Mechanics

Work - formula in LaTeX

The work of a constant force is the dot product of force and displacement, so a force perpendicular to the motion does no work. The dot is \cdot. Write trigonometric functions with a backslash (\cos): without it LaTeX sets three separate italic variables c, o, s.

W = \vec{F}\cdot\vec{s} = F s\cos\alpha

LaTeX code

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$$
W = \vec{F}\cdot\vec{s} = F s\cos\alpha
$$

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What the symbols mean

$W$: work (J)
$\vec{F}$: force (N)
$\vec{s}$: displacement (m)
$\alpha$: angle between the force and the displacement

A classical mechanics formula - it shows up in kinematics and dynamics problems and in physics lab reports.

Worked example

A sled pulled 10 m with a 50 N force at 60° to the horizontal. The degree sign is written 60^\circ, a small circle in a superscript.

W = 50\,\mathrm{N} \cdot 10\,\mathrm{m} \cdot \cos 60^\circ = 250\,\mathrm{J}

LaTeX commands in this formula

\vec: vector
\cdot: multiplication dot
\cos: cosine function in upright type
\alpha: Greek letter alpha

How to use this formula in LaTeX?

Copy the code with the button above - $$…$$ is centered display math.
Paste it into the CamteX editor, Overleaf or any LaTeX document.
Inside a sentence, use single $…$ instead of double.
The formula works without extra packages.

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