A uniform rope of mass 'i' per unit length is coiled on a table, one end s pulled straight up with constant speed Vo. a. find the force exerted on the end of the rope as a function of distance of the top of the rope above table (y). b. compare the power delivered to the rope with the rate of change of the ropes total mechanical energy. Part a seems to be pretty simple... F-mg = dp/dt, so F(y) = i*V^2+i*y*g. Now the problem is when i integrate F(y) with respect with y, I should get the total energy of the rope system. But i don't. The total energy = .5mv^2 + mgh = .5(i*y)(v^2) + .5(i*y)(y*g), which clearly isn't the integral of F. So what's going on???