Roller coasters are designed so that the riders will not experience more than a certain level of g-force during the ride. (The rider would experience B g's if hte normal force were Bmg where B is a number, i.e., if B=3 the rider would experience 3g's and the normal force owuld be 3 times his weight) In this, the car has a velcoity v1 at the crest of the at height h1 and drops to height h2 as it goes around the inside curve of radius p.
a) Find an expression for the minimum radius p if a design requirement limits the rider to B g's. (Hint: Use Newton's Second Law to determine the velocity at the bottom of the drop not that the roller coaster travels along a curved path. Then use work energy to relate this velocity to the velocity v1 and height of the crest h1. Your final expression for p should have the terms v1, h1, h2, and B)
b) How is the minimum radius affected if the inital velocity v1 increases? Explain why this does or does not make physical sense.
c) How is the minimum radius affected if the B decreases? In this case you would like the rider to experience less g's. Explain why this does or does not make physical sense.
d) Explain what happens to the minimum radius of p if B=1. Explain why this does or does not make sense.