Re: Inertia and third principle

Mikko il 15/08/2024 15:52:30 ha scritto:

There is some error in my previous post, which I have corrected here.
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The force compresses if it encounters a reaction and accelerates if it does not.

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In a typical collision the interaction first compresses both bodies and
then acclerates them. The amount of compression and acceleration of the
bodies need not be same. In come cases the direction of acceleration can
be opposite to the direction of motion so the speed is reduced.
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Sometimes one of the bodies is so massive that the acceleration is too
small to be detected, e.g. when someting falls to the ground.

These are generic considerations that demonstrate neither equality nor inequality between the action and reaction of the two bodies.

Instead, my animation https://www.geogebra.org/m/qterew9m (together with the numbers and correct reasoning), explains well what is the right relationship between the force that body A exerts on body B and what body B returns to body A.

First of all, this exchange of forces takes place in a limited and very specific area: it is the one at the point x=0 where the collision between the first rows of the two bodies occurs.

All the exchanges of forces that take place behind these two first rows do not take place between one body and another but within each individual body.

At instant 1, the forces are certainly equal and opposite (+3 and -3): body A exerts a +3 impulsive force on body B and body B exerts a -3 impulsive force on body A.

At instant 2, the second row of body A slams into the first, doubling the force it exerts on body B from +3 to +6 but the first row of body B also receives the "help" of its second row and can also oppose a doubled force -6, maintaining the equality between the action and the reaction unchanged.

Even at instant 3, the action remains the same as the reaction because both the first two rows receive help from the third rows and simultaneously increase each other's forces to +9 and -9.

At instant 4 the equilibrium breaks down.

The first two rows do not know what happened behind them, but the first row of body A receives the push of its fourth row and increases the force of its action towards the right from +9 to +12, while the first row of body B cannot do the same because he receives no help from his fourth row (which is not there) and cannot increase his reaction which remains unchanged at -9.

Thus, they face the first row of body A which acts to the right against body B with force +12 and the first row of body B which reacts to the left against body A with unchanged force -9 and is accelerated backwards .

Where is the equality between action and reaction predicted by Newton's 3rd law?

Luigi Fortunati.