{
  "aliases": [
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  "body": "\n## Summary\n\nThe work done by a force field $F$ on a particle that moves along a curve $\\gamma$ is the [[line integral|0H5MR9B6GT]] $W = \\int_\\gamma F \\cdot d\\mathbf{r}$.\nOnly the component of the force along the direction of motion contributes, positively when it points forward and negatively when it points backward.\n\n## Remarks\n\nFor a constant force $F$ and a straight displacement $d$, the work is $F \\cdot d$.\nFor a $C^1$ path, $W = \\int_a^b F(\\gamma(t)) \\cdot \\gamma'(t) \\, dt$. The integrand $F \\cdot \\gamma'$ is the power, the rate at which the force does work.\nIf $F = -\\nabla U$ for a potential energy $U$, then $W = U(\\gamma(a)) - U(\\gamma(b))$, and the work does not depend on the path. Gravity near the surface of the Earth is an example.\nA force that is always orthogonal to the velocity does no work.\n\n## Explanations\n\n### L1 human\n\nWork measures how much a force helps a motion.\nPushing a box forward does positive work, pushing against its motion does negative work, and pushing straight down on a sliding box does no work.\n",
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