Solving Variable Mass System Homework: Velocity of Chain Hanging Vertically

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Homework Help Overview

The problem involves a variable mass system where a chain is partially hanging through a hole in a table. The original poster is tasked with calculating the velocity of the chain as a function of the length that is hanging vertically.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to analyze the forces acting on a mass element of the chain and relates it to acceleration and velocity. Some participants suggest considering the force on the entire length of the chain hanging vertically.

Discussion Status

The discussion is ongoing, with participants exploring different approaches. The original poster has expressed difficulty in progressing from their initial analysis, and there is no clear consensus on the next steps or methods to pursue.

Contextual Notes

The original poster has provided an equation they believe to be the answer, but it remains unverified within the discussion. There is a lack of clarity on the assumptions regarding the mass distribution and forces involved.

anirudh dutta
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Homework Statement


a heap of chain is lying on a table with a hole. A small part of chain is released through the hole.calculate the velocity as a function of the length of the chain hanging vertically.



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Homework Equations





The Attempt at a Solution


if I take a mass element dm at a distance x from the hole,
then the force acting on it is
dF= (dm)g

then the acceleration is dF/m. this is equal to dV/dx

I am stuck now.


{ans is (2/3gy)1/2 }
 
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Hint: Consider the force acting on the entire length of the chain that is hanging vertically.
 
tried but didn't work
 
anirudh dutta said:
tried but didn't work
Show what you tried.
 

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