Find tangential velocity given radius and the coefficient of friction

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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.

 

[PeroK]

Can you post your working? Your method looks correct.

 

[jbriggs444]

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.

 

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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.