*38.   A ball is attached to one end of a wire, the other end being fastened to the ceiling. The wire is held horizontal, and the ball is released from rest (see the drawing). It swings downward and strikes a block initially at rest on a horizontal frictionless surface. Air resistance is negligible, and the collision is elastic. The masses of the ball and block are, respectively, 1.60 kg and 2.40 kg, and the length of the wire is 1.20 m. Find the velocity (magnitude and direction) of the ball (a) just before the collision, and (b) just after the collision.

 

To find velocity of the ball just before the collision is a conservation of energy problem

 

From diagram we can see h = L

 

 

From diagram the velocity is in the  direction

 

Now after the collision we find the velocity by conserving both momentum and kinetic energy

 

 

 

 

Now Conserve kinetic energy

 

 

 

 

 

Now use the equation from conservation of momentum

 

 

 

Now equate the two relationships

 

 

 

 

 

 

 

 

 

 

Before collision with block

After collision with block

 

 

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This page last updated on January 11, 2020