33.5 The Pole in the Barn: Quantitative Details

Problem

## Module 33: The Pole in the Barn: Quantitative Detailsâ€”Problem 2

Consider a pole and barn both of which have the same resting length $L_0=75 \,\textrm{meters}$. Let the pole rush through the barn at speed $v=\frac{4}{5}c$, with $\gamma=5/3$. As usual, according to Team Barn the pole is only $\frac{L_0}{\gamma}=\frac{75}{(5/3)}=45$ meters and so fits in the barn with 30 meters to spare. But, according to Team Pole, it is the barn that has length $\frac{L_0}{\gamma}=\frac{75}{5/3}=45$ meters and so it fails to fit inside the barn by a margin of 30 meters.