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 8.00 m work plank which weighs 111 N and is secured with a hinge on the opposite end. Worker B will stand on the plank 4.33 m from worker A. Worker B also brings up his paint can, mc = 3.56 kg, which he places 0.355 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

from the hinge

xb = L-4.33 = 8-4.33 = 3.67 m

xc = xb + 0.355 = 4.025 m

xa = 8m

xp = L/2 = 4m

net torque aboput the hinge = 0

Wp*xp + Wb*xb + Wc*xc = F*xa

(111*4)+(Wb*3.67)+(3.56*9.81*4.025) = (496*8)

Wb = 921.91 N

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