# Homework Help: Critical Velocity Problem

1. Oct 7, 2009

### JoshMP

1. The problem statement, all variables and given/known data

In an old-fashioned amusement park ride, passengers stand inside a 5.5m-diameter hollow steel cylinder with their backs against the wall. The cylinder begins to rotate about a vertical axis. Then the floor on which the passengers are standing suddenly drops away! If all goes well, the passengers will "stick" to the wall and not slide. Clothing has a static coefficient of friction against steel in the range 0.63 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. A sign next to the entrance says "No children under 30 kg allowed." What is the minimum angular speed, in rpm, for which the ride is safe?

2. Relevant equations

Critical velocity=SQRT(rg)
F=ma

3. The attempt at a solution

I know how to solve these kinds of problems in the absence of friction, but I don't understand what I need to do with these coefficients. Friction points tangentially to the circular motion in the free body diagram, but how does that influence the (Fnet)y?

2. Oct 7, 2009

### Staff: Mentor

Could you show us your FBD? If the force of gravity would normally pull the people down out of the ride, what force is resisting their movement?

3. Oct 7, 2009

### JoshMP

The normal force is what keeps people from falling- when the veolcity decreases such that the normal force is less than 0, the people would fall off the ride.

My FBD has gravity pointing down, normal force pointing down, and friction pointing to the left.

4. Oct 7, 2009

### Staff: Mentor

The forces on the FBD don't sound right. The normal force points toward the center of the circular motion, and is based on the centripital acceleration. The friction force is what opposes the falling-downward motion of the person, so it has to point _____

5. Oct 7, 2009

### JoshMP

Up? I thought friction points tangential to circular motion?

6. Oct 7, 2009

### Staff: Mentor

Up is correct in this problem. Now re-draw the forces on your FBD, and write the sum of forces equations in the vertical direction.

I have to bail for a few hours. Keep at it!

7. Oct 7, 2009

### JoshMP

I'm stuck. I've got an inequality set up, but I can't isolate the velocity. Am I even on the right track?

8. Oct 8, 2009

### Staff: Mentor

Beats me. Show us your FBD and equations.

9. Oct 8, 2009

### JoshMP

My FBD consists of Gravity pointing down, normal force pointing down, and static friction pointing up. (The net force along the radial axis is equal to Gravity + Normal force - static friction. This net force is equal to the mass multiplied by the radial acceleration, which = v^2/r. Using this equation I solved for the normal force, then used the inequality of n greater than or equal to 0. The inequality looks like this:

(m(v^2/r - g))/(1-mu static) is greater than or equal to 0. I need to solve for v. Any ideas?

10. Oct 8, 2009

### willem2

The normal force is always perpendicular to the surface that an object is being pushed against, no matter if it is by gravity or any other force, or to keep it on a circular path.