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AQA GCSE Physics (8463) · Topic 4.5 — Forces
Mini-Lesson

Forces

Forces is the biggest topic on the course. This mini-lesson walks you through the whole of AQA Topic 4.5 — Forces: scalars and vectors, contact and non-contact forces, work done, elasticity, moments, pressure, motion and momentum.

object 30 N 50 N resultant = 50 − 30 = 20 N to the right → it accelerates

Work through each screen, answer the questions as you go (some are wordy, some are calculations) and collect ⭐ stars. Press Start when you're ready.

Forces & interactions

Scalars and vectors

A scalar has size only (mass, distance, speed, energy). A vector has size and direction (force, weight, velocity, displacement, acceleration, momentum).

A force is a push or a pull on an object that results from its interaction with another object. Because it has a direction, a force is always a vector — we draw it as an arrow whose length shows the size.

Tip: if a quantity needs the word "north", "up", "to the right" to make sense, it's a vector. If just a number-and-unit is enough, it's a scalar.

Sort it

Scalar or vector?

Tap whether each quantity is a scalar (size only) or a vector (size + direction).

Contact & non-contact

Two families of force

Some forces only act when objects touch; others act at a distance through a field:

  • Contact forces — the objects are touching: friction, air resistance, tension, normal contact.
  • Non-contact forces — act through a field with no touching: gravitational, magnetic, electrostatic.
contact: a push 🌍 non-contact: gravity
Sort it

Contact or non-contact?

Tap a force, then tap the box it belongs in.

🤝 Contact

🌌 Non-contact

Equation 1

Weight

Weight is the force of gravity on an object. It depends on the object's mass and the gravitational field strength, g:

W = m gweight (N) = mass (kg) × gravitational field strength (N/kg)

On Earth g ≈ 9.8 N/kg. Weight is a vector that always acts straight down, as though all the object's mass were concentrated at one point — its centre of mass.

Don't confuse mass with weight. Mass (kg) is the amount of matter in an object and never changes. Weight (N) is the force of gravity on that mass, so it changes with location: an astronaut's mass is the same on the Moon, but their weight is about 1/6 of its Earth value because the Moon's g is smaller.

Worked example

A 5 kg bag of flour (g = 9.8 N/kg).

W = 5 × 9.8 = 49 N

Calculate

Your turn — weight

1A school bag has a mass of 7 kg. Using g = 9.8 N/kg, calculate its weight.
N
Hint: W = 7 × 9.8.
Resultant force

Free-body diagrams & the resultant

Usually several forces act on an object at once. A free-body diagram shows the object on its own with every force drawn as an arrow from it — the longer the arrow, the bigger the force. The single force with the same effect as all of them together is the resultant force.

box normal contact 200 N weight 200 N friction 30 N driving force 100 N
Up and down balance (200 N each, so no vertical motion). Horizontally 100 − 30 = a resultant of 70 N to the right — note the driving-force arrow is drawn far longer than the friction arrow.

Higher tier: a single force can be resolved into two forces (components) acting at right angles — and forces that act at an angle can be added tip-to-tail using a scale drawing to find the resultant.

Quick check

Reading the diagram

?A trolley is pushed forwards with 60 N while friction pushes back with 25 N. What is the resultant force?
Equation 2 · work & energy

Work done

When a force moves an object along the line of the force, it does work — transferring energy:

W = F swork done (J) = force (N) × distance moved along the line of the force (m)

One joule is the work done when a force of 1 newton moves an object 1 metre (1 J = 1 N·m). Work done against friction is transferred to the thermal store — the surfaces get warmer.

Worked example

A 40 N force drags a crate 6 m.

W = 40 × 6 = 240 J

Calculate

Your turn — work done

2A horizontal force of 25 N pushes a box 8 m across a floor. Calculate the work done.
J
Hint: W = 25 × 8.
Equation 3 · elasticity

Forces & elasticity — Hooke's law

For a spring, the extension is proportional to the force applied, up to the limit of proportionality:

F = k eforce (N) = spring constant (N/m) × extension (m)
limit of proportionality F ∝ e (straight) extension e (m) force F (N) 0
A straight line through the origin means F ∝ e. Past the limit of proportionality the graph curves away from that straight line and Hooke's law no longer holds.

