To carry a 500-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 the vertical component of each
Worker's force.Round your answer to two decimal places.

Question

To carry a 500-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 the vertical component of each
Worker's force.Round your answer to two decimal places.

Quizplus · Accepted Answer

Let's call the angles the ropes make with the vertical α and β. From the figure, we can see that:

sin(α) = opposite/hypotenuse = vertical component of force/500 pounds

sin(β) = opposite/hypotenuse = vertical component of force/500 pounds

Therefore, the vertical component of each worker's force is given by:

Vertical component of force = 500 pounds × sin(α) and Vertical component of force = 500 pounds × sin(β)

Plugging in the values given in the problem, we get:

Vertical component of force for the first worker = 500 pounds × sin(11°) ≈ 96.18 pounds

Vertical component of force for the second worker = 500 pounds × sin(79°) ≈ 485.80 pounds

Rounding each to two decimal places, we get:

Vertical component of force for the first worker ≈ 96.18 pounds

Vertical component of force for the second worker ≈ 485.80 pounds

Therefore, the correct answer is A), which is the only choice that matches these calculated values.

To Carry a 500-Pound Cylindrical Weight, Two Workers Lift on the Ends