(9 pts.) Suppose a 60 mm diameter stainless steel ball (see Ch. 3 for properties) is in contact with a plastic surface (E=2.8 GPa, =0.4). If the stainless steel ball is pressed against the plastic surface with a normal force of F= 120 N, what is the maximum pressure, pmax, for the following surface geometries for the plastic: (a) inside of a cup of diameter 61mm (conforming geometry, like in ball and socket joint), (b) flat plate (non-conforming), and (c) outside surface of a sphere of diameter 20 mm (non-conforming)