Why does a spring have potential energy compared to a rod?

Question

From what I understand, a solid body or rod should not add work to a system. This is because these bodies internal forces are passed through touch:

If the action and reaction forces are applied at the same point but on different stuck together body segments, the work of the action force will cancel out with that of the reaction since the internal forces are opposite and go through the same path(because they are passed through touch at the same point). Thus, it is clear the work of the internal forces is nullified.

This argument seems to apply to a spring system (for instance a spring with masses attached on both sides) since the spring's internal forces are passed by touch. Thus, apparently, a spring, in a system should not add to it work, which nullifys the need for a spring to have potential energy (since the potential energy comes to cancel out the spring's work).

In which way does the argument shown above fail in the spring's case while working in the solid body's case?

Answer 1

In practice there is no such thing as a perfectly rigid rod. All rods compress to some extent, so they are like extremely stiff springs, but they are such stiff springs that you can ignore the compression. Examples and exercises in physics are usually idealised (eg they might assume a perfectly round wheel or or a perfectly flat surface), so a rod might be considered to be perfectly incompressible for that reason.

If you bear in mind that work is force multiplied by distance, then when you compress a spring the distance through which it is compressed will usually be significant, but for a perfectly incompressible rod the distance will be zero, hence the work done when you apply a force to try to compress the rod is zero.

The explanation that internal forces, being passed through touch, do not add work, is simply misleading. At a microscopic level there is no such thing as touch. Forces are passed through solids as a consequence of electromagnetic forces which arise when the particles comprising the solid are perturbed from their equilibrium positions, either by compression or extension. The degree of compression or extension depends upon the physical properties of the material. In a stiff solid, a force can be propagated with very little compression, so little work is done. In a more flexible material, the particles in the solid move further from their equilibrium positions when a force is propagated through it, so the material compresses or extends more, and more work is done.