Relativistic CM frame Kinetic energy

Bigfoots mum
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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
 
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Hi Bigfoots mum! :smile:

(have a square-root: √ :wink:)
Bigfoots mum said:
… Not entirely sure about this, i took the obvious option and calculated (root3/2)c as my speed.

Yes, that's the right answer :-p …

but how did you get it? :confused:​
 
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
 
Bigfoots mum said:
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. :biggrin:
 

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