How Many Revolutions Does a Proton Complete in a Cyclotron?

[andrew410]

A cyclotron designed to accelerate protons has an outer radius of 0.477 m. The protons are emitted nearly at rest from a source at the center and are accelerated through 610 V each time they cross the gap between the dees. The dees are between the poles of an electromagnet where the field is 0.560 T.

(a) Find the cyclotron frequency.
(b) Find the speed at which protons exit the cyclotron.
(c) Find their maximum kinetic energy.
(d) How many revolutions does a proton make in the cyclotron?
(e) For what time interval does one proton accelerate?

So, I got the answer for parts a, b, and c. I'm stuck on part d though.
I know that I have to use the potential difference at this point in order to get the answer, but don't know how. I know the potential energy equals the charge of the proton times the potential difference, but don't know how to apply this to get the number of revs. Also, I changed the cyclotron frequency to rev/sec, but don't know what the time is.
I need some help putting the info together into an equation or something.
Please help, any help is great! thanks in advance ! :)

 

[stunner5000pt]

youk now the radius of the cyclotron
you knwo the linear speed of the protons

relate the two using $$a = \frac{v^2}{r} = \omega^2 r$$
what are the units of omega??

Note; this is one of MANY MANY approaches to this problem

 

[learningphysics]

You know the maximum kinetic energy. All the energy comes from being accelerated through the 610V(so every revolution the proton gains qV).

You know total energy gained. You know energy gained per revolution. So you should be able to get number of revolutions.

 

[andrew410]

thx guys! :)