What Is the Minimum Initial Velocity to Roll Up a Carpet?

[bobsmith601]

Homework Statement

Imagine a very long carpet, with a very small thickness of t, width W, length L and density of ρ,
which is partially rolled up to form a cylinder of radius r. Since the carpet is very thin, it can be
assumed that the rolled-up part of the carpet is a perfect cylinder. We decide to roll up the whole
carpet by just kicking the cylindrical part of the carpet with initial velocity v.
What is the minimum initial speed v, required for the cylindrical part to roll the whole carpet?

 

[tiny-tim]

welcome to pf!

hi bobsmith601! welcome to pf!

What is the minimum initial speed v, required for the cylindrical part to roll the whole carpet?

looks to me like a conservation of energy problem …

what energy is needed to end with the carpet fully rolled at zero speed?

 

[bobsmith601]

I'm not sure...

 

[tiny-tim]

(just got up :zzz:)

for initial speed v, what are the initial kinetic energy and potential energy?

for final speed 0, what are the final kinetic energy and potential energy?