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

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    Momentum Physics
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Homework Help Overview

The problem involves determining the minimum initial velocity required to roll up a carpet that has been partially rolled into a cylinder. The scenario includes considerations of the carpet's dimensions, density, and the mechanics of rolling motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the conservation of energy as a potential approach to the problem, questioning the necessary energy states at the beginning and end of the process.

Discussion Status

The discussion is ongoing, with participants exploring the relationship between initial and final energy states. Some guidance has been offered regarding the types of energy to consider, but no consensus has been reached yet.

Contextual Notes

Participants are considering the implications of initial and final kinetic and potential energy in the context of the problem, but specific values or formulas have not been provided.

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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?
 
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welcome to pf!

hi bobsmith601! welcome to pf! :smile:
bobsmith601 said:
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? :wink:
 
I'm not sure...
 
(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? :smile:
 

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