Centripetal acceleration of protons in an accelerator

  • Thread starter eftalia
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  • #1
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Homework Statement


In a certain accelerator, protons of kinetic energy 1.6 x 10^-7 J move round a circular path of diameter 2000m .
Calculate:
(a) the centripetal acceleration
(b) the mass

ans for a is 9x10^13 ms-2, for b is 1.78 x 10^-24 kg

Homework Equations


centripetal acceleration = v^2 / r
relativistic KE = (gamma - 1)mc^2

The Attempt at a Solution


I initially thought I could use the relativistic KE formula to find the velocity of the protons, then find the centripetal acceleration (and i got the answer, apparently, using the mass of protons as 1.67 x 10^-27, but this would contradict with the second part).

I'm not so sure why the mass of the protons would differ and how to go about getting the centripetal acceleration, otherwise ><..

thanks for any help :)
 

Answers and Replies

  • #2
Hootenanny
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Which formula did you use for the kinetic energy?
 
  • #3
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The (gamma-1)mc^2 one..
 
  • #4
Hootenanny
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The (gamma-1)mc^2 one..
Then in that case the mass in the formula represents the invariant mass of the proton, which you correctly used.

Part (b) refers to the relativistic mass.
 
  • #5
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OH! I see.. Okay I get the answer for the first part now but I'm confused as to how come the protons can be moving at the speed of light? Cos if so I can't find the relativistic mass since v = c and my denominator for gamma will be 0. Or is it a rounding error on my calculator?
 
  • #6
Hootenanny
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OH! I see.. Okay I get the answer for the first part now but I'm confused as to how come the protons can be moving at the speed of light? Cos if so I can't find the relativistic mass since v = c and my denominator for gamma will be 0. Or is it a rounding error on my calculator?
When I do the calculation, I get a value of velocity very close to c (0.99999C) - so it is probably a rounding error.
 
Last edited:
  • #7
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Ah I see. Alright then thanks a lot :)
 

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