Work, Energy & Power · Interactive

Work by a Variable Force

The work done by a force is the area under its force–position graph. Choose a force law, sweep the block from start to finish, and watch the shaded area fill in — that area, in joules, is exactly the work done and the kinetic energy the block gains.

▮ Shaded area = Work ● Force marker ▮ Block KE W = ∫ F dx

Force law

Force c 8.0 N
Displacement x_end 6.0 m
work done 48.0 J
W = F·d
48.0
work W (J) · area
8.0
force at x_end (N)
6.0
displacement (m)
8.0
avg force (N)
W = ∫ F dx = area const: W = F·d spring: W = ½k x²

Playback

Try this: a spring's F = kx gives a triangular area, so stretching twice as far costs 4× the work (W = ½k x²). A constant force gives a simple rectangle, W = F·d.