Cable Work - Bring That Load Up

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Work: Lifting A Load 100 ft Up From Below The Surface Of The Earth


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Strings (SiPjAjk) = S7P3A31     Base Sequence = 12735     String Sequence = 12735 - 3 - 31



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Work: Lifting A Load 100 ft Up To The Surface
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A cable weighing 2 lbs/ft is used to lift a 300 lbs load from the bottom of a well 100 feet deep.
Calculate the work done to raise the load to the surface.

The string:
(a) S7P3A31 (Force - Pull).
The math:
Cable Work Pull That Load
Pj Problem of interest is of type force. Work problems are generally of type force because force is the doer of work. In the case of white-collar work, intellectual force actuates materiality.
Consider the above diagram (fig. CW.1):
Let W be the work done to raise the load x feet.
Let k be the work done in raising the load h feet.
k = [300 + 2(100 - xavg)]h -------(1). xavg is the representative average of the partitions of the distance BC.
So, the rate of change of k with respect to h is:
k/h = [300 + 2(100 - xavg)] = 500 -2xavg
limit (k/h) as h → 0 = dW/dx (instantaneous change of W with respect to x)
So, limit (k/h) as h → 0 = 500 -2x. Since xavg → x.
So, dW/dx = 500 -2x.
So, W = 500x - x2 + C---------(2). Where C is a constant.
When x = 0, W = 0. So C = 0.
So, W = 500x - x2.
So, for x = 100,
W = 500(100) - (100)(100) = 40,000 ft-lb.

The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
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