Lifting a rope

A rope of length $$l$$ and mass density $$\lambda$$ lies in a heap on a floor. You grab one end of the rope and pull upwards with a force such that the rope moves at a constant speed $$v$$. What is total work you do, by the time the rope is completely off the floor? Assume that the rope is greased.

Details and Assumptions

• $$\lambda =\si{2\ \kilo\gram/\meter}$$
• $$L=\si{1\ \meter}$$
• $$v=\si{1\ \meter/\second}$$
• $$g=\si{10\ \meter/\second^2}$$
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