A bookcase weighing 1500 N rests on a horizontal surface for which the coefficient of static friction is p = 0.40. The bookcase is 1.80 m tall and 2.00 m wide; its center of gravity is at its geometrical center the bookcase rests on four short legs that are each 0.10 m from the edge of the bookcase. A person pulls on a rope attached to an upper comer of the bookcase with a force F that makes an angle 6 with the bookcase (Fig. 11.65).

(a) If6 = 90", so horizontal, show that as F is increased from zero, the bookcase will start to slide before it tips, and calculate the magnitude of F that will start the bookcase sliding.

(b) If 6 = 0°, so F is vertical, show that the bookcase will tip over rather than slide, and calculate the magnitude of F that will cause the bookcase to start to tip.

(c) Calculate as a function of 6 the magnitude of F that will cause the bookcase to start to slide and the magnitude that will cause it to start to tip. What is the smallest value that 6 can have so that the bookcase will still start to slide before it starts to tip?