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!   
      
   In article , I gave   
   an example where the body of mass 100m *does* bounce back.   
      
   I realise that although that example is a correct example of an   
   elastic collision of Newtonian point masses, it would be very hard to   
   actually do in an engineering sense, because the collision velocities   
   are very high (~ 1 km/second) and it's very hard to arrange elastic   
   collisions at such high speeds.   
      
   So, to make my example plausible in an engineering sense, let's scale   
   down all the velocities by a factor of 1000.  Now we have:   
     body A: mass m_A=100 kg, initial velocity v_A1=+0.001 m/s (moving right)   
     body B: mass m_B=1 kg,   initial velocity v_B1=-1.0 m/s   (moving left)   
   and these bodies (both point masses) have an elastic collision at position   
   x=0 m and t=0 s.   
      
   The final velocities (after the collision) are now   
     v_A2 = -0.0188 m/s      (body A recoils to the left)   
     v_B2 = +0.9822 m/s      (body B recoils to the right)   
      
   Again, we can check whether total linear momentum and kinetic energy are   
   conserved:   
      
   Total Linear momentum:   
     before the collision: m_A*v_A1 + m_B*v_B1 = -0.9 kg m/s   
     after  the collision: m_A*v_A2 + m_B*v_B2 = -0.9 kg m/s   
   i.e., total linear momentum is conserved.   
      
   Total kinetic energy:   
     before the collision: 1/2 m_A*v_A1^2 + 1/2 m_B*v_B1^2 = 0.50005 Joules   
     after  the collision: 1/2 m_A*v_A2^2 + 1/2 m_B*v_B2^2 = 0.50005 Joules   
   i.e., total 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           -0.003        +3.0   
     -2           -0.002        +2.0   
     -1           -0.001        +1.0   
      0            0.000         0.0        (collision happens here)   
     +1           -0.01882      +0.9822   
     +2           -0.03764      +1.9644   
     +3           -0.05647      +2.9465   
      
   Once again, we see that body A (mass 100 kg) does indeed bounce back   
   (final velociity is to the *left*) 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)