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.

(I.e., It would be possible to provide a piece of steel, whose force-modulus is higher than that of a Human bone, and yet, enough force could be exerted on that using a hydraulic press, to make it deform visibly, but not break. Such a body would be ‘less elastic’ / ‘more rigid’ than the bone, and yet bend. )

But, if I was able to measure the length of one of Francis’ bones with a micrometer, before and after I’ve applied a few pounds of force on it, the bone’s length will seem to change by a few microns – which is too small a difference to make out with the naked eye.

And so, the phenomenon that takes place inside the bone, by which ‘it knows to react to its environment with a force’, is actually this microscopic amount of compression, and the way this ultimately interacts with the Electrostatic Force. Mechanical rigidity, tensile strength, and resistance to compression, of ordinary matter, are all caused by the Electrostatic Force.

Francis chose not to believe this.

If the reader was to say, that he’s in possession of a body, that does not consist of atoms of matter, then what would cause it be be rigid, elastic, etc., would turn into another discussion entirely, because again, the macroscopic properties of that body, would be a function of what happens inside it microscopically.


 

I am assuming that what Francis was asking me each time, was what causes the bones inside our skeleton to act as rigid bodies, that can withstand force. If we wanted to know why we can move our arms – at a basic level – then I suppose that we’d need to explain that, at a molecular-biological level, our muscles act as ‘contraction engines’, that are fueled chemically by our nourishment, and those muscles exert force at certain points of our skeleton – that is always a tension, and that our skeleton acts as a natural system of levers, that can turn the pure ability of our bodies to make its muscles contract, into an ability to move at will.

(Edit On The Same Day: )

Because the Electrostatic Force, and the Magnetic Force, are understood to be part of the same Universal Force, I suppose a good question to ask might be: ‘Does magnetism on the subatomic scale, affect the phenomenon of mechanical rigidity on the macroscopic scale?’ And the honest answer would be ‘Yes, Indirectly.’

The magnetic force causes the electrons to form pairs. Without it, there would be no spin-spin decoupling. Single electrons are unable to form bonds between atoms. Thus, the existence of such bonds, owes to the existence of magnetism.

But that subject is harder for me to get in to.


 

A word of caution to some readers:

The fact should also be acknowledged, that where bones form joints, there is a piece of cartilage between the bones, that lubricates and cushions them.

When Humans walk upright, they become slightly shorter, than Astronauts become, who have spent a lot of time in space. This is due to the compression of the spinal cartilage, which has a much-lower force modulus than bone-matter.

While this is interesting from the perspective of Human Anatomy, it does little to help me explain the general workings of matter. If I press against a wall with my arm, the cartilage in my elbow certainly compresses by a greater distance, than either the bones in my forearm, or the bone in my upper arm do. Yet, as much as my cartilage does, these bones also need to translate force. And so my answer does not change, as to why bone-matter itself would.

Dirk

 

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