Kinetic energy distribution in high speeds and large scales

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Discussion Overview

The discussion revolves around the kinetic energy distribution in objects moving at high speeds, particularly focusing on large-scale structures like galaxy clusters. Participants explore how kinetic energy can be calculated and distributed in both homogeneous and non-homogeneous systems, considering relativistic effects and the implications of mass-energy equivalence.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests using a specific equation for calculating total energy in small, homogeneous objects, questioning how this applies to large-scale, non-homogeneous objects like galaxy clusters moving at relativistic speeds.
  • Another participant points out that a gold atom is not homogeneous but states that this does not affect the calculation of total energy, emphasizing the importance of considering the system's rest frame.
  • A participant raises a scenario involving a sphere with a specific volume and number of objects, questioning whether kinetic energy can be uniformly distributed within the sphere.
  • Responses indicate that the distribution of kinetic energy depends on the details of the object, with some suggesting that if the object is homogeneous, uniform distribution is meaningful.
  • Participants discuss the possibility of calculating energy for smaller volumes within a system, with one asking for equations or sources to support this approach.
  • Another participant references a previous post as providing a full description of the topic, indicating some level of agreement on the explanation provided.

Areas of Agreement / Disagreement

There is no clear consensus on how kinetic energy distributes in non-homogeneous systems, as participants express differing views on the implications of homogeneity and the applicability of certain calculations. The discussion remains unresolved regarding the specifics of energy distribution in complex systems.

Contextual Notes

Limitations include the assumptions about homogeneity and the dependence on the definitions of energy distribution. The discussion does not resolve how kinetic energy behaves in non-homogeneous scenarios or provide definitive equations for arbitrary volumes.

RyanH42
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We know that If object is homogenius and small (like gold atom) we can use this equation to calculate total energy of object when it moves very slow due to speed of light.And the equation is ##1/2(m_1v^2+m_2v^2+m_3v^2...=1/2Mv^2##, ##(M=m_1+m_2+m_3...)## here v is small and we are talking about a sphere.This means in every piece there's extra kinetic energy.And when we add them we get total energy

Now let's suppose we have a very large scale object, a galaxy cluster.Its not homogenius.So let's suppose that massive bigger object moves nearly speed of light.How can we calculate the the kinetic energy distrubition ?

Is this kinetic energy will distrubute the sphere in homogenius ways or just where the matter exist ?

If we take larger sphere radius How can this kinetic energy distrubition can be change ?
 
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A gold atom is not homogeneous. It does not matter, however.
RyanH42 said:
This means in every piece there's extra kinetic energy.
Depends on the way you count contributions to the total energy.

For the total kinetic energy, you can always consider the system in its rest frame first - calculate the total mass of the system there (energy divided by speed of light squared). Then calculate the total energy based on this mass and its speed. Both can be done with the usual relativistic formulas.
For the kinetic energy of individual components, just do the same thing as above but restricted to this component.
 
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So exaple we have extra 5mc^2 kinetic energy.Now our sphere volume is 100 m^3 and in the sphere there 10 objects.Is this kinetic energy can spread the sphere in homogenius ways.I mean can we say in every 1m^3 there's 5mc^2/100m^3 energy ? Or we need to say this kinetic energy inside the mass it gives extra mass to the rest mass ?
 
RyanH42 said:
.Is this kinetic energy can spread the sphere in homogenius ways.I mean can we say in every 1m^3 there's 5mc^2/100m^3 energy ?
That depends on the details of your object. If it is completely homogeneous, that is a meaningful statement.
 
Its not completely homogenius.So this time my other statemnet will true ?Or there's a theory which describes this non-homogenius situation ?
 
You can always calculate the energy of arbitrary smaller volumes in your system, in the same way you can do it for the whole system.
 
If I can calculate always smaller arbitary numbers can I get a equation ?Or a source ? Or can you describe me using my example ?
 
I think post 2 has a full description.
 
Then thank you.
 

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