Re: Newton's 3rd law is wrong

Mikko il 21/09/2024 19:21:13 ha scritto:

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.

Who tells you that equalities (where there are no net forces and not even acceleration) only apply to the ends of the rope?

I'll tell you: the 3rd law tells you and you repeat it trusting that the ends of the rope have particular characteristics that allow them not to accelerate while all the other points of the rope accelerate.

But this is not true at all because the ends of the rope accelerate exactly like everything else, proving that on the entire rope (ends included) a force acts to the right (that of the horse) greater than that which acts to the left (that of the stone).

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.

This is really bizarre!

What does it mean that there is no mass at the end of the rope?

What is there that acts as a bond between the rope and the horse and between the rope and the stone: a hole? A void?

It is obvious that the bond is between mass and mass, without jumps and without interruptions.

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.

I did not say that they move as a *rigid* body but as a *single* body where there are no interruptions, no voids and no detached parts.

[[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.

All this that you are saying here has nothing to do with the acceleration of the rope that depends *exclusively* on the horse and the stone.

The rope accelerates to the right *exclusively* because the horse's force (action) pulls it to the right *more* than the reaction of the stone pulls it to the left.

Otherwise, the rope would go forward at a constant speed, without accelerating.

Obviously.

Luigi Fortunati