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 8.49 m work plank which weighs 115 N and is secured with a hinge on the opposite end. Worker B will stand on the plank 4.22 m from worker A. Worker B also brings up his paint can, mc = 3.48 kg, which he places 0.385 m from where he is standing on the plank (between the two workers). Worker A unfortunately needs to supply 483 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. The answer needs to just be in Newtons. The torque produced by the weight of the plank is located at the planks center of gravity not along the entire length

Explanation / Answer

In order to keep the plank steady, all the torque must be balanced.

Torque applied by worker A = Torque applied by worker B and  the paint can system.

483 * 8.49 = mBg ( 8.49 - 4.22) + (3.48)(9.8) ( 8.49 - 4.22 + 0.37) + 115 * [8.49/2]

mB = 82.54 kg

Mass of worker, B = 82.54 kg

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