Problem 1 (75%): Design a clutch to transmit torques up to 1200 in.lb with speeds up to 30 rev/sec. The clutch operates dry with a woven friction material (Vall=60 ft/sec, PVall=40000 psi.ft/min) rubbing against smooth steel. The outside diameter of the friction disk may not exceed 9.0 in and the actuating force may not exceed 400 lb. A safety factor of 1.1 is required. If the least actuating force is desired, calculate the internal and external diameters of the friction disks, the number of the friction surfaces, and the actuating force.