# Length Contraction

1. Dec 5, 2008

### Aeighme

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

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?

2. Relevant equations

L=L1*(1/gamma)

3. 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.

2. Dec 5, 2008

### Staff: Mentor

Careful. Only the component parallel to the direction of motion contracts.

3. Dec 5, 2008

### Aeighme

So only the x component...is contracted. so L*cos(66.1)=L(x)?

4. Dec 5, 2008

### Staff: Mentor

Right. (That's L0, of course.)

5. Dec 5, 2008

### Aeighme

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

so L=3.8238

6. Dec 5, 2008

### Staff: Mentor

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.