To carry a 100-pound cylindrical weight, two workers lift on the ends of short ropes tied to an eyelet on the top center of the cylinder. One rope makes a angle away from the vertical and the other makes a angle as shown in the figure below. Find each rope's tension if the resultant force is vertical.Round your answer to two decimal places.

Question

To carry a 100-pound cylindrical weight, two workers lift on the ends of short ropes tied to an eyelet on the top center of the cylinder. One rope makes a  angle away from the vertical and the other makes a  angle as shown in the figure below. Find each rope's tension if the resultant force is vertical.Round your answer to two decimal places.

Quizplus · Accepted Answer

We can use the principles of equilibrium to solve the problem. The resultant force must be vertical because there is no motion in the horizontal direction. Therefore, the horizontal components of the tensions in the two ropes must cancel out.

Let T1 be the tension in the rope making the 30° angle and T2 be the tension in the rope making the 60° angle. Then we have;

T1cos(30°) = T2cos(60°)
T1sin(30°) + T2sin(60°) = 100 lbs

Substituting the values, we get;

0.87T1 = 0.5T2
0.5T1 + 0.87T2 = 100

Solving these equations, we get T1 = 41.94 lbs and T2 = 77.11 lbs. Rounding to two decimal places, we get T1 = 41.94 lbs and T2 = 77.11 lbs.

Therefore, the best choice is (A).

To Carry a 100-Pound Cylindrical Weight, Two Workers Lift on the Ends