Question

Two billiard balls with the same mass m move towards one another. Ball one moves in the positive x-direction with a speed of v1i, and ball two moves in the negative x-direction with a speed of v2i. The two balls collide elastically, and both balls change direction after the collision. Write an expression for the horizontal component of the system's final momentum, pf,x, in terms of m and the final speeds of ball one, v1f, and ball two, v2f.

Answer 1

The horizontal component of the final momentum for two billiard balls of the same mass undergoing an elastic collision is given by pf,x = m × v1f + m × (-v2f), where v1f and v2f are the final velocities of the balls.

Step-by-step explanation:

When two billiard balls with the same mass m collide elastically and change direction, the horizontal component of the system's final momentum, pf,x, can be expressed using the law of conservation of momentum. Since the collision is elastic, both momentum and kinetic energy are conserved. Therefore, the final horizontal momentum can be calculated as follows:

pf,x = m × v1f + m × (-v2f)

This expression takes into account the mass of the balls (m) and their final speeds after the collision (v1f and v2f), where v1f is the speed of ball one and v2f is the speed of ball two, taking the negative sign before v2f to account for its motion in the opposite direction.