The game of pool is an excellent showcase of interesting physics. One of the most common occurances occurences in a game of pool is an almost perfectly elastic collision between a moving cue ball and a stationary ball of equal mass. These collisions occur in two dimensions.
One very useful rule of thumb for pool players is the right angle rule: after the collision the cue ball's final velocity and the final velocity of the struck ball will make a right angle (assuming that both are moving).
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Note that this rule is only valid in the limit that ball spin can be ignored. If the cue ball has significant spin, then the rule will be violated. |
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When this rule applies, it is very powerful. The following examples showcase the utility of the right angle rule.
Part A
The cue ball is moving at 5.0 m/s when it impacts the 6 ball, which is at rest prior to the collision. The cue ball exits the (perfectly elastic) collision at an angle of 30 degrees from its original direction of motion. What are the final speeds of each ball?