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Problem 23 Medium Difficulty

Find the work done by the force field $ \textbf{F} $ in moving an object from $ P $ to $ Q $.

$ \textbf{F}(x, y) = x^3 \, \textbf{i} + y^3 \, \textbf{j} $; $ P(1, 0) $, $ Q(2, 2) $

Answer

$\frac{31}{4}$

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Video Transcript

So this question I asked us to find work down without special, without specifying the past. That means that it's kind of implication that the work should be independent path, and we should try to find a potential function. In this case, we wantto fine f e cause radiant off f little f potential function. So by definition that this should be excused and and this should be like you. And we shouldn't be hard to conclude that F. Ko's ex fourth over four plus why fourth over four, plus any constant, which doesn't matter because we're going to, um, to do a subtraction and cancel the constant thiss so the work down should be a difference of potential. So to Teo, so is sixteen over forth for four passports, eight minus one zero should be gives us one over four. So thirty two over four, minus one over for thirty one over four

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