Energy, work and power

O Level / IGCSE Physics · Motion, forces and energy. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.

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The idea

Energy is kept in stores: kinetic, gravitational potential, chemical, elastic, nuclear, electrostatic and internal (thermal). It moves from one store to another by a force doing work, by an electric current, by heating, or by waves such as light and sound.

Energy is never made or destroyed. The total stays the same, but in every transfer some is wasted, usually by heating the surroundings. Efficiency tells you what fraction is useful.

Power is how quickly energy is transferred. Energy resources are renewable (solar, wind, hydroelectric, tidal, wave, geothermal, biofuel) or non-renewable (fossil fuels, nuclear fuel).

Rules to remember

Common mistake

Forgetting to square the speed in ½mv2, or squaring the whole of ½mv. Square the speed first, then multiply by the mass and by ½.

Worked example

A pump lifts 30 kg of water through a height of 4.0 m in 6.0 s. What is the useful power of the pump? (g = 9.8 N/kg)

  1. Energy gained by the water: ΔEp = mgΔh = 30 × 9.8 × 4.0 = 1176 J
  2. power = energy transferred ÷ time taken = 1176 ÷ 6.0
  3. power = 196 W

Answer: 196 W (about 200 W).

Practice questions

Try each one, then open the answer.

1. A ball of mass 0.50 kg is thrown vertically upwards at 12 m/s. Ignoring air resistance, how high does it rise? (g = 10 N/kg)

  1. A
    1.2 m
  2. B
    3.6 m
  3. C
    7.2 m
  4. D
    14.4 m
Show answer

Answer: C. Kinetic energy = ½ × 0.50 × 122 = 36 J. At the top it is all gravitational potential energy: 36 = 0.50 × 10 × h, so h = 7.2 m. Forgetting the ½ gives 14.4 m; leaving out the mass gives 3.6 m.

2. A 5.0 kg box is lifted 2.0 m onto a shelf. What is the increase in its gravitational potential energy? (g = 10 N/kg)

  1. A
    10 J
  2. B
    20 J
  3. C
    50 J
  4. D
    100 J
Show answer

Answer: D. ΔPE = mgΔh = 5.0 × 10 × 2.0 = 100 J.

3. A motor does 3000 J of work in 20 s. What is its power?

  1. A
    0.0067 W
  2. B
    150 W
  3. C
    3020 W
  4. D
    60 000 W
Show answer

Answer: B. power = work done ÷ time = 3000 ÷ 20 = 150 W.

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