A large synchrotron at the famous Particle Accelerator in the deserts of Mexico has a diameter of 3.5 km. Protons that circle the synchrotron travel at the speed of light.
a.) how long does it take the proton to complete one revolution
b.) the protons enter the ring at an energy level of 10.0 GeV. They gain 1.5 MeV each revolution.
c.) how long does it take the protons to be accelerated to 1000 GeV
d.) how far do the protons travel dying this acceleration

Question

A large synchrotron at the famous Particle Accelerator in the deserts of Mexico has a diameter of 3.5 km. Protons that circle the synchrotron travel at the speed of light. 
a.) how long does it take the proton to complete one revolution 
b.) the protons enter the ring at an energy level of 10.0 GeV. They gain 1.5 MeV each revolution.
c.) how long does it take the protons to be accelerated to 1000 GeV
d.) how far do the protons travel dying this acceleration

aaronq · Answer

a) calculate the circumference, determine the time it would take to transit speed of light is 2.99 x10^8 m/s (though I'm pretty sure we can't reach the speed of light yet)

b) is not a question

c) if the enter with 10 GeV and gain 0.0015 GeV each revolution

1000  = 10  + 0.0015 x, x is number of revolutions

d) use the circumference you got in part a) and in part d), multiply them

anonymous · Answer

so for part a.) just calculate the circumference?

anonymous · Answer

@Compassionate

anonymous · Answer

k, i got 19.242 for the circumference :)

aaronq · Answer

you need units, always

aaronq · Answer

divide the circumference by the speed of light

anonymous · Answer

the speed of light is 2.99 x 10^8 m/s?

anonymous · Answer

what are the units?

aaronq · Answer

you're the one doing the calculation, you should know

anonymous · Answer

but is the speed of light 2.99 x 10^8 m/s? :P

anonymous · Answer

@Compassionate

compassionate · Answer

[One moment please...] 

[Processing question...]

anonymous · Answer

k btw i forgot to post up full question for part b.) its
The protons enter the ring at an energy level of 10.0 GeV. They gain 1.5 MeV each revolution. How many revolutions must they travel before they reach 1000 GeV of energy?

compassionate · Answer

>How long does it take the proton to complete one revolution 
$$t = \frac{ d }{ v }$$
$$t = \frac{ 3.5}{299,792.458  } \rightarrow 1.18\sec$$

10.0 GeV
Gain 1.5 GeV each revolution 

>How many must they travel before they get 1,000 GeV

$$1.5^{17} + 10 = 995.26GeV$$

So it must make 17 revolutions. 

>How long does it take the protons to be accelerated to 1000 GeV

They have to travel around 17 times, with a distance of 3.5km, at a speed of 299,792.458  km/s 

Using the time formula for time. 

17 x 3.5km = 59.5km$$t = \frac{ 59.5 }{ 299,792.458 } \rightarrow 1.98\sec$$

They travel 59.5 kilometers.

anonymous · Answer

thank you!! <33

anonymous · Answer

can you help me with another question?