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Conservation of Momentum in Two Dimensions

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Physics of The Stop Shot
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Physics of The Stop Shot

Credit: Jollytime
Source: http://en.wikipedia.org/wiki/File:8_ball_break_time_lapse.jpg
License: CC BY-NC 3.0

Everyone from kings to peasants have heard or played a game of billiards. Created in the 15th century, the game of billiards is played by attempting to place certain balls in any of the 6 pockets with the use of a cue ball. One of the most amazing things about billiards is how well every aspect of the game can be explained by classical physics.

Amazing But True

  • You don't need to be a physicist to be good at pool, but it can definitely help. Every aspect of the game of pool is based on classical mechanics. When you hit the ball with the cue stick, you are imparting a force on a stationary object. Depending on where the cue ball is hit, you are transferring both translational and rotational kinetic energy. Once the cue ball makes contact with another ball, it experiences an elastic collision, where there is a change in momentum and kinetic energy.
  • One of the many techniques that are needed in pool to master the game is the stop shot. The stop shot consists of hitting the cue ball with enough backward rotational so when it makes contact with a target ball, all the momentum and kinetic energy are transferred to the target ball. Doing so allows for a player to position the cue ball for their next shot.
  • Learn how the stop shot is done and how to practice it: 

http://www.youtube.com/watch?v=rUfmjPvzGX0

Can You Apply It?

Using the information provided above, answer the following questions.

  1. When the cue ball strikes a target ball what quantities are really conserved?
  2. Assuming a perfect elastic collision, what can be said about the momentum and kinetic energy of the cue ball during a stop shot?
  3. Another technique in pool would require you to have the cue ball roll backwards after it contacts the target ball. Using the information on how a stop shot is performed, how and where would you hit the cue ball to have it roll back to you after it contacts the target ball?

Image Attributions

  1. [1]^ Credit: Jollytime; Source: http://en.wikipedia.org/wiki/File:8_ball_break_time_lapse.jpg; License: CC BY-NC 3.0

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