*Originally posted by Ramiri15*

**True, there is no way the function can be described as a quadratic because eventually, due to the friction, the ball would reach a constant velocity.**

yes, i see it as an exponential rise-to-max type scenario, much like terminal velocity. but the probelm takes on vector-type difficulties early in the piece, since gravity is pulling the ball down, and the chain is pulling the ball sideways, with the chains force dependant on the angle between the line P1-P2 and the vertical. the combination of these will give the downward spped without friction. the friction u1 can be thought of as acting on the final sum of gravity and angle, so that should be easier to put in. i'm not fantastic at doing vector math...

Edit: ah ha, it seems galileo considered this probelm, and found for a ball rolling down a slope, the velocity at the end of the slope is v= sqrt((10g-h)/7), where g= accleration due to gravity, h= overall height dropped by ball. should give a start point anyway.