- #1

nothilaryy

- 7

- 0

## Homework Statement

Given the momentum p

_{1}and p

_{2}, find the distance of closest approach (b) also known as the impact parameter. I think we are also given charges q because I later have written solve for b

^{2}in terms of x

^{2}, q

^{2}, P

^{2}, p[tex]\bullet[/tex]x, q[tex]\bullet[/tex]x, and p[tex]\bullet[/tex]q. [those are supposed to be dot products but I think I fail at latex] I believe x is supposed to be relative position.

## Homework Equations

I'm not really sure which equations I'm supposed to be using at all, but my best guess is to use

E = mc

^{2}

E

^{2}= E'

^{2}- (pc)

^{2}

and maybe the lorentz transformations?

## The Attempt at a Solution

Ok so here's the deal. As much as I'd like an answer to this problem, I'd like to really understand what is going on much more. I've essentially been thrown into the world of special relativity without so much as a textbook for a side project I'm doing for a professor, and I understand the theory behind this weird stuff like time dilation and etc, but I don't understand most of the math behind it. So if anyone happens to know of a good online resource for this sort of stuff, I would greatly appreciate it.

That being said, I have actually given the problem a try! According to the hint my professor gave us, I'm supposed to solve it in the reference frame of the velocity of the center of mass, but I'm not really sure how to go about that. I thought about finding the center of mass like I would in mechanics, but not only can I not find enough information to be able to do that, I routinely mess up when I try to apply mechanics ideas when working with relativity.

I also looked at https://www.physicsforums.com/showthread.php?t=161767", because it seems really similar, but I cannot seem to convert between the information I was given and the information they were given. I did gather that I should be conserving total energy and momentum, but again, I'm not sure where to go from there.

Sorry for this wall of text- even the littlest bit of help or nudge in the right direction would be appreciated.

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