Conservation of energy for a system

AI Thread Summary
The discussion revolves around a physics problem involving the conservation of energy and momentum in a system with a massless wheel, a mass, and a chain. Participants express difficulty in framing the equations necessary to solve for the speed of the mass when it reaches a specific point. The conversation highlights confusion regarding the application of gravitational potential energy terms and the moment of inertia in the context of the problem. There is an emphasis on the need for clarity in deriving formulas and understanding the relationships between the variables involved. Overall, the focus is on correctly applying conservation principles to arrive at a solution.
Arka420
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Homework Statement


Figure shows a massless wheel of radius R on which at a point a mass m is fixed and a uniform chain of mass 2m is tied to it which passes over the rim of the wheel and half of its length is hanging on other side as shown in the figure. When a small clockwise jerk is given to the wheel, it starts rotating. Find the speed of the mass m when it reaches a point P directly opposite to its initial point.
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Homework Equations


The equations for conservation of energy and momentum (both angular as well as linear)

The Attempt at a Solution

[/B]Conservation of energy is the first attempt,but I am facing one hell of a trouble framing the equations. Conservation of momentum? Well,I don't have the inital velocity.
 
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Arka420 said:
Conservation of energy is the first attempt,but I am facing one hell of a trouble framing the equations.
Then show your attempt please.
Arka420 said:
Conservation of momentum? Well,I don't have the inital velocity.
The initial velocity is negligible, but conservation of momentum doesn't help here.
 
mfb said:
The initial velocity is negligible, but conservation of momentum doesn't help here.
Hmm. Looks like all I have to do is conserve energy.
 
mfb said:
Then show your attempt please.
Is the equation 2mgl = mgl + 1/2mv^2 + 1/2Iw^2 (I is the moment of inertia about the center of the pulley wheel,while w is the angular velocity) by any chance?
 
Where do 2mgl and mgl come from?
Arka420 said:
(I is the moment of inertia about the center of the pulley wheel
The moment of inertia of what?
 
mfb said:
Where do 2mgl and mgl come from?
They are the gravitational potential energy terms. Seeing that the length of the chain is not given,we can say that (pi)R = half times the length (which is given in the question itself).
mfb said:
The moment of inertia of what?
The moment of inertia of the mass m about the center of the pulley?

Am I doing something wrong?
 
Arka420 said:
They are the gravitational potential energy terms.
Sure, but potential of what relative to what? They don't look right in the way you used them.
Arka420 said:
The moment of inertia of the mass m about the center of the pulley?
Okay.
Arka420 said:
Am I doing something wrong?
Yes, and it is unclear what because you don't explain how you got your formulas.
 

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