Re: Newton e Hooke

Without a doubt, Newton relates force to acceleration and Hooke relates
it to elastic deformation.

If I push the end A of a spring, do I compress it or accelerate it?

Obviously I compress it and accelerate it at the same time, because I
am not pushing the elastic body of the spring but only its point A.

I ask myself: how much of my force is dedicated to compression and how
much to acceleration?

Here too the answer is simple: it depends on the mass of the spring.

If the mass of the spring is small enough to tend to zero (ideal
spring), the compression tends to zero and the acceleration tends to
100%.

If the mass is large enough to tend to infinity, the compression tends
to 100% and the acceleration tends to zero.

The difference between the force that compresses and the force that
accelerates depends exclusively on the force opposite to ours.

In the first case, our force is opposed by an increasingly smaller
opposing force (which tends to disappear) and then all our force
becomes a net force that accelerates according to the second law.

In the second case, the opposing force becomes increasingly larger
until it equals our force which becomes entirely Hooke's compressive
force where there is no longer any net accelerating force.

Well, what is this opposing force that opposes our force? Obviously it
is the inertia of the elastic body that we are pushing.

This inertia is a force that opposes our real force and, therefore,
this force must also be *real*, exactly as the force of friction is
real, because they have the same function: friction is a real force
because it opposes our real force and inertia is a real force because
it opposes our real force.

There are two inertias: there is the inertia of the body that persists
in its rectilinear and uniform motion and this is not a real force and
there is the inertia of the body that opposes the external force and
this is a real force.

Luigi Fortunati