Solving Variable Mass System Homework: Velocity of Chain Hanging Vertically

[anirudh dutta]

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 }

 

[Doc Al]

Hint: Consider the force acting on the entire length of the chain that is hanging vertically.

 

[anirudh dutta]

tried but didn't work

 

[Doc Al]

tried but didn't work

Show what you tried.

 

[paranormal]

Hello,

Thank you for sharing your attempt at solving this problem. It seems like you have a good start by considering the force acting on a small mass element and relating it to the acceleration and velocity. To continue, you can use the equation F=ma to find the acceleration as a function of the length of the chain hanging vertically. Then, you can use the kinematic equation v^2 = u^2 + 2ax, where u is the initial velocity (in this case, 0 since the chain is initially at rest) and a is the acceleration you found. Solving for v will give you the velocity as a function of the length of the chain. I hope this helps!