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Spring into Action

Stretch a spring and it pulls back — until you push it too far. Master Hooke's law, the limit of proportionality, and the energy stored in a stretched spring.

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What you'll cover

Spring into Action 🔩

Springs are everywhere — in pens, mattresses, car suspensions and bathroom scales. Their secret is that they **stretch in proportion to the force** you apply, then spring back. But push too hard and a spring never recovers. Let's find out exactly where that line is.

Two kinds of stretch 🔄

When a force changes an object's shape, the **deformation** is one of two kinds: • **Elastic** — the object **returns to its original shape** once the force is removed (a spring, a rubber band). • **Inelastic** — the object **stays deformed** even after the force is removed (a squashed lump of Plasticine).

Elastic or inelastic?

You bend a plastic ruler gently and it springs straight again. What kind of deformation is this?

  • Elastic — it returned to its original shape
  • Inelastic — it stayed bent
  • It is neither — rulers cannot deform
  • Both elastic and inelastic at once

Hooke's law 📏

For a spring, the extension is proportional to the force — this is **Hooke's law**: **F = k e** where **F** is the force in newtons (N), **k** is the **spring constant** in newtons per metre (N/m), and **e** is the **extension** in metres (m). A stiffer spring has a bigger k.

Find the force

An interactive activity.

Find the spring constant

An interactive activity.

The limit of proportionality 📈

In **Required Practical 6** you hang masses on a spring and plot **force against extension**. At first you get a **straight line through the origin** — Hooke's law holds. But at the **limit of proportionality** the line starts to **curve**. Beyond that point the spring stretches more for each newton, and **F = k e no longer applies**.

Plot the spring

An interactive activity.

About the limit

Select ALL THREE statements that are TRUE about a spring's force-extension graph.

  • Below the limit of proportionality the graph is a straight line
  • Below the limit, F = k e applies
  • Beyond the limit the line curves and F = k e no longer holds
  • The limit of proportionality is where the spring first starts to stretch
  • Beyond the limit the graph stays perfectly straight
  • F = k e works for any extension, however large

Energy in a spring ⚡

Stretching a spring stores energy in it — **elastic potential energy**. Provided you stay below the limit of proportionality, it is given by: **Ee = ½ k e²** with Ee in joules (J), k in N/m and e in metres (m). Note the extension is **squared**, so doubling the stretch stores four times the energy.

Find the stored energy

An interactive activity.

Spring summary

An object that returns to its original shape when the force is removed is _____ deformed. For a spring, force = spring constant × _____, written F = k e — but only below the limit of _____. The energy stored in a stretched spring is its _____ potential energy, Ee = ½ k e².

elastically extension proportionality elastic inelastically compression kinetic