A spray nozzle for a garden hose requires a force F = 5 lb. to open the spring-loaded spray chamber AB. The nozzle hand grip pivots about a pin through a flange at O. Each of the two flanges has thickness t = 1/16 in., and the pin has diameter dp = 1/8 in. [see figure part (a)]. The spray nozzle is attached to the garden hose with a quick release fitting at B [see figure part (b)]. Three brass balls (diameter db = 3/16 in.) hold the spray head in place under water pressure force fp = 30 lb. at C [see figure part (c)]. Use dimensions given in figure part (a).
(a) Find the force in the pin at O due to applied force F.
(b) Find average shear stress τaver and bearing stress σb in the pin at O.

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in Flange dp Top view at o Pin at O 0 a 0.75 in Spray nozzle Flange b 1.5 in c 1.75 in Sprayer hand grip Water pressure force on nozzle. fp Quick release fittings Garden hose 3 brass retaining balls at 120 diameter dy-16 in.