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Hooke's law and force-extension graphsEdexcel International A Level Physics: Flashcards

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State Hooke's law.

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State Hooke's law.
The extension of a spring is directly proportional to the force applied, provided the limit of proportionality is not exceeded.
Write Hooke's law as an equation and name each quantity.
F = kx: F is the force (N), k the stiffness (N m⁻¹), x the extension or compression (m).
What does the gradient of a force-extension graph give?
The stiffness k of the object, when force is on the vertical axis.
What shape is the force-extension graph for a spring obeying Hooke's law?
A straight line through the origin.
Define the limit of proportionality.
The point beyond which the extension is no longer proportional to the force, so Hooke's law is not obeyed.
Define the elastic limit.
The point beyond which the material does not return to its original length when the force is removed.
What is elastic deformation?
Deformation that disappears when the force is removed; the material returns to its original length.
What is plastic deformation?
Permanent deformation: the material stays longer after the force is removed.
What happens at the yield point?
A ductile material stretches a large amount for little or no increase in force.
How does the unloading line look if a wire is unloaded from the plastic region?
It is parallel to the initial straight line and meets the extension axis at the permanent extension.
Spring stiffness 40 N m⁻¹. What force gives an extension of 0.15 m?
F = kx = 40 × 0.15 = 6.0 N.
Which comes first on the graph, limit of proportionality or elastic limit?
The limit of proportionality comes first (or at the same point as the elastic limit).
What is a force-compression graph?
A graph of compressive force against compression; it is a straight line through the origin while Hooke's law is obeyed.

Exam questions on Hooke's law and force-extension graphs

  1. A student investigates a helical steel spring hung from a clamp. Masses are added one at a time to the lower end and the extension of the spring is measured after each addition. The spring obeys Hooke's law for all loads up to 8.0 N, at which load its extension is 0.20 m.
    The student adds further masses so that the force is 12 N. She finds that the extension is greater than the value predicted using the stiffness found from the first results. Explain this observation.2 marks
  2. Spring X has a stiffness of 60 N m⁻¹ and spring Y has a stiffness of 20 N m⁻¹. Both springs obey Hooke's law for all the forces used in a test.
    A force of 3.0 N is applied to spring Y. Calculate the force that must be applied to spring X to produce the same extension as in spring Y.2 marks
  3. A technician loads a metal wire, increasing the force steadily from zero. Up to 24 N the extension is directly proportional to the force, and at 24 N the extension is 1.2 mm. Between 24 N and 30 N the extension increases by larger amounts for each newton added, but the wire still returns to its original length when unloaded. Beyond 30 N the wire no longer returns to its original length when unloaded.
    Describe how the behaviour of the wire changes as the force is increased from zero to 30 N and beyond, using the terms limit of proportionality, elastic limit and plastic deformation.3 marks
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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).