Energy and its conservation

MDCAT Physics · Physics · Work, power 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, and a body raised above a chosen reference level has gravitational potential energy. Potential energy always depends on the level you measure the height from.

The work–energy principle says that the net work done on a body equals its change in kinetic energy. This often gives a force or a stopping distance more quickly than the equations of motion.

Energy is never created or destroyed. With no friction, the loss of potential energy equals the gain in kinetic energy. With friction or air resistance, part of the lost potential energy becomes heat, so the kinetic energy gained is smaller by the work done against friction.

Rules to remember

kinetic energy = ½ × mass × speed² (KE = ½mv² = p²/2m)
gravitational potential energy = mgh, with h measured from the chosen reference level
Work–energy principle: net work = change in KE (Fd = ½mv² − ½mu²)
No friction: loss of PE = gain in KE, so from rest v = √(2gh)
With friction: loss of PE = gain in KE + work done against friction (f × distance moved)
elastic potential energy of a spring = ½kx²

Common mistake

On a slope, students use the length of the slope in mgh. Use the vertical height for potential energy and the distance along the slope for the work done against friction.

Worked example

A 0.50 kg ball is dropped from rest from a height of 20 m and reaches the ground at 18 m s⁻¹. Taking g = 10 m s⁻², find the work done against air resistance.

Loss of PE = mgh = 0.50 × 10 × 20 = 100 J.
Gain in KE = ½mv² = ½ × 0.50 × 18² = 0.25 × 324 = 81 J.
Work done against air resistance = 100 − 81 = 19 J.

Answer: 19 J, which becomes heat in the air and the ball.

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