Mass and inertia

Forces and motion · level 5, lesson 2 of 6

A question to start

On the International Space Station, everything floats, and a bathroom scale reads zero. Yet doctors need to know if astronauts are losing mass. How do you weigh someone who weighs nothing?

The idea

Mass is the amount of matter in something, measured in kilograms. It is also a measure of inertia: how hard it is to change the thing's velocity. Twice the mass needs twice the force to get the same change of speed in the same time.

Weight is different. It is the force of gravity on the mass, and it depends on where you are. On Mars it is 0.38 of Earth's; in orbit things are in free fall and feel weightless.

A 70 kg astronaut Mars surface Earth surface In orbit
Mass 70 kg 70 kg 70 kg
Weight felt 260 N 687 N none (free fall)
Force to give 1 m/s² sideways 70 N 70 N 70 N

That last row is the key. Inertia does not depend on gravity, so it can be used to measure mass anywhere. On the space station, astronauts strap into a device called SLAMMD, the Space Linear Acceleration Mass Measurement Device: a spring pulls them along a short track, and the device times how fast they accelerate. From \(m = F/a\) it works out their mass.

m: speeds up by a2m: speeds up by a/2

Worked examples

1. SLAMMD. A spring pulls an astronaut with 140 N, and they accelerate at 2.0 m/s². Mass \(= 140 \div 2.0 = 70\) kg.

2. A full and empty trolley on Mars. The full one has three times the mass. With the same push it speeds up a third as fast, exactly as on Earth.

3. Shaking a box. You can tell an empty box from a full one in space by shaking it: the full one fights back harder. That is inertia, with no weight at all.

Try it

  1. What is the difference between mass and weight?
  2. Does a rock have more inertia on Earth or on Mars?
  3. A device pulls with 90 N and the astronaut accelerates at 1.5 m/s². What is the astronaut's mass?
  4. Why can't a bathroom scale measure mass on the space station?
Answers
  1. Mass is the amount of matter and measures inertia; weight is the force of gravity on it.
  2. The same: inertia depends only on mass.
  3. \(90 \div 1.5 = 60\) kg.
  4. Everything there is in free fall: the person does not press on the scale, so it reads zero.

Common mistake

"Things are weightless in orbit because there is no gravity." Gravity on the space station is about 90% of Earth's. Everything there is falling round the Earth together, so nothing presses on anything.

Where it leads