**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

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