Overview
What you’ll learn
- Identify and distinguish contact forces (friction, air resistance, tension, normal force) from non-contact forces (gravitational, electrostatic, magnetic).
- State that mass is a measure of the amount of matter in a body and distinguish mass from weight.
- Describe a gravitational field and define gravitational field strength as the gravitational force per unit mass.
- Apply weight = mass × gravitational field strength to solve problems.
- Apply density = mass / volume to solve problems.
- Define pressure in terms of force and area and apply pressure = force / area to solve problems.
Key points
- 1Contact forces need touching: friction, air resistance, tension, normal force. Non-contact act at a distance: gravitational, electrostatic, magnetic.
- 2Mass (kg) = amount of matter — scalar, same everywhere. Weight (N) = the gravitational force on it — vector, changes with the field.
- 3Gravitational field strength g = gravitational force per unit mass, about 10 N/kg near Earth.
- 4W = mg: a 2.0 kg mass weighs 2.0 × 10 = 20 N near Earth.
- 5Density ρ = mass ÷ volume, in kg/m³ (or g/cm³); <1000 kg/m³ floats in water.
- 6Pressure = force ÷ area, in pascals (Pa) — 1 Pa = 1 N/m²; smaller area → bigger pressure for the same force.
Notes · 1 of 5
Contact and non-contact forces
A force is a push or pull — with or without touching.
A force is a push or a pull, measured in newtons (N). Contact forces act only when objects touch: friction between sliding surfaces, air resistance pushing against moving objects, tension in a stretched rope or cable, and the normal force a surface pushes back with. Non-contact forces reach across empty space: gravitational attraction, electrostatic forces between charges, and magnetic forces between magnets or magnetic materials.
| Contact (touching) | Non-contact (at a distance) |
|---|---|
| friction between surfaces | gravity pulling a dropped ball |
| air resistance on a cyclist | electrostatic attraction of a rubbed balloon to hair |
| tension in a tow rope | magnets attracting iron pins |
| normal force from the floor | Earth holding the Moon in orbit |
Spotting the family is a one-mark skill: ask do the objects need to touch? A book resting on a table feels the table's normal force (contact) and the Earth's gravity (non-contact) at the same time — most everyday situations mix both.
Notes · 2 of 5
Mass, weight and gravitational field
Same body everywhere; different weight where the field is weaker.
Mass is a measure of the amount of matter in a body, in kilograms: a scalar that never changes with location. Weight is the gravitational force acting on that mass, in newtons: a vector, always pointing towards the Earth's centre (downwards). The Earth is surrounded by a gravitational field — a region where masses feel that force — and its strength is defined as the gravitational force per unit mass: about 10 N/kg near the Earth's surface.
That definition gives the working equation: W = mg. A 2.0 kg bag of sugar weighs 2.0 × 10 = 20 N on Earth; on the Moon, where g is about 1.6 N/kg, the same 2.0 kg weighs only about 3.2 N. Astronauts on the Moon are not massless — their mass is unchanged — the field is weaker, so the force is smaller.
Notes · 3 of 5
Density
How tightly mass is packed: ρ = m ÷ V.
Density measures how much mass is squeezed into each unit of volume: density = mass ÷ volume, symbol ρ. In SI it comes out in kg/m³; lab work often uses g/cm³, and 1000 kg/m³ = 1 g/cm³. Water is 1000 kg/m³ (1.0 g/cm³): objects less dense than water float in it; denser objects sink. A block of wood (≈600 kg/m³) floats; the same-sized block of lead (≈11 000 kg/m³) sinks.
Notes · 4 of 5
Pressure
Force spread over area: p = F ÷ A.
Pressure is the force acting per unit area: pressure = force ÷ area, measured in pascals (Pa), where 1 Pa = 1 N/m². The same force makes a bigger pressure on a smaller area: a drawing pin's tiny point concentrates your thumb's push into a huge pressure — enough to pierce the board — while the broad head keeps the pressure on your thumb small. Snowshoes and wide tractor tyres increase the area to reduce pressure and stop sinking.
Notes · 5 of 5
Rearranging the three equations
One triangle of habits for W = mg, ρ = m/V, p = F/A.
| Equation | Find the first quantity | Find a second quantity |
|---|---|---|
| W = mg | weight from mass | mass = W ÷ g |
| ρ = m ÷ V | density from mass and volume | mass = ρ × V; volume = m ÷ ρ |
| p = F ÷ A | pressure from force and area | force = p × A; area = F ÷ p |
Revise
Key terms
The words examiners expect you to use precisely.
- force
- A push or a pull, measured in newtons (N).Contact forces need touching; non-contact forces act across space.
