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 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 = 3.48 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 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/s^2.

Explanation / Answer

Here ,

Length , L = 8.98 m

weight of plank , W = 1.1 *10^2 N = 110 N

mc = 3.48 Kg

x = 0.475 m

FA = 509 N

let the weight of worker B is WB

balancing the torque about the support of wall

FA * 8.98 - W * 8.98/2 - WB * (8.98 - 4.66) - 3.48 * 9.8 * (8.98 - 4.66 + 0.475) = 0

509 * 8.98 - 110* 8.98/2 - WB * (8.98 - 4.66) - 3.48 * 9.8 * (8.98 - 4.66 + 0.475) = 0

solving for WB

WB = 905.9 N

the weight of the worker B is 9.06 *10^2 N

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