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 114 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, mc = 3.52 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 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

=> 522N*8.98m - 114N*(8.98m/2) - B*(8.98-4.11)m – [3.52kg*9.81m/s²*(8.98-4.11+0.355)m] = 0

B * 4.87m = 3995.274 N·m

B = 820.38 N

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