Re: Inertia and third principle

I had the audacity to point out a case in which Newton's 3rd law is wrong, citing numbers, formulas and drawings.

It is something extraordinary: a law considered perfect is not always so.

Yet, there was no one who found a single mistake in what I wrote.

So, I'll go ahead and propose my latest animation
https://www.geogebra.org/m/azp3jkja
in which body A of mass m=15 (15 particles of mass m=1) collides with body B of mass m=9.

The impact lasts only a very small fraction of time but it is still sufficient to be able to divide it into 5 successive instants.

In the first instant the 3 blue surface particles of body A and the 3 red surface particles of body B collide.

The action of the blue particles and the reaction of the red ones occurs according to Newton's 3rd law: the 3 pulses of the blue particles push to the right, the 3 pulses of the red particles push to the left in the same way.

It is the equality of the 3 opposing blue and red forces that guarantees the stopping of the contact particles on the vertical of the y axis, which would not happen if these opposing action and reaction forces were not equal.

In this first phase, the remaining particles of the 2 bodies are not yet affected by the collision.

In the second instant, the 3 particles that are just behind the first ones collide with the particles in front (which have stopped) and push them, adding the force of their impulse.

And since the forces of the 2 second rows are also equal and opposite (always according to Newton's 3rd law), they cancel each other out and, even at the second instant, the first particles stop on the vertical of the y axis.

The same thing happens at time 3.

At instant 4 things change, because the fourth row of red particles (in body B) is not there and the lack of their strength prevents any reaction to the push of the fourth row of blue particles of body A.

These blue particles of the fourth row of B act on the other blue particles in front and their impulse propagates until it reaches the blue particles of the first row, where the respective red counterforce does not reach!

In this way, this blue force becomes a preponderant net force that accelerates the (now) unified body AB towards the right.

And the same happens at instant 5 when the impulsive force of the fifth row also arrives on the surface of body A without encountering any reaction and, thus, contributes to increasing the speed towards the right even further.

As you have noticed, the equality provided by Newton's 3rd law is valid only as long as the reaction can resist it and, obviously, it ceases to be valid when the reaction can no longer resist it.

It is the point of impact that we must observe to understand if the action is equal to the reaction: if it stays still, the equality is there, if it moves it is not.

And here, I want to remind you that Newton, speaking of the third principle, says that the horse pulls a stone tied to a rope with the same force with which the stone pulls the horse.

But this is only true while the horse pulls the stone at a constant speed and not when, at the start, the horse has to accelerate the stone from zero speed to speed v!

Luigi Fortunati