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 113 N and is secured with a hinge on the opposite end. Worker B will stand on the plank 4.77 m from worker A. Worker B also brings up his paint can, mc = 3.58 kg, which he places 0.265 m from where he is standing on the plank (between the two workers). Worker A unfortunately needs to supply 522 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

Sum the moments about the hinge:
M = 0 = 113N*9.96m/2 + B*(9.96-4.77)m + 3.58kg*9.81m/s²*(9.96-4.77+0.265)m - 522N*9.96m
0 = B*5.19m - 3882N·m
B = 748 N

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