Two particles have equal kenetic energies

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Discussion Overview

The discussion revolves around the relationship between kinetic energy and momentum for two particles that have equal kinetic energies. It explores whether having the same kinetic energy implies that the particles also have the same momentum, touching on both classical and relativistic perspectives.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions if two particles with equal kinetic energies must have the same momentum.
  • Another participant asserts that equal kinetic energy does not guarantee equal momentum, citing various influencing factors.
  • A participant provides a specific example using classical mechanics, calculating kinetic energy and momentum for two different masses and speeds, demonstrating that they can have the same kinetic energy but different momenta.
  • A later reply introduces the concept of relativistic kinetic energy, suggesting that for particles, the kinetic energy formula may be K = (\gamma - 1) mc^2, which aligns with the classical definition under certain conditions.

Areas of Agreement / Disagreement

Participants do not reach a consensus; there are competing views regarding the relationship between kinetic energy and momentum, with some emphasizing classical mechanics and others introducing relativistic considerations.

Contextual Notes

The discussion includes assumptions about the conditions under which kinetic energy and momentum are compared, and it highlights the differences between classical and relativistic frameworks without resolving these complexities.

napier212121
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if two particles have equal kenetic energies, do they have the same momentum?
 
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NO! Just because something has the same kinetic energy doesn't mean it has the same momentum. There are a number of factors that could affect it.
 
Kinetic energy of an object with mass m and velocity v is (1/2)mv2. Momentum is mv.

Take for example, an object with mass 4kg and speed 1 m/s. Its kinetic energy is (1/2)(4)(1)2= 2 Joules and its momentum is (4)(1)= 4 kgm/s. Take a second object with mass 1kg and speed 2 m/s. It has kinetic energy (1/2)(1)(2)2= 2 Joules also but its momentum is (1)(2)= 2 kgm/s.
 
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Originally posted by HallsofIvy
Kinetic energy of an object with mass m and velocity v is (1/2)mv<sup>2</sup>. Momentum is mv.

Take for example, an object with mass 4kg and speed 1 m/s. Its kinetic energy is (1/2)(4)(1)<sup>2</sup>= 2 Joules and its momentum is (4)(1)= 4 kgm/s. Take a second object with mass 1kg and speed 2 m/s. It has kinetic energy (1/2)(1)(2)<sup>2</sup>= 2 Joules also but its momentum is (1)(2)= 2 kgm/s.

Well, kinetic energy (for particles, as the question originally asked) is probably more likely to be [itex]K = (\gamma - 1) mc^2[/itex], i.e. relativistic kinetic energy, which reduces to the Newtonian expression in the limit of small v.
 

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