A young work crew is trying to quickly finish some touch-up painting to complete

Question

A young work crew is trying to quickly finish some touch-up painting to complete a job. Rather than setting up a secure work area, they decide to try a shortcut. Worker A will hold the far end of a 9.96 m work plank which weighs 112 N and is secured with a hinge on the opposite end. Worker B will stand on the plank 4.99 m from worker A. Worker B also brings up his paint can, mc = 3.44 kg, which he places 0.415 m from where he is standing on the plank (between the two workers). Worker A unfortunately needs to supply 483 N of force to hold the end of the plank. How much does worker B weigh? The acceleration due to gravity is g = 9.81 m/s2. Find Wb=N

Explanation / Answer

Let normal reaction forces by the hinge be Rx and Ry
and normal reaction at the floor be N
From force balance N + Ry = W + 112 + 3.44 g
and F = Rx

from moment balance abouit hinge
N*9.96cos(theta) = F*9.96*sin(theta) + W*(9.96-4.99)cos(theta) + 3.44*9.8*(9.96 - 4.99 - 0.415)cos(theta) + 112*9.96*cos(theta)/2
now, theta is not known so this equation cannot be further soplved, but W can be known from thjis equation by plugging in values

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