- #1

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## Homework Statement

## Homework Equations

## The Attempt at a Solution

Suppose length of upper portion is ##x## and that of lower portion is ##L-x## .

In time ##dt## , ##dm## mass of rope starts moving abruptly with speed ##v## .

The kinetic friction acting on the upper part of the rope is ##f = \mu M(x)g## , where M(x) = Mx/L .

dx = Mdx/L

Applying impulse momentum theorem ,

##(F-\mu \lambda xg)dt = (m+dm)(v) - mv##

##(F-\mu \lambda xg)dt = vdm##

I don't know how to proceed from here .

I would appreciate if someone could guide me .

Thanks

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