Hooke's Law and Elasticity

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CognitoHooke's law and spring constant

Key facts & equations

Hooke's Law

Force = spring constant × extension. F = ke.
k = spring constant (N/m). e = extension (m). F = force (N).
Hooke's law applies up to the limit of proportionality.
Within this limit: extension is directly proportional to force (F ∝ e).
Graph of force vs extension: straight line through origin (obeying Hooke's law).

Elastic and plastic deformation

Elastic deformation: object returns to original shape when force is removed.
Plastic deformation: object is permanently deformed — does not return to original shape.
Elastic limit (elastic potential energy): beyond this point, deformation becomes plastic.
For elastic deformation: E_elastic = ½ke² (elastic potential energy stored).
Spring: good example of elastic deformation up to its limit.

Force-extension graphs

Straight line through origin = Hooke's law obeyed. Gradient = spring constant k.
Curve (steepening) beyond limit of proportionality = no longer linear.
After elastic limit: permanent deformation occurs.
Area under F-e graph = work done (elastic potential energy stored).
Compare springs in series vs parallel: parallel is stiffer (higher k).

Required practical — springs

Hang spring vertically. Measure natural length (no load).
Add known masses. Measure new length. Calculate extension = new length − natural length.
Plot force (N) vs extension (m). Draw best-fit line through origin.
Gradient = spring constant k.
Identify the point where graph starts to curve (limit of proportionality).

Exam questions — 4 questions · 11 marks · AQA 8463 style

3 marksHooke's law calculationAQA 8463 P1 style 🔢 Calculator

A spring has a spring constant of 40 N/m. (a) Calculate the extension when a force of 12 N is applied. (b) Calculate the elastic potential energy stored. (3 marks)

Hint: (a) Rearrange F = ke to get e = F/k. (b) Elastic PE = ½ke² (or ½Fe since F=ke).

+30 XP

1 markLimit of proportionalityAQA 8463 style

On a force-extension graph, what happens at the limit of proportionality?

A The spring snaps

B The line begins to curve — extension is no longer proportional to force

C The spring constant doubles

D The spring immediately becomes permanently deformed

3 marksElastic vs plasticAQA 8463 style

Explain the difference between elastic and plastic deformation, and state which type of deformation a rubber band shows when it returns to its original shape. (3 marks)

+30 XP

1 markSpring constant from graphAQA 8463 style

A force-extension graph shows that a force of 30 N produces an extension of 0.15 m. What is the spring constant?

A 4.5 N/m

B 0.005 N/m

C 200 N/m

D 450 N/m

Hooke's Law and Elasticity

Hooke's Law

Elastic and plastic deformation

Force-extension graphs

Required practical — springs

Module complete! 🎉