Work, energy and power

Physics · Space, time and motion. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

Work is energy transferred by a force. Only the part of the force along the direction of movement does work, so a force at right angles to the motion does no work at all.

Energy is never created or destroyed. It is only transferred from one store to another, so the total before equals the total after. If friction or air resistance acts, some energy goes to thermal energy, and you must include it. A Sankey diagram shows this: the width of each arrow is proportional to the energy.

Power is the rate of doing work. Efficiency is the useful fraction of the input. For fuels, specific energy is the energy per kilogram and energy density is the energy per cubic metre.

Rules to remember

Common mistake

Students use W = Fs with the whole force when the force is at an angle to the motion. Always multiply by cos θ, and remember that cos 90° = 0, so a force at right angles does no work.

Worked example

A sledge of mass 20 kg starts from rest on frictionless ice. It is pulled 10 m by a rope with a tension of 50 N at 30° above the horizontal. What is its final speed?

  1. Work done = Fs cos θ = 50 × 10 × cos 30° = 500 × 0.866 = 433 J.
  2. With no friction, all of this becomes kinetic energy: ½mv2 = 433.
  3. v2 = 2 × 433 ÷ 20 = 43.3, so v = √43.3.

Answer: About 6.6 m s−1.

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