1. Kinematics of a Rubber Bouncy Ball A Simulation of a Rubber Bouncy Ball Yun Chung Lu Physics 210 Final Project Presentation Affiliation: University of British Columbia 17/11/08

2. Abstract This project explores a way to simulate a mathematical description of the trajectory of a rubber bouncy ball in a box with no gravity A script was designed to calculate various components of the rubber bouncy ball’s trajectory, and a graph was made to show this trajectory.

3. Outline Discussion of classical mechanics Discussion of the association of classical mechanics equations with the kinematics of a rubber bouncy ball Presentation of script’s capabilities Conclusion

4. Classical Mechanics A mathematical model of the ball can be described through F=ma=kx, where x is the compression of the ball as it hits the ground Energy conservation is also important, with total energy = to the sum of kinetic and potential energy Due to friction, loss of energy through sound, etc, the ball slowly “loses” its kinetic and potential energy, and will eventually stop bouncing The ball will also spin, the description of its trajectory and the angle it bounces from the ground will be partially determined by it’s angular momentum. The project was designed such that there was no gravity involved. In this case, the ball will just travel in a straight line until a collision.

5. Relation Between Classical Kinematics and the Description of the Rubber Bouncy Ball After some derivations, it can be found that a ball bouncing off a horizontal surface can have its velocity described in three simple formulas

6. Script The simulation of the rubber bouncy ball was made by writing a script in Matlab Calculates for the initial bounce at time T

7. What the Script Does Not Do/Improvements Due to the storage of variables in Matlab, it seems that the script will not be able to calculate for any bounces other than the initial bounce Due to this problem, a graph of the trajectory can not be displayed. Intend to find a way to fix such a problem.

8. Conclusion I accomplished most of what I set out to do There should be an easy way to fix the storing of variables that I have not figured out (I intend on finding a way to solve this) There is potential to add more balls into the simulation (ex. to see what would occur if the ball struck each other)