Newton's Cradle: Fascinating Momentum & Kinetic Energy

[John_RB]

I have always found the Newton's Cradle that my daughter bought for me fascinating. With the steel balls as identical as possible then the analysis of the process is simple. Both the momentum and kinetic energy are conserved (assuming negligible losses) on collision. The only way(?) this can occur is for the the same number of balls to move away from the collision as cause the collision; what is fascinating to me is how the balls which are hit move away as though glued together. Certain conditions must be met to get this nice simple behaviour. Both the receiving balls and the striking (raised) balls must be stationary and touching. If you do that then you can get several repeated collisions before the behaviour becomes "not so nice".
Is there an easy solution if the balls are not of equal mass and is the resulting collision always "not nice"?

 

[AYPHY]

you can use the direct formula which is based on conservation of linear momentum and Newton law of restitution (e) its a propert of colliding materials