A 1.0 kg mass, hanging vertically from the bottom of an inverted cone, is held in place by a 2.0 kg wheel that is rolling (without slipping) with a constant speed in a horizontal circle on the inside of the cone, as shown in the figure. They are attached by a string that passes through a pulley and a hole in the middle of the cone. If the cone makes an angle of 20 degrees with respect to the horizontal and the wheel is always 1.0 m from the center line of the cone.
What is the maximum and minimum speed with which the wheel can go to keep the hanging mass in place, given the coefficient of static friction between the cone and the wheel is 0.40.