A. Consider a circular vertical loop-the-loop on a roller coaster. A car coasts without power around the loop. Determine the difference between the normal force exerted by the car on a passenger with a mass of m at the top of the loop and the normal force exerted by the car on her at the bottom of the loop.

b. This difference of 6mg, 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 h above the ground increases in order to have this constant centripetal acceleration? The radius and the speed at the ground are Ro and vo respectively. Express your answer as a function: R = R(h).