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Hooke's law and springs Cambridge International AS & A Level Physics revision

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In plain words

Hang a weight on a spring and it stretches. Hang twice the weight and it stretches twice as far, up to a point. That simple rule is Hooke's law, and the number that says how stiff the spring is, is called the spring constant.

Three things to know

  1. A tensile force stretches an object; a compressive force squashes it. The load is the force applied, and the extension is the increase in length.
  2. Hooke's law: force is proportional to extension, F = kx, up to the limit of proportionality. k is the spring constant (the stiffness), in N/m.
  3. On a force–extension graph, Hooke's law holds along the straight part through the origin, and the gradient there is k.

Worked example

A spring is 12.0 cm long with no load, and 15.0 cm long with a 6.0 N load. Find its spring constant, and its length under a 10 N load. (The limit of proportionality isn't passed.)

  1. Extension = 15.0 − 12.0 = 3.0 cm = 0.030 m.
  2. k = F ÷ x = 6.0 ÷ 0.030 = 200 N/m.
  3. For 10 N: x = 10 ÷ 200 = 0.050 m = 5.0 cm, so the length is 17.0 cm.

Tips and tricks

  • Extension is the change in length, not the total length.
  • Convert centimetres or millimetres to metres before you find k in N/m.
5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Hooke's law and springs: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. What does the gradient of the straight part of a force–extension graph give?
    • the spring constant (the answer)
    • the Young modulus
    • the strain
    • the energy stored

    k = F ÷ x.

  2. A spring of spring constant 40 N/m is stretched by 0.20 m. What force is stretching it?
    • 0.0050 N
    • 8.0 N (the answer)
    • 40.2 N
    • 200 N

    F = kx.

  3. What is the limit of proportionality?
    • the point beyond which force is no longer proportional to extension (the answer)
    • the point where the spring breaks
    • the longest the spring can be
    • the point where the spring has no load

    Beyond it the force–extension graph is no longer straight.

  4. A spring is 10 cm long with no load and 14 cm long with a 2.0 N load. What is its extension under that load?
    • 4 cm (the answer)
    • 10 cm
    • 14 cm
    • 24 cm

    Extension is the increase in length.

  5. What are the units of the spring constant?
    • N/m (the answer)
    • N m
    • N
    • m/N

    Force divided by extension.

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