# Relativistic Momentum

1. Mar 10, 2017

### Blue Kangaroo

1. The problem statement, all variables and given/known data
How much work is required to accelerate a proton from rest up to a speed of 0.999c?
What would be the momentum of this proton?

2. Relevant equations
p=γmv

3. The attempt at a solution
I got part A, which was the momentum. I found that to be 20.1 GeV. Now for part B I have to find the momentum in units of GeV/c. I'm down to my last attempt on Mastering Physics. First, I tried going the simplest route and divided the 20.1 GeV from part A by c to get 6.7e-8 and that was wrong. I also tried using p=γmv to find an answer of 1.12e-5 J, which I converted to 7.01e-8 GeV, then divided that by c and got an incorrect figure of 2.34e-16.

Any help would be greatly appreciated.

2. Mar 10, 2017

### PeroK

Can you find a formula that relates the energy to the momentum of a particle?

3. Mar 10, 2017

### Blue Kangaroo

Would that be E^2=p^2c^2 + m^2c^4? If that is the correct equation, I came up with an answer of 1.35e-6.

4. Mar 10, 2017

### PeroK

You could use that one. But, what about using $E = \gamma mc^2$ and $p = \gamma mv$?

5. Mar 10, 2017

### Blue Kangaroo

Honestly, I'm not quite sure what I would do with those equations. I saw that a guy on Yahoo Answers did K/c=mvγ and that led me to an answer of 7.01e-8. I'm not confident that that is right though. Any idea if my answer of 1.35e-6 from my previous post is right?

6. Mar 10, 2017

### PeroK

I think your problem is probably understanding $eV$ units. The mass of a particle is normally given in $MeV/c^2$. For example, the proton mass is about $938 MeV/c^2$.

The energy of a particle is, therefore, $E = \gamma m$ where $E$ is in $MeV$ and $m$ is the mass in $MeV/c^2$.

Momentum is given in units of $MeV/c$ and we have $p = \gamma mv/c$ in these units.

In this case $v/c = 0.999 \approx 1$ so we have $p \approx \gamma m = E$.

These units take a bit of time and practice to get used to, but you can see how using them can simplify the calculations.

7. Mar 10, 2017

### Blue Kangaroo

Yes, thank you it makes sense now.