[continued from previous message]   
      
   because the whole system is accelerating.  In fact, because we're taking   
   m1 = m2 = m3 and and all three masses have the same common acceleration,   
   it must be the case that F_net_on_m1 = F_net_on_m2 = F_net_on_m3.   
      
      
   On the other hand, suppose that m1=10, m2=80, and m3=10.  Then (11) gives   
     F3 = - ((m2+m3)/(m1+m2+m3)) F1 + (m1/(m1+m2+m3)) F2   
        = -0.9 F1 + 0.1 F2   
        = -95   
   and (19) gives   
     F4 = (m3/(m1+m2+m3)) F1 -   (m1+m2)/(m1+m2+m3) F2   
        = 0.1 F1 - 0.9 F2   
        = +55   
   This means the net forces on the three bodies are now   
     F_net_on_m1 = F1 + F3 = 100-95 = +5   
     F_net_on_m2 = -F3 - F4 = -(-95) - (55) = 95-55 = +40   
     F_net_on_m3 = F2 + F4 = -50 +55 = +5   
   The forces are now different from the equal-mass case (which is not   
   surprising, since we've changed the mass of each individual body).   
   Notice that the forces are in the ratio   
     F_net_on_m1 = F_net_on_m3 = (1/8) F_net_on_m2   
   which just match the ratios of the masses,   
     m1 = m3 = (1/8) m2   
   This is just what we would expect from Newton's 2nd law, since all   
   all three masses have the same common acceleration.   
      
      
      
   So, the simple answer to Luigi's questions is "it depends on the body's   
   internal mass distribution".   
      
   --   
   -- "Jonathan Thornburg [remove -color to reply]"    
      (he/him; currently on the west coast of Canada)   
       "Totalitarianism in power invariably replaces all first-rate talents,   
        regardless of their sympathies, with those crackpots and fools whose   
        lack of intelligence and creativity is still the best guarantee of   
        their loyalty."     -- Hannah Arendt, "The Origins of Totalitarianism"   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)