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DYNAMICS - EXAMPLE


Collision of Two Balls
  Example

 

Two balls, A and B, impact each other as shown. If the coefficient of restitution, e, is 1.0 (perfectly elastic), what is the velocity magnitude of ball B after impact?

   
    Solution


Velocity of Balls
Before and After Collision

 

Ball B only has a velocity in the y-direction, so first consider y-direction momentum. Conservation of momentum before and after impact gives

     mAvA1y + mBvB1y = mAvA2y + mBvB2y
     4 cos30 - 3 = -vA2y + vB2y
     0.4641 = -vA2y + vB2y

There are still unknowns, so the impact equation needs to be used,

     e = (vB2y - vA2y)/(vA1y - vB1y)
     1 = [vB2y - (-vA2y)] / [4 cos30 - (-3)]
     3.464 + 3 = vB2y + vA2y
     6.464 = vB2y + vA2y

Combining both equations
     0.4641 = -(6.464 - vB2y) + vB2y
     0.4641 + 6.464 = 2vB2y
     vB2y = 3.464 m/s

vB2y = vB2 = 3.464 m/s

     
   
 
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