# 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 $$a+b+c$$

I got this question from Deepanshu.

:D

×