(a) Consider a circular vertical loop-the-loop on a roller coaster. Show that if a car coasts without power around the loop, the difference between the normal force exerted by the car on a passenger at the top of the loop and the normal force exerted by the car on her at the bottom of the loop is six times the gravitational force exerted on her.

(b) This difference of \(6 m g\), referred to as "six gees," is quite a difference for the body to tolerate. To avoid this stress, vertical loops are teardrop-shaped rather than circular, designed so that the centripetal acceleration is constant all around the loop. How must the radius of curvature \(R\) change as the car's height \(b\) above the ground increases in order to have this constant centripetal acceleration? Express your answer as a function: \(R=R(h)\).