World Science Scholars
25.7 Combining Velocities

Module 25: Combining Velocities — Problem 2

In this problem we reconsider the light-clock, and ask ourselves the following question: What if we have a version of the light-clock in which the bouncing projectile is not a photon, but is instead a ping pong ball bouncing between two horizontal surfaces? (Neglect air resistance, etc.) Will the rate of slowing on such a “ping pong ball clock” agree with the rate of slowing on a light-clock?

To this end, let the speed of the ping-pong ball in the stationary clock be $w$, so the duration of a tick-tock in the stationary ping pong ball clock is $\Delta t_{\rm stationary}= \frac{2L}{w}$. Let the time for a “tick”; on the moving clock, from our stationary vantage point, be $\Delta t$. That is, let $\Delta t$ be the time for the ping pong ball to travel the diagonal trajectory from the lower surface to the upper surface, from the viewpoint of the stationary observer.

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