Gravity mass, weight and gravitational field strengths

SPEC 4.5.1.3 • FORCES — GRAVITY, MASS & WEIGHT

Gravity, Mass & Weight

The most-reliably-examined topic in Module 5. Get the W = m g equation, the units, and the centre-of-mass definition exact — three easy marks every series.

Quick Recap — From 5.01

You already know the key distinction. This lesson builds on it.

Mass

Scalar · measured in kg · the amount of matter

Weight

Vector · measured in N · a force due to gravity

This lesson answers the questions: where does weight come from, how do we calculate it, and where on an object does it act?

Mass and Weight — Tight Definitions

Mass

The amount of matter in an object. Measured in kilograms (kg). Constant wherever the object is taken.

Weight

The force acting on an object due to gravity. Measured in newtons (N). Changes with location because gravitational field strength changes.

Exam Tip

If a question gives a value in kilograms, it's a mass. If it gives a value in newtons, it's a weight. Units are the giveaway — and the most-tested part of this topic.

Where Weight Comes From

Weight isn't a separate "thing" inside an object — it's caused by the gravitational field around the Earth. Any object placed in that field experiences a pulling force toward the Earth's centre. That force is what we call weight.

Spec wording

"The force of gravity close to the Earth is due to the gravitational field around the Earth." The strength of that field at a point determines how much weight an object will have there.

The Equation You Must Recall

W = m × g

W (weight, N) = m (mass, kg) × g (gravitational field strength, N/kg)

Gravitational field strength (g)

The force per unit mass at a point in a gravitational field, in newtons per kilogram (N/kg). The bigger g is, the more weight any object has at that location.

Locationg (N/kg)Note

Earth's surface9.8The standard value AQA uses

Moon's surface1.6About 1/6 of Earth's value

Mars' surface3.7About 3/8 of Earth's value

Don't memorise g

The spec guarantees: "In any calculation the value of the gravitational field strength (g) will be given." Always read the question to find the value to use — don't assume 9.8.

ESUA — The Calculation Framework

For every numerical question in Physics, lay out your working with ESUA. The mark scheme awards each step separately, so showing work earns partial marks even if you slip on the final answer.

EEquationWrite it in full from memory.

SSubstitutePut numbers in (after converting units).

UUnitState the unit of the answer.

AAnswerFinal value, sensible sig figs.

The mark-scheme reality

A 3-mark calculation usually marks: 1 mark for equation, 1 mark for correct substitution (units converted!), 1 mark for correct answer with unit. Skip any step and you cap your marks.

Worked Example — Weight on Earth

Calculate the weight of a 60 kg person on Earth.

Take g = 9.8 N/kg. 2 marks

E

Equation: W = m × g

S

Substitute: W = 60 × 9.8

U

Unit: newtons (N)

A

Answer: W = 588 N ≈ 590 N (2 sig fig)

Sig figs

Where the question doesn't specify, round to 2 or 3 significant figures — match the precision of the values you were given. Here g was given to 2 sig fig, so 590 N is the cleanest answer.

Same Person, Different Worlds

The classic exam framing. The same 60 kg person travels to the Moon and Mars. Mass stays constant — the amount of matter doesn't change. But weight changes because g changes.

LocationMass (kg)g (N/kg)Weight = m × g (N)

Earth609.860 × 9.8 = 588 N

Moon601.660 × 1.6 = 96 N

Mars603.760 × 3.7 = 222 N

The exam-ready sentence

"Mass is constant wherever the object is taken, because the amount of matter doesn't change. Weight depends on g, so weight is smaller on the Moon (g is smaller) than on Earth, even though the mass is the same."

Weight is Proportional to Mass

At a fixed location (so g is constant), doubling the mass doubles the weight. The spec uses the symbol ∝ to mean "is proportional to":

W ∝ m

(at constant g)

∝ symbol

The spec explicitly says you should "recognise and be able to use the symbol for proportionality, ∝". Two quantities are proportional when their graph is a straight line through the origin.

Centre of Mass

Weight acts on every part of an object — but for calculations and free-body diagrams, we say it all acts at one single point. That point is the centre of mass.

Centre of Mass

The point at which the weight of an object can be considered to act.

Mark-scheme accepts any of these 4 forms

The point from which the weight may be considered to act

The point where the mass appears to be concentrated

The point through which the line of action of the weight acts

The point at which the mass is concentrated

Pick whichever you find easiest to remember. The key idea: a single point, not a vague region.

