You can't spell Physics without Pi

Collisions between two masses $m_{1}$ and $m_{2}$ have two important quantities: momentum and energy, respectively given by

$$ p = m_{1}v_{1} + m_{2}v_{2}$$


$$E = \frac{1}{2}m_{1}v_{1}^2 + \frac{1}{2}m_{2}v_{2}^2.$$

Momentum is always conserved, energy is sometimes not (e.g. lost to friction). Imagine a small mass $m$ and a larger mass $M$. Mass $M$ hits $m$, small $m$ hits a wall, bounces back, and hits $M$ again. Mass $m$ continues to bounce back and forth between $M$ and the wall, while $M$ continues moving forward towards the wall (in turn, the collisions become more and more frequent). If energy and momentum are both conserved and $M/m$ is the right ratio, the number of times the two masses collide (before $M$ changes direction) is related to the digits of pi!

Tuesday, March 19, 2019 - 12:00 to 13:00

Thackeray 703

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