Even some seasoned roller coaster riders blanch at the thought of riding the Rotor, which is essentially a large, hollow cylinder that is rotated rapidly around its central axis. Before the ride begins, a rider enters the cylinder through a door on the side and stands on a floor, up against a canvas covered wall. The door is closed, and as the cylinder begins to turn, the rider, wall, and floor move in unison. When the rider's speed reaches some predetermined value, the floor abruptly and alarminglly falls away. The rider does not fal with it but instead is pinned to the wall while the cylinder rotates, as if an unseen (and somewhat unfriendly) agent is pressin the body to the wall. Later, the floor is eased back to the rider's feet, the cylinder slows. and the rider sinks a few centimeters to regain footing on the floor. (Some riders consider all this to be fun.)
Suppose that the coefficient of static friction `mu_(s)` between the rider's clothing and the canvas is 0.40 and that the cylinder's radius R is 2.1 m.
a. What minimum speed v must the cylinder and rider have if the rider is not to fall when the floor drops?
b. If the rider's mass is 49 kg, what is the magnitude of the centripetal force on her?

Explanation

To solve the problem step by step, we will break it down into two parts as specified in the question.

### Part (a): Minimum Speed \( v \)

1. **Understanding Forces Acting on the Rider**:
- When the floor drops, the rider is pinned against the wall due to the frictional force and the normal force. The forces acting on the rider are:
- Gravitational force \( F_g = mg \) acting downwards.
- Normal force \( N \) acting towards the center of the cylinder.
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