Key Stage 3 science · Physics – Motion and forces

KS3 Hooke’s Law, springs and friction: a guide for parents

In Key Stage 3, children measure forces in newtons and study what happens when forces stretch, squash, rub against and push through things. The central investigation is stretching a spring: the extension grows in proportion to the force, which is Hooke’s Law, until a limit is reached. They also study friction and resistance from air and water, and learn that doing work with a force transfers energy.

Deformation, friction and Hooke’s Law, explained

Forces can change the shape of things. Stretching a spring, squashing a sponge or bending a ruler are all deformations. Children measure force in newtons (N) using a newton meter, a spring with a scale, and record how much an object stretches or is compressed as the force changes. As a rough guide, the weight of a 100 g mass on Earth is about 1 N, which makes it easy to build a set of known forces from small masses.

The key measurement is the extension, which is the new length minus the original (natural) length. A graph of the spring’s length against force is a straight line, which is called a linear relationship, but it does not start at zero because the spring already has a length. Plotting extension against force instead gives a straight line through the origin: double the force and the extension doubles. That special case, where extension is directly proportional to force, is Hooke’s Law. It holds only up to the limit of proportionality. Beyond that, the line bends, and if the spring is overstretched it may not return to its original length.

Other forces resist motion. Friction acts where two surfaces rub or try to slide past each other, and it opposes the motion or the attempt to move. Air resistance and water resistance (drag) act on an object moving through a fluid and get bigger with speed and with the area pushing through. Pushing something out of the way takes a force too. These forces are useful and annoying: friction makes brakes, shoes and walking possible, while drag slows a swimmer and a cyclist.

The last strand links forces to energy. In science, work is done when a force moves something in the direction of the force, and the energy transferred is measured in joules. Stretching a spring means doing work, which is stored as elastic energy and can be released again. Dragging a box along a rough floor does work against friction, but here the energy goes to the thermal store of the floor and box, so you can’t get it back as movement. Work done is the force multiplied by the distance moved, for example 20 N over 3 m is 60 J.

Words your child will hear

Newton (N): The unit of force. A 100 g mass has a weight of about 1 N on Earth.
Extension: How much longer a spring or elastic object becomes: new length minus natural length.
Hooke’s Law: The extension of a spring is directly proportional to the force, up to a limit.
Limit of proportionality: The point beyond which a spring no longer follows Hooke’s Law.
Friction: A force between surfaces that opposes sliding or the attempt to slide.
Air resistance: The friction-like force of air pushing against a moving object. Also called drag.
Work done: Energy transferred when a force moves an object, found by force × distance moved in the direction of the force.

What the National Curriculum says

The programme of study for Key Stage 3 says:

Pupils should be taught about forces associated with deforming objects; stretching and squashing (springs); with rubbing and friction between surfaces; with pushing things out of the way; and resistance to motion of air and water
Pupils should be taught about forces measured in newtons, and measurements of stretch or compression as force is changed
Pupils should be taught about the force-extension linear relation; Hooke's Law as a special case
Pupils should be taught about work done and energy changes on deformation

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

A spring has a natural length of 10.0 cm. Masses are added and its length is measured. Does the spring obey Hooke’s Law, how long will it be with a 3.5 N force, and what happens at 6 N?

Work out the extension for each force: extension = length - natural length (10.0 cm).

force   length   extension
(N)     (cm)     (cm)
0       10.0     0.0
1       12.0     2.0
2       14.0     4.0
3       16.0     6.0
4       18.0     8.0
5       20.0     10.0
6       23.5     13.5

Look at the pattern in the extension, not the length. From 0 N to 5 N, each extra newton adds 2.0 cm, and 2 N gives double the extension of 1 N. A graph of extension against force would be a straight line through the origin.
That is Hooke’s Law for this spring: extension = 2.0 cm for every 1 N. Note that the length is not proportional to the force, because the spring starts at 10 cm; 2 N gives 14 cm, not double 12 cm.
Predict for 3.5 N. Extension = 3.5 × 2.0 = 7.0 cm, so the length is 10.0 + 7.0 = 17.0 cm.
Check 6 N. Following the pattern, the extension should be 12.0 cm, but it is 13.5 cm. The spring has gone past its limit of proportionality, so the line bends and the spring may now be permanently stretched.

Yes, up to 5 N the extension is proportional to the force (2.0 cm per newton). With 3.5 N the spring is 17.0 cm long. At 6 N it has passed its limit of proportionality, so Hooke’s Law no longer applies.

Common mistakes and how to help

Using the total length instead of the extension

The length is the number read off the ruler, so children check whether that doubles when the force doubles.

What helps: Always subtract the natural length first. If the length at 1 N is 12 cm and at 2 N is 14 cm, the lengths don’t double, but the extensions (2 cm and 4 cm) do.

Thinking every stretchy object follows Hooke’s Law all the way

Children generalise from one good result with a spring to elastic bands, bungee cords and everything else.

What helps: Test it. A rubber band gives a curved graph rather than a straight line. Every material has a limit, and past it the object may not return to its original shape.

Believing friction is always a nuisance, or only happens when something is moving

Friction is mostly noticed when it slows or wears things out, and the word is linked with sliding.

What helps: Ask your child how they could walk on perfectly smooth ice. Friction between shoes and ground is what pushes you forwards. A parked car on a slope stays put because of friction even when nothing is moving.

Thinking that holding something heavy is doing work in the science sense

Holding a heavy bag is tiring, and in everyday language that is work.

What helps: In science, work needs a force that moves something in the direction of the force. Holding a bag still involves no movement, so no energy is transferred to it, even though the muscles tire. Lifting it onto a shelf is work.

How to help at home

Rubber band stretch test. Hang a rubber band from a hook or the edge of a table, and add small known masses (coins or washers in a bag) one at a time. Measure the length with a ruler after each addition, and compare with a spring if you have one. Keep your face away from the band in case it snaps, and keep feet clear of falling masses.
Spring from a pen. Take the spring out of a spare clicker pen if you have one, stand it on kitchen scales and press down on it gently with a pencil. Watch the reading rise as the spring is squashed further (100 g on the display is about 1 N). Ask your child how the compression changes with the force, and whether twice the squash seems to need twice the force.
Friction slide. Rest a book on a board and slowly raise one end until the book starts to slide. Repeat after covering the board with different materials such as a tea towel, baking paper or sandpaper. Which surface needs the steepest slope?
Drag in a bowl. Fill a washing-up bowl with water and push a flat piece of card through it, face-on and then edge-on. Feel the difference. Then drop a flat sheet of paper and a scrunched-up one from the same height and watch air resistance at work.
Say where the energy went. For anything your child pushes, pulls or stretches, ask whether work is being done and where the energy ends up. Rubbing a hand on a carpet makes it warm, a stretched spring stores energy, and a ball thrown upward stores it in height.

Leads on to

Key Stage 4: Forces, fields, work done and pressure
Key Stage 4: Motion, acceleration and road safety