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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.

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What a learner can do afterwards

  • 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

1 · Read

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.

Try it together

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.

Good to know

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.

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

2 · Watch

Take it off screen

Print a worksheetA4 with an answer key page for grown-ups. No screen, no internet.

Where it sits

Where this leads

Jobs that lean on this skill. Follow one to see everything it is built on.

Then practise

8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.

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Work Done by a Force at an Angle · Science, ages 16 to 18 · LightMySky