Re: Newton's 3rd law is wrong

Luigi Fortunati il 15/09/2024 19:01:35 ha scritto:

[[Mod. note -- 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)

 
This alternation of greater and equal cannot be correct because where
there is "greater" it means that there are net forces (and
accelerations) and where there is "equal" there are not.

Those formulas are for situation where there is acceleration and
therefore net forces. The equalities only apply to forces from the
ends of the same interaction. The force at on the horse side end of
the rope must be equal to the froce on the rope side end of the horse
because there is no mass between the horse and the rope. Likewise
there is no mass between the rope and the stone.

The three bodies move as a single body and, therefore, nowhere can
there be areas (small or large) that accelerate together with areas
that do not accelerate.

They do not move like a single rigid body. In particular, there are areas
of the horse that do not accelerate (hoofs when they touch the ground) and
areas that do accelerate (hoofs when they don't touch the ground). When
the force in the rope vaires the length of the rope varies so the
accleretions at the two ends of the rope differ.

[[Mod. note -- In my analysis I idealized the rope as non-stretching,
so that the stone, rope, and non-hoof parts of the horse all share
a common acceleration.  -- jt]]

[[Mod. note -- *If* we approximate the rope as having zero mass, then
(2)   (F_rope_right  - F_rope_left  = m_rope  a)
says that
the rope tension is the same at both ends, i.e.,
F_rope_right = F_rope_left.                    (9)

 
No! If the mass decreases, (2) says something else.

The accleration of the rope is roughly constant and fully determined
by the acclereations of the horse and stone. Therefore, wen the mass
decreaces so does the difference of F_rope_right and F_rope_left. The
difference is zero if the mass of the rope is zero, regardless of
acceleration.

...

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]]

 
This sentence is not mine, it is Newton's and you can find it in his
book "Principles of natural philosophy" under "law III".

It isn't Newton's as Newton wrote his "Principia" in Latin. It isn't
Motte's, either, but uses the word "motion" in the same sense. The
full term is "quantity of motion" but Motte uses plain "motion" as a
shorter term for the product of mass and speed. In today's English the
usual word is "momentum".

He means to say (I think) that: "the collision of body A determines a
variation of the linear motion of body B equal to the variation of the
linear motion of body A in the opposite direction".

Instead of "variation" Motte uses "change". Newton's focus is on initial
and final states although conservation of momFentum also apply during
the collision.

--
Mikko