the problem we got in class was that an object of mass m was sliding down a quarter-circle ramp (or "quarter pipe) that had a radius a, and a coefficient of kinetic friction "mu". if the mass began down the ramp from rest and continued to the bottom, what would it's final velocity be? i had no idea how to solve it by the time the teacher worked it out on the board. she simplified it converting it to a flat ramp at an angle of 45 deg above the horizontal. i understand more than well how to work problems of that sort... but how would you go about it the "correct" way?? i've tried integrating the normal force of m*g*cos("theta") WRT theta from "pi" to 3*"pi"/2... which obviously didn't work. i've also tried calculating the unit normal vector of the line r("theta")=a*cos("theta")i+a*sin("theta")j and ("pi" <= "theta" <= 3*"pi"/2) and using that with the normal force which also didn't work. i don't need this answer for class... i just don't like only knowing how to figure this out the "simplified" way. if you could explain how to do figure this out, i'd appreciate it. thanks.