Course: Combined Science + Separate Physics | Tier: Foundation + Higher | Equation sheet: W = m g is given in the exam
📌 KEY DEFINITIONS – learn them word for word
Mass is the amount of matter in an object. Unit: kilogram (kg). Mass is the same everywhere.
Weight is the force acting on an object due to gravity. Unit: newton (N). Weight changes if the gravitational field strength changes.
Mass and weight side by side
| Mass | Weight | |
|---|---|---|
| What is it? | The amount of matter in an object | The force on an object due to gravity |
| Unit | kilograms (kg) | newtons (N) |
| Scalar or vector? | Scalar (size only) | Vector (size and direction – always down, towards the centre of the planet) |
| Changes on the Moon? | No – stays the same | Yes – smaller, because g is smaller |
| Measured with | A balance (e.g. top-pan balance) | A newtonmeter (calibrated spring balance) |
The equation
weight = mass × gravitational field strength W = m g
Rearranged: m = W ÷ g | g = W ÷ m | On Earth, g = 9.8 N/kg
Weight is directly proportional to mass: double the mass and the weight doubles (as long as g stays the same).
Use FIFA for every calculation: Formula, Insert, Fix (rearrange), Answer with a unit.
Foundation: aim for Q1–13. Higher: aim for Q7–17.
Part 1: Know the difference
Q1 (F) Which one is a force: mass or weight?
Show answer
Weight. Weight is the force on an object due to gravity. Mass is the amount of matter, not a force.
Q2 (F) Give the unit for: (a) mass (b) weight (c) gravitational field strength.
Show answer
(a) kilograms (kg)
(b) newtons (N)
(c) newtons per kilogram (N/kg)
Q3 (F) Name the piece of equipment used to measure: (a) mass (b) weight.
Show answer
(a) A balance (e.g. a top-pan balance)
(b) A newtonmeter (a calibrated spring balance)
Q4 (F) True or false?
(a) An astronaut’s mass is smaller on the Moon than on Earth.
(b) An astronaut’s weight is smaller on the Moon than on Earth.
(c) Weight is a vector quantity.
(d) In deep space, far from any planet, an object has zero mass.
Show answer
(a) False – mass is the same everywhere.
(b) True – g on the Moon is smaller, so weight is smaller.
(c) True – weight has a size and a direction (downwards).
(d) False – it has (almost) zero weight, but its mass does not change.
Part 2: Rearranging practice
Q5 (F) Rearrange W = m g to make m the subject.
Show answer
W = m × g
m is being multiplied by g, so divide both sides by g:
m = W ÷ g
Q6 (F) Rearrange W = m g to make g the subject.
Show answer
W = m × g
g is being multiplied by m, so divide both sides by m:
g = W ÷ m
Part 3: Calculations
Use g = 9.8 N/kg on Earth unless the question says otherwise.
Q7 (F) A student has a mass of 60 kg. Calculate the student’s weight on Earth.
Show solution
F: W = m g
I: W = 60 × 9.8
F: W is already the subject
A: 588 N
Q8 (F) A cat has a mass of 4.5 kg. Calculate its weight on Earth.
Show solution
F: W = m g
I: W = 4.5 × 9.8
F: W is already the subject
A: 44.1 N
Q9 (F) A box of books has a weight of 98 N on Earth. Calculate its mass.
Show solution
F: W = m g
I: 98 = m × 9.8
F: m = 98 ÷ 9.8
A: 10 kg
Q10 (F) An apple has a mass of 200 g. Calculate its weight on Earth.
Show solution
Convert first: 200 g = 200 ÷ 1000 = 0.2 kg
F: W = m g
I: W = 0.2 × 9.8
A: 1.96 N
Q11 (F) An astronaut has a mass of 75 kg. On the Moon, g = 1.6 N/kg.
(a) What is the astronaut’s mass on the Moon?
(b) Calculate the astronaut’s weight on the Moon.
Show solution
(a) 75 kg – mass does not change.
(b) F: W = m g
I: W = 75 × 1.6
A: 120 N
Q12 (F/H) A 2 kg mass is hung from a newtonmeter on Jupiter. The newtonmeter reads 49.6 N. Calculate the gravitational field strength on Jupiter.
Show solution
F: W = m g
I: 49.6 = 2 × g
F: g = 49.6 ÷ 2
A: 24.8 N/kg
Q13 (F/H) A lorry has a weight of 147 kN on Earth. Calculate its mass.
Show solution
Convert first: 147 kN = 147 000 N
F: W = m g
I: 147 000 = m × 9.8
F: m = 147 000 ÷ 9.8
A: 15 000 kg
Q14 (H) An astronaut weighs 833 N on Earth. Calculate the astronaut’s weight on the Moon, where g = 1.6 N/kg.
Show solution
Step 1 – find the mass (the same on Earth and the Moon)
F: W = m g
I: 833 = m × 9.8
F: m = 833 ÷ 9.8 = 85 kg
Step 2 – weight on the Moon
I: W = 85 × 1.6
A: 136 N
Watch out: you cannot use 833 as the mass – it is a weight in newtons.
Q15 (H) A 5 kg rock is taken from Earth to Mars, where g = 3.7 N/kg. Calculate how much its weight decreases by.
Show solution
Weight on Earth: W = 5 × 9.8 = 49 N
Weight on Mars: W = 5 × 3.7 = 18.5 N
Decrease: 49 − 18.5 = 30.5 N
The mass is still 5 kg on Mars.
Q16 (H) A lift can safely carry a maximum weight of 7.35 kN. The average mass of a person is 70 kg. What is the greatest number of people the lift can safely carry?
Show solution
Convert first: 7.35 kN = 7350 N
F: W = m g
I: 7350 = m × 9.8
F: m = 7350 ÷ 9.8 = 750 kg
A: 750 ÷ 70 = 10.7… → 10 people
Round down – 11 people would be over the safe limit.
Part 4: Explain it
Q17 (H) [3 marks] A student says: “When I go to the Moon I will weigh less, so my mass will be less too.” Explain why the student is only partly correct.
Show answer
Any three of:
• The student is right that their weight will be less.
• This is because the gravitational field strength on the Moon is smaller than on Earth (1.6 N/kg compared to 9.8 N/kg).
• Mass is the amount of matter in the student, which does not change.
• So their mass stays the same – only their weight changes.
Want more practice? Try the 10 W = mg calculation questions, or go back to Forces.