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 111 N and is secured with a hinge on the opposite end. Worker B will stand on the plank 4.77 m from worker A. Worker B also brings up his paint can, mc = 3.60 kg, which he places 0.475 m from where he is standing on the plank (between the two workers). Worker A unfortunately needs to supply 4.70 × 102 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

given

W_plank = 111 N

L = 9.96 m

F_A = 4.7*10^2 N = 470 N

As the plank is in equilibrium, net force and net torque acting on the plank must be zero.

Apply, net torque about hinge = 0

WB*4.77 + W_plank*(9.96/2) + 3.6*9.81*(4.77 + 0.475) - FA*9.96 = 0

WB*4.77 + 111*(9.96/2) + 3.6*9.81*(4.77 + 0.475) - 470*9.96 = 0

WB*4.77 -3943.2 = 0

WB = 3943.2/4.77

= 827 N <<<------------Answer

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