The pulley in the figure is fixed to a 45 mm shaft by a rectangular sunk key 14 mm wide and 9 mm deep (half the depth in the shaft, half in the hub). The shaft transmits the power at the speed given in the figure, and the allowable stresses for the key are also given there. Determine (a) the torque transmitted (answer in N·m), (b) the key length required to resist shear (answer in mm) and (c) the key length required to resist crushing (answer in mm). State which length must be provided.