An aluminum sphere with a diameter of 20 mm is pressed with a load of 300 N against a hard-plastic sphere with a diameter of 40 mm. The elastic modulus of aluminum is 69 GPa and that of the plastic is 82 GPa. The Poisson's ratios for aluminum and plastic are respectively 0.33 and 0.206. Determine:
(a) The contact circle diameter
(b) Maximum contact pressure
(c) Maximum shear stress in the wheel using stress curves for contacting spheres