# What Is the Minimum RPM Needed for Safety on This Amusement Park Ride?

• JoshMP
In summary: So in this case the normal force is pointing towards the center of the circle, because it is being pushed against the wall. The static friction is pointing up, because it is opposing the force of gravity pushing the people downward. As for your inequality, I'm not sure what you're trying to do. But remember that the normal force and the friction force depend on each other, so you can't just set an inequality for one and expect to solve it. You need to find a way to relate the two forces, so that when one changes, the other changes as well.I have to bail for a few hours. Keep at it!Okay, I'll keep at it. Thanks for all your help!In summary, the
JoshMP

## Homework Statement

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?

## Homework Equations

Critical velocity=SQRT(rg)
F=ma

## 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?

JoshMP said:

## Homework Statement

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?

## Homework Equations

Critical velocity=SQRT(rg)
F=ma

## 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?

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?

berkeman said:
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?

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.

JoshMP said:
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.

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 _____

berkeman said:
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 _____

Up? I thought friction points tangential to circular motion?

JoshMP said:
Up? I thought friction points tangential to circular motion?

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!

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

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

Beats me. Show us your FBD and equations.

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?

JoshMP said:
My FBD consists of Gravity pointing down, normal force pointing down, and static friction pointing up.

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.

## What is the "Critical Velocity Problem"?

The Critical Velocity Problem is a concept in fluid mechanics that refers to the minimum velocity required for a fluid to flow through a pipe without causing turbulence or cavitation.

## Why is the Critical Velocity important?

The Critical Velocity is important because it helps determine the maximum flow rate that a fluid can maintain without causing damage to the pipe or equipment. It also affects the efficiency and performance of fluid systems.

## How is the Critical Velocity calculated?

The Critical Velocity is calculated using the equation Vc = (p/ρ)^0.5, where Vc is the Critical Velocity, p is the pressure of the fluid, and ρ is the density of the fluid.

## What factors can affect the Critical Velocity?

The Critical Velocity can be affected by the density and viscosity of the fluid, the diameter and length of the pipe, and the roughness of the pipe's inner surface.

## What happens if the fluid velocity exceeds the Critical Velocity?

If the fluid velocity exceeds the Critical Velocity, it can cause turbulence and cavitation, which can lead to damage to the pipe or equipment. It can also decrease the efficiency of the fluid system and increase energy consumption.

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