Work Done Calculations

Work is done when a force moves an object in the direction of the force. Work done equals the energy transferred.

The equation

$W = Fd$

Symbol	Quantity	Unit
$W$	Work done	J
$F$	Force in the direction of motion	N
$d$	Distance moved in the direction of the force	m

1 joule = 1 newton x 1 metre.

Important conditions

• The force and the distance must be in the same direction. If you push a box horizontally, only the horizontal component of the force counts; the vertical component (perpendicular to the motion) does no work.
• If there is no movement, no work is done, regardless of how large the force is.

Worked example

A student pushes a trolley with a force of 50 N over a distance of 8.0 m. Calculate the work done.

$W = 50 \times 8.0 = 400\text{ J}$

The student transfers 400 J of energy to the trolley.

Work done against friction

When friction opposes the motion, work is done against friction. This energy is transferred to the thermal energy store of the surfaces and surroundings.

If the trolley above also experiences 15 N of friction, the work done against friction over 8.0 m is:

$W_{\text{friction}} = 15 \times 8.0 = 120\text{ J}$

The remaining energy (400 - 120 = 280 J) goes to the kinetic energy of the trolley.

Common errors and how to correct them

Using the total force when only the component in the direction of motion should be used. If a force acts at an angle, find the horizontal component for horizontal work.

Confusing work done and force. Work has the unit joules (energy transferred), not newtons.

How to apply this in an exam

Write the equation, substitute force and distance, calculate, and state the unit (J). If the question asks where the energy goes, name the energy store(s) that receive it.