(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A proton (rest mass 1.67x10^-27 kg) has total energy that is 3.2 times its rest energy. What is:

a) the kinetic energy of the proton (in joules)

b) the magnitude of the momentum of the proton (in kg*m/s)

c) the speed of the proton (in terms of the speed of light "c")

2. Relevant equations

E(0) = m(0)c^2

where E(0) is rest energy, m(0) is rest mass and c is the speed of light (approximately 3.00x10^8 m/s)

E = mc^2

where E is the total energy (im not too sure if thats the formula for total energy) and m is the relativistic mass

p=mv

where p is the momentum

E^2 = (p^2)(c^2) + (m(0)^2)(c^2)

Ke = E - m(0)c^2

where Ke is the kinetic energy

3. The attempt at a solution

I found the rest energy E(0) = m(0)c^2 = 1.503x10^-10 and since my total energy = 3.2 times the rest energy, E = 3.2E(0) = 4.81x10^-10.

And because E = mc^2, i can use the previously calculated value to find m which gave me m= 5.344x10^-27.

I used these values and the equation E^2 = (p^2)(c^2) + (m(0)^2)(c^2)to find the momentum which gave me 1.603x10^-18, which is correct.

But when i use the formula p = mv and rearrange it as v = p/m, i get 0.9999c m/s which according to my homework isn't correct.

And also, when i use the equation Ke = E - m(0)c^2 to find the kinetic energy, i get 3.307x10^-10, which is also incorrect.

I know it's long but a little help would be appreciated.

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# Homework Help: Special relativity: find speed and kinetic energy

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