Classical Mechanics

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Difficult

Work in a Non-Uniform Field

CLMECH-H5BNEB

Imagine an external force field is described by $\vec{F}\left(\vec{r}\right) = (y^2\hat{i})\,N$, where $\vec{r} = (x\hat{i} +y\hat{j})$ is the position.

How much work is done pushing against this force to move along a straight line from the point (0, 0) to (-4.0, 2.0)?

A

$W = 16\sqrt{5}\,J $

B

$W = 6.0\,J$

C

$W = 19\,J$

D

$W = 130\,J$