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Problem 39 Hard Difficulty

Given the force field $\mathbf{F}$, find the work required to move an object on the given oriented curve.
$\mathbf{F}=\langle y,-x\rangle$ on the path consisting of the line segment from (1,2) to (0,0) followed by the line segment from (0,0) to (0,4)

Answer

$$w=\int_{0}^{1} d t=0$$

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Video Transcript

all right. Given force field, I find the work of art. Two moving objects. Ah, given curve. It's a we have. Ah, is why Come on. Negative X and the path C is gonna be, ah, line segment from Want to come out to 20 comma zero and then from zero comma zero 20 come before. All right, so see, it's gonna be from one comma. 2 to 0. Comma. Zero. We're gonna get one comma too. Plus t time. Zero minus ones. Like the ones they're almost too. Get to This comes out to one Manistee coma to minus two t therefore and and f so taking. This is X, and this is why f a zero to minus two t. Come on. Negative Won t can also calculate our prime right here. That's equal to negative one common negative too. All right. Putting this in her in a girl from 0 to 1, uh, to minus two Teoh car. Negative one plus t. Thought that was They could have wanted Colin *** to t t We have the integral from 0 to 1 for negative two plus two t plus two minus two t DT and that's equal to zero now for the second part from 00 deserve four we have are other Parametric equations is a source of 00 zero plus tee times. Um, zero My zero Ethan four minus zero, which is zero coma 40 again. When? If f is, you know why? Kind of a negative X. They plug in 40 by zero racks. No way. Progress into the integral the same forms before. Except now it's 40. Come on. Zero 0.0 comma four and the Article zero. So for the two lines, were you both, uh, zero? So the total line and grow zero.

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