Rotating Cylinder, Centripital Motion, and Coeffients of friction.

[Imatree]

Homework Statement

So, in a popular amusement park ride, a cylinder with a radius of 3.00 meters is set in rotation. The floor then drops away, and leaves riders suspended against the wall in a vertical position.

a. If the Cylinder rotates at 50 RPM, what minimum coefficient of friction between a rider's clothing and the wall of the cylinder is necessary to keep the rider from slipping?
b. If the coefficient of friction between the rider's clothing and the wall of the cylinder is 0.200, at what minimum rotational speed (in RPM) must the ride rotate?

Homework Equations

a = V² / r
F_f= μF_n
V = 2πrRPM / 60
F = ma

The Attempt at a Solution

So, I started with Drawing a diagram of this situation. I drew a cylinder with a radius of 3m, and spinning at 50RPM. The forces I drew were F_a, so the centripetal force, and the force of gravity on the rider. Then I used the V = 2πrRPM / 60 to get my velocity of 15.71 m/s, plugged that into the a = V² / r to get an acceleration of 82.246 m/s², then plugged that into the F = ma equation. I assumed a mass of 10kg for the rider (no mass was given), and got an inward force of 822.467N. Now I'm completely stuck. I have the F_f= μF_n equation, but I do not have a force of Friction, and I need to solve for Mu. I'm also not sure if I need to use the inward force for this equation, instead of the force of gravity.

 

[JaWiB]

I assumed a mass of 10kg for the rider (no mass was given), and got an inward force of 822.467N.

Don't do this. It will work out in the end, but it's better to leave "m" in the equations and see if it cancels out at the end (as you would expect).

I have the Ff= μFn equation, but I do not have a force of Friction, and I need to solve for Mu. I'm also not sure if I need to use the inward force for this equation, instead of the force of gravity.

Fn is the normal force. Have you drawn a free body diagram, or can you visualize all the forces on the rider? When you add up the frictional force, the weight force, and the normal force, what do you get?