Roller Coaster Circular Motion Problem

Roller coasters use a hill for riders to gain speeds followed by an upside-down loop. The loops are designed with large radius bottoms and small radius tops (this shape is called a clothoid). Answer the following in order to find out why the clothoid is used: The speed of the roller coaster is 22 m/s at the bottom of the loop (r1 = 10m) and 8 m/s at the top of the loop (r2 = 5m). Construct a quantitative force diagram for the passenger when they are at the bottom of Loop 1. Include the sum of the forces equation. Construct a quantitative force diagram for the passenger when they are at the top of Loop 2. Include the sum of the forces equation. Construct a quantitative force diagram for the passenger when they are at the bottom of Loop 1. Include the sum of the forces equation. Construct a quantitative force diagram for the passenger when they are at the top of Loop 2. Include the sum of the forces equation. Why is the clothoid shape used in roller coasters?