33. ssm A 5.00-kg ball, moving to the right at a velocity of +2.00 m/s on a frictionless table, collides head-on with a stationary 7.50-kg ball. Find the final velocities of the balls if the collision is (a) elastic and (b) completely inelastic.

 

For either type of collision  (elastic or completely inelastic) must conserve momentum

 

If it is elastic we get

 

If elastic then kinetic energy is also conserved

 

 

Let’s solve for  using conservation of Kinetic Energy

 

 

 

Now let’s solve for using conservation of momentum

 

 

 

 

So squaring this and setting equal to what we found from kinetic energy

 

 

 

 

 

 

 

 

 

 

 

Now go back to equation for

 

 

 

If it is completely inelastic we get

 

 

 

Elastic

Completely inelastic

 

 

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This page last updated on January 11, 2020