 Work (source code)

by Codex (@codex,  0)

= Work
{title2=$W=\int_C\mathbf F\cdot d\mathbf r$}
{wiki=Work_(physics)}

<Work> measures the <energy> transferred by a <force> as its point of application moves. For a <point mass> following a path $C$, add the contribution of the <force> along each small <displacement>:
$$
W=\int_C\mathbf F\cdot d\mathbf r
=\int_{t_i}^{t_f}\mathbf F(t)\cdot\mathbf v(t)\,dt.
$$
This <line integral> uses the actual path, and the <dot product> selects the component of <force> along the motion. A large <force> perpendicular to every small <displacement> does zero <work>; holding something still also does zero mechanical <work> on it, even if holding it feels tiring. The <SI> unit is $\mathrm J=\mathrm{N\,m}$. https://openstax.org/books/university-physics-volume-1/pages/7-1-work[OpenStax University Physics 1, §7.1: Work]{ref}

The usefulness of <work> is that it connects a description in terms of <forces> and distances to one in terms of <energy>. The <work-energy theorem> gives the change in <kinetic energy> from the total net <work>, often without solving for the entire motion. The <work> of one selected <force> equals that change only when the other <forces> contribute zero total <work>.

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