Suppose a box whose mass m(t) increases at a constant rate moves with constant velocity v. The force necessary to keep this object at constant velocity is F = dp/dt = dm/dt*v. Now we try to find the work done by the force from time 0 to time t. The force is constant, so W = F*d = F*v*t = dm/dt *v*v*t = (m(t)-m(0))*v^2. (since dm/dt is constant, t*dm/dt = dm). Now if we calculate the change in kinetic energy from time 0 to time t, it should be the same as the work done, if energy is conserved. So KE = .5*m(t)*v^2 - .5*m(0)*v^2 = .5 (m(t)-m(0))*v^2. It's not equal to the work done! Am I making a stupid mistake, or is energy indeed not conserved in this system?