Elastic Bodies. Force.

A certain person named Francis used to ask me repeatedly,

“When my arm pushes against a wall, or when anything pushes against my arm, what causes the force?”

I always answered his question exactly the same way.

When we think of the bone inside the arm, or of components used to build houses and walls, we think of those as ‘rigid bodies’. But in reality, rigid bodies are just special cases of ‘elastic bodies’, and one needs to understand why elastic bodies exist, in order to understand rigid bodies, in the way He asked.

The molecules that make up an elastic body, generally consist of atomic nuclei that are separated by electron-pairs, or chemical bonds. These bonds act as ‘microscopic springs’.

When the distance between two nuclei that are part of a molecule is at its neutral distance, the electrostatic repulsion between the nuclei equals, or cancels with, the electrostatic attraction caused by the electron-pair itself.

If the distance between the nuclei decreases slightly, then the electrostatic repulsion increases, but the attraction caused by the electron-pair – i.e. caused by the chemical bond – stays about the same. And so a net repulsive force results, that tries to restore the distance between them to their neutral distance.

If the distance between the nuclei increases slightly, then the electrostatic repulsion decreases, but the attraction caused by the electron-pair – i.e. caused by the chemical bond – stays about the same again. And so a net attractive force results, that tries to restore the distance between them to their neutral distance.

One reason why the folly is still undertaken today, to teach Newtonian Bodies to Students, prior to teaching more-advanced concepts, is the fact that what happens on the macroscopic scale in Newtonian Mechanics, also tends to approximate what happens on the microscopic scale, and vice-versa. With Quantum-Mechanics, Relativity, etc., this can no longer be guaranteed. And it helps explain why Newton was able to ‘understand his world’ so well, even though the subatomic world wasn’t known yet, in his era.

Elastic bodies are made out of a huge number of atoms, but their macroscopic behavior derives from their microscopic behavior, in that If the distance between their end-points decreases slightly, from its neutral distance, a net repulsive force results, while if the distance between their end-points increases, a net attractive force results. This latter, net attractive force is also due to their ‘tensile strength’.

When such elastic bodies are only modeled as having two end-points, then they are also simplified as ‘springs’. And springs have a so-called ‘force-modulus’, which is a linear factor, by which a small change in distance, results in some change in force. If a spring has a very low force-modulus, then it is very ‘soft’ or elastic. If it has a very high force-modulus then it is very ‘stiff’ or inelastic.

Beyond some amount of compression the spring will fracture, and this behavior is known as ‘brittleness’. If the spring is very brittle, then it won’t compress much, before it breaks.

The fact to understand about rigid bodies, is that they are just elastic bodies, whose force-modulus is so high, that we don’t humanly observe them deform. And the brittleness is also so weak, that to try to apply enough force to them to make them (appear to) deform, is impractical and just results in their breaking.

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