Calculate Velocity of Protons in CM Frame After Elastic Collision

[latentcorpse]

proton mass 938MeV/c^2. Consider an elastic collision between two protons. IN the centre of mass frame the kinetic energy of each proton is equal to its rest energy.

calculate the speed of the protons in the CM frame.

clearly they will be equal and opposite velocities so the two speeds should be the same.

E=mc^2
then equate that to relativistic energy momentum relationship $E=\sqrt{c^2p^2+m^2c^4}$ but then i get p=0 so I am going wrong somewhere...

 

[nicksauce]

I assume you set E = the rest energy leading to p = 0. But it says the kinetic energy is equal to the rest energy, there's also it's rest energy!

(Kinetic energy + Rest energy) = sqrt(p^2 + m^2)

 

[latentcorpse]

do you mean i should have $c^2p^2=m^2c^4$