Dynamics Problem: Spinning cone with mass!?
The sides of a cone make an angle "THETA" with the vertical. A small mass "m" is placed on the inside of the cone and the cone, with its point down, is revolved at a frequency "f" about its symmetry axis. If the coefficient of static friction is "MU", at what positions on the cone can the mass be placed without sliding on the code? (Give the maximum and minimum distances, "r", from the axis)
I guess what it boils down to is what forces are acting on the mass... what am I missing. So far I have these forces:
Centripetal, friction, and gravity. Is that it? And is (f/(2*pi*r)) equal to velocity?
The Attempt at a Solution
set up two equations, set normal force equal to each other, and solve for r?
(F_n)*cos(THETA) = (F_centrip) - (F_friction)*sin(THETA)
m*g = (F_n)*sin(THETA) + (F_friction)*cos(THETA)
i'm missing something :( what is it?!-