A 650-N billboard worker stands on a 4.00-m scaffold weighing 600 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 660 N in that rope?
A)1.78 m
B)2.00 m
C)1.90 m
D)0.06 m
E)0.93 m

Question

Quizplus · Accepted Answer

The total weight acting downward is the sum of the worker's weight and the scaffold's weight, which is 650 N + 600 N = 1250 N. To find the distance $x$ from one of the supporting ropes where the tension is 660 N, we can use the principle of moments (torque). Let $x$ be the distance from the rope with 660 N tension, and $4.00 - x$ be the distance from the other rope. The moment around one rope is equal to the moment around the other rope because the system is in equilibrium. Therefore, $660N \times x = (1250N - 660N) \times (4.00 - x)$. Solving for $x$ gives approximately 1.78 meters.

A 650-N Billboard Worker Stands on a 4