How Does the Velocity of a Carpet's Axis Change as It Unrolls?

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Homework Help Overview

The discussion revolves around a physics problem involving a carpet unrolling from a cylindrical shape on a rough floor. The problem focuses on determining the horizontal velocity of the carpet's axis as its radius changes from R to R/2, while considering factors like energy conservation and angular momentum.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss energy conservation in the context of friction and question whether angular momentum is conserved during the unrolling process. There is also a focus on the relationship between the radius and mass of the carpet as it unrolls.

Discussion Status

Some participants have shared their attempts and results, with one noting a discrepancy between their answer and the book's answer. Others are engaging in clarifying the assumptions made regarding mass and radius, leading to further exploration of the problem.

Contextual Notes

Participants are considering the implications of kinetic energy and the relationship between the dimensions of the carpet as it unrolls, which may affect their calculations. There is an acknowledgment of the complexity involved in the problem setup.

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Homework Statement


A carpet of mass M made of in-extensible material is rolled along its length in the form of a cylinder of radius R an is kept on a rough floor. The carpet starts unrolling without sliding on the floor when a negligible small push is given to it. Calculate the horizontal velocity of the axis of the cylindrical part of the carpet when its radius reduces to R/2

The Attempt at a Solution



I tried conserving energy since friction won't be doing any work, my answer came out to be √(4gR/3)

The answer in the book is √(14gR/3). Is anyone getting this answer?

(Also, will angular momentum be conserved? I'm thinking yes.)
 
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Hi AlchemistK! :wink:
AlchemistK said:
The answer in the book is √(14gR/3). Is anyone getting this answer?

Yup!

Show us what you did. :smile:​
 
Hint: Careful with kinetic energy considerations.
 
x.x I got the answer, I made the mistake of assuming that since the radius dropped by half, even the mass dropped by half, while in fact it drops by a factor of 4.
Thanks for your help! I'd never have even tried it again if didn't get to know that the answer was correct.
 

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