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 9.47 m work plank which weighs 112 N and is secured with a hinge on the opposite end. Worker B will stand on the plank 4.00 m from worker A. Worker B also brings up his paint can, mc = 3.54 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 496 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 = 496N*9.47m - 112N*9.47m/2 - B*(9.47-4.00)m - 3.54kg*9.81m/s²*(9.47-4.00+0.2)m

B * 5.47m =3439.57N·m

B =628.80N

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