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Work is done when a force acts over a distance. Its units are given in Newton-metres, or Joules (J). If force is variable and given as a function $ \vec{F} = f(x) $ (with x being the position), and b - a is the interval over which the force acts, work is given by

$ W = \int^b_a f(x)dx $

or more generally (as a vector line integral)

$ \int_a^b \vec{F} \cdot d \vec{r} $

If the force is constant and always parallel to the displacement vector, this simplifies to

$ W = | \vec{F} | d $ or

Formulae for workEdit

  • $ W = -\Delta U $, where U is potential energy
  • $ W = \int^b_a P(t)dt = P_\mathrm{avg} t $ where P is power
  • $ W = \int_{\alpha}^{\beta} \tau\, d \theta $ where τ is torque and θ is the angle across which torque is applied
  • $ W = \tau \theta $ (if τ is constant)
  • $ W = \frac{1}{2} k x^2 $ for a spring obeying Hooke's law
  • $ W = \int^b_a P \ dV $ where P is pressure and a and b are initial and final volumes