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putongren
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- The work done is independent of path if the infinitesimal work ๐นโ โ
๐๐โ
is an exact differential.
I was researching about conservative and non-conservative forces, and there is some information in a website that sates that the work done is independent of path if the infinitesimal work ๐นโ โ
๐๐โ is an exact differential. It further states that in 2 dimensions the condition for ๐นโ โ
๐๐โ = Fxdx + Fydy to be an exact differential is:
๐๐น๐ฅ/๐๐ฆ=๐๐น๐ฆ/๐๐ฅ.
My question is this: why is a force conservative if the work is an exact differential? How can we deduce from the definition of a conservative force that this force is conservative if the work done to it is an exact differential?
๐๐น๐ฅ/๐๐ฆ=๐๐น๐ฆ/๐๐ฅ.
My question is this: why is a force conservative if the work is an exact differential? How can we deduce from the definition of a conservative force that this force is conservative if the work done to it is an exact differential?