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aerospacedout
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Homework Statement
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.
Homework Equations
PE = mgy
KE= 1/2mv^2
Ac=V^2/r
W=Fd= change in KE
2piR=C
Work done by friction(?)= Fnu(c)
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.