Find tangential velocity given radius and the coefficient of friction

AI Thread Summary
The discussion focuses on calculating tangential velocity using centripetal force and friction. The initial approach incorrectly equated centripetal force to gravitational force without considering the role of friction. It was clarified that the normal force, which contributes to centripetal force, must be derived from frictional forces rather than simply using weight. The correct relationship involves setting the frictional force equal to the gravitational force, leading to a revised normal force calculation. This adjustment allows for the accurate determination of tangential velocity.
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Homework Statement
A student is in a giant trash can which is set on top of a revolving plate. The coefficient of friction between the student and the wall is 0.32, and the can has a radius of 10m. The can is set turning and the floor drops out. How can I find the tangential velocity of the can needed for the student to "stick" to the wall?
Relevant Equations
Fc = (mv^2)/r, Fn = mg, Ff = Mu (Fn)
I have attempted to solve for the velocity by setting the centripetal force (mv2)/r to the normal force pointed to the center of rotation (mg). This approach seems to give the incorrect solution and I am unsure of my misunderstandings.
 
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Can you post your working? Your method looks correct.
 
Send-Help said:
I have attempted to solve for the velocity by setting the centripetal force (mv2)/r to the normal force pointed to the center of rotation (mg). This approach seems to give the incorrect solution and I am unsure of my misunderstandings.
The normal force is horizontal. Gravity is vertical.
 
Thank you for all the replies. I realized the normal force (also the force making up the centripetal force) cannot simply be accounted for by (mg) but has to be calculated from the frictional forces opposing the force of gravity. This means that (Mu*Fn = mg) which gives Fn=(mg)/Mu; This can be set equal to the centripetal force equation and the correct answer could then be found.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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