Forces and motion · GCSE Physics
Weight and mass
Teacher-written GCSE Physics revision on weight and mass: mass in kilograms, weight W = mg in newtons, gravitational field strength, centre of mass, and why weight changes on the Moon but mass does not.
Mass is the amount of matter, in kilograms. Weight is the gravitational force on that mass, W = mg, in newtons. Mass does not change on the Moon; weight does.
The important bits
What you need to know
- 1
Mass m is a scalar measured in kilograms (kg). It is the quantity of matter and also a measure of inertia: how hard it is to change the object’s motion.
- 2
Weight W is a force, a vector, measured in newtons (N). It is the pull of a gravitational field on a mass.
- 3
W = mg, where g is gravitational field strength in N/kg. On Earth g is about 9.8 N/kg (papers may tell you to use 10 N/kg).
- 4
g is also the acceleration of free fall in m/s². 9.8 N/kg is the same size as 9.8 m/s² because 1 N = 1 kg m/s².
- 5
Weight acts at the centre of mass, towards the Earth (or the planet you are on). On a diagram that is a downward arrow from the centre of the object.
- 6
Mass is the same everywhere. Weight changes if g changes: on the Moon g ≈ 1.6 N/kg, so you weigh less but your mass, and your inertia, stay the same.
- 7
A newton meter (spring balance) measures weight. A balance that compares masses can be calibrated to show kilograms, which is mass.
- 8
“Weightless” in orbit means the astronaut and the spacecraft are in free-fall together, not that g is zero. There is still gravity; it provides the centripetal force.
Quotations worth analysing
Short evidence. Real method.
“Weight = mass × gravitational field strength”
Mass in kilograms, g in N/kg, weight in newtons. Using grams, or calling the answer “kg”, is the standard unit fault.
“Mass is a scalar; weight is a vector.”
Weight has a direction: towards the centre of the planet. Mass has size only. That is why they cannot be the same quantity.
Go deeper
g is both a field strength and a free-fall acceleration
Gravitational field strength is the force per kilogram: 9.8 N on every 1 kg at Earth’s surface. Drop that kilogram and the resultant force (if drag is tiny) is 9.8 N, so a = F/m = 9.8 m/s². The same number wears two units. On a planet where g = 4.0 N/kg, a 2.0 kg rock weighs 8.0 N and falls at 4.0 m/s² if air is ignored. Students treat g as “gravity” without a number, then cannot substitute. Write g = 9.8 N/kg in the data line. If the paper says use g = 10 N/kg, do that: the mark scheme will. Weight on a slope still acts vertically down, not down the slope; the component down the slope is what may cause acceleration. Keep the arrow vertical on the free-body diagram.
Go deeper
The Moon is the cleanest mass-versus-weight question
Your mass on the Moon is unchanged: same number of kilograms, same inertia, same resistance to F = ma. A 10 N push still gives the same acceleration. Your weight is about one-sixth because the Moon’s g is about 1.6 N/kg. A newton meter would read less; a properly used mass balance comparing you with kilogram masses would still agree. In orbit, people say “zero gravity” as slang. GCSE Physics wants: gravity is a little weaker up there, but the main point is free-fall. The satellite is accelerating towards Earth even if its speed is constant, because direction keeps changing. Mass still appears in F = ma and in p = mv. Do not put weight into those formulae unless you have converted with W = mg first.
See the idea in action
An astronaut has mass 80 kg. On Earth, g = 9.8 N/kg, so weight W = mg = 80 × 9.8 = 784 N. On the Moon, g = 1.6 N/kg, so W = 80 × 1.6 = 128 N. Mass is still 80 kg. A 40 N resultant force on the Moon gives a = F/m = 40 / 80 = 0.50 m/s², the same acceleration as on Earth for that resultant, because inertia has not changed. Using 784 N as if it were mass in F = ma would be a catastrophic unit error.
Exam technique
Turn knowledge into marks
State mass in kg and weight in N. Write W = mg with the value of g from the paper. On other planets, change g, not m. On diagrams, draw weight from the centre of mass, vertically down.
Common mistakes
Do not give these marks away
- 01
Using mass in grams in W = mg, or quoting weight in kilograms.
- 02
Saying mass is less on the Moon, or that there is no gravity in space.
- 03
Putting weight into F = ma without converting, or drawing weight down a slope instead of vertically.
A 5.0 kg package is taken to a planet where g = 4.0 N/kg. What is its mass and its weight there?
AMass 5.0 kg, weight 20 N
BMass 20 kg, weight 5.0 N
CMass 1.25 kg, weight 5.0 N
DMass 5.0 kg, weight 49 N
Show the answer
Mass 5.0 kg, weight 20 N. Mass does not change. W = mg = 5.0 × 4.0 = 20 N. 49 N would be using Earth’s 9.8 N/kg by mistake.
Quick questions
If this is the bit you searched
What is the difference between mass and weight?
Mass is the amount of matter in kilograms. Weight is the gravitational force on that mass, W = mg, in newtons.
What are the units of g?
Newtons per kilogram (N/kg) as gravitational field strength, or metres per second squared (m/s²) as acceleration of free fall. The number is the same.
Does a balance measure mass or weight?
A spring newton meter measures weight. A comparison balance can be marked in kilograms (mass). In everyday speech people say “weight in kilos”; in Physics you must separate them.
Why do astronauts float?
They are in continuous free-fall around the Earth with their spacecraft. Gravity is still acting; they and the cabin accelerate together, so they feel weightless.