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 8.49 m work plank which weighs 115 N and is secured with a hinge on the opposite end. Worker B will stand on the plank 4.11 m from worker A. Worker B also brings up his paint can, mc = 3.48 kg, which he places 0.430 m from where he is standing on the plank (between the two workers). Worker A unfortunately needs to supply 496 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.

Explanation / Answer

Let WB be the weight of worker B.

The net moment of all forces from the hinge point is zero. So,

496*8.49 - WB*(8.49 - 4.11) - mcg(8.49 - 4.11 + 0.43) - 115*(8.49/2) = 0

=> 4.38WB = 496*8.49 - 3.48*9.81*(8.49 - 4.11 + 0.43) - 115*(8.49/2)

=> WB = 812.5 N

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