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

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{3}A_{31} 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) S_{7}P_{3}A_{31} (Force - Pull).
**The math**:

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 - x_{avg})]h -------(1). x_{avg} 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 - x_{avg})] = 500 -2x_{avg}

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 x_{avg} → x.

So, dW/dx = 500 -2x.

So, W = 500x - x^{2} + C---------(2). Where C is a constant.

When x = 0, W = 0. So C = 0.

So, W = 500x - x^{2}.

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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