A rope of length L and mass density lies in a heap on the floor. You grab

Question:

A rope of length L and mass density σ lies in a heap on the floor. You grab one end of the rope and pull upward with a force such that the rope moves at constant speed v. What is the total work you do, by the time the rope is completely off the floor? How much energy is lost to heat, if any? Assume that the rope is greased, so that it has no friction with itself.