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 112 N and is secured with a hinge on the opposite end Worker B will stand on the plank 4.99 m from worker. A Worker B also bongs up his paint can, m_c = 3.44 kg, which he places 0.415 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/s^2. W_B =

Explanation / Answer

Solution:

Sum of the vertical forces is 0.

Weight of the person B = FB

Support force by A = Fa = 483 N

weight of plank = W=112 N

weight of paint bucket = 3.44 x 9.8 = 33.712 N

Torque due to weight of plank from left end = (112)(9.96/2) Nm = 557.76 Nm

Torque due to B's weight = Fb*( 9.96- 4.99) Nm = Fb(4.97)

Torque due to paint bag = 33.712 *(4.97 + 0.415) = (33.712) (5.385) = 181.54 Nm

483 * 9.96 = 4.97 Fb + 557.76 + 181.54

=> Fb = 4071.38 / (4.97) = 819.2 N =weight of B

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