B What is m in Kinetic Energy? Relativistic mass or Rest mass?

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In discussions about kinetic energy and total energy for particles moving at relativistic speeds, the consensus is that only rest mass should be used, as relativistic mass leads to confusion. The correct expression for total energy is E = γm₀c², where γ is the Lorentz factor, and the kinetic energy is given by (γ - 1)m₀c². The Newtonian approximation of kinetic energy, 1/2 mv², is valid only at low velocities compared to the speed of light. The use of relativistic mass is discouraged in modern physics, as it complicates understanding and does not provide any advantages over using rest mass. Overall, clarity is achieved by consistently referring to rest mass in calculations.
  • #51
The problem here is that the OP isn't trying to learn physics, but to score well enough in an exam so he can start graduate school and THEN learn some physics. Hopefully learning physics and doing well on the exam are correlated, but probably not 100%. In particular, if relativistic mass is on the test, he better learn it.

Of course this cuts both ways - if it's not on the test, he's not just wasting his time, he's actually making negative progress. While he can not afford.
 
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  • #52
I know, today it's more important to earn some "credit points" and have other idiosyncratic burocracy fulfilled than learning the actual physics. In Europe it's the "Bologna process", turning our universities to schools...
 
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  • #53
Vanadium 50 said:
The problem here is that the OP isn't trying to learn physics, but to score well enough in an exam so he can start graduate school and THEN learn some physics. Hopefully learning physics and doing well on the exam are correlated, but probably not 100%. In particular, if relativistic mass is on the test, he better learn it.

Of course this cuts both ways - if it's not on the test, he's not just wasting his time, he's actually making negative progress. While he can not afford.
You have very accurately described my situation.
 
  • #54
Vanadium 50 said:
if relativistic mass is on the test, he better learn it
Yes, unfortunately that is true.
 
  • #55
Slimy0233 said:
Professor probably doesn't use it when he is doing actual problem, but he does use it when he is teaching us, he probably thinks this is easier to grasp than the alternative.
He is probably using an older book that is no longer in print. See if you can find out what it is and buy a used one somewhere. This happened to me once and about half way through the semester we found an old copy of the textbook. It was like having a light come on, illuminating the course material!
 
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  • #56
Ibix said:
Don't say that, then. Use ##E=mc^2## to refer to the rest energy of something and ##E=\gamma mc^2## for the total energy (which reduces to ##mc^2## when ##v=0## and hence ##\gamma =1##). There is nothing expressed in terms of the relativistic mass that cannot be expressed in terms of the rest mass times the Lorentz gamma factor. And then it is always crystal clear what ##m## means - the rest mass.

The rest mass is also an invariant quantity, which makes it much easier to deal with when you use more sophisticated tools.

Lev Okun (https://en.wikipedia.org/wiki/Lev_Okun). Sadly he passed away a few years ago, but he posted here a few times.
In the spirit of Okun's good article, better to write
##E_0=mc^2##
to avoid confusion.

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lightarrow