Re: Inertia and third principle

Luigi Fortunati il 05/08/2024 20:41:20 ha scritto:

[[Mod. note --
To analyze a collision at the level of granularity you're trying to
achieve (i.e., forces acting on the individual mass particles which
make up bodies A and B, you need to include the inter-particle forces
between the particles which make up each body.  That is, if we label the
columns of particles in your animations from left to right as A5, A4,
A3, A2, A1 (comprising body A) and B1, B2, B3 (comprising body B),
then we need to take into account that the actual structure is
effectively
   A5 <--> A4 <--> A3 <--> A2 <--> A1    B1 <--> B2 <--> B3
where each '<-->' denotes a spring...

Exactly, between the particles there are elastic forces that act like springs.

And as in all springs, if there is compression there are forces, if there is no compression there are no forces.

Before the collision there are no forces because there is no compression, during the collision suddenly the forces are there because the compression is there: this is why I talk about forces that are activated.

To analyze the collision, we really need to write out Newton's 2nd
law for all the particles, taking into account all the forces.  It's
a bit of a mess, but it will give a precise answer.
-- jt]]

Great, I use Newton's 2nd law F=ma.

In my animation https://www.geogebra.org/m/qterew9m the force that brakes body A is F=ma=15*-3/4=-11.25.

The one that stops body B and then accelerates it backwards is F=9*(1/4--1)=9*+5/4=+11.25.

Therefore, the forces acting on bodies A and B during the collision are equal and opposite.

This result was tormenting for me because I was certain (and I am certain!) that the action of body A on body B cannot be equal to the reaction of body B on body A.

But my certainty was shattered on the rock of the mathematical result mentioned above.

With these doubts, I spent days and days trying to clarify every little thing, I consumed an entire notepad filling it with notes, numbers, formulas and concepts.

And finally, I understood where the solution was.

The forces acting on bodies A and B are (as I have already said) certainly equal to +11.25 and -11.25.

But how much of that +11.25 is action force exerted by A against B and how much of that -11.25 is reaction force exerted by B against A?

Certainly, the force +11.25 on body B is exerted entirely by body A.

However, not all of the -11.25 force on body A is exerted by body B.

In fact, body B can only exert a force equal to -9 on body A, which is all the force it has and with which it manages to stop body A in the first 3 instants of my animation.

After the first 3 moments, body B no longer reacts against body A and, therefore, retreats and goes away!

So, the action and reaction ends here, with the action being worth +11.25 and exceeding the -9 reaction by +2.25 (+11.25-9).

Obviously, the matter does not end here because the answer to the question is missing: if body A, during the collision, receives a force equal to -11.25, who provides the remaining force -2.25 that body B does not provide (since it limits to -9)?

It's an answer that I will have to give but I can't give it here because the post would become too long and I will do it in the next post (if the moderators allow me to do this double intervention).

Luigi Fortunati.