Need Formula: 2D Relativistic (hopefully) Collisions with COR (e)

Click For Summary

Homework Help Overview

The discussion revolves around finding a formula for the speed and angle after a 2D collision that incorporates the coefficient of restitution (e) in a relativistic context. The original poster expresses difficulty in locating such a formula despite extensive research in various mechanics texts and online resources.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the potential to adapt non-relativistic equations for velocity and the coefficient of restitution to a relativistic framework. There are questions about the independence of speed from incident angles and how the coefficient of restitution affects the angle of collision.

Discussion Status

Some participants have suggested methods for deriving the necessary equations, including replacing non-relativistic momentum conservation with relativistic principles. There is an acknowledgment of the complexity involved in such derivations, and a collaborative spirit is present as participants encourage the original poster to attempt the calculations and share their findings for further assistance.

Contextual Notes

The original poster indicates a lack of mathematical confidence in approaching the problem, which may affect their ability to engage with the suggested methods. There is also a reference to specific resources that may not directly address the relativistic aspect of the problem.

Sunmaz
Messages
8
Reaction score
0
I need a formula that yields the speed and angle after a 2D collision that uses the coefficient of restitution (e). Preferably this would also be relativistic. I have searched EVERYWHERE for this and could not find it.
To "prove" that I have indeed tried I have read the collision sections of Classical Mechanics by R. Douglas Gregory, Mechanics, Volume 4
By Ted Graham, Aidan Burrows, Brian Gaulter, Physics for Scientists and Engineers, Volume 2
By Lawrence S. Lerner, Impact Mechanics
By W. J. Stronge, Engineering Mechanics: Dynamics
By Russell C. Hibbeler, and MANY more...I have also searched extensively online to no avail. Please find/derive this formula for me! Thanks!

The most useful thing I have found so far is: http://books.google.ca/books?id=oVL...icient of restitution collision angle&f=false

This gives a non-relativistic speed using COR but I need the angle too but not for the scenario I describe (a 2D collision between two spheres) - perhaps someone could also explain how to get that from the formula there. Does the COR only effect v and not the angle? Shouldn't a speed formula be independent of the incident angles (and that be factored in with the calculation of the exiting angle)?

Thank you for any and all help!
 
Last edited:
Physics news on Phys.org
39 views and no posts?! Come on - please help!
 
Someone must have something to say regarding this?!
 
Take a look at Wikipedia:
http://en.wikipedia.org/wiki/Coefficient_of_restitution
The article shows the non-relativistic equations for velocity perpendicular to the collision plane, together with the procedure for deriving them, starting from the definition of COR and the law of conservation of momentum. I imagine that you could take those equations, replace the non-relativistic law of conservation of momentum as used in the Wikipedia article with the relativistic one, and derive a relativistic equation for the perpendicular component of velocity in a collision. You should also be able to assume that the parallel component of velocity remains the same, as in NR collisions, and from that obtain the formulas for speed and angle. I wouldn't be surprised if they look pretty ugly, though.

I've written http://www.ellipsix.net/blog/post.84.html about a special case of inelastic collisions that you could look at, basically as an example of manipulating the collision equations - but it's not particularly relevant to your situation.
http://www.ellipsix.net/blog/post.84.html
 
Thanks. I was hoping that someone would know it but I guess I'll have to try that.
 
In all honesty I'm not sure I'm mathematically capable of it but I can try :P.
 
Give it a try and post it here, maybe we can help you fix it up. It'll be good learning experience too. (If it's not obvious to you how to do so, I'd suggest first trying to reproduce the collision equations given on the Wikipedia page as practice.)
 
I will follow your advice and post it here when I get the time (hopefully within the next week and a half). I looked at what you wrote and it is very well written and quite enlightening (although like you said it is not of much use to me). Thanks for the advice and well done!