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Mass and weight
Everyday English uses mass and weight interchangeably, and physics never does. One is an amount of matter that goes everywhere with you; the other is a force that depends on where you are standing.
Builds on Newton's laws and the resultant force.
IN THIS TOPIC
- Distinguish mass, a scalar measured in kilograms, from weight, a force measured in newtons.
- Use W = mg, with g as the gravitational field strength of the location.
- Explain what a balance and a newton meter each measure, and how their readings change off Earth.
WHAT YOU PROBABLY THINK
Mass and weight are two words for the same thing.
Two different quantities
Mass is the amount of matter in an object: a scalar, measured in kilograms, the same wherever the object goes. It is also the measure of an object's inertia, its resistance to acceleration, which is the m in F = ma.
Weight is a force: the gravitational pull on that mass, a vector pointing toward the centre of the planet, measured in newtons. The two are related by
where g is the gravitational field strength of wherever you happen to be, about 9.81 N kg−1 at the Earth's surface. Written that way, the units make the meaning plain: g is the newtons of pull per kilogram of mass, and it belongs to the location, not to the object.
Take a 70 kg astronaut to the Moon, where g is 1.62 N kg−1, and the mass is still 70 kg while the weight falls from about 687 N to about 113 N. Nothing about the astronaut changed. The location did.
Why Earth blurs the two
On Earth the conflation is almost harmless, because g is nearly the same everywhere on the surface: weight is always the same multiple of mass, so a single number seems to do both jobs, and bathroom scales exploit exactly that. The distinction only bites when g changes, which is precisely what exam questions arrange.
The two instruments split cleanly along the same line. A balance compares one mass against standard masses; gravity pulls on both sides equally, cancels out, and the balance reads the same on the Moon. A newton meter measures the gravitational force directly through a stretched spring, so on the Moon it reads a sixth of its Earth value. Which instrument “lies” depends entirely on which quantity you wanted.
THE EXAM BIT
- State the units with the definitions: mass in kilograms, weight in newtons. An answer giving a weight in kg has answered a different question.
- Mass is a scalar; weight is a vector, directed toward the planet's centre. The scalar/vector classification of this pair is a routine opener.
- g doubles as the gravitational field strength, and its units N kg−1 are identical to m s−2. Use whichever form the question speaks in.
- “The same object is taken to planet X” means: mass unchanged, weight rescaled by the new g. Both halves of that sentence carry marks.
- In free fall the object still has weight; what vanishes is the support force. “Weightless” in orbit is the absence of the normal contact force, not of gravity.
CHECK YOURSELF
An astronaut has a mass of 70 kg. On the Moon, g = 1.62 N kg−1. What are the astronaut's mass and weight on the Moon?
Show a hint
One of the two quantities never changes.
Show the answer
Mass: 70 kg, exactly as on Earth. Mass is the amount of matter and travels with the astronaut.
Weight: W = mg = 70 × 1.62 = 113 N, about a sixth of the 687 N weight on Earth, because the Moon's field strength is about a sixth of the Earth's.
Mass travels with you.
Weight belongs to where you are.
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