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 111 N and is secured with a hinge on the opposite end. Worker B will stand on the plank 4.11 m from worker A. Worker B also brings up his paint can, mc = 3.48 kg, which he places 0.250 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

Sum moments about the hinge to zero.
Assume the plank is uniform

Let Wt be the weight of worker B

Wt[8.98 - 4.11] + 3.48(9.81)[8.98 - 4.11 + 0.250] + 111[898 / 2] - 4.70(10²)[8.98] = 0

Wt = 45798.0
Wt = 45798 N

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