Why this matters — direction and line of action

When you draw a weight arrow on a free-body diagram, the tail starts at the centre of mass, and the arrow points vertically downward (toward the Earth's centre). The vertical line drawn from the centre of mass through the arrow is called the line of action of the weight — a term that comes up again in the moments lesson (5.05).

How Weight is Measured

Weight is a force, so it's measured with a force-measuring device: a calibrated spring-balance, also called a newton-meter. The scale reads directly in newtons.

Kitchen scales vs newton-meter

Everyday "weighing scales" (bathroom, kitchen) typically show mass in kg or g — not weight. They're calibrated for Earth's g but they're measuring mass. A newton-meter measures weight directly, in N.

Examiner Alert — Wrong Unit on Weight

The single biggest error on this topic

Students reliably write things like "weight = 60 kg" or treat the kilogram reading on a scale as a weight. Weight is a force — its unit is always the newton (N). If the answer line ends in "kg", you've given a mass, not a weight, and the mark is lost regardless of working.

Check before you write the final line: the unit of the answer must match what the question asked for. "Calculate the weight" → answer in N. "Calculate the mass" → answer in kg. Never confuse them.

The unit-conversion trap

If the question gives mass in grams (or you read it off a kitchen scale in g), you must convert to kilograms before substituting into W = mg. Real exams report ~80% of students losing a mark from skipping this step. Rule: ÷ 1000 to go from g to kg.

Examiner Alert — Centre of Mass

Only 1 in 4 students score this 1-marker

On a real exam, when asked "what is meant by centre of mass?", only ~25% of students got the mark. The reason is subtle: students know roughly what it means, but write it in a way that's not specific enough.

✓ Accepted by mark scheme

"…where the weight may be considered to act"

"…where the mass appears to be concentrated"

"…through which the line of action of weight acts"

"…where the mass is concentrated"

✗ Rejected by mark scheme

"the centre of an object" — not all objects are symmetrical

"where most of the mass is" — vague, doesn't specify a point

The exam-winning pattern

Every accepted form starts with "the point…" — emphasising it's a single, specific point. Rejected forms refer to a region ("the centre", "where most mass is") rather than a point. Lead with "the point at which…" and you've half-secured the mark.

Practice Question

A bag of apples is placed on a kitchen balance. The balance reads 450 g.

Calculate the weight of the apples. Use gravitational field strength g = 9.8 N/kg. 3 marks

CONV

Convert mass to kg: 450 g ÷ 1000 = 0.45 kg(the trap step — most marks lost here)

E

Equation: W = m × g

S

Substitute: W = 0.45 × 9.8

U

Unit: newtons (N)

A

Answer: W = 4.41 N (or 4.4 N to 2 sig fig)

Watch out — real exams chain extra steps

Real Paper 2 questions often add a step before W = mg. Common framings: "Calculate the mean weight of one tomato" (read balance → convert → divide by N items → apply W = mg) or "Find the weight on the Moon" (read mass → apply W = mg with different g). Read carefully — the calculation might be 4 steps, not 3.

Weak vs Strong Answers

Same question, two student responses. Mark-scheme language matters as much as the maths.

Q: Calculate the weight of a 250 g block on Earth. g = 9.8 N/kg. (3 marks)

✗ Weak

"W = m × g = 250 × 9.8 = 2450"

No unit conversion (250 g treated as kg). No unit on answer. Two marks lost — only the equation mark scores.

✓ Strong

"Mass = 250 g = 0.25 kg

W = m × g = 0.25 × 9.8 = 2.45 N"

Conversion shown. Equation, substitution, answer, and unit all present. Full 3 marks.

The pattern that always wins

Check the units. Convert before substituting. Show the equation. Put the unit on the final answer. Four small habits that secure marks across every calculation in Module 5.

Summary & Checkpoint

The definitions

Mass: the amount of matter in an object · scalar · kg · constant

Weight: the force on an object due to gravity · vector · N · varies with g

g (gravitational field strength): force per unit mass at a point in a gravitational field · N/kg

Centre of mass: the point at which the weight of an object can be considered to act

The equation

W = m × g

W (N) · m (kg) · g (N/kg) — and W ∝ m at constant g

The exam-winning habits

Check units of the answer match what was asked (force → N, not kg)

Convert g → kg before substituting into W = mg

Show E·S·U·A separately so partial marks score

Memorise the centre of mass definition verbatim

Weight acts at the centre of mass, pointing downward