# Work - Integration and vectors

1. Oct 18, 2011

### Sefrez

I have this very simple problem, I am just a little unsure of the notation of the integral.
I am given that a force vector F = (5x i + 4y j) N is applied to a mass and it moves by the vector r = (5.08 i) m. So in other words, there is a variable force and the mass moves only along the x axis.

This problem is ridiculously easy when noting that fact as you simply integrate 5x from 0 to 5.08 as the j component does no work (no r in the j direction.) You get about 64.5 J

That is what I did to solve the problem, but I noticed that it showed this:
w = ∫F dr where F and r are the vectors defined above.

So my question is, how do you go about integrating that considering F and r are vectors? And also, what does dr represent when r is a vector? I am just a bit confused so any help would be appreciated.

Thanks.

2. Oct 19, 2011

### Nesk

In w = ∫F dr, the F dr part is a dot product, i.e., the scalar Fx dx + Fy dy. dr = i dx + j dy is an infinitesimal vector along the path.