Special relativity: rectangular box moving 0.5c

[scustin]

Homework Statement

A rectangular box at rest in S' has sides a'=2m, b'=2m, c'=4m. The side c' is parallel to z' axis of S'; the side b' forms an angle 45deg with x' axis of S'. S' moves with v=0.5c with respec to S, along its x axis. Find the volume of the box in S and S'.

Homework Equations

gamma= 1/sqrt(1-v^2/c^2)
gamma= Lp / L
V=l*w*d

The Attempt at a Solution

gamma = 1.33333
L(a') = 1.06066
V(S') = 12m^3
V(S) = 16m^3
am I right about S' ??

 

[vela]

No, you made a couple of mistakes. First, your value for gamma isn't correct. Second, length contraction should affect both a' and b' since neither side is parallel to the y' axis.

You should have also realized your answer was wrong because the volume of the box is largest in its rest frame. In a frame where it's moving, it'll be length-contracted, so its volume will decrease. V(S') should be bigger than V(S).

 

[scustin]

I had it backwards, 16m^3 was my S', 12 was what i got for S.

 

[scustin]

Ok i found the mistake, gamma should be 1.1547, making L(a) 1.22456m, and the area 13.85m^3, if i am right