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 115 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 = 3.58 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 509 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.

Worker B = __?__Newtons

Explanation / Answer

Taking torque about the hinge point H. Let weight be Wb

Let the hinge point be H

center of the beam be O (at distance 8.98/2 = 4.49 m from hinge)

Paint bucket be at point P (OP = 8.98-4.445)

Person B pont be B and A be point A (OB = 8.98-4)

Balancing torque

(4.49 x 115)+[(8.98-4.445) x (3.58 x 9.81)]+[(8.98-4) x Wb] = (8.98 x 509)

Wb(Worker B) = 782.169 N

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