Conservation of Linear momentum and Kinetic energy

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Discussion Overview

The discussion revolves around the conservation of linear momentum and kinetic energy in a system involving two masses attached by a string, particularly in the context of removing one mass while the system is in motion. Participants explore the implications of this action on energy conservation and the definitions of equilibrium in the scenario described.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant proposes a scenario where two masses are attached to a string and moved away from an equilibrium position, suggesting that removing one mass should lead to an increase in kinetic energy.
  • Another participant questions the definition of "equilibrium position" and requests a more complete description of the scenario.
  • A later reply clarifies that the system involves simple harmonic motion and discusses the forces at play when the masses are moved and released.
  • One participant argues that conservation laws apply only to closed systems and that removing a mass would not allow for the conservation of momentum, suggesting that the remaining mass would not change velocity.
  • Another participant acknowledges the oversight regarding the closed system requirement and expresses regret for the confusion in their initial question.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of conservation laws when one mass is removed from the system. There is no consensus on the implications of this action for energy conservation or the definitions involved.

Contextual Notes

Participants highlight the need for clearer definitions and scenarios, particularly regarding the concept of equilibrium and the conditions under which conservation laws apply. There is also a lack of clarity about the system's configuration, which may affect the discussion.

Who May Find This Useful

This discussion may be of interest to those studying mechanics, particularly in the context of conservation laws, simple harmonic motion, and system dynamics.

eonden
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Suppose that we are working with a horizontal string with two masses attached. There is no friction on the floor and we move those two attached masses away from the equilibrium position by an undefined distance.
Once the string with those two attached masses passes through the equilibrium possition, we remove one of the attached masses.
As there are no forces present in that moment (as we are in the equilibrium position), we should apply the conservation of the linear momentum such that:
(m1 + m2 ) * v_slow = m1 *v_fast (as we remove the m2 with no speed)
So, we move from an initial Kinetic energy = ((m1+m2)*v_slow^2)/2
To a final Kinetic energy = (m1*v_fast^2)/2 from which we can derive using the conservation of the linear momentum --> ((m1+m2)^2 * v_slow^2)/(2*m1) and as ((m1+m2)^2)/m1 > (m1+m2), we have essentialy given energy to the system.
Can someone explain me where does this "extra" energy come from?
Thanks
 
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eonden said:
Suppose that we are working with a horizontal string with two masses attached. There is no friction on the floor and we move those two attached masses away from the equilibrium position by an undefined distance.
What do you mean by "equilibrium position"? Please define the scenario you have in mind more completely.
 
Doc Al said:
What do you mean by "equilibrium position"? Please define the scenario you have in mind more completely.

https://ecourses.ou.edu/ebook/dynamics/ch10/sec101/media/d0121.gif

We start from an original position and move the masses away from the origin to the maximum amplitude of the Simple Harmonic Motion. Once we get to that position, we let it contract by the spring force.
Sorry for not including a simple diagram with the doubt.
 
If I understand you correctly, you want to remove part of the moving mass from the system at some point?
If so, then you can't use conservation laws - these work only for close systems.

In other words, if you magically remove one of the masses, the other one will not change velocity.
 
eonden said:
https://ecourses.ou.edu/ebook/dynamics/ch10/sec101/media/d0121.gif

We start from an original position and move the masses away from the origin to the maximum amplitude of the Simple Harmonic Motion. Once we get to that position, we let it contract by the spring force.
Sorry for not including a simple diagram with the doubt.
I see one mass attached to a wall by a spring. Your first post mentions two masses attached by a string. Are you changing the scenario?

You pull the mass from the equilibrium position and let it go. So what? (I don't see what this has to do with conservation of momentum.)

Please restate your question with reference to the diagram.
 
Bandersnatch said:
If I understand you correctly, you want to remove part of the moving mass from the system at some point?
If so, then you can't use conservation laws - these work only for close systems.

In other words, if you magically remove one of the masses, the other one will not change velocity.

Thanks, completely forgot that when talking about closed systems no matter can be exchanged.
Sorry for the stupid question.
 

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