Physics › Mechanics › Mass and weight
Mass and weight
Everyday English uses mass and weight interchangeably, and physics never does. One is a measure of inertia that goes everywhere with you; the other is a force that depends on where you are standing.
Pick your board and the few notes written for the other boards quietly fold away, here and in the practice players. Nothing is deleted: every folded piece reopens on a tap.
Builds on Newton's laws and the resultant force.
IN THIS TOPIC
- Separate mass, a scalar in kilograms, from weight, a force in newtons.
- Use W = mg with g as the field strength of wherever you are standing, and say what a balance and a newton meter each really measure.
COMMON MISCONCEPTION
Mass and weight are two words for the same thing.
Two different quantities
Mass is a scalar measure of an object's inertia, its resistance to acceleration: the m in F = ma, measured in kilograms, the same wherever the object goes. The everyday picture of mass as an amount of matter is a fair first idea, but inertia is the definition that earns the mark.
Weight is a force: the gravitational pull on that mass, a vector pointing towards 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 in those units the meaning is plain. g counts the newtons of pull per kilogram of mass, and it belongs to the location. The object has no say in it. Note that the AQA and OCR A booklets print g among the constants without printing W = mg, so on those boards it is yours to remember; Edexcel's formulae sheet does print it.
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. g barely varies across the surface, so weight is always the same multiple of mass and one number appears to do both jobs. Bathroom scales are built on exactly that convenience. The distinction only bites once g changes, which is precisely the situation exam questions arrange.
The two instruments split along that same fault line. A beam balance compares one mass against standard masses, and since gravity pulls equally on both sides it cancels out, so it reads identically on the Moon. An electronic balance actually senses the force on its pan and is calibrated to report the mass that force implies, so it needs recalibrating anywhere g differs. 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 one “lies” depends entirely on which quantity you wanted.
INDEPENDENT PRACTICE
Weighed on another world
A 180 kg probe weighs 668 N on the surface of another planet. Find the gravitational field strength there, and state what has and has not changed since the probe left Earth.
Show the working
g = W/m = 668/180 = 3.7 N kg−1, which happens to be Mars.
The mass never moved. 180 kg there, 180 kg here, 180 kg anywhere at all. Only the weight changed, because weight is the field's grip on an unchanging mass.
ASSESSMENT FOCUS
- State the units with the definitions. Mass in kilograms, weight in newtons. A weight quoted in kg has answered a different question, and it is a routine opener worth two easy marks.
- “The same object is taken to planet X” means mass unchanged and weight rescaled by the new g. Both halves of that sentence carry marks. Note that g doubles as the gravitational field strength, and N kg−1 is the identical unit to m s−2, so answer in whichever form the question uses.
- In free fall the object still has weight. What vanishes is the support force, so “weightless” in orbit means no normal contact force, not no 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
The mass is 70 kg, exactly as on Earth. Mass measures inertia, and it travels with the astronaut.
The weight is = 70 × 1.62 = 113 N, about a sixth of the 687 N it was on Earth, because the Moon's field strength is about a sixth of ours.
Mass travels with you; weight belongs to where you are.
WORKBOOK
Printable practice for this topic: original exam-style questions with room to work, and a fully worked answer book. Free to use; please do not redistribute or sell.
Or read them with their mark schemes on the mass and weight questions page.
WHERE TO GO NEXT
- Required practical 3: measuring g by free fall puts this topic in the lab, and the written papers ask about it.
CHECK YOUR PROGRESS
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- Separate mass, a scalar in kilograms, from weight, a force in newtons.
- Use W = mg with g as the field strength of wherever you are standing, and say what a balance and a newton meter each really measure.
Open the full revision checklist to track your progress across the whole unit.