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From: Luigi Fortunati <fortunati.luigi@gmail.com>
Newsgroups: sci.physics.research
Subject: Newton's 3rd law is wrong
Date: Mon, 16 Sep 2024 00:01:35 PDT
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Approved: Jonathan Thornburg [remove -color to reply]" <dr.j.thornburg@gmail-pink.com (sci.physics.research)
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I realize the enormity of the title of this article that refutes a law 
that is more than three centuries old and that has never been contested 
until now, but before presenting this work, I have carefully checked 
all the concepts, numbers and formulas and I am ready to present this 
article of mine in all other possible venues if it is rejected by 
Physics Review.

Mine will be a logical, physical and mathematical demonstration.

Newton writes: If a horse pulls a stone tied to a rope, the horse is 
also equally pulled towards the stone: in fact the rope stretched 
between the two parts, by the same attempt to loosen, will push the 
horse towards the stone and the stone towards the horse; and it will 
impede the advance of the one by as much as it will promote the advance 
of the other.

But this is not always true!

Indeed, it is true only in the one case in which the horse moves with a 
rectilinear and uniform motion.

The explanation is simple.

The rope is subjected to two opposing forces, on one side there is the 
action of the horse that pulls to the right and on the other there is 
the reaction of the stone that pulls to the left.

If the two opposing forces are equal, the rope moves in a rectilinear 
and uniform motion but if the horse accelerates, the rope also 
accelerates and, therefore, during the acceleration the action of the 
horse is necessarily greater (and not equal) to the reaction of the 
stone and, therefore, what Newton says is true *only* when the horse 
does not accelerate.

[[Mod. note -- You're missing some forces here.  If you account for
*all* the forces, Newton's 3rd law remains correct.

Let's look at this case (the horse, rope, and stone are all accelerating)
a bit more carefully.  For convenience of exposition, I'll take the
velocity and acceleration of all three bodies to be to the right.
And, I'll idealise the rope as having a constant length, i.e., as
not stretching.  (This means that the accelerations of the horse,
rope, and stone are all the same.)

Then we have the following free-body diagrams for the horizontal forces:

  <---stone------>   <------rope------->   <-------horse--------->

Each of the three objects has *two* distinct forces acting on it:
Stone:
  F_stone_left: friction of the ground on the stone
                (force pulling left to the left)
  F_stone_right: rope tension at the stone's end of the rope
                 (force pulling right on the stone)
Rope:
  F_rope_left = rope tension at the stone's end of the rope
                (force pulling left on the rope)
  F_rope_right = rope tension at the horse's end of the rope
                 (force pulling right on the rope)
Horse:
  F_horse_left = rope tension at the horse's end of the rope
                 (force pulling left on the horse)
  F_horse_right = force applied to horse by horse's legs acting on ground
                  (force pulling right on the horse)

By Newton's 2nd law,
  F_stone_right - F_stone_left = m_stone a			(1)
  F_rope_right  - F_rope_left  = m_rope  a			(2)
  F_horse_right - F_horse_left = m_horse a			(3)
where /a/ is the (common) acceleration.

Since we've assumed /a > 0/ (acceleration to the right), we can infer
several things:

Since the stone is accelerating to the right, there must be a net force
to the right acting on it, i.e., we must have
  F_stone_right > F_stone_left.					(4)

And, since the rope is accelerating to the right, there must be a net
force to the right acting on it, i.e., we must have
  F_rope_right > F_rope_left.					(5)

And, since the horse is accelerating to the right, there must be a net
force to the right acting on it, i.e., we must have
  F_horse_right > F_horse_left.					(6)

Notice that Newton's 3rd law only relates the forces of bodies that
are directly exerting forces on each other.  That is, Newton's 3rd law
says that
  F_stone_right = F_rope_left,					(7)
and that
  F_rope_right = F_horse_left.					(8)
But in general Newton's 3rd law does NOT itself say anything about the
relationship between F_stone_right and F_horse_left, becauase the stone
and the horse aren't directly exerting forces on each other.

Combining (4), (5), (6), (7), and (8), we have that
  F_horse_right > F_horse_left		(this is just (6) again)
		  = F_rope_right	(by (8))
		    > F_rope_left	(by (5))
		      = F_stone_right	(by (7))
			> F_stone_left	(by (4)
i.e., we conclude that
  F_horse_right > F_stone_left					(9)
In other words, the force-to-the-right applied to the horse by the
horse's legs acting on ground must be larger than the friction
force-to-the-left of the ground acting on the stone.  This is just
what we'd expect for acceleration to the right.

*If* we approximate the rope as having zero mass, then (2) says that
the rope tension is the same at both ends, i.e.,
  F_rope_right = F_rope_left.					(9)
We can then combine (7), (8), and (9) to infer that
  F_stone_right = F_horse_left

Regardless of whether we approximate the rope as having zero mass,
or we treat the rope's mass as nonzero, in either case there's no
violation of Newton's laws.  In particular, in either case the forces
F_stone_right and F_horse_left *act on different objects* (the stone
and the horse, respectively).  Each object (still) has a net force
acting on it which points to the right.
-- jt]]

Newton also says: If some body, colliding with another body, will in 
some way have changed with its force the motion of the other, in turn, 
due to the opposing force, will undergo an equal change in its own 
motion in the opposite direction.

[[Mod. note -- This statement is a bit ambiguous: I can't tell what
you mean by "motion".  Are you referring to velocity?  Acceleration?
Force?  Linear momentum?  Angular momentum?
-- jt]]

It is true and it is also obvious: the motions are modified in opposite 
directions to the same extent because the sum of the forces that push 
to the right is always exactly equal and opposite to the sum of the 
forces that push to the left.

But if all this is true, it is not equally true that all the forces 
that push to the right are actions of body A on body B and all those 
that push to the left are reactions of body B on body A.

I will demonstrate this with two animations and the related 
calculations.

In the first animation I will show what, in all likelihood, was the 
main cause of the error that underlies the third law: believing that a 
property valid for single particles can be extended with impunity also 
to bodies.

In the animation https://www.geogebra.org/m/d667egkq we can (with the 
appropriate sliders) collide and rotate the two particles A and B to 
realize that the action and the reaction are *always* equal and 
opposite because it is geometrically impossible to make the blue area 
(action) greater or less than the red area (reaction): no particle A 
can ever act on particle B more or less than particle B reacts on 
particle A.

All true, as the third law prescribes.

But if we transfer this law from particles to bodies, it is no longer 
correct and I demonstrate this with the second animation 
https://www.geogebra.org/m/gd8uqyff where there is body A (mass m=2) 
formed by the two particles A1 and A2 and body B (mass m=1) formed by 
the particle B1 alone.

With the appropriate slider we can collide the two bodies to see how 
(during the collision) the 4 forces F1, F2, F3 and F4 arise and grow 
until the maximum compression.

The vector sum of all these forces is zero (and this is why the total 
momentum is conserved) but not all these forces are actions and 
reactions between bodies A and B.

So, what are the action and reaction forces between bodies A and B?

Certainly the forces F1=+1 and F2=-1 which cancel each other out are.

Certainly *not* is the force F4=-0.67 which is internal to body A and 
does not concern body B.

The force F3=+0.67 is only at half so because the particle A2, pushing 
towards the right, acts on everything it finds on the right and, 
========== REMAINDER OF ARTICLE TRUNCATED ==========