From: fortunati.luigi@gmail.com   
      
   On Fri, 13 Feb 2026 18:05:38 PST, kaukasoina3dore73js4@sci.fi (Petri   
   Kaukasoina) wrote:   
    >Luigi Fortunati   wrote:   
    >>A body of mass 2m cannot bounce back (in place!) when it collides with a   
    >>body of mass m, otherwise a body of mass 3m, 10m, or 100m would also   
    >>bounce back.   
    >   
    >3m will stop. Less than 3m will bounce back. More than 3m will only   
   slow down.   
      
   On Fri, 13 Feb 2026 18:05:45 PST, pa@see.signature.invalid (Pierre   
   Asselin) wrote:   
    >Luigi Fortunati  wrote:   
    >> Il 12/02/2026 07:30, Luigi Fortunati ha scritto:   
    >> > The Wikipedia entry for "Elastic collision"   
    >> > https://en.wikipedia.org/wiki/Elastic_collision   
    >> > contains the following animation   
    >> > https://youtu.be/wl0c6NMysY4   
    >> > where the two bodies collide at point x and instantly reverse   
   direction.   
    >> [ ... ]   
    >   
    >> I dispute what the moderator wrote.   
    >   
    >> A body of mass 2m cannot bounce back (in place!) when it collides   
   with a   
    >> body of mass m,   
    >   
    >And yet, it bounces back, though with a reduced velocity.   
    >   
    >> otherwise a body of mass 3m, 10m, or 100m would also bounce back.   
    >   
    >No, a body of mass 3m would stop cold, and bounce the body of mass m   
   with velocity 2*v.   
    >More massive bodies would continue forward with reduced velocity, and   
   bounce the smaller   
    >body with increased velocity.   
    >   
    >> It's obvious that a body of mass 100m, colliding with a body of mass m,   
    >> can only slow down but not stop in place and bounce back!   
    >   
    >Slows down a bit and bounces the smaller body with velocity   
   approaching 3*v.   
    >The formulas are in the text above the animations. (Mind the signs of   
   the vA1,vB1 and vA2,vB2.)   
      
   Yes, even in the newsgroup free.it.scienza.fisica the discussion has   
   reached this point: the 3m mass body stops, the smaller mass body moves   
   backward, the larger mass body slows down but continues forward without   
   stopping.   
      
   The problem is determining where the body stops, because my objection   
   doesn't concern the initial and final velocities, but only the location   
   of the rebound.   
      
   In the animation, the two bodies rebound exactly at the point of   
   contact, and this is only true when the masses of the two bodies are equal.   
      
   The reason is simple: if the two bodies have the same mass, the system's   
   center of mass is stationary and, during the compression and subsequent   
   springback, remains stationary (as required by the law of conservation   
   of momentum), so, in the end, the rebound occurs at the same point of   
   contact.   
      
   However, in our animation, where the masses are different, the system's   
   center of mass moves continuously to the right (due to the law of   
   conservation of momentum), even throughout the entire collision.   
      
   Consequently, when the rebound ends, the two bodies are no longer where   
   they began the contact but are further to the right.   
      
   All of this is missing in our animation, where body "2m" returns to the   
   same point of contact and not from a later point, as it should in reality.   
      
   Luigi Fortunati   
      
      
   [[Mod. note --   
   As I pointed out earlier, the animation assumes that the bodys'   
   accelerations are nonzero for only a short time.  This implies that   
   the bodies move only a very short distances (so short that we can   
   neglect them) during the time interval that their accelerations are   
   nonzero.   
   -- jt]]   
      
   --- SoupGate-Win32 v1.05   
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