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## Homework Statement

A cutting tool under microprocessor control has several forces acting on it. One force is [itex]\vec{F}[/itex]=-αxy

^{2}[itex]\hat{j}[/itex], a force in the negative y-direction whose magnitude depends on the position of the tool. The constant is α=2.50 N/m

^{3}. Consider the displacement of the tool from the origin to the point x=3.00m, y=3.00m.

(a) Calculate the work done on the tool by [itex]\vec{F}[/itex] if this displacement is along the straight line y=x that connects these two points.

## Homework Equations

W=∫[itex]\vec{F}[/itex][itex]\cdot[/itex]d[itex]\vec{l}[/itex]

## The Attempt at a Solution

I'm trying to use the equation above, so here's what I know:

d[itex]\vec{l}[/itex]=dx[itex]\hat{i}[/itex]+dy[itex]\hat{j}[/itex]

[itex]\vec{F}[/itex]=-αxy

^{2}[itex]\hat{j}[/itex]

Since it's the dot product,

[itex]\vec{F}[/itex][itex]\cdot[/itex]d[itex]\vec{l}[/itex]=dx+-αxy

^{2}dy.

I'm confused as to why the right side of that equation is equal to -αy

^{3}dy, as the textbook solution suggests. Any help is appreciated.