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 114 N and is secured with a hinge on the opposite end. Worker B will stand on the plank 4.33 m from worker A. Worker B also brings up his paint can, mc = 3.52 kg, which he places 0.325 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/s2.
let mass of worker B be m kg.
let the point where worker A is holding the plank be x=0
total forces acting on the plank are:
1. weight of worker B=m*g, in downward direction , at x=4.33 m
2. weight of the plank=114 N, in downward direction, at x=4.49 m
3. weight of the paint can=3.52*9.81=34.531 N, in downward direction , at x=4.33-0.325=4.005 m
4. normal force from the hinge, let it be T N, at x=8.98 m, in upward direction
5. force applied by A=522 N in upward direction at x=0
balancing total toqrue about the hinge:
m*g*(8.98-4.33)+114*(8.98-4.49)+34.531*(8.98-4.005)=522*8.98
==>m=(522*8.98-34.531*(8.98-4.005) -114*(8.98-4.49))/((8.98-4.33)*g)=87.773 kg
A young work crew is trying to quickly finish some touch-up painting to complete a job....
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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 8.00 m work plank which weighs 114 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 brings up his paint can, mc=3.58 kg, which...
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