I am having hard time proving this either right or wrong.
Let's take for example a river, does the water flowing down follow the least resistant path?
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asked Oct 16, 2015 at 23:22
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$\begingroup$ Nature is lazy... Principle of least action $\endgroup$– raulCommented Oct 16, 2015 at 23:25
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2 Answers
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The river will not always follow along the path of least resistance because as water flows, its momentum increases. If a river follows a bend/curve in the land, it may slosh against the bank or even go over the bank--but eventually, it will lose some of its momentum & then flow to a lower elevation or seep through the earth to a lower elevation. So as you can see the direction & momentum of water movement depends on other factors.
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$\begingroup$ yes, those factors define the path that require less energy from the river. $\endgroup$– raulCommented Oct 16, 2015 at 23:49
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$\begingroup$ But least effort would not guarantee path of least resistance. @raul $\endgroup$ Commented Oct 16, 2015 at 23:51
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$\begingroup$ That's why the rivers has curves. To flow with the less resistance. $\endgroup$– raulCommented Oct 17, 2015 at 0:03
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1$\begingroup$ Since when straight rivers are sexy? Kill the stereotypes, real rivers have curves. $\endgroup$– raulCommented Oct 17, 2015 at 0:09
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Not necessarily. Imagine two containers connected by a narrow hose that is just below the water line, and a big hose (like a syphon) above the water line.
The path of least resistance would be the large hose - but you need to "prime" the hose for the water to find / choose that. If you don't, then the water will flow through the small hole. Not the path of least resistance. The "most available" path of least resistance.
And if you have more than one hole under the water line, the water will flow through all of them; it may flow more through the wider hose, and less through the narrow one - but it will use all of them. It won't find the "path of least resistance", but the distribution of flow that will lead to the least "total" resistance.
Of course you might have to define "path of least resistance" more carefully...
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$\begingroup$ Nah!, bad example. It would require more energy to get to the biggest hole than let the gravity do all the work $\endgroup$– raulCommented Oct 16, 2015 at 23:47