Re: inelastic collision (was: Re: Newton e Hooke)

Luigi Fortunati il 16/03/2025 10:28:35 ha scritto:

The animation https://www.geogebra.org/classic/hxvcaphh shows how two
rigid bodies interact when they collide head-on.
>
...

>
So, the new law is defined as follows: "For every action there is a
corresponding opposite reaction depending on the ratio between the two
masses expressed by the equation FA_B=-F_BA(1+(mA-mB)^2/(mA+mB))".

Surprisingly and referring to inertia, Newton said something very
similar: "The vis insita, or innate force of matter, is a power of
resisting, by which every body, as much as it lies, endeavors to
persevere in its present state, whether it be of rest, or of moving
uniformly forward in a right line. This force is __proportional__ to
the body whose force it is...".

Proportional and not equal!

In the collision this is exactly what happens: each of the bodies A and
B endeavors to persevere in its current state of motion and rebels with
a force proportional to the other body that tries to modify it.

Now that I think I have found this proportionality I realize that I
still have a long way to go.

First of all, why does the proportionality depend on
(1+(mA-mB)^2/(mA+mB)) and not on anything else?

I found it indirectly starting from the conservation of momentum and
knowing how the velocities of bodies vary after the collision but I
would need to compare myself with someone who is better than me to find
the direct explanation, to check that everything is correct, to fix
every imperfection or error and to transcribe everything with the
correct scientific language suitable for an official publication.

Is there anyone willing to collaborate with me to fine-tune everything
together or to find any errors that I may have missed?

Luigi Fortunati