# Length contraction equation. what am i doing wrong?

1. Sep 20, 2005

### Sneil

Length contraction equation determining v. what am i doing wrong???

OK,

L=L*(1-v2/c2)1/2 (to the power of 1/2)

L=.75m L*=1.0m

now i need to find v and for the life of me i always end up with a value greater then c which is obviously impossible.

ill simplify to v=

L/L*=(1-v2/c2)1/2
(L/L*)squared = 1-v2/c2
1+(L/L*)squared = v2/c2
(1+(L/L*)squared )to the 1/2=v/c
c((1+(L/L*)squared )to the 1/2)=v

and thus i break the barrier of the speed of light and go back in time i guess...

Last edited: Sep 20, 2005
2. Sep 20, 2005

### LeonhardEuler

Your mistake is on line 3. It should go:
$$(\frac{L}{L*})^2=1-\frac{v^2}{c^2}$$
$$(\frac{L}{L*})^2-1=-\frac{v^2}{c^2}$$
$$\frac{v^2}{c^2}=1-(\frac{L}{L*})^2$$

3. Sep 20, 2005

Staff Emeritus
Let's see. L/L* is .75

(1 - v^2/c^2)^1/2 -.75
1 - v^2/c^2 = .5625
-v^2/c^2 = .5625 -1 = -.4375
v^2/c^2 = .4375
v/c = sqrt(.4375) = .661437828

So v is about 661/7 % of c.

Your error was in going from your second equation to your third. You got the signs wrong in simplifying. Check it out.

4. Sep 20, 2005

### Sneil

ah, great. bad mistake on my part. Thank you very much for the quick replies!