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Lesson 18 · Work is a push through a distance
A push, through a distance
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A push, through a distance

Work is not effort — it is a force times the distance it acts through: W=FdW = Fd, W equals F d: the work WW in joules, the force FF in newtons, the distance dd in metres. No distance, no work: lean on a wall all afternoon and the wall owes you nothing.

The fine print is direction. Only the part of the push ALONG the motion counts — the full law is W=Fdcos⁡θW = Fd\cos\theta (W equals F d cosine theta, where θ\theta — the Greek letter theta — is the angle between the push and the direction the thing actually moves), and in this lesson force and motion are aligned, so cos⁡θ=1\cos\theta = 1 and the fine print sleeps. It wakes for the last question: a force at right angles to the motion has cos⁡90∘=0\cos 90^\circ = 0, so carrying a suitcase across a level floor does zero work on it. Carried is not worked.

And run the free check before any arithmetic: newtons times metres cancel to joules, so W=FdW = Fd survives. Units guide the way — they don't confess.

Fθd

W=Fdcos⁡θW = F d \cos\theta

  • WW= Work (energy)
  • FF= Force (force)
  • dd= Displacement (length)
  • θ\theta= Angle between force and motion (angle)
Work (W = Fd cos θ) solver →