A small block with mass m is placed inside an inverted cone that is rotating about a vertical axis such that the time for one revolution of the cone is T (Figure 1). The walls of the cone make an angle B with the horizontal. The coefficient of static friction between the block and the cone is µg. If the block is to remain at a constant height h above the apex of the cone, what are (a) the maximum value of T and (b) the minimum value of T? (That is, find expressions for Tmax and Tmin in terms of B and h.)

A small block with mass m is placed inside an inverted cone that is rotating about a vertical axis such that the time for one revolution of the cone is T (Figure 1). The walls of the cone make an angle B with the horizontal. The coefficient of static friction between the block and the cone is µg. If the block is to remain at a constant height h above the apex of the cone, what are (a) the maximum value of T and (b) the minimum value of T? (That is, find expressions for Tmax and Tmin in terms of B and h.)