Protons in an accelerator at the fermi national laboratory near chicago are accelerated to a total energy that is 400 times their rest energy.
(a) what is the speed of these protons in terms of c?
(b) what is their kinetic energy in mev?

(a) 0.99999687c

The relationship between total energy (E) and rest energy () is

where is the relativistic factor. In this problem, we know that the total energy is 400 times the rest energy: this means that

The formula for the relativistic factor is

where v is the speed of the proton and c is the speed of light. By isolating the term v/c, we find the speed of the protons in terms of c:

(b)

Given the rest mass of a proton:

its rest energy is the energy equivalent to this mass:

The protons in the Fermi Laboratory have energy that is 400 times their rest energy, so their total energy is

The total energy is also sum of rest energy and kinetic energy:

So the kinetic energy is

And since the conversion factor is

This kinetic energy converted into MeV () is

i had this question and the answer was 3.15 miles.

martina travels from school to her mom's office. from there, she walks to school. after school, she walks to the library and then to a friends house before finally ending back at home. find martina's total distance traveled.

a) 0 miles  

b) 0.4 miles  

c) 1 mile  

d) 3.15 miles

god i hope this !