a young work A young work crew is trying to quickly finish some touch-up paintin

Question

a young work 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 8.96 m work plank which weighs 1.10 Times 10^2 N and is secured with a hinge on the opposite end. Worker B will stand on the plank 4.66 m from worker A. Worker B also brings up his paint can, m_c = 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 522 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/s^2.

Explanation / Answer

Sum the moments about the hinge:
M = 0 = ( 522 ) ( 8.98 m ) - (110 N ) ( 8.98m / 2 ) - ( Wn ) (8.98 - 4.66)m
- ( 3.46 kg ) ( 9.81 m/s² ) (8.98-4.66+0.445 )m

Solve the equation

Wn ( 4.32m ) = 3538 N·m
Wn = 818.98 N

Round off the result to 3 signficant digits

Wn  = 819 N

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