An engineer is designing a conveyor system for loading hay bales into a wagon (Fig. 11.57). Each bale is 0.25 m wide, 0.50 m high, and 0.80 m long (the dimension perpendicular to the plane of the figure), with mass 30.0 kg. The center of gravity of each bale is at its geometrical center. The coefficient of static friction between a bale and the conveyor belt is 0.60, and the belt moves with constant speed.
(a) The angle f3 of the conveyor is slowly increased. At some critical angle a bale will tip (if it doesn't slip first), and at some different critical angle it will slip (if it doesn't tip first). Find the two critical angles and determine which happens at the smaller angle.
(b) Would the outcome of part (a) be different if the coefficient of friction were 0.40?

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0.25 m 0.50 m cg AB