From: fortunati.luigi@gmail.com   
      
   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   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)