From (Marion 5th ed. Problem 9-15) A smooth rope is placed above a hole in a table. One end of the rope falls through the hole at t = 0, pulling steadily on the remainder of the rope. Find the velocity and acceleration of the rope as a function of the distance to the end of the rope x. Ignore all friction. The total length of the rope is L. I attempt to solve it by lagrangian L = T - U T = 1/2 (λx) v^2 U = -(λx)g(x/2) where λ is mass density But someone said it is not correct. He claimed that if T depends on generalized coordinate explicitly(in this case x), then it violates Newton's Second Law. So, lagrangian mechanics cannot be used in open system ? Marion's Solution F = dp/dt = m(dv/dt) + v(dm/dt) (see Fig) I learnt that we cannot differentiate m (i.e. dm/dt) if the system is open. So, which one is correct ?? Can anyone explain to me in detail ?