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 1.10 × 102 N and is secured with a hinge on the opposite end. Worker B will stand on the plank 4.44 m from worker A. Worker B also brings up his paint can, mc = 3.44 kg, which he places 0.400 m from where he is standing on the plank (between the two workers). Worker A unfortunately needs to supply 496 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 the moments about the hinge:

M = 0

Write net force equation about hinge and equate to zero.

( 496 N ) (9.96 ) - (110N ) ( 9.96 m /2 ) - ( B ) (9.96 - 4.44) m - ( 3.44kg ) ( 9.81m/s² ) (9.93 - 4.44 + 0.4 ) m = 0

B ( 5.52 m ) = 4193.59 N·m

Solve for B

B = 759.7 N

Round off the result to 3 significant digits

B = 760 N

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