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Problem 75 Medium Difficulty

The conductor of a high-speed train uses a meter stick to measure the length of her train at 200 m while the train is stopped at the station. The train then travels at $80 \%$ of the speed of light (this is a super-supersonic train!). If she repeats the measurement on the moving train, what answer will she get?

Answer

$200 \mathrm{~m} $

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Video Transcript

in this exercise, we have a conductor of the train that measures the train when it's at rest and finds that the train is 200 meters long. Then the train starts moving with the speed of 0.8 times the speed of light with relation to the ground and the conductor whose inside a train wants to measure. He train again, and we have to find what is the value L prime that the conductor finds in this case? Well, I noticed that, as I said before, the length off the train at Breast is 200 meters, and when the conductor is inside the train in her reference rain, the train is at rest. It doesn't matter that it's moving with relation to the earth or to the ground, because there's no preferential reference train in special relativity. So for that reason, her reference frame the reference frame other conductor is just as good as any reference frame. And she can very well say that with relation to her reference frame, the speed of the Train V prime is just zero. And for that reason our prime will be just equal to okay, so the length that she will measure will be the length off the train at Breast and this is equal to 200 meters.

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