# Centripetal acceleration of protons in an accelerator

## 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 :)

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Hootenanny
Staff Emeritus
Gold Member
Which formula did you use for the kinetic energy?

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

Hootenanny
Staff Emeritus
Gold Member
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.

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
Staff Emeritus