- #1
joriarty
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Homework Statement
Consider a force field F = c(iy - jx). From the force field calculate the work required to move a particle from the origin to the point 2i + 4j without acceleration along the two different paths:
- From the origin to 2i then to 2i + 4j
- From the origin to 4j then to 2i + 4j
Comment whether the force field is conservative or not
2. The attempt at a solution
I'm just slightly confused by the notation used in the question. I know that i and j are just the unit vectors in the x and y directions, but what is c in the force field expression? And if i and j are already noted in this expression, why are x and y used as well?
Assuming c is just some arbitrary constant, then is the work done simply 6c J for both paths? My logic for this is that for the first path the work done is 2c J along the x-axis and then 4c J along the y-axis (and the other way around for the second path).
Thus the force field is conservative (work done is independent of the path taken).
Is my logic correct, or am I missing something? Thank you