I have this problem, which I think I can solve in 2 ways, but only 1 of them seems to be correct, but I don't understand why the other isn't correct. The problem is as follows:(adsbygoogle = window.adsbygoogle || []).push({});

"A bar with the rest length L_0 moves in its length direction with the velocity v through a lab. A particle moves along the same line but in opposite direction with the same speed v [velocity -v]. How long will it take the particle to pass the bar, [time] mearsured from the lab."

The easy way to do this, is by saying that if L is the length of the bar seen from the lab, then the time the particle will take to pass the bar will be

[tex] T = \frac{L}{2v} = \frac{L_0}{2v\gamma} [/tex]

(this is also the result given in the solutions manual)

But if we look at the situation from the bars reference frame, then the particle will be moving with a velocity

[tex] v' = \frac{2v}{1+v^2/c^2} [/tex]

So the time the particle will take to pass the bar seen from the bars intertial frame will be

[tex] T' = \frac{L_0}{v'} = \frac{L_0(1+v^2/c^2)}{2v} [/tex]

This time T' seen from the lab most be

[tex] T = \gamma T' = \gamma(1+v^2/c^2)\frac{L_0}{2v} [/tex]

But this last result ain't equal to the first one. Why is that so? Where did I make a mistake in my last calculations?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Relativity: disagreement between two results

**Physics Forums | Science Articles, Homework Help, Discussion**