Question

Two billiard balls of equal mass are travelling straight towards each other with the same speed. They meet head on in an elastic collision. What is the total momentum of the system contains the two balls before the collision??

Answer 1

Zero

Step-by-step explanation:

The momentum of an object is a vector quantity given by

`p=mv`

where

m is the mass of the object

v is its velocity

Being a vector, momentum has also a direction, which is equal to the direction of the velocity.

In this problem, we have two balls of equal mass, so

`m_1=m_2=m`

And they have the same speed: this means that the magnitude of their velocity is the same, but their direction is opposite, so

`v_2=-v_1`

Therefore, the momentum of ball 1 is

`p_1=m_1 v_1 = mv_1`

While the momentum of ball 2 is

`p_2=m_2 v_2 = m(-v_1)=-mv_1`

Therefore, the total momentum before the collision is

`p=p_1+p_2=mv_1-mv_1=0`

Because the two balls have same momentum but in opposite directions.