Length Contraction Homework: Find Length of Moving Rod

AI Thread Summary
To find the length of a moving rod with a rest length of 10.4 m at a speed of 0.42c, only the component parallel to the direction of motion contracts. The x-component of the rod's length is calculated using the formula L = L0 * (1/gamma), where gamma is derived from the speed. The x-component is found to be approximately 3.82 m. The y-component remains unchanged, and the total length of the rod as measured by a stationary observer requires combining both components. The final step involves calculating the full length using the Pythagorean theorem to account for both x and y components.
Aeighme
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Homework Statement



A rod of rest length L0 = 10.4 m moves with a speed v = 0.42c along the x axis. The rod makes an angle of q0 = 66.1° with respect to the x' axis (primed frame is moving with the rod). What is the length of the rod as measured by a stationary observer?

Homework Equations



L=L1*(1/gamma)


The Attempt at a Solution


I have tried this several times, but can't seem to get it right.
L0=L1=10.4
gamma=(1-.422)-.5
Just solved for L..but didn't work.
 
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Careful. Only the component parallel to the direction of motion contracts.
 
So only the x component...is contracted. so L*cos(66.1)=L(x)?
 
Aeighme said:
So only the x component...is contracted. so L*cos(66.1)=L(x)?
Right. (That's L0, of course.)
 
Doc Al said:
Right. (That's L0, of course.)

now I multiply that by 1/gamma or (1-Beta2).5
and beta = .42...

so L=3.8238
 
Aeighme said:
now I multiply that by 1/gamma or (1-Beta2).5
and beta = .42...

so L=3.8238
OK so far, but realize that this is just the x-component, Lx not the full L. What's the y-component? Then calculate the measured length of the rod.
 
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