A uniform 23kg door that is 2.0m high by 0.90m wide is hung from two hinges that

Question

A uniform 23kg door that is 2.0m high by 0.90m wide is hung from two hinges that are 20cm from the top and 20cm from the bottom. If each hinge supports half the weight of the door, find the magnitude and direction of the horizontal components of the forces exerted by the two hinges on the door. (Take the direction of forcing the door away from the hinges to be positive and the direction of forcing the door toward the hinges to be negative). _________ Upper Hinge _________ Lower Hinge Show all work and steps and solution please.

Explanation / Answer

Let upper hinge be A and lower hinge be B now Fa = horizontal force on door at A (away from hinge) Fb = horizontal force on door at B (away from hinge) net horizontal force = 0 thus Fa + Fb = 0 also net moment about hinge B =0 thus 23*9.81*(0.9/2) + Fa*(2-0.2-0.2) = 0 solve to get answer

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