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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