Determine the work done by the Force F = yi(hat) - xj(hat) on an object that travels from point A (a,0) to point B (-a,0)
a) along an elliptical path described by x=acosθ, y=bsinθ
b) along a straight line from A to B
c) From these results, can we determine whether or not the force is conservative?
W=∫F ° dl
dl=dxi(hat) + dyj(hat)
The Attempt at a Solution
a) W=∫(a to -a) bsinθi(hat)dl - ∫(0 to 0) acosθj(hat)dl
so that just gives me ∫(a to -a) bsinθi(hat)dl which equals 0. This doesn't seem right to me. What's mainly confusing me is that the y is corresponding to the i(hat) vectors and vice versa for the x. I don't really know what to do with the b.
b) dl = dxj(hat)
W = ∫(a to -a) xdy = 0
c) I know that you can tell if a force is conservative if the work depends on the path. Therefore this is probably not conservative.