Serway & Jewett — Circular Motion and Other Applications of Newton's Laws: Problem 32

Why is the following situation impossible? A mischievous child goes to an amusement park with his family. On one ride, after a severe scolding from his mother, he slips out of his seat and climbs to the top of the ride’s structure, which is shaped like a cone with its axis vertical and its sloped sides making an angle of \(\theta = 20.0^\circ\) with the horizontal as shown in Figure P6.32. This part of the structure rotates about the vertical central axis when the ride operates. The child sits on the sloped surface at a point \(d = 5.32 \text{ m}\) down the sloped side from the center of the cone and pouts. The coefficient of static friction between the boy and the cone is 0.700. The ride operator does not notice that the child has slipped away from his seat and so continues to operate the ride. As a result, the sitting, pouting boy rotates in a circular path at a speed of 3.75 m/s.