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 4.33 m from worker A. Worker B also brings up his paint can, mc = 3.50 kg, which he places 0.295 m from where he is standing on the plank (between the two workers). Worker A unfortunately needs to supply 509 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

w = 112 N, L = 9.96 m , mc = 3.50 kg

When the system is under equilibrium then the force and torque actingon the system is zero

sigma torque = FA L - w (L/2) - FB(L - 4.33) - mc g(L - 4.035) = 0

FB(L - 4.33) =  FA L - w (L/2) - mc g(L - 4.035)

Therefore the weigh of worker B

FB = [FA L - w (L/2) - mc g(L - 4.035)] / (L - 4.33)

= [509 * 9.96 - 112 (9.96/2) - 3.5 * 9.8(9.96 - 4.035)] / (9.96 - 4.33)

= 765.3 N

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