Further Mathematics · AQA 7367 · Option M · Topic MC

Work, energy and power

Work, energy and power, including elastic strings and springs.

  • 7 sub-topics
  • Taught in Year 12
  • 90 practice questions
  • 7 animated lessons
Practice questions (90) Lessons Worksheets All AQA Further Mathematics topics

What the specification says

Every sub-topic AQA 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. MC1Work done by a force, WD = Fd cos θY12
  2. MC2Gravitational potential energyY12
  3. MC3Kinetic energyY12
  4. MC4Hooke's law and modulus of elasticityY12
  5. MC5Work done by a variable force, WD = ∫F dxY12
  6. MC6Elastic potential energyY12
  7. MC7Power, P = FvY13

Try 3 questions

Easy, medium and hard questions from this topic, each with a worked solutions and the mark for every step. All 90 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}

Total5

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Work, energy and power

Hard

Work, energy and power · Year 12 · 8 marks

A car of mass 1000 kg moves up a straight road inclined at an angle α\alpha to the horizontal, where sin⁡α=130\sin\alpha = \frac{1}{30}. The resistance to motion is constant, of magnitude 600 N, and the engine works at a constant rate of 20 kW.
  1. (a)
    Find the maximum speed of the car up the hill.
    (4)
  2. (b)
    Find the acceleration of the car when its speed is 13 m s⁻¹.
    (3)
  3. (c)
    The car reaches the top of the hill and moves onto level road, with the same resistance and power. Find its new maximum speed.
    (1)
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Part (a)4 marks

  1. At maximum speed the driving force balances resistance and the weight component.20000v\frac{20000}{v}=600{}= 600+1000×9.8×130{}+ 1000 \times 9.8 \times \frac{1}{30}
  2. v=21.6 m s−1v = 21.6\text{ m s}^{-1}

Part (b)3 marks

  1. F=maF = ma along the slope.2000013−600−327\frac{20000}{13} - 600 - 327=1000a{}= 1000a
  2. a=0.612 m s−2a = 0.612\text{ m s}^{-2}

Part (c)1 mark

  1. 20000600\frac{20000}{600}=33.3 m s−1{}= 33.3\text{ m s}^{-1}

Total8

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