Special Relativity, Length Contraction

AI Thread Summary
The discussion revolves around calculating the rest length of a rocket moving at 0.95c, with marks made on a stationary axis indicating a distance of 100 m apart. The proper length equation L = Lp / gamma is applied, leading to a proposed answer of 240 m, which is contested by another participant who calculates approximately 400 m. The discrepancy arises from differing interpretations of the movement of the rocket's back end during the marking process, specifically whether to add or subtract 25 m. Ultimately, it is confirmed that the original answer key may have mixed up the front and back of the rocket. The conversation highlights the complexities of applying special relativity principles in practical scenarios.
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Homework Statement


As a rocket ship moves by at 0.95c a mark is made on a stationary axis at the front end of the rocket and 9 × 10^−8 s later a mark is made on the axis at the back end. The marks are found to be 100 m apart. The rest length of the rocket is:
A. 31m
B. 78m
C. 100m
D. 240m
E. 320m


Homework Equations


L = Lp / gamma, where Lp is the proper length.


The Attempt at a Solution



The answer given is 240 m, but I get about 400 meters for my answer and the discrepancy lies in whether you use 100+25 m or 100 - 25 m.

My explanation goes something like this: In the time before the second person marks the end of the rocket, the back of the train has moved an additional 25 meters, so we have the total length measured in the stationary axis frame as 100 + 25 (that is my L value). Plugging into the above equation gives about 400 meters.

Is this a correct argument or am I going wrong somewhere? Thanks a lot ahead of time.
 
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Your argument is correct. It looks like the answer key got the front and back of the rocket mixed up.
 

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