From Newsgroup: sci.physics.research

The corpuscle P is stationary at the point x_P=0, while the bodies A
and B approach at the same velocity from the left and right, arriving simultaneously on the corpuscle P, as can be seen in the animation https://www.geogebra.org/classic/fyymjr9s

During the collision, the crushing of the spherical corpuscle P always
occurs (regardless of the mass of the two bodies A and B) because the
forces F1 and F2 are convergent.

Instead, the acceleration of the corpuscle P may or may not occur,
because P, after the collision, can start moving to the right or to the
left (varying its speed from zero to +v or -v) or it can remain
stationary in its initial place x_P=0, leaving its zero speed
unchanged.

What conditions must be met for the corpuscle P to accelerate to one
side or the other and what conditions for it to remain stationary in
its place?

Luigi Fortunati

[[Mod. note -- If (and only if) A and B have the same mass, then the
system is left-right symmetric, so P will remain stationary.
-- jt]]
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From Newsgroup: sci.physics.research

[[Mod. note -- I'm sorry, I mistakenly posted an earlier draft of this
article. The mistake was mine, not the author's. I believe this is the correct version.
-- jt]]

The small body P is at rest at the point x_P=0, while the bodies A and
B approach at the same speed from the left and right, arriving at P at
the same time, as shown in the animation https://www.geogebra.org/classic/ptkfwqh5

During the collision, the crushing of the tiny body P is always there (regardless of the mass of the two bodies A and B) because the forces
F1 and F2 are convergent.

Instead, the acceleration of P may or may not be there because, after
the collision, P can start moving to the right or to the left (changing
its speed from zero to +v or -v) or it can remain at its initial place
x_P=0, leaving its zero speed unchanged.

What conditions must be met for P to accelerate to one side or the
other and what conditions for it to remain at rest in its place?

If the small body P is not there and the points A and B collide
directly with each other, do the forces F1 and F2 stop being
convergent?

Luigi Fortunati

[[Mod. note -- We are given that A and B have the same speed. So, if
(and only if) A and B have the same mass, then the system is left-right symmetric, so P will remain stationary.
-- jt]]
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From Newsgroup: sci.physics.research

Luigi Fortunati il 27/04/2025 17:23:11 ha scritto:

The small body P is at rest at the point x_P=0, while the bodies A and
B approach at the same speed from the left and right, arriving at P at
the same time, as shown in the animation https://www.geogebra.org/classic/fyymjr9s

During the collision, the crushing of the tiny body P is always there (regardless of the mass of the two bodies A and B) because the forces
F1 and F2 are convergent.

Instead, the acceleration of P may or may not be there because, after
the collision, P can start moving to the right or to the left (changing
its speed from zero to +v or -v) or it can remain at its initial place x_P=0, leaving its zero speed unchanged.

What conditions must be met for P to accelerate to one side or the
other and what conditions for it to remain at rest in its place?

If the small body P is not there and the points A and B collide
directly with each other, do the forces F1 and F2 stop being
convergent?

Luigi Fortunati

[[Mod. note -- We are given that A and B have the same speed. So, if
(and only if) A and B have the same mass, then the system is left-right symmetric, so P will remain stationary.
-- jt]]

If A and B have the same mass, will only P remain stationary or will
the entire system A+P+B remain stationary?

Are the internal forces of the system A+P+B (F1 and F2) in equilibrium
only if A and B have the same mass or are they also in equilibrium when
their masses are different?

Luigi Fortunati
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From Newsgroup: sci.physics.research

Luigi Fortunati il 30/04/2025 09:04:27 ha scritto:

The small body P is at rest at the point x_P=0, while the bodies A and
B approach at the same speed from the left and right, arriving at P at
the same time, as shown in the animation
https://www.geogebra.org/classic/fyymjr9s

During the collision, the crushing of the tiny body P is always there
(regardless of the mass of the two bodies A and B) because the forces
F1 and F2 are convergent.

Instead, the acceleration of P may or may not be there because, after
the collision, P can start moving to the right or to the left (changing
its speed from zero to +v or -v) or it can remain at its initial place
x_P=0, leaving its zero speed unchanged.

What conditions must be met for P to accelerate to one side or the
other and what conditions for it to remain at rest in its place?

If the small body P is not there and the points A and B collide
directly with each other, do the forces F1 and F2 stop being
convergent?

Luigi Fortunati

[[Mod. note -- We are given that A and B have the same speed. So, if
(and only if) A and B have the same mass, then the system is left-right
symmetric, so P will remain stationary.
-- jt]]

To the left of P there is only the force of the action to the right of
body A, to the right of P there is only the force of the reaction to
the left of body B.

On the tiny body P the forces of the action of A and the reaction of B *converge*.

These two converging and opposite forces are F1 and F2.

If F1 and F2 were ALWAYS equal and opposite (as Newton's third law
states), body P should never start moving, should never accelerate and
should always remain stationary at x_P=0.

Instead, you have just stated (correctly) that P remains stationary if
(and only if) the masses of the two bodies A and B are equal and NOT
when they are different.

Therefore Newton's third law is wrong.

The forward action of the Newton's horse on the rope and the backward
reaction of the stone on the rope are equal when the rope is
stationary, they are also equal when the rope moves with uniform motion
but they are NOT equal when the rope accelerates and, therefore, the
third law is wrong.

In tug-of-war, the leftward action of team A equals the rightward
reaction of team B only when the rope is stationary and when it is
moving uniformly but not when the rope is accelerating.

How many more ways do I have to prove that Newton's third law is wrong?

Luigi Fortunati.
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