Einstein's Electrodynamics of moving Bodies

[jselms99]

Homework Statement

Okay guys I’m lost:

I have a train measured as being 100 meters in length standing in the station. Once its pulled out and it reaches a constant speed, the length measured by observers who are alongside the tracks is 50 meters. How fast is it traveling?

I have to calculate this for different distances; for example, 10 meters, 50 meters, 100 meters and represent the answer as a fraction of c.

Relevant Equations

The problem is, I don’t know what equation I should be using!

Okay I’m assuming I have to use √1- v^2/c^2 multiplied by some coefficient of length but I don’t understand any of this and could really use help understanding the process and/or reference material that might point me in the right direction

 

[BvU]

Hello @jselms99 ,

$\qquad$ !​

Here at PF we have some rules and guidelines, which please read. In particular: we need some attempt from you before we can help.

The problem is, I don’t know what equation I should be using!

Okay I’m assuming I have to use √1- v^2/c^2 multiplied by some coefficient of length but I don’t understand any of this and could really use help understanding the process and/or reference material that might point me in the right direction

Do you have a textbook, lecture notes, anything relevant for this exercise ?
If not, why are you doing this ?

Perhaps you can read up on 'length contraction' ?

$\$

 

[jselms99]

Hello @jselms99 ,

$\qquad$ !​

Here at PF we have some rules and guidelines, which please read. In particular: we need some attempt from you before we can help.Do you have a textbook, lecture notes, anything relevant for this exercise ?
If not, why are you doing this ?

Perhaps you can read up on 'length contraction' ?

$\$

I don’t have notes or anything except Einstein’s 1905 paper “On the Electrodynamics of Moving Bodies” which is currently breaking my brain…. From what I’ve read about length contraction, the equation L = Lo √1- v^2/c^2 may apply but I’m having difficulty identifying Lo

 

[BvU]

$L_0$ is length in rest frame (i.e. when measured in frame where train stands still, for example standing at the station).

 

[jselms99]

$L_0$ is length in rest frame (i.e. when measured in frame where train stands still, for example standing at the station).

How would I account for varying distances traveled though? I was thinking of using the equation x=vt and t=x’/(c-v) but I don’t know if that’s helpful

 

[hmmm27]

Could you transcribe the entire problem : as is, the "different distances... for instance...." makes no sense to me without quite a bit of context.

 

[PeroK]

I don’t have notes or anything except Einstein’s 1905 paper “On the Electrodynamics of Moving Bodies” which is currently breaking my brain…. From what I’ve read about length contraction, the equation L = Lo √1- v^2/c^2 may apply but I’m having difficulty identifying Lo

That's a great paper, but it's not a good source for you to learn SR from. As is evidenced by your helplessness in the face of a length contraction problem.

Try this. The first chapter is free.

https://scholar.harvard.edu/david-morin/special-relativity

 

[Frabjous]

Here’s a good free book.
Taylor and Wheeler - Spacetime Physics
https://www.eftaylor.com/spacetimephysics/