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Module 24: Lorentz Transformation: Examples - Problem 9
In this problem, you’ll analyze how, in a particular example, an observer moving on a train makes sense of a platform observer’s claim that the train is Lorentz contracted.
Here’s the set up: A train whose resting length is 1,000 feet rushes by a platform at speed . The platform observers measures the train’s length to be contracted by a factor of , namely 800 feet. To prove to everyone that this is the train’s length, the platform observers make an 800 foot bronze statue of the train, and place it right next to the tracks. The next day, the train rushes by the platform again and as it does platform observer F, situated at the front of the statue, and platform observer R, situated at its rear, agree that at one moment in time the train and the statue exactly align, showing that the train is in fact 800 feet long.
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1. Question
According to those on the train, how long is the statue?
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2. Question
According to those on the train, what is the time difference between when the two platform observers assessed the location of the front and rear of the train?
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3. Question
According to those on the train, observer F first assesses the location of the front of the train first and only later does observer R assess the location of the rear of the train (with the time difference between the two measurements having been calculated in the previous part). According to those on the train, how far does observer R move during this interval?
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4. Question
Using the results of the previous parts, determine how far apart, according to those on the train, the measurements of observer F and observer R took place.
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5. Question
What general equation involving (the rest length of an object), and , best characterizes the general relationship illustrated by the example in this problem? (Write the equation in units where , for simplicity.)