Mass-energy conversion

[Guest Gabriel]

I have a question about mass-energy conversions in accelerators. I usually think of mass being converted to energy, or vice-versa, as in a cloud/bubble chamber or a nuclear reactor. However, in an accelerator, I was taught that the mass of the particle increases as well as its speed, and by the amount corresponding to E = m.c^2, so that E is its gain in energy and m is its gain in mass. My teacher said that this could happen because work was being done on the particle. Is this correct?

[timo]

The correct formula would be E = g*m*c², where g = (1-v²/c²)^-0.5. In this formula m is allways constant for a particle since it´s a property of it. If you do a Tayolor Expansion of this formula it leads you to E = m*c² + 0.5*m*v² + X, where X is small for nonrelativistic velocities. Thats the normal Ekin= 0.5*m*v² you might know from basic Newtonian Physics.

 

However:

For some reasons some people still use E=m'*c², where m'=g*m. I don´t really know why people use that notation because it doesn´t make much sense for reasons I don´t want to discuss on this board. One reason might be that "E=mc²" is easier to remember. Another might be that this is the one that you allways read in the press. Maybe you can even find some shortcuts for certain conditions with using m'. In this picture m' increases as velocity increases (of course: g increases) so the people using m' say that the mass of a particle increases.

 

To avoid confusion with these two notations one usually calls

m the "rest mass" and

m' the "relativistic mass"

 

To come back to what your teacher said: If work is done on the particle then, in this case, it´s energy increases => E increases => g increases (all other factors are constant) => m' increases.

[[Tycho?]]

The correct formula would be E = g*m*c²' date=' where g = (1-v²/c²)^-0.5. In this formula m is allways constant for a particle since it´s a property of it. If you do a Tayolor Expansion of this formula it leads you to E = m*c² + 0.5*m*v² + X, where X is small for nonrelativistic velocities. Thats the normal Ekin= 0.5*m*v² you might know from basic Newtonian Physics.

 

However:

For some reasons some people still use E=m'*c², where m'=g*m. I don´t really know why people use that notation because it doesn´t make much sense for reasons I don´t want to discuss on this board. One reason might be that "E=mc²" is easier to remember. Another might be that this is the one that you allways read in the press. Maybe you can even find some shortcuts for certain conditions with using m'. In this picture m' increases as velocity increases (of course: g increases) so the people using m' say that the mass of a particle increases.

 

To avoid confusion with these two notations one usually calls

m the "rest mass" and

m' the "relativistic mass"

 

To come back to what your teacher said: If work is done on the particle then, in this case, it´s energy increases => E increases => g increases (all other factors are constant) => m' increases.[/quote']

 

 

Well, the first part of that post was quite beyond me, but the last sentace is what I was going to say.

[Guest Gabriel]

I haven't studied this in enough detail (I am beginning Physics in university later this year), but now I can at least see how this effect is a result of the equation. Thank you very much for your detailed reply.