Conservation of energy for a system

In summary, the conversation discusses finding the speed of a mass m attached to a massless wheel with a uniform chain of mass 2m tied to it. A small clockwise jerk is given to the wheel, causing it to rotate. Conservation of energy and momentum equations are mentioned as possible solutions, but the initial velocity is unknown. The equation 2mgl = mgl + 1/2mv^2 + 1/2Iw^2 is suggested, but it is unclear where the terms 2mgl and mgl come from and the moment of inertia is also not specified. It is concluded that there may be an error in the equations used.
  • #1
Arka420
28
0

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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  • #2
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.
 
  • #3
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.
 
  • #4
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?
 
  • #5
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?
 
  • #6
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?
 
  • #7
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.
 

FAQ: Conservation of energy for a system

1. What is the conservation of energy for a system?

The conservation of energy for a system is a fundamental principle in physics that states that energy cannot be created or destroyed, but can only be transferred or transformed from one form to another.

2. Why is conservation of energy important?

Conservation of energy is important because it helps us understand how energy behaves and is transferred in different systems. It also allows us to make accurate predictions and calculations in various scientific fields, such as engineering and thermodynamics.

3. How is energy conserved in a closed system?

In a closed system, energy is conserved through various processes such as mechanical work, heat transfer, and chemical reactions. This means that the total amount of energy in the system remains constant, even though it may change forms.

4. Can energy be lost in a system?

No, according to the law of conservation of energy, energy cannot be lost in a system. It can only be transferred or transformed into another form. However, some energy may be lost due to inefficiencies in the system, such as friction or heat loss.

5. How does conservation of energy apply to real-life situations?

Conservation of energy applies to almost all real-life situations, from the movement of a pendulum to the functioning of a car engine. It helps us understand and predict the behavior of natural phenomena and is crucial in developing sustainable energy solutions.

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