An 800-N billboard worker stands on a 4.0-m scaffold weighing 500 N and supported by vertical ropes at each end.How far would the worker stand from one of the supporting ropes to produce a tension of 770 N in that rope?
A) 1.4 m
B) 2.0 m
C) 2.5 m
D) 2.7 m

Question

Quizplus · Accepted Answer

To find the distance, use the principle of moments (torque). The sum of moments around one rope must equal zero for equilibrium. Let x be the distance from the worker to the rope with 770 N tension. The moment due to the worker is 800x, and the moment due to the scaffold is 500(2.0) since the scaffold's weight acts at its center. The tension in the other rope is 800 + 500 - 770 = 530 N. Setting the sum of moments around the 770 N rope to zero: 800x + 500(2.0) = 530(4.0). Solving for x gives x = 1.4 m.

An 800-N Billboard Worker Stands on a 4