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

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The discussion revolves around calculating the horizontal velocity of a carpet's axis as it unrolls from a cylinder with radius R to R/2. A participant initially used energy conservation but arrived at an incorrect answer of √(4gR/3), while the correct answer is √(14gR/3) as stated in the textbook. Another participant pointed out that the initial calculation mistake involved incorrectly assuming the mass dropped by half instead of by a factor of four. The conversation highlights the importance of careful consideration of kinetic energy and mass changes during the unrolling process. Ultimately, the correct understanding of these principles led to the right solution.
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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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