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 8.98 m work plank which weighs 112 N and is secured with a hinge on the opposite end. Worker B will stand on the plank 4.11 m from worker A. Worker B also brings up his paint can, m_c = 3.44 kg, which he places 0.475 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/s^2.

Explanation / Answer

Sum the moments about the hinge:
M = 0 = 522N*8.98m - 112N*8.98m/2 - B*(8.98-4.11)m
- 3.44kg*9.81m/s²*(8.98-4.11+0.475)m
B * 4.1m = 3915 N·m
B =718.98N

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