Real life elastic collision and variation of kinetic energy

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Discussion Overview

The discussion revolves around the criteria for determining when a collision can be considered elastic, particularly in real-life scenarios. It explores the concept of elastic collisions, the significance of the time interval ##\Delta T##, and the acceptable error margins in energy measurements.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions how small ##\Delta T## should be for a collision to be classified as elastic, noting that only atomic collisions are typically regarded as perfectly elastic.
  • Another participant suggests that ##\Delta T## should be small enough that the error from ignoring it is negligible for the intended application.
  • A participant proposes using a criterion where if the percentage of ##\Delta T## from the initial time ##T_i## is less than 10%, it could be considered acceptable, although they express uncertainty about this approach.
  • It is noted that tolerating a 10% error in energy measurements may be acceptable, but the definition of a purely elastic collision is described as an approximation, with no definitive answer on the usefulness of approximations depending on context.

Areas of Agreement / Disagreement

Participants express varying opinions on the criteria for classifying collisions as elastic, with no consensus reached on a specific threshold for ##\Delta T## or error margins.

Contextual Notes

The discussion highlights the dependence on specific applications and the subjective nature of what constitutes an acceptable approximation in the context of elastic collisions.

velvetmist
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How small should ##\Delta T## be in a collision to be considered elastic? In elastic collisions ##\Delta T =0##, but as far as I know, just atomic collisions are considered perfectly elastic. Then, which criterias are used to considere a collision between two objects elastic?
 
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It should be small enough that you don't care about the error from ignoring it for whatever your application is.
 
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Ibix said:
It should be small enough that you don't care about the error from ignoring it for whatever your application is.
I don't have any specific application. I was thinking in taking the percentage of ##\Delta T## from ##T_i##, and if it's ##<10\%## it's acceptable, but I'm not sure if it could be a valid criteria.
 
If you can tolerate an error of 10% in your energy measure, sure.

A purely elastic collision is an approximation to reality. There's no single answer to "how good does an approximation have to be to be useful" - it depends on how big the error is and how precise an answer you need.
 
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