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Practice questions · Hooke's law

Proportional, up to a point.

Six original Cambridge-style questions on Hooke's law and F = kx, finding the spring constant, reading the load-extension graph, and naming the limit of proportionality correctly.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.
The essentials

F = kx, while the line stays straight.

01
[2 marks]

State Hooke's law.

  • The extension of a spring is directly proportional to the load applied. ✓
  • This holds up to the limit of proportionality. ✓
02
Analysis
[3 marks]

Describe the shape of the load-extension graph for a spring that is loaded beyond the point where Hooke's law stops holding. Name that point.

  • A straight line through the origin at first (extension proportional to load). ✓
  • After the limit of proportionality the line curves (extension increases more rapidly per unit load). ✓
  • The point named is the limit of proportionality. ✓
03
Calculation
[2 marks]

Within the proportional region, a load of 6.0 N produces an extension of 0.040 m. Calculate the spring constant.

k = F ÷ x = 6.0 ÷ 0.040

k = 150 N/m

04
Calculation
[2 marks]

A spring has a spring constant of 25 N/m. Calculate the load needed to produce an extension of 0.20 m, assuming it stays within the proportional region.

F = k x = 25 × 0.20

F = 5.0 N

05
Analysis
[2 marks]

On a load-extension graph, a student labels the end of the straight-line section the "elastic limit." State the term the syllabus expects here, and note whether the two are the same point.

  • The expected term is the limit of proportionality. ✓
  • It is not the same as the elastic limit; they are different points on the graph. ✓
06
Calculation
[3 marks]

A spring has an original length of 12.0 cm. With a 1.5 N load it stretches to 15.0 cm, within the proportional region.

(a)Calculate the extension. (b)Calculate the spring constant in N/m.

(a) extension = 15.0 − 12.0 = 3.0 cm = 0.030 m ✓

(b) k = F ÷ x = 1.5 ÷ 0.030

k = 50 N/m