Further Mathematics · Pearson Edexcel 9FM0 · Option FM1 · Topic 3

Elastic strings and springs and elastic energy

Hooke's law for strings and springs, the energy they store, and problems that combine elastic energy with other energies.

  • 2 sub-topics
  • Taught in Year 13
  • 33 practice questions
  • 2 animated lessons
Practice questions (33) Lessons Worksheets All Edexcel Further Mathematics topics

What the specification says

Every sub-topic Pearson Edexcel can examine in this topic, with its reference number from the official specification. The Y12 and Y13 tags show when each sub-topic is usually taught.

  1. 3.1Hooke's lawY13
  2. 3.2Elastic potential energyY13

Try 3 questions

Easy, medium and hard questions from this topic, each with a worked solutions and the mark for every step. All 33 questions in this topic, free, no account needed.

Elastic strings and springs and elastic energy

Not needed for Year 12Easy

Hooke's law · Year 13 · 1 mark

  1. An elastic string has natural length 0.5 m and modulus of elasticity 20 N. What is the tension when its extension is 0.2 m?
    (1)

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  1. T=λxlT = \dfrac{\lambda x}{l}.A: 8.00 N8.00\ \mathrm{N}

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Elastic strings and springs and elastic energy

Not needed for Year 12Medium

Hooke's law · Year 13 · 5 marks

A light elastic string has natural length 0.5 m and modulus of elasticity 49 N. One end is fixed at a point OO and a particle of mass 2 kg hangs in equilibrium from the other end.
  1. (a)
    Find the extension of the string.
    (3)
  2. (b)
    Find the elastic potential energy stored in the string.
    (2)

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Part (a)3 marks

  1. Hooke's law.T=λxlT = \frac{\lambda x}{l}
  2. Resolve vertically: T=mgT = mg.49x0.5=2×9.8\frac{49x}{0.5} = 2 \times 9.8
  3. x=0.200 mx = 0.200\text{ m}

Part (b)2 marks

  1. λx22l\frac{\lambda x^2}{2l}
  2. =1.96 J= 1.96\text{ J}

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Elastic strings and springs and elastic energy

Not needed for Year 12Hard

Elastic potential energy · Year 13 · 5 marks

A particle PP of mass 0.5 kg is attached to one end of a light elastic string of natural length 0.8 m and modulus 20 N. The other end is fixed to a point AA on a rough horizontal table. PP is held at rest on the table with AP=1.2AP = 1.2 m and released. The coefficient of friction between PP and the table is 0.25.
  1. Find the speed of PP when the string first becomes slack.
    (5)
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  1. EPE\text{EPE}=20×0.422×0.8{}= \frac{20 \times 0.4^2}{2 \times 0.8}=2 J{}= 2\text{ J}
  2. F=μRF = \mu R, R=mgR = mg, over the distance 0.4 m.work against friction\text{work against friction}=0.25×0.5×9.8×0.4{}= 0.25 \times 0.5 \times 9.8 \times 0.4=0.49 J{}= 0.49\text{ J}
  3. Work–energy principle.12(0.5)v2=2−0.49\tfrac{1}{2}(0.5)v^2 = 2 - 0.49
  4. v=2.46 m s−1v = 2.46\text{ m s}^{-1}

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