Variably Solving for Minimum Tangential Speed

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To find the minimum tangential speed for a rider to stick to the side of a rotating carnival ride, the relationship between the radius (R), coefficient of static friction (u), and gravitational force (g) must be established. The equations of motion indicate that the centripetal force required to keep the rider in circular motion is provided by the frictional force. The normal force acting on the rider is equal to the gravitational force, and the frictional force acts towards the center of the circle. The condition for the rider not to fall involves ensuring that the frictional force is sufficient to counteract the gravitational pull. Clarifying these relationships will lead to the correct expression for minimum tangential speed.
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Homework Statement


A ride at a carnival rotates about a vertical axis. When spinning fast enough the bottom is dropped and the rider sticks to the side. Find the minimum tangential speed so that the rider does not fall. R=radius of circle, u= coefficient of static friction and g represents gravity. The answer must be in these terms.


Homework Equations


F = ma
F = un
Ca = v^2/r

The Attempt at a Solution


V = sqrt (Ca*r)

I think I am missing something here, as it is not with respect to the right variables. Any hints on what to do next, or if I am heading down the wrong path?
 
Physics news on Phys.org
What is the normal reaction of the surface?
In which direction the frictional force acts?
What should the condition so that rider does not fall?
 

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