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Weighing on Mars

Forces and motion · level 3, lesson 6 of 6

A question to start

An astronaut packs two things for Mars: a bathroom scale, and an old-fashioned balance with two pans, like the ones in pictures of the scales of justice. On Mars, she weighs a bag of rice on each. Do they agree?

The idea

The two kinds of scale do different jobs.

  • A balance compares two masses. Rice goes in one pan; known masses, like 1 kg blocks, go in the other. When it balances, the masses are equal. Gravity pulls both pans, and on Mars it pulls both less, by the same amount. So a balance gives the same answer on Mars as on Earth.
  • A spring scale (and a bathroom scale, and a kitchen scale) measures the force pushing down on it. It turns that force into "kilograms" using Earth's gravity. On Mars, the force is only 0.38 as big, so the scale shows only 38% of the real mass.
balance: 1 kgspring scale: 0.38 kg
A 1 kg bag of rice Mars Earth
On a two-pan balance 1 kg 1 kg
On a kitchen scale made for Earth 0.38 kg 1 kg
The force on the scale 3.7 N 9.8 N

So a kitchen scale on Mars would need to be set up for Mars gravity, multiplying its reading by about 2.6. Or the cook could use a balance, which never needs changing.

Worked examples

1. A bathroom scale. A person of 60 kg stands on a bathroom scale from Earth, on Mars. The force is \(60 \times 3.7 = 222\) N. The scale divides by Earth's 9.8: it shows about 23 kg.

2. Fixing the reading. A Mars kitchen scale from Earth shows 0.95 kg of flour. The real mass is \(0.95 \div 0.38 = 2.5\) kg.

Try it

  1. Which kind of scale works the same on Mars as on Earth?
  2. What does a spring scale really measure?
  3. An Earth bathroom scale on Mars reads 30 kg. About what is the person's mass?
  4. On the Moon, gravity is about 0.17 of Earth's. What would a balance say for a 1 kg bag there?
Answers
  1. A two-pan balance.
  2. The force pushing on it (the weight).
  3. \(30 \div 0.38 \approx 79\) kg.
  4. 1 kg. A balance compares masses, so gravity does not matter.

Common mistake

"On Mars I would lose weight, so my mass would go down." Your weight, the force, goes down. Your mass, the amount of you, stays exactly the same. Only scales that measure force are fooled.

Where it leads