Why Does Kinetic Energy Change Near Light Speed?

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SUMMARY

The discussion centers on the limitations of the classical kinetic energy equation KE = ½ m ⋅ v² at speeds approaching the speed of light (c). It highlights that as an object's speed increases, its effective mass changes according to the Lorentz factor, necessitating the use of the relativistic kinetic energy formula KE = (\gamma - 1)mc². Participants emphasize that the concept of relativistic mass is not essential for understanding these principles, as physicists primarily utilize rest mass in their calculations.

PREREQUISITES
  • Understanding of classical mechanics and kinetic energy principles
  • Familiarity with special relativity concepts, particularly the Lorentz factor
  • Knowledge of momentum in both Newtonian and relativistic contexts
  • Basic calculus for understanding integrals and derivations in physics
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  • Study the derivation of the relativistic kinetic energy formula KE = (\gamma - 1)mc²
  • Explore the implications of the Lorentz factor on mass and energy
  • Learn about the differences between relativistic and classical momentum
  • Investigate the role of reference frames in both Newtonian and relativistic physics
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Students of physics, educators teaching relativity, and anyone interested in advanced mechanics and the behavior of objects at relativistic speeds.

julianwitkowski
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I'm curious as to the reasons why KE = ½ m ⋅ v2 only works at speeds much less than c?

Also, how does the equation change?

Thank you!
 
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Shyan said:
This thread may help.
Is it because you have to compensate for the increasing mass of the object which is proportional to the Lorentz factor, and then the integrals give you the the accurate change in mass over the entire distance with acceleration/deceleration and other factors compensated for?
 
julianwitkowski said:
Is it because you have to compensate for the increasing mass of the object which is proportional to the Lorentz factor, and then the integrals give you the the accurate change in mass over the entire distance with acceleration/deceleration and other factors compensated for?

I prefer not to use relativistic mass at all and in fact its not needed. Physicists don't use it too. Its just that in both Newtonian and Relativistic mechanics, linear momentum and kinetic energy depend on the reference frame, but with different forms. In relativity we have KE=(\gamma-1)mc^2 and \vec p=\gamma m \vec v. By m, I mean rest mass and this is the only concept of mass I use.
These forms are dictated by consistency with special relativity and actually they can be derived. See e.g. this paper!
 
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