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Chapter 1: Q20DQ (page 159)

To keep the forces on the riders within allowable limits, many loop-the-loop roller coaster rides are designed so that the loop is not a perfect circle but instead has a larger radius of curvature at the bottom than at the top. Explain.

Short Answer

Expert verified

The larger radius of curvature at the bottom controls the effective force on the rider within the allowable limit at the bottom.

Step by step solution

01

Explanation of the physics of an object moving in a circular path:

When an object travels in a circle, centripetal acceleration is applied to it from the circumference of the route in a radial direction. Centripetal force is the result of this centripetal acceleration acting on an object. The force acting on an object changes according to the circular path's speed and radius of curvature.

02

Reason for the larger radius of curvature at bottom of a roller coaster than at the top of a roller coaster:

The apparent weight of the rider on a roller coaster is maximum at the bottom and minimum at top of the roller coaster. The centripetal force on the rider is controlled by increasing the radius of curvature at the bottom to limit the effective force on the rider.

The loop cannot be a perfect circle due to different the radius of curvature at the bottom and top of the roller coaster. This different radius of curvature is chosen to limit the effective forces at the bottom and top within allowable limits for the rider.

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