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 1.10 × 102 N and is secured with a hinge on the opposite end. Worker B will stand on the plank 4.44 m from worker A. Worker B also brings up his paint can, mc = 3.40 kg, which he places 0.340 m from where he is standing on the plank (between the two workers). Worker A unfortunately needs to supply 4.70 × 102 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

Net torque about the hinge = 0

worker B is at rB = 8 - 4.4 = 3.6 m from worker A

can is at rc = 3.6+0.34 = 3.94 m

WB*rB + mc*g*rc + Wp*L/2 - FA*L = 0

WB*3.6 + 3.4*9.81*3.94 + 1.1*10^2*8/2 - 4.7*10^2*8 = 0

weight of worker B = WB = 885.7 N

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