Lifting a rope

A rope of length ll and mass density λ\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 vv. 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

  • λ=2 kg/m\lambda =\si{2\ \kilo\gram/\meter}
  • L=1 mL=\si{1\ \meter}
  • v=1 m/sv=\si{1\ \meter/\second}
  • g=10 m/s2g=\si{10\ \meter/\second^2}

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