A 1600-lb elevator is suspended by a 200-ft cable that weighs 10 lb/ft. How much work is required to raise the elevator from the basement to the third floor, a distance of 30 ft?
Please show all steps, thank you.
Please show all steps, thank you.
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Since you're going to life the elevator 30 feet, the bounds will be from 0 to 30. The weight of the cable as you lift it up is given by 10(200 - x), where x is the number of feet lifted. Note that the weight of the elevator is never going to change. Therefore the work done is given by:
30
∫ 1,600 + 10(200 - x) dx = 1,600x + 2,000x - 5x^2 [0 , 30]
0
1,600(30) + 2,000(30) - 5(30^2) =
48,000 + 60,000 - 4,500 = 103,500 foot-pounds.
Hope this helped.
30
∫ 1,600 + 10(200 - x) dx = 1,600x + 2,000x - 5x^2 [0 , 30]
0
1,600(30) + 2,000(30) - 5(30^2) =
48,000 + 60,000 - 4,500 = 103,500 foot-pounds.
Hope this helped.