Work Done and Energy Transfer

Work done by a force on an object equals the magnitude of the force multiplied by the distance the object moves in the direction of the force:

$W = F \, s$

• $W$ in joules (J).
• $F$ in newtons (N).
• $s$ in metres (m).

1 joule = 1 newton-metre. They are exactly the same unit, but J is preferred for energy and N·m for torque.

Worked example. A 50 N push moves a box 4 m.

$W = 50 \times 4 = 200\,\text{J}$

200 J of energy has been transferred from the pusher's chemical store to the kinetic and/or thermal stores of the box and floor.

Worked example. Lifting a 5 kg load 2 m up.

• Force needed (against gravity): $F = mg = 5 \times 9.8 = 49\,\text{N}$.
• Work done: $W = 49 \times 2 = 98\,\text{J}$.
• Where it goes: 98 J of gravitational potential energy gained ($E_p = mgh = 5 \times 9.8 \times 2 = 98\,\text{J}$). Consistent!

Work done by a force always equals the energy it transfers. The destination depends on the situation:

Force does work…	Energy goes to
Lifting against gravity	Gravitational PE store
Stretching a spring	Elastic PE store
Accelerating an object	Kinetic store
Against friction	Thermal store of surfaces
Against air resistance	Thermal store of air

Worked example. Pushing a 10 kg box at constant velocity across a rough floor with a 30 N force, distance 5 m.

• Work done: 30 × 5 = 150 J.
• Since velocity is constant, kinetic store doesn't change.
• The 150 J therefore goes to the thermal store of the floor and box (friction).

If the force is perpendicular to motion (e.g. centripetal force on an orbiting satellite), no work is done — distance in the force direction is zero.