Oblique impact of smooth spheres?

AI Thread Summary
A sphere of mass m collides obliquely with a stationary sphere of mass M, with a coefficient of restitution e. The discussion centers on demonstrating that if m equals eM, the resulting motion directions after impact will be perpendicular. Participants suggest using vector representations and conservation of momentum to analyze the collision dynamics. One user shares a link to a helpful article that clarifies the concepts involved. The conversation emphasizes the importance of understanding the relationship between mass, velocity, and the coefficient of restitution in collision scenarios.
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1. A sphere of mass m impinges obliquely on a sphere of mass M, which is at rest. The coefficient of restitution between the spheres is e. Show that if m=eM, the directions of motion after impact are at right angles



2. Coefficient of restitution -
442cb57fc9daffed79a534632d0a5aad.png




3. I really don't think I have a clue with this one, so far I have taken e and substituted it into m=eM to give

m = M x V_{}2f-V_{}1f/V_{}1

Can anyone give me any clues as to where to go next or am I going completely wrong with what I have?

Thanks in advance for any help
 
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Have you tried to draw a vector representation of your problem? Try this and make use of the conservation of momentum.
 
dlgoff said:
Have you tried to draw a vector representation of your problem? Try this and make use of the conservation of momentum.

This is what I have for the problem,

http://img156.imageshack.us/img156/2310/questioncb9.jpg

Do I have the right idea of what the collision looks like?

And how would I use the momentum conservation here, as in U1 (speed of m before) = V2 (speed of M after)?
 
Last edited by a moderator:
Well, that's not exactly what I had in mind.

Could you read over this http://instruct.tri-c.edu/fgram/web/elastic.htm" and let me know if it helps?
 
Last edited by a moderator:
Ah, that article was exactly what I needed, thanks for your help :D
 

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