A force vec(F) = - k (y hat(i) + x hat(j)), 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 positive y - axis to a point (a, a). Calculate the total work done by the force on the particle.

A force vec(F) = - k (y hat(i) + x hat(j)), where k is a positive cons

1.	A force vec(F) = - k (y hat(i) + x hat(j)), 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 positive y - axis to a point (a, a). Calculate the total work done by the force on the particle.
Answer» Solution :DISPLACEMENT vector, `d vec(s) = d x vec(i) + dy vec(J)` `therefore` Work done `W = int vec(F).d vec(s) = int - k(y hat(i) + x hat(j)).(d x hat(i) + dy hat(j))` `= - k int_((0,0))^((a,a)) (YDX + xdy) = - k int_((0,0))^((a,a)) d (xy) = - k\|(xy)\|_(0,0)^(a,a) = - k (a xx a) = - KA^(2)`