Understanding the Coefficient of Restitution in 2-D Inelastic Collisions

[Sythalist]

Hello,

This concerns a collision between two spherical balls of equal mass and radius. The collision is two dimensional and not completely elastic. The secondary ball begins stationary. The primary ball travels along the horizontal axis with a given velocity. After the collision, the speed and components of velocity of both balls are observed.

u0 = initial velocity of primary ball
v0 = initial velocity of secondary ball = 0

u1x = horizontal component of velocity of primary ball post collision
u1y = vertical component of velocity of primary ball post collision
|u1| = post collision speed of primary ball

v1x = horizontal component of velocity of secondary ball post collision
v1y = vertical component of velocity of secondary ball post collision
|v1| = post collision speed of secondary ball

The question is about the coefficient of restitution. What is, if any, the relationship between all or some of the above variables in terms of the coefficient of restitution? Or how can we determine the coefficient of restitution from the above variables? Thank you!

 

[Sythalist]

aaah n/m sorry, I just hit a mind block back there, I did more research and figured out you must use the speeds along the axis of the normal of the collision. And that the secondary ball's direction IS along the normal of collision axis. Then you simply find the ratio between the difference of speeds before and after the collision. oops

hehe talking to myself in my ooooown thread