When Least Is Best by Paul J. Nahin

Author:Paul J. Nahin [Nahin, Paul J.]
Language: eng
Format: epub
ISBN: 9780691218762
Publisher: PrincetonUP
Published: 2021-07-15T00:00:00+00:00

This quadratic in x is now easy to solve (and I’ll do that in just a bit), and our question (where is point C, the location of the pulley?) is answered.

Now, let’s return to that f(x) function derived earlier (which tells us how far below the ceiling the weight hangs). The new minimum principle I mentioned before is now applied—the system is in stable equilibrium when its potential energy is minimum. (We’ll use this same argument again, in the next chapter, to solve a much more famous problem than this one.) That is, stable equilibrium occurs when the weight hangs as far below the ceiling as possible, which occurs when f(x) is maximum. So, all we need to do is set the derivative of f(x) equal to zero and solve for x, i.e.,

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