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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.
Module 33: The Pole in the Barn: Quantitative Details—Problem 2
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Question 1 of 4
1. Question
Team Barn carefully analyzes the measurements undertaken by Team Pole, and notes that Team Pole first assesses the location of the pole’s rear and later assesses the location of the pole’s tip. How far apart in space does Team Barn claim these two measurements are?
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Question 2 of 4
2. Question
Assume Team Pole assesses the location of the pole’s rear just as it enters the barn. According to Team Barn, how far outside the barn will the tip of the pole be when Team Pole subsequently assesses its location?
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Question 3 of 4
3. Question
Team Barn claims that its team members located at the front and the rear of the barn work together to determine whether the rear end of the pole is inside the barn at the very moment that the tip of the pole is about to exit the barn. Team Pole claims that these two members of Team Barn do not carry out their assessments simultaneously. Hence, the barn moves between the two measurements. How far apart in space does Team Pole claim these two measurements are?
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Question 4 of 4
4. Question
Assume Team Barn assesses the location of the pole’s tip just as it is about to exit the barn. According to Team Pole, how far inside the barn will the end of the pole be when Team Barn subsequently assesses its location?
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