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 4.22 m from worker A. Worker B also brings up his paint can, mc = 3.52 kg, which he places 0.340 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

torque across the hinge is equal to zero

T = 0

diatance at which worker B is standing from hinge = 8- 4.22 = 3.78 m

distance of can from hinge = 3.78+.340 = 4.12 m

-483*8 + mc*g*4.12 + Mb*g*3.78+ 111*4 = 0

-3864 + 142.2685 + 37.082*Mb + 444 = 0

m= 88.4 kg

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