Relativistic CM frame Kinetic energy

[Bigfoots mum]

Now then, this is a past paper question for only 3 marks but its annoying me.

2 identical spheres undergoing an elastic relativistic collision. The spheres move with a speed such that their CM frame kinetic energy is equal to their rest energy. Calculate the speed the spheres in the CM frame.
Not entirely sure about this, i took the obvious option and calculated (root3/2)c as my speed.

Any ideas?
Thanks

 

[tiny-tim]

Hi Bigfoots mum!

(have a square-root: √ )

… Not entirely sure about this, i took the obvious option and calculated (root3/2)c as my speed.

Yes, that's the right answer …

but how did you get it? ​

 

[Bigfoots mum]

I used Kinetic Energy T = E - mc^2

where E is the total particle energy and mc^2 is the rest energy. Therefore gamma is 2, and we're away with the mixer.
I just wasnt sure if this method would apply in the CM frame, but then I am not sure why it wouldnt!
Thanks for the response

 

[tiny-tim]

I just wasnt sure if this method would apply in the CM frame, but then I am not sure why it wouldnt!

All your favourite formulas apply in any inertial frame.