Gravitational Potential Energy

Summary

Gravitational potential energy is the amount of work against gravity to move a mass from a reference point to a chosen point.

Key equation:
$Δ U = m g y$

Read Time

⏱ 1 min

Definition

Gravitational potential energy is the amount of work you must do against gravity to move a mass from a chosen reference point to another point.

If masses naturally want to remain at the reference point, the higher the mass it moves, the more potential energy it has and the more work that must be done.

Derivation

Assumptions

To derive the gravitational potential energy, assume the following:

The potential energy is related to work as $Δ U = - W$
The total work is from the ground to some height $y$ value
Assume the ground (0 position) has no potential energy
Let upwards be positive

Use the image below as visual aid ^[1]
!300

\begin{aligned} Δ U & = - W \\ = - \int_{0}^{y} F_{g} d y \\ = - \int_{0}^{y} - m g \cdot d y \\ = m g \int_{0}^{y} d y \\ = m g y \end{aligned}

Taken from https://tikz.net/dynamics_gravity/ by Izaak Neutelings (Febuary 2022) ↩︎