The spring constant k measures stiffness. Bending the spring back into shape afterwards means the deformation was elastic; if it stays bent, it was inelastic.

Elastic potential energy stored in a stretched spring is Ee = ½ k e². Required practical: hang masses on a spring and plot force against extension.

Calculate

Your turn — Hooke's law

3A spring has a spring constant of 30 N/m. What force is needed to stretch it by an extension of 0.4 m?
N
Hint: F = k × e = 30 × 0.4.
Equation 4 · physics only

Moments, levers & gears

A force can turn an object about a pivot. The turning effect is the moment, and it depends on the force and how far from the pivot it acts:

M = F dmoment (N·m) = force (N) × perpendicular distance from pivot to the line of force (m)
pivot effort F large distance d load small distance
Balanced: clockwise moment = anticlockwise moment. A small effort at a large distance d can balance a much bigger load close to the pivot — that is how a lever multiplies force.

This is the principle of moments: when balanced, the total clockwise moment equals the total anticlockwise moment. Levers and gears use a long distance to multiply the effect of a force.

Think of a spanner. A long-handled spanner loosens a stiff bolt far more easily than a short one, even with the same push — because the moment is force × distance, so a longer handle (bigger d) gives a bigger turning effect for the same force.

Calculate

Your turn — moment

4A spanner is turned by a 50 N force applied 0.3 m from the bolt (at right angles). Calculate the moment.
N·m
Hint: M = F × d = 50 × 0.3.
Pressure in fluids · physics only

Pressure

A fluid (liquid or gas) pushes on every surface it touches. The pressure is the force spread over the area:

p = F ÷ Apressure (Pa) = force (N) ÷ area (m²)

In a column of liquid the pressure increases with depth, density and gravity:

p = h ρ gpressure (Pa) = height of column (m) × density (kg/m³) × g (N/kg)

Floating & sinking: a submerged object feels greater pressure on its bottom than its top, giving an upthrust. If upthrust ≥ weight it floats. Atmospheric pressure falls as you go higher, because there is less air above you pressing down.

Quick check

Diving deeper

?A diver swims from 5 m deep down to 15 m deep in the same lake. What happens to the water pressure on her?
Forces & motion

Describing motion

  • Distance is a scalar; displacement (distance in a straight line, with direction) is a vector.
  • Speed is a scalar; velocity is speed in a given direction (a vector).
  • Typical speeds: walking ≈ 1.5 m/s, running ≈ 3 m/s, cycling ≈ 6 m/s.

Acceleration is how quickly velocity changes:

a = Δv ÷ tacceleration (m/s²) = change in velocity (m/s) ÷ time (s)

Higher tier: for uniform acceleration, v² − u² = 2 a s (final² − initial² = 2 × acceleration × distance).

Calculate

Your turn — acceleration

5A car speeds up from 8 m/s to 20 m/s in 6 s. Calculate its acceleration.
m/s²
Hint: a = (20 − 8) ÷ 6.
Motion graphs

Velocity–time graphs

On a distance–time graph the gradient is the speed. On a velocity–time graph the gradient is the acceleration and the area under the line is the distance travelled.

Δt Δv gradient = acceleration constant velocity decelerating area under line = distance time (s) velocity (m/s)
The gradient (Δv ÷ Δt) of the sloped part is the acceleration; the shaded area under the whole line is the distance travelled. A flat line means constant velocity.
Calculate

Your turn — read the graph

6On a velocity–time graph, an object's velocity rises in a straight line from 0 to 18 m/s over 9 s. Find its acceleration (the gradient).
m/s²
Hint: gradient = change in velocity ÷ time = 18 ÷ 9.
Newton's laws

Newton's three laws

  • First law: if the resultant force is zero, a still object stays still and a moving object keeps a constant velocity. The tendency to resist a change in motion is inertia.
  • Second law: a resultant force makes an object accelerate — F = m a.
  • Third law: when two objects interact, they exert equal and opposite forces on each other (an action–reaction pair).
F = m aresultant force (N) = mass (kg) × acceleration (m/s²)

Biggest misconception: a moving object does not need a resultant force to keep moving. By Newton's first law, with zero resultant force it carries on at a constant velocity forever. A force is only needed to change motion (speed up, slow down or turn) — not to maintain it. Things on Earth slow down only because friction and drag provide a resultant force.

