1. (25 pts). A pen oflength i 2 12a and weight W=125 N rests in a thin-walled cylindrical cup of diameter 4a, height 3a, and weight 4W. The lower end of the pen contacts the corner at the bottom of the cup, shown in the gure. The contact points between the cup and the pen are labeled A and B. The pen is thin and we simplify it as a line segment. All surfaces are smooth. (a) (10 pts). Draw the free body diagram of the pen. (b) (15 pts). Apply the equilibrium condition to determine the contact forces on the pen at A and B