NOTE: To keep things simple, I neglected air resistance and friction in my discussion.
When Jordan and I were playing pool at Senior Camp this year, she said to me, “You should use this for your next physics blog! The collisions between the pool balls are nearly elastic.” At the time, I had no idea what an elastic collision was so I responded to her with a simple “Yeah, that’s a great idea!” Now, with a solid background in momentum and collisions, I would have whipped out my Casio Fx-CG10 as soon as Jordan reminded me about elastic collisions and I would have calculated the final velocities of the balls right there on the spot!
In pool, as Jordan pointed out, the collisions between the balls are nearly elastic. That is, both momentum AND kinetic energy are conserved. In pool, you start with two balls: your attack ball and your target ball. Once you set the attack ball into motion, one of your balls is moving while the other remains stationary. Soon enough, your attack ball hits your target ball and both balls scatter in different directions at different velocities! How exciting, right?!
![A picture of me getting excited about elastic collisions at Senior Camp while Jordan watches me fail to shoot the pool ball in the pocket.](https://physicsjack.wordpress.com/wp-content/uploads/2013/11/photo-1.jpg?w=600&h=450)
A picture of me getting excited about elastic collisions at Senior Camp while Jordan watches me fail to shoot the pool ball in the pocket.
To find the new magnitude and direction of the balls’ velocities, we would need their angles of separation, which we could then use to componentize both balls in to their respective x- and y-velocity components. Assuming we have all of the necessary information and assuming that we are able to find the resultant vector of each ball’s velocities, we can observe conservation of momentum and kinetic energy in elastic collisions through the following relationships. Because both balls have the same mass and because ball 2 is initially stationary, the conservation of momentum equation (M1V1i + M2V2i = M1V1f + M2V2f) simplifies to V1i = V1f + V2f. Similarly, the conservation of kinetic energy equation (1/2M1V1^2i = 1/2M1V1^2f + 1/2M2V2^2f) simplifies to V1^2i = V1^2f + V2^2f.
Through the above relationships, we can see that both momentum and kinetic energy are conserved in pool (and all other examples of elastic collisions for that matter). Undoubtedly, Senior Camp would have been a much better experience if I had already known how to calculate the velocities of the pool balls. Oh well, at least I know what I’m going to do the next time I play pool.