Work-energy principle and conservation of energy

Physics · Work and energy. 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

A moving body has kinetic energy. A body raised to a height has gravitational potential energy. Both are measured in joules, the same unit as work.

The work-energy principle says that the work done on a body equals the change in its kinetic energy. So a force that speeds a car up, or brakes that stop it, can be found from the kinetic energy change and the distance.

Energy is never created or destroyed. It only changes form. When a body falls freely, its loss of potential energy equals its gain in kinetic energy. If friction acts, part of the potential energy lost becomes heat, so less is left as kinetic energy.

Rules to remember

Common mistake

Kinetic energy depends on v2, so the work needed to go from 10 to 20 m s−1 is not found from (20 − 10)2. Work out ½mv2 at each speed and then subtract.

Worked example

A 0.20 kg ball is thrown straight up at 14 m s−1 and rises to a height of 9.0 m. How much work is done against air resistance on the way up?

  1. K.E. at the start = ½mv2 = ½ × 0.20 × 142 = 19.6 J.
  2. P.E. at the top = mgh = 0.20 × 9.8 × 9.0 = 17.64 J (the K.E. there is zero).
  3. Work done against air resistance = 19.6 − 17.64 = 1.96 J.

Answer: About 2.0 J

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