Re: Inertia and third principle

There is some error in my previous post, which I have corrected here.

The force compresses if it encounters a reaction and accelerates if it does not.

If the reaction exists but is insufficient, the force compresses until the reaction is canceled out and then (with what remains, i.e. with the "net" force F=ma of Newton's 2nd law) accelerates.

If I push against the wall I only generate compression because my force does not overcome the wall's reaction and there is no net residual force left to accelerate.

Instead, if I push a cart, I obtain both compression (at the point of contact where the cart reacts) and acceleration with what remains of my force net of what was used for the compression.

The sum of my force that compresses plus the residual "net" force that accelerates is exactly equal to the overall force I exerted on the cart.

This division between compression and acceleration can be clearly seen in the animation https://www.geogebra.org/m/qterew9m where there are two bodies A (mass=15) and B (mass=9) colliding at speed v= 1 and v=-1.

At instant 3, the action of body A (+9) and the reaction of body B (-9) are exactly equal and opposite and, therefore, compress the contact zone without accelerating.

In fact, the 18 particles involved were globally still before (+9v and -9v) and are still after (+0 and -0).

Instead, at instant 5, the impulsive force +15 (in some unit of measurement) of body A on body B generates a further opposite reaction which increases from -9 (what it was at instant 3) to -12.75, so that the remaining force +2.25 (+15-12.75) which finds no reaction, instead of compressing, accelerates body B.

At the end of the collision, the +6 sum of the momentum of body A (+3.75) and body B (+2.25) is perfectly equal to what it was before the collision (+15-9=+6), in accordance with the law of conservation of momentum.

The equality of the opposite action and reaction forces exerted by body A on body B and vice versa is valid if it is limited to only the two opposite compressive forces (+12.75 and -12.75) but not if we consider the entire impulsive force (action ) of body A (+15) and the entire reaction of body B (-12.75).

The forces that compress are equal and opposite, those that accelerate are not.

Luigi Fortunati