Work Done

Work done is the energy transferred when a force makes an object move. If there is no movement, no mechanical work is done.

Key idea and equation

Work done links forces and energy:

$$W = F d = \Delta E$$

• W is work done (in joules, J)
• F is the force (in newtons, N)
• d is the distance moved in the direction of the force (in metres, m)

One joule is the work done when a force of one newton moves something one metre: $1\,\text{J} = 1\,\text{N m}$.

Understanding what counts as distance

• Only the distance along the force counts. Pushing a box forward: the forward distance counts.
• Holding a heavy bag still: the bag does not move, so $W = 0$ on the bag (even though your muscles use energy).
• Lifting raises gravitational potential energy, so work done equals the increase in GPE.

Mechanical and electrical work

Mechanical work is done by forces making things move (pushing, pulling, lifting). Electrical work is energy transferred by an electric current (for example, a lamp transfers electrical energy to light and heat). In both cases, work done equals energy transferred.

Common misconceptions

• “Pushing hard means large work.” Not unless the object moves. No movement means $W=0$.
• “Any distance counts.” Only the distance in the force’s direction counts.
• “Friction does no work.” Friction can do work that removes kinetic energy and warms surfaces.
• “Centimetres are fine.” Use metres in $W = Fd$.