Interactive Dynamics
Billiards Activity

Introduction

	Pocket Billiards has been described in many ways. According to Jim Meador, an avid pool player, pool "...at its best, it is Swan Lake. The player is the conductor, the cue stick his baton, and the balls are dancers on a stage of green felt." Billiards is a game grounded in physics and mechanics. France, Italy, China, England, and Spain have been credited with the invention of billiards, but not much is known of the early days of billiards. Records of the game of billiards exist as far back as the 1400's. The actual mechanics and physics of the game are very complex and exceed the realm of this course. However, a good approximation can be made using the techniques covered in EMch 12.

Part A

The World 9-Ball Championship is quickly approaching, and the pros are chalking up their cues. This year Fransisco Bustemante is determined to win. He has been practicing many different shots to analyze the dynamics behind his playing, to improve his accuracy and precision. View the following QuickTime movies, and analyze the pool ball interactions. Try and find the coefficients of restitution for various types of collisions, an equivalent value for the friction of the table, and any other properties that may be useful.

Two ball collision Ball in pocket

Straight two ball collision Ball and wall collisions

Ball coming to a stop

Part B

Now Fransisco needs some advice. After the initial break, the table is arranged as shown in detail here. In 9 ball each player must hit the balls in order (from 1-9) with the intent being to hit the 9 into a pocket on a ricochet or by first knocking in the other 8 balls and then playing the 9. The 1 ball was hit and knocked into a pocket on the break. Now the blue number 2 ball must be the first ball hit on the next shot. What initial conditions must be given to pocket the blue ball legally? Additionally, Fransisco doesn't want to waste any energy, so the blue ball should be given just enough velocity so that it just barely rolls in. Use the information gathered in Part A to determine the answer.

Specifications of a Billiard Ball
Mass (kg)	0.1598
Circumference (m)	0.184

Activity Report

In your report you will provide a summary of the problems and objectives stated. For Parts A and B include the equations and supporting diagrams. Be sure to answer all posed questions.

[EMch 12] [ESM] [Faculty] [PSU Engineering] [Penn State]

people have accessed this page since July 1, 1998.

Prepared by Molly Riley and Chris Watterson.

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