Easy Special Relativity Question, Exam two days

[mmmboh]

[PLAIN]http://img811.imageshack.us/img811/3199/trainv.jpg

I have to find how long it takes the ball to travel the distance of the train in the ground frame.

In the train's frame, it is L₀/u₀.

Is the answer in the ground's frame simply (L₀/u₀)/(1-v²/c²)^(1/2)?

 

[kuruman]

Use the formula of relativistic addition of velocities to find the speed of the ball relative to the ground.

*** On edit ***
It would help us help you if you posted the sub problems that you have to solve before answering the question.

 

[mmmboh]

All we had to do was find the time it would take if spacetime was galilean, and the time it took for the ball to reach the end of the train in the train's frame, both of which are just L₀/u₀.

The relativistic velocity addition method is messy because the train moves so I can't just divide the length of the in ground frame by that velocity, I'll have to find the total distance it travels, but if your saying my answer is wrong I'll do that...so I can't just take the time an event took in a moving frame and multiply it by gamma?

 

[mmmboh]

Actually I can just use a simple Lorentz transform on this problem right? I'll take t'=L₀/u₀, and x'=L₀, and for the velocity in gamma I'll use the velocity of the train. That should be right, right?

 

[vela]

Yes, that'll work.

 

[kuruman]

You might consider that the velocity of the ball with respect to the train is also relativistic. Then you would have to find the contracted length of the train in the ball's reference frame and from it the (proper) time it takes the ball to reach the other end. Once you have that, you can use addition of velocities to find the gamma of the ball relative to the ground and then use this gamma to time-dilate the proper time.

 

[mmmboh]

But that would be a lot more work than just using the lorentz transform equation, wouldn't it..and what do you mean by the velocity of the ball with respect to the train is relativistic? Because the speed of the ball is given with respect to the train, so in that frame we just take it as u₀.

 

[kuruman]

But that would be a lot more work than just using the lorentz transform equation, wouldn't it..

It most certainly would be more work. Are you concerned with quantity or quality of work?

and what do you mean by the velocity of the ball with respect to the train is relativistic? Because the speed of the ball is given with respect to the train, so in that frame we just take it as u₀.

I mean what if u₀ = 0.9c? You are not given u₀ so you may have to assume the more general case. That's why I asked you to post the sub problems mentioned in the statement of the problem.

 

[mmmboh]

Of course I'm concerned with quality, but I meant if the Lorentz Transform works then why do it the other longer way?...what I mean is...are you saying what I think is wrong, or are you just suggesting another way to do it?

 

[kuruman]

Of course I'm concerned with quality, but I meant if the Lorentz Transform works then why do it the other longer way?...what I mean is...are you saying what I think is wrong, or are you just suggesting another way to do it?

OK. Is Newtonian mechanics as opposed to the Special Theory of Relativity right or is it wrong? The answer is "It depends on the speed of things as compared with the speed of light, c." When you say "I'll take t'=L₀/u₀, and x'=L₀", you are correct if u₀ << c, but you are wrong if u₀ is comparable to c. So what do you think about how u₀ compares with c? It is always safe to use special relativity because Newtonian Mechanics is a limiting case of it. It is not always safe to use Newtonian Mechanics when you don't know whether the speeds are close to the speed of light or not, That's what I'm saying.

 

[vela]

Of course I'm concerned with quality, but I meant if the Lorentz Transform works then why do it the other longer way?...what I mean is...are you saying what I think is wrong, or are you just suggesting another way to do it?

If I were you, I'd try calculating the time in all three frames, mostly to satisfy my curiosity to see if it really works out consistently. It also helps to get practice analyzing the same two events in different reference frames, especially a simple problem like this where it doesn't require a lot of effort to do it each way.

 

[vela]

OK. Is Newtonian mechanics as opposed to the Special Theory of Relativity right or is it wrong? The answer is "It depends on the speed of things as compared with the speed of light, c." When you say "I'll take t'=L₀/u₀, and x'=L₀", you are correct if u₀ << c, but you are wrong if u₀ is comparable to c.

No, he's correct. In the train's rest frame, the length of the train is L₀, and the ball moves with speed u₀ and thus reaches the front when t'=L₀/u₀.

 

[kuruman]

No, he's correct. In the train's rest frame, the length of the train is L₀, and the ball moves with speed u₀ and thus reaches the front when t'=L₀/u₀.

Of course. I guess I had a mental lapse.