Re: Inertia and third principle

Il 06/07/2024 12:17, Luigi Fortunati ha scritto:

[[Mod. note --
1. At *every* time during the collision, the force A exerts on B is equal
to precisely -1 times the force B exerts on A (this is just Newton's 3rd
law).

In this way, you (without proof) assume that Newton's 3rd law is correct.

Instead, I will *prove* that it is incorrect.

First of all, I'll start with the fundamental error in your calculations, which is to base yourself on the variations between the final and initial speeds, as if they depended only on the action and reaction forces.

If this were really the case, it is obvious that the third principle would be right in all cases but this is not the case and I demonstrate it to you visually and mathematically with my animation https://www.geogebra.org/m/tmwxph9z where there is the body A with mass mA=2 and body B with mass mB=1.

At the moment of the inelastic collision, the momentum of half the mass of A (mAv/2=+1) and the momentum of the full mass of B (mBv=-1) cancel each other's effects and half the mass of A and the entire mass of B come to rest.

So far, the forces of the two impulses are effectively equal and opposite, and are, without a doubt, action and reaction forces between A and B.

Instead, the force of the impulse of the remaining half mass of A (mAv/2=+1) not only acts on body B (now stationary) but also on the entire mass of body A!

In fact, this +1 impulse is divided proportionally into a part (+1/3) which acts on body B accelerating it from zero to 1/3 of v to the right and a part (+2/3) on the mass of the same body A.

The first part (+1/3) is an action and reaction force between A and B, the second part (+2/3) is not.

The second part (which you use unduly to make balance the accounts) is an *internal* force in body A that has nothing to do with the action and reaction between bodies A and B!

Luigi Fortunati

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