Question

A ball is travelling towards another ball which is at rest. The ball that is travelling has a speed of 3.5 m/s and weighs 22 g. The ball that is at rest weighs 27 g. There is a head on elastic collision between the balls. What is the velocity of each ball after the collision? Show all steps for full marks

Answer 1

Let m1 = 22g = 0.022 and m2 = 27g = 0.027kg. The initial speed of m1 is u1 = 3.5m/s and that of m2 is u2 = 0. Let v1 and v2 be their respective speeds after elastic collision. In an elastc collision momentum and kinetic energy of the system is conserved. Applying law of conservation of momentum,

Applying law of conservation of kinetic energy,

Dividing both the final equations, we get

Substituting this in the final equation of momentum conservation, we get

Similarly, it can be shown that,

The above equations gives the velocities of m1 and m2 after the elastic collision.

Substituting the values in the above equations, we get

So the magnitude of velocty of m1 after the elastic collision is 0.36m/s. Since its value is negative, the direction of m1 after collision is opposite to the initial direction of m1 before collision.

So the magnitude of velocty of m2 after the elastic collision is 3.14m/s. Since its value is positive, the direction of m2 after collision is same as the initial direction of m1 before collision.