# Special relativity: rectangular box moving 0.5c

1. Sep 14, 2010

### scustin

1. The problem statement, all variables and given/known data

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'.

2. Relevant equations

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

3. 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' ??

2. Sep 14, 2010

### vela

Staff Emeritus
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).

3. Sep 14, 2010

### scustin

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

4. Sep 14, 2010

### 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