# Centripetal acceleration of protons in an accelerator

1. Nov 15, 2008

### eftalia

1. The problem statement, all variables and given/known data
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

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

3. 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 :)

2. Nov 15, 2008

### Hootenanny

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

3. Nov 15, 2008

### eftalia

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

4. Nov 15, 2008

### Hootenanny

Staff Emeritus
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. Nov 15, 2008

### 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?

6. Nov 15, 2008

### Hootenanny

Staff Emeritus
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: Nov 15, 2008
7. Nov 15, 2008

### eftalia

Ah I see. Alright then thanks a lot :)

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