Conservation of energy for a system

[Arka420]

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.

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.

 

[mfb]

Conservation of energy is the first attempt,but I am facing one hell of a trouble framing the equations.

Then show your attempt please.

Conservation of momentum? Well,I don't have the inital velocity.

The initial velocity is negligible, but conservation of momentum doesn't help here.

 

[Arka420]

The initial velocity is negligible, but conservation of momentum doesn't help here.

Hmm. Looks like all I have to do is conserve energy.

 

[Arka420]

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?

 

[mfb]

Where do 2mgl and mgl come from?

(I is the moment of inertia about the center of the pulley wheel

The moment of inertia of what?

 

[Arka420]

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).

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?

 

[mfb]

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.

The moment of inertia of the mass m about the center of the pulley?

Okay.

Am I doing something wrong?

Yes, and it is unclear what because you don't explain how you got your formulas.