Show that the total relativistic energy of a proton

AI Thread Summary
The discussion focuses on calculating the total relativistic energy of a proton in a moving bunch, demonstrating that it equals 5mc². Participants clarify the use of the equations for energy and relativistic factors, particularly emphasizing the importance of the Lorentz factor, γ. They confirm that the speed of the proton can be derived from the given ratio of v²/c² = 24/25, leading to the expression v = c√(24/25). The conversation highlights the simplicity of substituting values into the energy equation without needing exact mass or speed of light figures. Ultimately, the correct approach and understanding of the relativistic energy concept are achieved.
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Homework Statement



The mass of a proton when at rest is m. According to an observer using the
detector frame, the speed of the anticlockwise moving bunch, A, is such that
va^2/c^2=24/25
Show that the total relativistic energy of a proton in bunch A, as observed in
the detector frame, is exactly 5mc^2, and work out the speed of the proton,
expressed as a decimal multiple of c, (to 5 significant figures).

Homework Equations


Right I think its these
E=mc^2
Etot=mc^2/√1-v^2/c^2
Etrans=mc^2/1-v^2/c^2
and maybe
E^2tot=p^2c^2+m^2c^4
p=mv/1-v^2/c^2

The Attempt at a Solution


Now I know that to get Etot you need e=mc^2 and Etrans and so maybe combing these equations will give the answer but I think this IS not the right to get 5mc^2.
So maybe its E^2tot equation I have to use.
Im just not sure.
 
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well if \frac{v^{2}}{c^{2}}=\frac{24}{25}

and the mass of the proton is m, and Etot = mc2\gamma

where \gamma=\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}

then why don't you just try plugging the values in?

I'm not sure what Etrans is supposed to beand to solve for the velocity of the proton all you need is \frac{v^{2}}{c^{2}}=\frac{24}{25}
 
Yeah getting that wrong about Etrans, just looked at my textbooks and was reading it wrong . I have an asnwwer for the last bit not sure if rights but this is what I have for that.
24/25 x 3.00 x10^8 =2.88000 x 10^8 ?

So are you saying just add the values for a proton = 1.67 x 10^-27
the speed of light 3.00 x 10^8
and then add 24=v and 25=c into the gamma part
 
if \frac{v^{2}}{c^{2}}=\frac{24}{25}

then v=c\sqrt{\frac{24}{25}}

and just leave it as a multiple of c


for the first part all you need to write is

E_{tot}=\frac{mc^{2}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}

and then substitute \frac{v^{2}}{c^{2}} for \frac{24}{25}

you should be able to do it in your head, no need to put in the mass of the proton or the exact speed of light, since the answer you want is just 5mc2 where m is the mass of the proton and c is the speed of light
 
Thank you very much I have now , its taken two days for that to sink in !
 
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