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Find the work done by a person weighing 124 lb walking exactly half a revolution up a circular, spiral staircase with a radius of 5 ft, if the person rises 19 ft after one full revolution.

Work = ___ ft-lb

Answer :

Final answer:

To find the work done by the person, uplift the sum of horizontal and vertical distances walked and multiply this distance by his weight. The result of work done is (5π + 9.5) * 124 ft-lb.

Explanation:

The first step in this Physics problem is to find the distance up the circular spiral staircase, by calculating the length of the circular path. One full revolution on the circular path equates to a circumference of 10π feet. Since in this case only half a revolution was walked, the path distance will be half of that, which equals 5π ft.

Next, we consider the vertical rise. After one full revolution, the person rises a total of 19 feet. Therefore, after half a revolution, the person must rise half of that, which equals 9.5 ft.

Because work done is the distance traveled multiplied by the force acting (which is the person's weight), we combine the vertical and horizontal distances, which sum to 5π + 9.5 ft. Then we multiply by the person's weight (124 lb) to get the total work done, resulting in an answer of (5π + 9.5) * 124 ft-lb.

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