Question

A force vecF(yhatl+xhatJ), where K is a positive constant, acts on a particle moving in the XY-Plane. Starting from the origin, the particle is taken along the positive X-axis to a point (a,0) and then parallel to the y-axis to the point (a,a). Calculate the total work done by the force on the particle.

Answer 1

Answer:

F = -k(yi+xj)

W = F.dr              (dot product of force & displacement)displacement vector(dr) is of line joining initial & final position vectors...

W = -k(yi+xj).(dxi+dyj)d

W = -k(ydx + xdy)d

W = -kd(xy)  (exact)integrating both sides ,

W = -k [xy] lim from (0,0) to (a,a)

W  = -ka2

Answer 2

W= -ka²

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