Question

A 16 g ball is fired horizontally with speed v0 toward a 111 g ball hanging motionless from a 0.9-m-long string. The balls undergo a head-on, perfectly elastic collision, after which the 111 g ball swings out to a maximum angle θmax=53°. What was v0?

Answer 1

Given , the masses of the two balls are : m = 0.016 kg and M = 0.111 kg . M > m .

The initial velocity of smaller ball is .

And the heavier ball was in rest initially.

Let, the final velocity (just after collision) of smaller ball is

and final velocity (just after collision) of heavier ball is .

Now from conservation of energy we know that, the kinetic energy of heavier ball just after the collision must be equals to its total potential energy (when it reaches its maximum height).

where,

Applying conservation of energy for heavier ball after collision (between points A and B).

  

or,   

In elastic collision momentum and energy remains conserved.

Now applying conservation of momentum after and before the collision :

or,    ................................(1)

  

Eccentricity(e) is defined as the velocity of separation divided by velocity of approach . And for elastic collision e = 1 .

So,

  

or,

or,    .................................(2)

Solving equation (1) and (2), we get