Question

Find the work done when a force F⃗ = (x 2 − y 2 +x)i⃗+ (−2xy − y)j⃗ moves a particle from origin to (1,1) along a parabola y 2 = x

Answer 1

Answer:

This force is conservative, it comes from the potential:

V(x,y)=x3/3−y2x+x2/2−y2/2

So the work done is the potential difference between the endpoints:

W=V(1,1)−V(0,0)=1/3−1+1/2−1/2=−2/3