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 8.00 m work plank which weighs 111 N and is secured with a hinge on the opposite end. Worker B will stand on the plank 4.44 m from worker A. Worker B also brings up his paint can, mc = 3.60 kg, which he places 0.280 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.

Explanation / Answer

This is done by equilibrium of the torques ( = FL)

The plank has a torque downward of (111)(4) = 444 down

The worker has a torque of (W)(3.56) = 3.56 W down

The paint can has a torque of (3.6)(9.81)(3.84) = 135.6 down

The supply force torque is (483)(8) = 3864 upward

So, 3864 = 444 + 3.56 W + 135.6

W = 922.6 N

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