Chapter 6, Problem 93A

To determine

To Explain:The physics behind the vertical loops on most roller coasters are not circular in shape.

Explanation of Solution

Introduction:Centripetal acceleration is directed towards the center of a circle whose magnitude is equal to square of angular velocity divided by the distance from the center of the circle.

First if the shape of the roller coaster is circular, then centripetal acceleration experienced by the rider in roller coaster is large and for circular loop,roller coaster requires greater entry speeds to complete the loop. So, the vertical loops of the roller coaster are made clothoid shape. In clothoid shape the radius is constantly changing. The radius at the bottom of the shape is larger than the radius at the top. Thus, it requires less speed to complete the loop.