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 9.96 m work plank which weighs 114 N and is secured with a hinge on the opposite end. Worker B will stand on the plank 4.55 m from worker A. Worker B also brings up his paint can, mc = 3.46 kg, which he places 0.445 m from where he is standing on the plank (between the two workers). Worker A unfortunately needs to supply 4.70

Explanation / Answer

This is done by equilibrium of torques, where torque = FL

Using the pivot point at the hinge location, the beam has a 'downward' torque of (114)(4.98) - The weight is concentrated at its center

Worker B has a 'downward torque of (W)(9.96 - 4.55)   - We are going to find W

The paint can has a 'downward' torque of (3.46)(9.81)(9.96 - 4.55 + .445)

Worker A supplies an 'upward' torque of (470)(9.96)

So

(114)(4.98) + (W)(5.41) + (3.46)(9.81)(5.855) = (470)(9.96)

W = 723.6 N

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