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.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.