Mechanics

Potential energy - formula in LaTeX

Gravitational potential energy near the Earth's surface, measured from a reference level you choose. LaTeX typesets adjacent letters as a product; if you want a visible multiplication sign, put \cdot between them.

E_p = m g h

LaTeX code

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$$
E_p = m g h
$$

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What the symbols mean

$E_p$: potential energy (J)
$m$: mass (kg)
$g$: gravitational acceleration, about 9.81 m/s²
$h$: height above the reference level (m)

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

Worked example

A 2 kg backpack carried up one floor, 5 m above the ground floor, which you take as the zero level. The unit m/s² is written \mathrm{m/s^2}: superscripts work inside \mathrm as well.

E_p = 2\,\mathrm{kg} \cdot 9.81\,\mathrm{m/s^2} \cdot 5\,\mathrm{m} = 98.1\,\mathrm{J}

LaTeX commands in this formula

x_{0}: subscript; wrap several characters in braces

How to use this formula in LaTeX?

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The formula works without extra packages.

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