Work Done

Key Stage 3

Work Done is the amount of energy transferred by the action of a force.

Work Done is measured in Joules.

Work Done can only be calculated for objects moving in the direction of the force.

Work Done = Force X Distance moved in the direction of the force \[ W = F \times d\] \[ W = Fd\]

Work done is written with a capital W. Force is written with a capital F. Distance is written with a lower case d.

A person lifts a 40N box by a height of 1.2m. Calculate the work done by the person against gravity.	The brakes on a car apply a force of 10,000N. The car travels a distance of 15m braking. Calculate the work done by the brakes.	A person carries a 20N box along a horizontal path of 20m.
Force = 40N Distance moved in the direction of the force = 1.2m \( W = Fd\) \( W = 40 \times 1.2\) \( W = 48J\)	Force = 10,000N Distance moved in the direction of the force = 15m \( W = Fd\) \( W = 10,000 \times 15\) \( W = 15,000J\)	Force = 40N Distance moved in the direction of the force = 0m \( W = Fd\) \( W = 20 \times 0\) \( W = 0J\) No work has been done because the movement is not in the direction of the force. The weight acts downwards but the movement was horizontal.

When an object is deformed, such as a spring being stretched, work is done to transfer energy into its Elastic Potential Energy Store.


Work is done to stretch this spring.

The Force needed to stretch a spring is proportional to the extension of the spring (Hooke's Law). Force = Spring Constant x Extension

The Work Done on an object is proportional to the force and the distance traveled. Work Done = Force x Distance

The distance moved is the same as the extension 'x'.

These two equations can be combined:

1. \( F = kx\)

2. \( W = Fx\)

Substitute 1 into 2. \[W = (kx) \times x\] \[W = kx^2\]