- normal force
- The perpendicular push a surface exerts on an object resting on it.A contact force: the table pushing up on the book.
- tension
- The pulling force transmitted through a stretched rope, cable or string.A contact force carried along the rope.
- mass
- A measure of the amount of matter in a body, in kilograms — a scalar.Unchanged by location: 70 kg on Earth or the Moon.
- weight
- The gravitational force on a body, W = mg, in newtons — a vector pointing downwards.Changes when the gravitational field changes.
- gravitational field strength
- The gravitational force per unit mass, about 10 N/kg near the Earth.Numerically the free-fall acceleration: 10 N/kg = 10 m/s².
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- density
- Mass per unit volume, ρ = m ÷ V, in kg/m³ or g/cm³.Less dense than water → floats; denser → sinks.
- pressure
- Force per unit area, p = F ÷ A, in pascals (1 Pa = 1 N/m²).Small area concentrates a force into high pressure.
Revise
Common mistakes
Where students most often lose marks in this chapter — and what to do instead.
Mistake: Using mass in kg directly in p = F/A.
Pressure needs a force, not a mass.
Instead: Convert first: F = mg (×10 N/kg), then p = F ÷ A.
Mistake: Saying weight is measured in kilograms.
Kilograms measure mass; weight is a force.
Instead: Weight is in newtons (N); mass in kg.
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Mistake: Claiming an astronaut on the Moon is massless.
Weaker gravity shrinks weight, never mass.
Instead: Mass is unchanged; weight = mg drops because g is smaller.
Mistake: Treating friction as a non-contact force.
Friction needs surfaces touching and sliding (or trying to).
Instead: Friction is contact; gravity, magnetism and electrostatic force are non-contact.
Mistake: Forgetting 1 cm² = 10⁻⁴ m².
Squaring the cm→m factor is missed.
Instead: 1 m² = 10 000 cm², so 1 cm² = 0.0001 m².
Mistake: Dividing force by the area of one foot when the person stands on two.
The force spreads over both soles.
Instead: Use the total contact area supporting the weight.
Mistake: Mixing g/cm³ and kg/m³ mid-calculation.
A factor of 1000 hides between the two units.
Instead: 1 g/cm³ = 1000 kg/m³ — convert once, clearly.
Mistake: Expecting the heavier object always to have the higher density.
Density is mass per volume — size matters too.
Instead: Compare mass-to-volume ratios: a big polystyrene block can out-mass a coin yet still float.
Mistake: Quoting pressure in newtons.
Newtons measure force; pressure is force per area.
Instead: Pressure units are pascals — N/m².
Mistake: Thinking a larger area increases pressure.
Area is the divisor.
Instead: Same force spread over more area gives less pressure — that is why snowshoes work.
Mistake: Naming air resistance as a non-contact force.
Air molecules physically strike the moving object.
Instead: Air resistance is contact — the object collides with air particles.
Mistake: Using W = mg with g = 10 m/s² and calling the answer a mass.
The number comes out in newtons — it is a weight.
Instead: Track units: kg × N/kg = N, a force.
Check yourself
Quick quiz
20 questions with instant explanations. About 5 minutes.
Question 1 of 3
- Question 1: current question
- Question 2: not answered
- Question 3: not answered
Identify and distinguish contact forces (friction, air resistance, tension, normal force) from non-contact forces (gravitational, electrostatic, magnetic).
Which list contains only contact forces?
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Practise
Topical questions
Exam-style practice in three tiers, from recall to data questions.
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12 questions worth 61 marks, each with a model answer, mark scheme and examiner tips.
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Question paper
Chapter 3 Practice Paper
30 marks · 40 min · 4 pages
5 multiple-choice questions and structured questions with answer lines. Chapter 3 (contact and non-contact forces, mass vs weight with W = mg, density = m/V, pressure = F/A).
Mark scheme
PROChapter 3 Practice Paper — mark scheme
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Model answers with a mark for each creditworthy point — for marking at home or in class.
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Questions
Frequently asked questions
Why does weight change but mass never does?
Mass counts the matter in you — the same atoms everywhere. Weight is the gravitational force on those atoms, so it shrinks wherever the field (g) is weaker, like the Moon.
How do I remember which equation is which?
W = mg links the two "amount" ideas (kg ↔ N). ρ = m ÷ V packs mass into volume. p = F ÷ A spreads force over area. Units give them away if you forget.
What decides floating — weight or density?
Density. Compare the object's density with the fluid's (water = 1.0 g/cm³): less dense floats, denser sinks. A huge ship floats; a tiny coin sinks.
Why do drawing pins and knives work?
Pressure = force ÷ area. Concentrating a modest force onto a tiny area creates a huge pressure — enough to pierce wood or slice food.