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Re: Thanks Zephram - One More?

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Posted by Zephram Cochrane/">Zephram Cochrane on January 5, 2000 21:28:12 UTC

: I also used the Lorentz transform to work out the distances in the rocket frame and they come out to xA' = 20.9 and xB' = 31.5. What gives? I thought distance in the rocket frame contracted in the direction of motion?

What you worked out here was the rocket frame coordinates at which the flashes took place, but remember that they took place at different times and according to the rocket frame, it is not the rocket but the bulbs on the ground that are in motion. During the time between the flashes they moved. Flashbulb B went off at t'B = -9.4 at x'B = 31.5 Flashbulb A went off at t'A = -6.3 at x'A = 20.9

To find the length between the bulbs according to the rocket frame we must find out were one of the bulbs were when the other went off. When flashbulb B went off flashbulb A was actually at x'Ainitial = 20.9 + 0.3(9.4 - 6.3) = 21.8 So the length between them is L' = 31.5 - 21.8 = 9.7 The ground frame length between them was L0 = 30 - 20 = 10 So indeed there was a length contraction on the distance between the flashbulbs. The easier way to get it you probably already know is L' = L0/g = 10/(1 - 0.32)1/2 = 9.5 (The difference is purely due to rounding errors building up in the previous method.)


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