Question

A portion of a chain of length L and mass m stands at rest on an incline with an angle ? while the rest of the chain hangs down from the edge of the inline as seen in the figure below. The incline is fixed at the edge of a table. There is no friction between the chain and the incline and the incline has a constant linear mass density ? . (a) Show that the hanging part of the chain has a length y_0 = (L sin ?) / (1 + sin ?) . (b) Assuming that the potential energy at the top of the incline is zero, find the total potential energy of the chain. (c) Now, the hanging part of the chain is pulled down very slightly (with almost zero force) and released. Calculate the change ?V in the potential energy at the moment the chain clears the incline? (d) What is the velocity of the chain at that moment?

          A portion of a chain of length L and mass m stands at rest on an incline with an angle ? while the rest of the chain hangs down from the edge of the inline as seen in the figure below. The incline is fixed at the edge of a table. There is no friction between the chain and the incline and the incline has a constant linear mass density ? .
(a) Show that the hanging part of the chain has a length y_0 = (L sin ?) / (1 + sin ?) .
(b) Assuming that the potential energy at the top of the incline is zero, find the total potential energy of the chain.
(c) Now, the hanging part of the chain is pulled down very slightly (with almost zero force) and released. Calculate the change ?V in the potential energy at the moment the chain clears the incline?
(d) What is the velocity of the chain at that moment?

A portion of a chain of length L and mass m stands at rest on an incline with an angle ? while the rest of the chain hangs down from the edge of the inline as seen in the figure below. The incline is fixed at the edge of a table. There is no friction between the chain and the incline and the incline has a constant linear mass density ? .
(a) Show that the hanging part of the chain has a length y0 = (L sin ?) / (1 + sin ?) .
(b) Assuming that the potential energy at the top of the incline is zero, find the total potential energy of the chain.
(c) Now, the hanging part of the chain is pulled down very slightly (with almost zero force) and released. Calculate the change ?V in the potential energy at the moment the chain clears the incline?
(d) What is the velocity of the chain at that moment?

Added by John H.

Question

Please give Ace some feedback