Meter Stick Special Relativity Problem

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SUMMARY

The discussion centers on calculating the length of a meter stick in special relativity as observed from different frames of reference. The meter stick in frame S' is at a 30° angle and moves at 0.82c relative to frame S. The Lorentz factor (γ) is calculated as 1.747, leading to a contracted length of 0.572 meters. To find the correct length in frame S, the x-component must be calculated separately, and the Pythagorean theorem applied to determine the total length after contraction.

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  • Study the derivation and application of the Lorentz factor in various scenarios.
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harrietstowe
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Homework Statement



A meter stick in frame S' makes an angle of 30° with the x' axis. If that frame moves parallel to the x-axis with speed 0.82c relative to frame S, what is the length of the stick as measured from S?

Homework Equations



Length contraction: L=Lo/γ

The Attempt at a Solution


Relative to s, the length of this meter stick will contract. γ=1.747
Lo = 1m
L = .572
I then multiplied this by the cosine of 30 degrees to get .088 m but this is not the right answer. Multiplying by the cosine of 30 degrees was sort of a guess as I am unsure of what to do with it.
Thanks

Thanks
 
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harrietstowe said:
Relative to s, the length of this meter stick will contract. γ=1.747
Lo = 1m
L = .572
I then multiplied this by the cosine of 30 degrees to get .088 m but this is not the right answer. Multiplying by the cosine of 30 degrees was sort of a guess as I am unsure of what to do with it.
Work with the x-component and y-component separately. Calculate the x-component and the y-component of the meter stick in its own frame of reference (the S' frame). Only the x-component will contract in the S frame. Then use the Pythagorean theorem to find the total length (in the S frame) after contraction. :wink:
 

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