An amusement park ride called the Rotor consists of a room in the shape of a vertical cylinder (2.10 m in radius) which, once the riders are inside, begins to rotate, forcing them to the wall. When the room reaches a speed of one rotation every 1.36 s, the floor suddenly drops out. What is the minimum coefficient of static friction between riders and wall necessary to prevent them from sliding down the wall?

This problem seems to be asked every week. Only the numbers change now and then.

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To find the minimum coefficient of static friction between the riders and the wall, we need to consider the forces acting on the riders when the floor drops out.

1. Determine the gravitational force acting on each rider:
The gravitational force on each rider can be calculated using the formula Fg = mg, where m is the mass of each rider and g is the acceleration due to gravity (approximately 9.8 m/s^2).

2. Determine the net force acting towards the center of the circular wall:
When the floor drops out, the only force acting in the horizontal direction is the static friction force between the riders and the wall. This static friction force must be sufficient to provide the centripetal force needed to keep the riders against the wall. The centripetal force can be calculated using the formula Fc = (mv^2) / r, where m is the mass of each rider, v is the speed of rotation, and r is the radius of the cylinder.

3. Set up the static friction equation:
The static friction force is equal to the product of the coefficient of static friction (μs) and the normal force (Fn). The normal force is equal to the gravitational force acting on each rider.

4. Equate the net force to the static friction force:
Set up the equation: Fc = Fs, where Fc is the centripetal force and Fs is the static friction force. Rearrange the equation to solve for the coefficient of static friction (μs): μs = Fc / Fn.

5. Substitute the values and solve for the minimum coefficient of static friction:
Insert the values for m, v, and r into the equation and calculate the gravitational force (Fn). Then substitute the gravitational force and the centripetal force into the equation to find the minimum coefficient of static friction (μs).

Remember to convert units to ensure consistent calculations.

With these steps, you should be able to find the minimum coefficient of static friction between the riders and the wall necessary to prevent them from sliding down.