Do I use an arc length formula? How do I go about solving this problem?

Question

A simple pulley of radius r=0.5 ft is used to lift a heavy object. Determine the height to which the object is lifted when the pulley rotates 810 degrees.

Answer 1

The first step to solving this problem is understanding what it is really asking.

 

The distance that the pulley rotates through, will be the height that the object is lifted to. Therefore, the problem is really asking you to determine how far the outside edge of the pulley will travel as it rotates 810 degrees.

 

In order to determine that, you will need to multiply the number of revolutions that the pulley passes through, by the distance traveled per revolution - that is, the circumference. So, there are two, relatively straightforward steps to this problem: determining how many revolutions it has gone through, and determining its circumference.

 

To determine the number of revolutions, divide 810 degrees by the number of degrees in one complete revolution (360).

 

To determine the circumference, use the formula C = 2*r*PI.

 

Once you have both of those parts, simply multiply them together, and you will have your answer.

 

Good luck!

Answer 2

810°/360° = 2.25

 

circumference of circle is 2∏r

 

since pully rotated 2.25 times we have:

 

2.25 * 2 *∏ * r

 

2.25 * 2 * 3.14 * .5  ≈ 7.065 feet