Mass, weight and weightlessness
Mass is the amount of matter and never changes. Weight is the earth's pull, W = mg, so it changes with g; on the moon it is about one sixth.
Mass vs weight
Worked example: weight on the earth and on the moon
A small rover has a mass of 30 kg. Find its weight on the earth (g = 9.8 m s⁻²) and on the moon (g = 1.63 m s⁻²). What is its mass on the moon?
- On the earth: W = mg = 30 kg × 9.8 m s⁻² = 294 N.
- On the moon: W = 30 kg × 1.63 m s⁻² = 48.9 N.
- Compare: 294 ÷ 48.9 ≈ 6, so its weight on the moon is about one sixth.
- Mass does not change, so on the moon it is still 30 kg.
294 N on the earth and about 49 N on the moon; the mass stays 30 kg
Worked example: from weight to mass
A sack of rice weighs 245 N. Find its mass. (g = 9.8 m s⁻²)
- W = mg, so m = W/g.
- m = 245 N ÷ 9.8 m s⁻² = 25 kg.
25 kg
Weightlessness
A weighing machine does not measure the earth's pull directly. You press down on it, and it pushes back up on you with an equal force (third law). The machine shows this reaction. Now imagine you and the machine falling freely together. You both fall with the same acceleration, so you press on nothing. The machine reads zero. So a body falling freely under gravity is weightless. Astronauts in an orbiting spacecraft are always falling freely round the earth, so they float.
Activity: feel a book become lighter
You need one heavy book.
- 1Hold a heavy book flat on your open palm. Feel how hard it presses down.
- 2Now move your hand down quickly with a sudden drop.
- 3★Observe: the book seems to press less, as if it has become lighter.
- 4Conclude: when your hand speeds up downward, the book presses less on it. If your hand fell freely at g, the book would press with zero force.
★ key step
Quick checks on mass and weight
- At one place g is fixed, so weight is directly proportional to mass there.
- You weigh slightly more at the poles than at the equator, because g is larger at the poles.
- In a lift that starts moving up, you feel heavier. When it starts moving down, you feel lighter.
- When we say 'my weight is 50 kg' in daily talk, we really mean mass. A shop scale is simply marked in kg.
A 60 kg person weighs about 588 N on the earth but only about 98 N on the moon. A sack of atta in your kitchen has the same mass anywhere; only its weight would change.
2 marks: “Your mass is 50 kg. Will it change if you go to the moon? Will your weight change? Explain.” Mass stays 50 kg, because it is the amount of matter. Weight = mg changes, because g on the moon is about one sixth of the earth's. It falls from 490 N to about 82 N.
2 marks: “Why does a person in a freely falling lift feel weightless?” The person and the lift fall with the same acceleration g. The person does not press on the floor, so the floor gives no reaction, and the weight felt is zero.
3 marks: “The value of g on a planet is 3.7 m s⁻². A box weighs 196 N on the earth (g = 9.8 m s⁻²). Find its mass and its weight on the planet.” Mass m = W/g = 196 ÷ 9.8 = 20 kg. Weight on the planet = 20 × 3.7 = 74 N. The mass stays 20 kg there.
Mass is matter and stays; weight is a pull and sways with g.