---
title: "Work Done by a Force at an Angle"
description: "Only the part of a force along the displacement does work, which gives W = Fs cos theta. A force at right angles to the motion, such as the string tension on a whirled object, does none at all."
canonical: https://lightmysky.com/learn/science/work-done-by-a-force-at-an-angle-mt_OvBtur6dW5
source: https://lightmysky.com/learn/science/work-done-by-a-force-at-an-angle-mt_OvBtur6dW5.md
retrieved: 2026-09-12
---

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# Work Done by a Force at an Angle

Only the part of a force along the displacement does work, which gives W = Fs cos theta. A force at right angles to the motion, such as the string tension on a whirled object, does none at all.

Subject: Science · Area: Energy · Ages 16 to 18
Page: https://lightmysky.com/learn/science/work-done-by-a-force-at-an-angle-mt_OvBtur6dW5

## Ready when they can

- Calculates work done when the force and the displacement are not in line
- States the work done by a perpendicular force as zero and gives a worked example of one
- Reads work done off a force-displacement graph as the area beneath it

## Lesson: Work when the push is at an angle

Work is the component of force along the motion times the distance. That gives W equals F d cos theta, where theta is the angle between the force and the displacement.

**Example.** You drag a sledge with a rope held at 30 degrees to the ground. Only the along-ground part of the pull does work. A person carrying a briefcase on level ground does no work on it, because the lifting force sits at right angles to the motion.

A force at right angles to the motion does zero work, since cos 90 is zero. A force that opposes the motion does negative work, like the generator lowering a briefcase at steady speed. Work is also the area under a force against displacement graph.

**Tip.** The joule is one newton acting through one metre in its own direction. Split any angled force into parallel and perpendicular parts, keep the parallel part, and drop the rest.

**Recap.** Only the along-motion part of a force works, and right angles give zero.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Moments, Couples and the Conditions for Equilibrium](https://lightmysky.com/learn/science/moments-couples-and-the-conditions-for-equilibrium-mt_EDsdTZ0BNO)
- [Calculating Work Done and Power](https://lightmysky.com/learn/science/calculating-work-done-and-power-mt_udulQxseg1)

## Opens up

- [Power as Force Times Velocity, and Efficiency](https://lightmysky.com/learn/science/power-as-force-times-velocity-and-efficiency-mt_2FFGLIjgV6)
- [Work as a Line Integral Along a Path](https://lightmysky.com/learn/science/work-as-a-line-integral-along-a-path-mt_UFuQUPGAt7)