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How do springs stretch under a force, what is Hooke's law, and how is energy stored in a stretched spring?

Elastic and inelastic deformation, Hooke's law and the force on a spring, the limit of proportionality, the energy stored in a stretched spring, and the force-extension practical.

A focused answer to OCR Gateway GCSE Physics A topic P2 on springs and elasticity, covering elastic and inelastic deformation, Hooke's law and the force on a spring, the limit of proportionality, the energy stored in a stretched spring, and the force-extension practical.

Generated by Claude Opus 4.89 min answer

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  1. What this topic is asking
  2. Elastic and inelastic deformation
  3. Hooke's law
  4. The force-extension graph and the practical
  5. Energy stored in a stretched spring
  6. Try this

What this topic is asking

OCR wants you to describe elastic and inelastic deformation, apply Hooke's law (the force on a spring), identify the limit of proportionality, find the energy stored in a stretched spring, and carry out the force-extension practical. This is topic P2.3 of the OCR Gateway Physics A (J249) specification.

Elastic and inelastic deformation

To stretch, compress or bend an object you always need more than one force acting on it (otherwise it would simply accelerate away). A spring being stretched, for example, has the pulling force at one end balanced by the support at the other.

Hooke's law

The extension is the increase in length, not the total length, so always subtract the original (natural) length first. Hooke's law holds only up to the limit of proportionality; beyond that point the spring extends more for each extra newton, the graph curves away from a straight line, and the spring may deform inelastically.

The force-extension graph and the practical

In the P2 force-extension practical you hang a spring from a clamp stand, measure its natural length, then add masses one at a time and record the force (the weight of the masses) and the new length, finding the extension by subtraction. Plotting force against extension gives:

  • a straight line through the origin while the spring obeys Hooke's law (force proportional to extension), and
  • a line that curves beyond the limit of proportionality.

The gradient of the straight section equals the spring constant kk. A systematic error to mention is not measuring from the unloaded length, which shifts every extension value.

Energy stored in a stretched spring

This stored energy is recovered when the spring returns to its original shape, which is how a spring in a toy or a trampoline launches objects back. If the spring is stretched beyond its limit of proportionality, some energy is used in permanently deforming it and is not recovered.

Try this

Q1. A spring stretches by 0.10 m0.10\,\text{m} when a force of 4 N4\,\text{N} is applied within its limit of proportionality. Calculate the spring constant. [2 marks]

  • Cue. Rearrange F=kxF = kx: k=Fx=40.10=40 N/mk = \dfrac{F}{x} = \dfrac{4}{0.10} = 40\,\text{N/m}.

Q2. State what is meant by the limit of proportionality. [1 mark]

  • Cue. The point beyond which the extension is no longer directly proportional to the force.

Exam-style practice questions

Practice questions written in the style of OCR exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

OCR 20193 marksA spring has a spring constant of 25 N/m25\,\text{N/m}. A force stretches it by 0.20 m0.20\,\text{m} within its limit of proportionality. Calculate the force applied to the spring.
Show worked answer →

A P2 Calculate question on the given equation F=kxF = kx. Write the values: spring constant k=25 N/mk = 25\,\text{N/m} and extension x=0.20 mx = 0.20\,\text{m} (1 mark for selecting and stating the equation). Substitute: F=kx=25×0.20=5 NF = kx = 25 \times 0.20 = 5\,\text{N} (2 marks for the calculation and the answer with units). Markers reward the correct equation, substitution, and answer in newtons. A common error is to forget that xx is the extension (the increase in length), not the total length of the spring.

OCR 20214 marksDescribe how you would investigate the relationship between the force applied to a spring and its extension, and explain how the results show whether the spring obeys Hooke's law.
Show worked answer →

A P2 practical question worth four marks. Method: hang the spring from a clamp stand, measure its original length, then add masses one at a time, recording the force (weight) and the new length each time, and find the extension by subtracting the original length (2 marks for a clear method with repeated measurements). Plot a graph of force against extension. If the graph is a straight line through the origin, the force is directly proportional to the extension, so the spring obeys Hooke's law (1 mark). The point where the line starts to curve is the limit of proportionality, beyond which Hooke's law no longer holds (1 mark). Markers reward the method, the straight-line test for proportionality, and identifying the limit of proportionality.

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