Lifting Rope.

Classical Mechanics Level 3

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 upward with a non-impulsive constant force \({ F }_{ o }\). Find the time period require to completely lift off the rope.

Assume that the rope is greased.

The answer is in the form \(\displaystyle{{ T=\cfrac { a }{ g } (\sqrt { \cfrac { { F }_{ o } }{ \lambda } } -\sqrt { \cfrac { { F }_{ o } }{ \lambda } -\cfrac { bgl }{ c } } })}\)

Find \(a+b+c\)

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