1. The problem statement, all variables and given/known data A rollercoaster has an initial hill that leads to a circular loop of radius R. (a) Show that the top of the hill must be at least 1/2 R higher than the highest part of the loop. (b) Discuss additional factors that must be considered in the design of an actual rollercoaster of this type. 2. Relevant equations PE = mgy KE= 1/2mv^2 Ac=V^2/r W=Fd= change in KE 2piR=C Work done by friction(?)= Fnu(c) 3. The attempt at a solution A) I started by realizing that the loop must be lower than the hill due to conservation of energy, because PEi=KEf(assuming no friction). What I don't understand is if there only needs to be enough energy to get the rollercoaster to the top of the loop and a little past it, why is the question telling me that it has to be at least 1/2 R greater? Why not 1/5 R? If there is friction, I don't know the coefficient so I have no idea whether or not this extra 1/2R of distance is needed to overcome friction. I'd appreciate some guidance as to where to go from here, thanks in advance.