What is the energy here refers to?

[cks]

The original design of the Berkeley 184 inch synchrocyclotron was able to product a pulsed beam of 350 MeV protons by using a magnetic field of 1.5T and a voltage amplitude across the 'dees' of 10,000 eV.

My question is the 350MeV the proton has refers to the total energy of just the kinetic energy?

Let's say

E^2=p^2m^2+m^2c^4

Is total energy , E=350MeV

Or

Kinetic energy = sqrt(p^2m^2+m^2c^4)-mc^2=350MeV

 

[jtbell]

E^2=p^2m^2+m^2c^4

Correction: E^2 = p^2 c^2 + m^2 c^4

Is it even possible for a proton to have a total energy of 350 MeV, under any circumstances?

Hint: what is mc^2 for a proton? (m here being the rest-mass)

 

[DrGreg]

The original design of the Berkeley 184 inch synchrocyclotron was able to product a pulsed beam of 350 MeV protons by using a magnetic field of 1.5T and a voltage amplitude across the 'dees' of 10,000 eV.

My question is the 350MeV the proton has refers to the total energy of just the kinetic energy?

Let's say

E^2=p^2m^2+m^2c^4

Is total energy , E=350MeV

Or

Kinetic energy = sqrt(p^2m^2+m^2c^4)-mc^2=350MeV

If you were talking about electrons instead of protons, the answer would be that the rest mass energy of an electron is tiny compared with 350 MeV so, as the figure is only approximate, it doesn't matter either way.

However if you really do mean protons, then something else in your question must be wrong, as jtbell has hinted...

 

[JANm]

Dear jtbell
If there was 0 MEV administered the protons would be at rest. So p=0. Since the first energy you mention: total energy = m*c^2 and the second energy you mention: kinetic energy = 0. I would say: the kinetic energy is the right answer.

 

[DrGreg]

However if you really do mean protons, then something else in your question must be wrong, as jtbell has hinted...

Oops, I withdraw that sentence. What I should have said was:

However if you really do mean protons, then jtbell has given you a big hint that only one of your answers could possibly be correct...​

 

[cks]

I see. It's very easy to know whether the 350MeV refers to the total energy or Kinetic energy.

For proton, its rest mass energy is 935MeV.

So, the total energy should be at least more than the rest mass energy. So, 350MeV which is less than 935MeV can't possibly be total energy. It has to be kinetic energy.

I think physically, it's intuitive. Because the detector can stop the proton and thus measure its energy. If a proton is stopped, then all its kinetic energy converted as signal to the detector,while its rest mass energy can't be converted. So, a detector usually will detect Kinetic energy, I guess.

Thank you you guys.