GCSE Physics, Unit 6, Lesson 4 of 6

Springs, elasticity and the force-extension practical

GCSE Physics, Forces, work, elasticity, moments and pressure, 25 minutes

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Elastic and inelastic deformation, F = ke and the limit of proportionality, elastic potential energy ½ke², and the required practical on a spring.

What you will learn

  • Tell elastic from inelastic deformation
  • Use F = ke with extensions in cm or m
  • Find k from a force-extension graph and spot the limit of proportionality
  • Use E = ½ke²
  • Plan and analyse the spring practical

Stretch it and let go

To stretch, squash or bend an object you need more than one force on it; one force alone would just move it.

  • Elastic deformation: it goes back to its original shape and length when the forces are removed (a rubber band, a squeezed tennis ball).
  • Inelastic deformation: it stays changed (a crushed can, squashed modelling clay).

For a spring, the extension is directly proportional to the force, up to a point:

force = spring constant × extension
F = k e

F in N, k in N/m, e in m. AQA and OCR: recall. Edexcel writes it F = k × x: recall too. The same equation works for compression.

  1. A spring with k = 40 N/m is stretched 5 cm
  2. e = 5 ÷ 100 = 0.05 m
  3. F = 40 × 0.05 = 2 N

Extension is the increase in length: new length − original length. It is not the new length.

Rearranged: spring constant k = F ÷ e, and extension e = F ÷ k. If you know the extension, the new length is the original length + the extension.

  1. A 30 cm spring with k = 50 N/m holds a 2 N load.
  2. e = F ÷ k = 2 ÷ 50 = 0.04 m = 4 cm
  3. new length = 30 + 4 = 34 cm

For a hanging load, the force on the spring is its weight: change grams to kilograms and use W = m g.

The rest of this lesson and its 11 practice questions are locked.

In this lesson

  1. Stretch it and let go
  2. The limit of proportionality
  3. Energy stored in a stretched spring
  4. Required practical: force and extension
  5. Try it: Find k from a stretch
  6. Try it: F = ke

11 practice questions, marked as you go; about 25 minutes in all.

Key terms

More than one force, Limit of proportionality, Elastic potential energy

In this unit: Forces, work, elasticity, moments and pressure

Weight and resultant forces, work done, stretching springs and their required practical, moments, levers and gears, and pressure in fluids.

All of Forces, work, elasticity, moments and pressure

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