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.
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 $E$ and its mass $m$. Definition:

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

The number $\mathcal{U} \:$ is called the total potential energy of P. Recall that if the motion of a material particle 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 strongly on the mass. Then remember that for heavy particles, a sensory interpretation of the mass relates mainly to thermal sensations. And so for Newtonian particles, the potential energy is mostly associated with thermal sensations too.

Right.png Next step: dynamic equilibrium.
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