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Stretching and Hooke's law Cambridge IGCSE Combined Science revision

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In plain words

Pull on a spring and it gets longer. For a while the stretch is fair: double the pull, double the extension. That's Hooke's law. Pull too hard and you pass the limit of proportionality: the spring stretches more than it should, and may not go back.

Three things to know

  1. For a spring, extension is proportional to load up to the limit of proportionality (Hooke's law): F = kx.
  2. The spring constant k is the force per unit extension, in N/m or N/cm. A stiffer spring has a bigger k.
  3. Extension is the stretched length minus the original length, not the total length.

Worked example

A spring stretches 4 cm with a 2 N load. What is its spring constant?

  1. k = force ÷ extension.
  2. = 2 ÷ 4 = 0.5 N/cm.

Tips and tricks

  • Extension is the extra length, not the total length. Subtract the original length first.
  • On a graph, Hooke's law holds only while the line is straight and passes through the origin.
6 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Stretching and Hooke's law: 6 questions and answers

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

  1. A spring stretches 2 cm with a 1 N load. If it obeys Hooke's law, how far does it stretch with 3 N?
    • 3 cm
    • 5 cm
    • 6 cm (the answer)
    • 9 cm

    Three times the load gives three times the extension.

  2. What does a larger spring constant tell you?
    • The spring is longer.
    • The spring is stiffer. (the answer)
    • The spring is easier to stretch.
    • The spring has been stretched too far.

    More force is needed for each metre of extension.

  3. A load–extension graph for a spring is a straight line through the origin. What does this show?
    • The spring has passed its limit of proportionality.
    • Extension is proportional to load. (the answer)
    • The spring constant is zero.
    • The spring will not return to its original length.

    A straight line through the origin means one doubles when the other does.

  4. A spring of original length 10 cm is 16 cm long when loaded. What is its extension?
    • 26 cm
    • 16 cm
    • 10 cm
    • 6 cm (the answer)

    Extension = new length − original length.

  5. A force of 12 N extends a spring by 0.30 m. What is its spring constant?
    • 3.6 N/m
    • 12.3 N/m
    • 40 N/m (the answer)
    • 400 N/m

    k = F ÷ x = 12 ÷ 0.30.

  6. What happens to a spring stretched beyond its elastic limit?
    • It breaks immediately.
    • It does not return to its original length. (the answer)
    • It becomes stiffer.
    • Its mass increases.

    It is permanently deformed.

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