Stopping on a cone

When viewed from the side, a cone subtends an angle 2theta at its tip. A block of mass m is connected to the tip by a massless string and moves in a horizontal circle of radius R around the surface. If the initital speed is v0, and if the coefficient of kinetic friction between the block and the cone is u, how much time does it take the block to stop? Hint: The answer is a little messy, but there are some limits you can check that will make you feel about it.

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