- #1

vco

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In textbooks, the total potential energy is defined as the sum of the elastic energy of the body and the potential energy of the external forces. The elastic energy is a well-defined concept, but I have been wondering for years what exactly is the physical interpretation of the "potential energy of the external forces", and consequently, the physical interpretation of the total potential energy itself.

A simple example of the application of the method: for a linear spring with stiffness ##k## loaded with a force ##F##, the elastic energy is [tex]U=\frac{1}{2}ku^2,[/tex] and the potential energy of the external force is defined as [tex]V=-Fu,[/tex] where ##u## is the displacement of the spring. The total potential energy of the system is [tex]\Pi=U+V=\frac{1}{2}ku^2-Fu,[/tex]and by minimizing ##\Pi## with respect to ##u## we end up with the obvious equilibrium equation [tex]ku-F=0.[/tex] In every textbook I have seen, the total potential energy and the associated principle are introduced as if they were some fundamental physical concepts that need no explanation or derivation. Even the name "total potential energy" sounds confusing since it cannot be the energy stored in the system; the stored energy is the elastic energy, is it not?

Also, the Wikipedia article says something about the lost potential energy being turned into heat, how does this fit in? Is this related to the forces being applied instantaneously vs quasi-statically?

So, could someone please explain what is the

*physical meaning*of the

- potential energy of the external forces?
- total potential energy?