A 40kg ball moving to the right at 50 ms collides headon wit

A 4.0kg ball moving to the right at 5.0 m/s collides head-on with a 2.0kg ball moving to the left at 4.0 m/s. If the collision is elastic, determine the direction and speed of each ball after the collision.

Solution

Masses m = 4 kg

   M = 2 kg

Initial velocities u = 5 i

                      U = -4 i

Where i = unit velctor along right direction.

Let the velocities of m and M after collision be v and V respectively.

The collision is elastic.So, coefficient of restitution e = 1

i.e., relative velocity after collision / relative velocity before collision = 1

    ( V - v ) /( u - U ) = 1

                  V - v = u - U

                         = 5i -(-4i)

                         = 9 i

                       V = v + 9i

From law of conservation of linear momentum ,

mu + MU = mv + MV

4(5i) +2(-4i) = 4(v) + 2( v+9i)

                 = 4v + 2v +18 i

   20 i -8 i = 6v + 18 i

           12 i = 6 v + 18 i

            6v = -6 i

              v = -1 i

i.e., the ball of mass 4 kg moves with a speed 1 m/s along left direction

We know V = v+ 9i

                   = -1i +9i

                   = 8 i

i.e., ball of mass 2 kg moves with a speed of 8 m/s along right direction.