Centripetal acceleration of protons in an accelerator

[eftalia]

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 :)

 

[Hootenanny]

Which formula did you use for the kinetic energy?

 

[eftalia]

The (gamma-1)mc^2 one..

 

[Hootenanny]

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.

 

[eftalia]

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?

 

[Hootenanny]

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.

 

[eftalia]

Ah I see. Alright then thanks a lot :)