Energy, work & power

Work done, kinetic and gravitational potential energy, conservation of energy, power and efficiency.

7 min read

Work done = force × distance moved in the direction of the force: $W = F d$ . Doing work transfers energy, so work and energy share the unit, the joule (J).

Two key stores: gravitational potential energy $E_{p} = m g h$ and kinetic energy $E_{k} = \frac{1}{2} m v^{2}$ .

Worked example

A $2 kg$ ball is lifted $5 m$ ( $g = 10$ ). Find the GPE gained.

$E_{p} = m g h = 2 \times 10 \times 5 = 100 J .$

Energy is conserved; it is transferred between stores, never created or destroyed. A falling object converts GPE into KE, so $m g h = \frac{1}{2} m v^{2}$ (ignoring air resistance).

Power is the rate of transfer: $P = \frac{energy transferred}{time}$ . Efficiency measures how much input energy ends up useful: $efficiency = \frac{useful output}{total input} \times 100%$ .

Worked example

A motor takes in $500 J$ and outputs $300 J$ usefully. Find its efficiency.

$\frac{300}{500} \times 100 = 60%.$

Exam tip

For "how fast is it going at the bottom?" drops, set $m g h = \frac{1}{2} m v^{2}$ . The mass cancels, giving $v = 2 g h$ , a clean non-calculator result.

Using the total distance for work when only the distance *in the direction of the force* counts.
Forgetting the $\frac{1}{2}$ in kinetic energy.
Giving efficiency above 100%, which signals a calculation slip.

Energy, work & power

Work & energy

Conservation, power & efficiency

Common mistakes