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 $20 ^ { \circ }$ angle away from the vertical and the other makes a $30 ^ { \circ }$ 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

Quizplus · Accepted Answer

Let T1 and T2 be the tensions in ropes making 20° and 30° angles with the vertical, respectively.

Consider the forces acting on the weight:

- The weight W acts downward with a force of 100 lb.
- T1 acts at an angle of 20° away from the vertical.
- T2 acts at an angle of 30° away from the vertical.
- There is no horizontal force acting on the weight.

Resolve forces horizontally and vertically to get

Horizontal forces: T1 cos 20° = T2 cos 30°

Vertical forces: T1 sin 20° + T2 sin 30° = W

Substituting W = 100 lb, we get

T1 cos 20° = T2 cos 30°     ….. (1)

T1 sin 20° + T2 sin 30° = 100 lb     ….. (2)

Solving (1) and (2) simultaneously, we get

T1 = 44.65 lb

T2 = 65.27 lb

Therefore, the tensions in the ropes are 44.65 lb and 65.27 lb, respectively. Rounded to two decimal places, we get the answer (A).

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