From: dr.j.thornburg@gmail-pink.com   
      
   In article <10mlemh$1pima$1@dont-email.me>, Luigi Fortunati writes:   
   > 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!   
      
   No, it's not obvious, in fact it's not even always true.  Here's a   
   specific example where the body of mass 100m *does* bounce back:   
      
   Suppose we have   
     body A: mass m_A=100 kg, initial velocity v_A1=+1 m/s (moving right)   
     body B: mass m_B=1 kg, initial velocity v_B1=-1000 m/s (moving left)   
   and these bodies have an elastic collision at position x=0 m and t=0 s.   
      
   The formulas in the previously-cited Wikipedia article   
    give the final   
   velocities after the collision as:   
     v_A2 =  -18.822 m/s       (body A recoils to the left)   
     v_B2 = +982.178 m/s      (body B recoils to the right)   
      
   But we don't have to trust the Wikipedia article!  We can check for   
   ourselves whether or not these v_A2 and v_B2 are correct by checking   
   whether or not both linear momentum and kinetic energy are conserved:   
      
   Linear momentum:   
     before the collision: m_A*v_A1 + m_B*v_B1 = -900 kg m/s   
     after  the collision: m_A*v_A2 + m_B*v_B2 = -900 kg m/s   
   i.e., linear momentum is conserved.   
      
   Kinetic energy:   
     before the collision: 1/2 m_A*v_A1^2 + 1/2 m_B*v_B1^2 = 500050 Joules   
     after  the collision: 1/2 m_A*v_A2^2 + 1/2 m_B*v_B2^2 = 500050 Joules   
   i.e., kinetic energy is conserved.   
      
   Since we find that these values of v_A2 and v_B2 conserve both linear   
   momentum and kinetic energy, we know that these are in fact the correct   
   v_A2 and v_B2 for an elastic collision.   
      
   From the initial & final velocities, it's easy to calculate the   
   bodies' positions:   
     t (s)        x_A (m)       x_B(m)   
     -3           -3.0        +3000.0   
     -2           -2.0        +2000.0   
     -1           -1.0        +1000.0   
      0            0.0            0.0        (collision happens here)   
     +1          -18.822       +982.178   
     +2          -37.644      +1964.356   
     +3          -56.465      +2946.535   
      
   So in this case, yes, a body of mass 100 kg does "bounce back" (final   
   velociity is of the opposite sign to initial velocity) after colliding   
   with a body of mass 1 kg.   
      
   --   
   -- "Jonathan Thornburg [remove -color to reply]"    
      (he/him; on the west coast of Canada)   
      "All models are wrong, but some are useful" -- George E. P. Box   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)