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Relativistic momentum proof

  • #1

Homework Statement


Show that

1/[itex]\sqrt{1-(u'/c)^2}[/itex]=[itex]\gamma[/itex](1-(vu/c^2)/[itex]\sqrt{1-(u/c)^2}[/itex]


Homework Equations





The Attempt at a Solution



Since I'm terrible with Latex I took a picture of what I have so far. I'm not sure where to go next or if I'm even on the right track.

My professor gave a hint that u'^2=(ux')^2+(uy')^2+(uz')^2

And that (u'/c)^2[itex]\Rightarrow[/itex]1-(u'/c)^2[itex]\Rightarrow[/itex] 1/(1-(u'/c)^2)^1/2

which I think just confused me more.

Thanks a lot

EDIT: Here's a link to the photo turned rightside up

http://i307.photobucket.com/albums/nn310/nilesthebrave/2012-09-27_20-22-26_35.jpg
 

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Answers and Replies

  • #2
938
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That's very difficult to show without knowing what u, v and u' are :)
 
  • #3
Unfortunately, there are no values for anything. I turned the homework in today and my professor showed me how to do it. It was pretty messy.
 
  • #4
vela
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Clamtrox's point was without knowing the complete problem statement, the relation in your original post is meaningless to us. We're not in the class you're taking, and we can't read your mind. You have to provide all of the relevant information.
 
  • #5
And as I said, this is the EXACT problem I was given. This is all I had to work with, which is why I posted it here.

But my professor showed me how to do it after I turned it in so it's not an issue now.
 
  • #6
vela
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I doubt that. There is some context to the problem that you (or your professor) omitted. The question, as it is now, is like "Show that a+b = c+d" without defining what a, b, c, and d are.

I can infer that your problem probably had something to do with velocity addition, but that would only be a guess.
 
  • #7
Ah, sorry I guess I didn't realize I didn't explain that. :redface:

It was something to do with a Lorentz transform for momentum. I always forget that the same symbols and letters aren't used universally. I thought you were asking for values for each of the letters.

I guess that's where I was getting confused since the u's and v's are velocities(I think) and the c is the speed of light.

I don't know I've been looking at it a little today but it's not on the exam I have Monday so I'm saving it for after that.

Thanks for the responses, sorry I misunderstood what you were saying.
 
  • #8
938
9
Ah, sorry I guess I didn't realize I didn't explain that. :redface:

It was something to do with a Lorentz transform for momentum. I always forget that the same symbols and letters aren't used universally. I thought you were asking for values for each of the letters.

I guess that's where I was getting confused since the u's and v's are velocities(I think) and the c is the speed of light.

I don't know I've been looking at it a little today but it's not on the exam I have Monday so I'm saving it for after that.

Thanks for the responses, sorry I misunderstood what you were saying.
If you really were given the problem in the form above, then I feel sorry for you... But maybe the problem relates to something done in lecture notes, maybe something where the details were left as an exercise? If you can't understand what the symbols mean, then what hope do you have of actually showing that?
 

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