A chain with length L and linear mass densituy kg/m lies in a heap at the edge of a table. One end of the chain initially sticks out an infintessimal distance from teh heap. You grab this end and pull it down with constant acceleration . Assume there is no friction as the chain unravels. What force as a function of time must you apply to the end of the chain? Find the value of for which the force from your had is zero (that is, the chain falls naturally).

If same chain is now lying on the floor. You grab one end and pull upward such that the end of the chain moves upward with constant speed v. What is the total work you do by the time the chain is off the floor?