4.11-4.13 - Work done and gravitational potential energy

What counts as work done

A force does work when its point of application moves with a component along the force. A resistive force can do negative work even though it opposes rather than causes the motion. If there is a force but no movement in the direction of the force, no work is done by that force. For example, if you hold a heavy bag still at the same height, your upward force does no work on the bag, because the bag does not move.

The important distance is the distance moved in the direction of the force. If a horizontal force pushes a box along a floor, use the horizontal distance moved. If an upward force lifts a mass, use the vertical height moved. Do not automatically use the total journey length if the force is not acting along that whole journey.

Here, $W$ is work done in joules, $F$ is force in newtons, and $d$ is distance moved in the direction of the force in metres.

The unit joule links work to energy. One joule of work is done when a force of one newton moves through one metre in the direction of the force.

Work done as energy transferred

Work done is equal to energy transferred. This means a work done calculation tells you how much energy has been transferred by the force.

For example, if you push a crate along a rough floor, work is done by your pushing force. Energy is transferred from your chemical store to other stores, including thermal stores of the crate and floor. In this lesson, the key calculation is the amount of energy transferred, not the detailed path through every store.

Worked example:

A constant force of $40 N$ moves a trolley $3.0 m$ in the direction of the force.

So $120 J$ of work is done, meaning $120 J$ of energy is transferred by the force.

You can rearrange the equation when a question gives energy transferred or work done:

Keep units consistent: force in $N$, distance in $m$, work done or energy transferred in $J$.

Lifting objects and GPE

When an object is lifted, work is done against gravity. In the diagram, assume constant speed and negligible resistance: the lifting force balances weight and its work becomes GPE. The energy transferred increases the object's gravitational potential energy, often shortened to GPE.

[DIAGRAM: asset_name: Lifting a crate and gaining GPE; asset_slug: p38_work_done_and_gravitational_potential_energy__diagram_01; recommended_method: image_gen; description: NovaLearn pale-palette vertically lifted crate with upward force F, a dashed higher crate position and height h measured exactly between the two bottom edges; work done by F leads to energy transferred and a GPE gravitational-store box.]