Potential Energy

Tampan, Paminggir people. Lampung region of Sumatra, 19th century, 50 x 56 cm. From the library of Darwin Sjamsudin, Jakarta. Photograph by D Dunlop. |

Consider a particle P, that is described by its kinetic energy $K$, its mechanical energy $E$, its momentum $p$ and its mass $m$. Definition: the number $\mathcal{U} \:$ is called the **total potential energy** of P

$\mathcal{U} \equiv E - K$

Recall that if motion is not relativistic then the mechanical energy can be approximated as

$\begin{align} E &\simeq m c^{2} \left( 1 + \frac{p^{2}}{2m^{2}c^{2}} \right) \\ &\simeq m c^{2} \left( 1 + \frac{K}{mc^{2}} \right) \\ &\simeq m c^{2} +K \end{align}$

And so

$\mathcal{U} \equiv E - K \simeq m c^{2}$

For slowly moving Newtonian particles, the potential energy depends very strongly on the mass.

page revision: 82, last edited: 27 May 2017 03:31