**Educational Text on Roller Coaster Physics**The roller coaster at Six Flags Great America amusement park in Gurnee, Illinois, features innovative design technology and fundamental physics principles. Each vertical loop of the coaster is teardrop-shaped rather than circular (see Figure P6.13). The cars ride on the inner side of the loop at the top, traveling at speeds sufficient to keep them on track. The largest loop is 40.0 meters high. Assuming the speed at the top of the loop is 13.0 m/s with a corresponding centripetal acceleration of the riders at 2g, consider the following questions:(a) What is the radius of the arc of the teardrop at the top?(b) If the total mass of a car plus riders is \( M \), what force does the rail exert on the car at the top?(c) Assuming the roller coaster had a circular loop of radius 20.0 m and the cars maintain a speed of 13.0 m/s at the top, what is the centripetal acceleration of the riders?(d) Discuss the normal force at the top in the situation described in part (c) and the benefits of teardrop-shaped loops.**Figure P6.13 Description:**The image shows a roller coaster with a teardrop-shaped loop. This shape is designed to enhance the ride’s safety and performance by maintaining ride comfort and speed efficiency. The track construction ensures that cars ride smoothly on the inside edge as they move through the loop.

since the question contains more than 3 subparts, the solution for the first three is provided here.…

Answered: 13. A roller coaster at the Six Flags…

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