1. The problem statement, all variables and given/known data So a mass m is placed on a ramp at a height given by h_1. This portion of the trip is frictionless. Then, at the bottom of the ramp the mass encounters a rough patch of levelled ground with a µk given my µ. This strip has a length of size "d" meters. After traveling across this surface, the mass encounters yet again, another frictionless ramp. The question wants to know how far up the second ramp the ball will get. Call this variable h_2. There were no ø given for either of the two ramps. 2. Relevant equations ΔE=W GPE=mgh KE=½mv^2 W+KE_1+GPE_1=KE_2+GPE_2+E_loss (due to friction) KE_1=0 KE_2=0 (when it reaches it max height on the second hill) 3. The attempt at a solution If someone could confirm this or explain why this is incorrect it would be very helpful. Im thinking, Since W=F*D and I know the only force acting against the ball is that of friction (negative work), can I equate that to ΔGPE? So; -µmgd=mgh_2-mgh_1 -µd+h_1=h_2 But now that I think about it, would there also be work done by the x component of gravity when the ball is rolling down and up the first and second hills? If anyone could clarify this it would be much appreciated.