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.

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.

[[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.

It says that F_rope_right - F_string_left = m_rope_verysmall*acceleration, because very small and zero are not the same thing at all!

You cannot make the acceleration disappear by decreasing the mass!

The rope, no matter how small its mass, always accelerates exactly as much as the horse and the stone.

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".

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".

Luigi Fortunati