Physics
posted by Marissa .
OK, so I'm having some serious problems with this one question. It's on relativity. Here it is:
Calculate the mass of a proton (m0 = 1.67E27 kg) whose kinetic energy is one sixth its total energy. How fast is it traveling?
THANKS!!

Total energy is then
Etotal = m0c^2 + KE = (6/5) m0 c^2
= m0 c^2/sqrt[1  (v/c)^2]
6/5 = 1/sqrt[1  (v/c)^2]
25/36 = 1  (v/c)^2
(v/c)^2 = 11/36
v/c = 0.306
v = 9.17*10^7 m/s
You don't need to use the rest mass.
There is a nonrelativistic way to do this also, but you will get a different (and wrong) answer. That would be to calculate m0c^2, take 1/5 of it for the kinetic energy, and set that equal to
(1/2) m0 v^2, then solve for v. 
wait, aren't we lookng for the mass, too?

Whoops, you are right. They asked for mass, too. It is the rest mass times the factor 1/sqrt[1  (v/c)^2], which is (6/5) m0.

m = m0 / √ [1  v^2/c^2]
Kinetic energy = [mm0] c^2.
Total energy = mc^2.
It is given that [mm0] c^2 = mc^2/6
m = [6/5] *m0 = [6*1.67e27/5] = 2.004e27 kg.
…
v^2 /C^2=[ m^2 m0^2] / m^2 =[ 2.004e27 ^2 1.67e27^2] /2.004e27^2
v = 0.553 C where C = 3e8m/s.
================================= 
what would happen if it became 1/4 the total energy instead? how would the equation be set up?
Respond to this Question
Similar Questions

Physics
Zero, a hypothetical planet, has a mass of 1.0x10^23 kg, a radius of 3.0x10^6 m, and no atmosphere. A 10 kg space probe is to be launched vertically from its surface. (a) If the probe is launched with an initial kinetic energy of 5.0x10^7 … 
Physics
A proton moving with a constant speed has a total energy 2.5 times its rest energy. What is the proton's: a. speed b. kinetic energy 
physics
A beam of protons is moving toward a target in a particle accelerator. This im trying to study for my exam by doing problems, however im stuck with this one. any help is appreciated beam constitutes a current whose value is 0.39A. … 
Physics
In protonbeam therapy, a highenergy beam of protons is fired at a tumor. The protons come to rest in the tumor, depositing their kinetic energy and breaking apart the tumor’s DNA, thus killing its cells. For one patient, it is … 
Physics
A relativistic proton has a momentum of 1.0×10^17 kg ∙ m/s and a rest energy of 0.15 nJ. What is the kinetic energy of this proton? 
Physics
A relativistic proton has a momentum of 1.0×10^17 kg ∙ m/s and a rest energy of 0.15 nJ. What is the kinetic energy of this proton? 
Physics
A bowling ball of mass 7.45 kg is rolling at 2.56 m/s along a level surface. (a) Calculate the ball's translational kinetic energy. J (b) Calculate the ball's rotational kinetic energy. J (c) Calculate the ball's total kinetic energy. … 
physics
A bowling ball of mass 7.45 kg is rolling at 2.56 m/s along a level surface. (a) Calculate the ball's translational kinetic energy. J (b) Calculate the ball's rotational kinetic energy. J (c) Calculate the ball's total kinetic energy. … 
physics relativistic energy
I'm not too good with these special relativity problems :/ The question is: A 20 kiloton bomb releases 8 x 10^13 joules. How much mass must be converted into other forms of energy? 
physics
the mass of a proton is 1836 times the mass of an electron a)a proton is traveling at speed v. at what speed (in terms of v) would an electron have the same kinetic energy as the proton?