Inertia is like a loaded shopping trolley. A full trolley (large mass) is much harder to get moving — and once moving, much harder to stop or steer — than an empty one. More mass means more inertia: a greater resistance to any change in motion.

Action–reaction pairs act on different objects, so they never cancel. Push off a wall on a skateboard: you push the wall (action) and the wall pushes you back (reaction). The two forces are equal and opposite but act on different bodies — the force on you is what sends you rolling away.

Worked example

A resultant force of 60 N acts on a 4 kg trolley.

a = F ÷ m = 60 ÷ 4 = 15 m/s²

Calculate

Your turn — Newton's second law

7A resultant force accelerates a 1200 kg car at 2.5 m/s². Calculate the size of the resultant force.
N
Hint: F = m × a = 1200 × 2.5.
Stopping distance

Stopping a car

Stopping distance = thinking distance + braking distance. Thinking distance is travelled during the driver's reaction time; braking distance is travelled once the brakes are applied.

thinking braking thinking + braking = stopping distance reaction time grows fast with speed
  • Thinking distance increases with speed and a longer reaction time (tiredness, alcohol, drugs, distractions).
  • Braking distance increases with speed, and with poor road, tyre or brake conditions (wet, icy, worn).
Terminal velocity

Terminal velocity

A falling object speeds up until the upward air resistance grows to balance its downward weight. With the forces balanced the resultant force is zero, so it stops accelerating and falls at a steady maximum speed — its terminal velocity.

🪂 air resistance weight forces balanced resultant = 0
A skydiver: at terminal velocity the air-resistance arrow and the weight arrow are equal in length — they cancel.

Terminal velocity ≠ no forces. At terminal velocity the resultant force is zero (so acceleration is zero), but weight and air resistance are both still acting — they simply balance. Opening a parachute hugely increases air resistance, so it briefly exceeds weight, the skydiver decelerates, and they settle to a new, slower terminal velocity.

Quick check

What affects stopping?

?A driver has been awake for 20 hours and is very tired. Which part of the stopping distance does tiredness directly increase?
Momentum · physics only

Momentum

A moving object has momentum — a vector that depends on mass and velocity:

p = m vmomentum (kg·m/s) = mass (kg) × velocity (m/s)

In a closed system (no outside forces), total momentum is conserved: the total momentum before an event equals the total momentum after it.

Higher tier: force equals the rate of change of momentum, F = Δp ÷ Δt. Spreading a collision over a longer time (crumple zones, air bags) reduces the force.

Worked example

A 0.5 kg ball moves at 4 m/s.

p = 0.5 × 4 = 2 kg·m/s

Calculate

Your turn — momentum

8A 1500 kg car travels at 12 m/s. Calculate its momentum.
kg·m/s
Hint: p = m × v = 1500 × 12.
Recap

The equations to know

Weight: W = m g

Work done: W = F s

Hooke's law: F = k e  (elastic p.e. Ee = ½ k e²)

Moment: M = F d

Pressure: p = F ÷ A  (column: p = h ρ g)

Acceleration: a = Δv ÷ t  (HT: v² − u² = 2 a s)

Newton's 2nd law: F = m a

Momentum: p = m v  (HT: F = Δp ÷ Δt)

You've covered the whole of AQA 4.5 — scalars & vectors, contact & non-contact forces, work, elasticity, moments, pressure, motion, Newton's laws, stopping distance and momentum. Press Finish to see your score.

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