Relativistic Momentum and Kinetic Energy

[erok81]

Homework Statement

What is the speed of an electron (m_e=0.511 MeV/c²) with a momentum p=5 MeV/c.

Homework Equations

Starting with momentum:

$$p=\gamma mu$$

Then solving for u:

$$u=\pm\frac{cp}{\sqrt{c^2m^2+p^2}}$$

The Attempt at a Solution

I've never dealt with these units before (MeV/c² and MeV/c) so I am not sure what to do with them. Can one use those values to solve for speed? I solved it (getting 0.993c) but I converted everything to kg and kg*m/s and the solved from there.

Is there an easy way to convert (if I have to)? I ended up using a calculator online to find values. But I'd rather understand them better.

 

[tiny-tim]

hi erok81!
(have a gamma: γ and a square-root: √ and try using the X² and X₂ icons just above the Reply box )

I've never dealt with these units before (MeV/c^2 and MeV/c) so I am not sure what to do with them. Can one use those values to solve for speed?

yes

if in doubt, look at the units given to you …

the whole of that square-root bracket is in units of MeV/c² squared times c², and (MeV/c)², which are the same, and the top line is the square-root of that …

everything is in the same units, so the whole thing is just a dimensionless number, just like v/c (you don't even need to convert from MeV to eV)

 

[erok81]

Oh hey, what do you know, it worked.

I tried it once before after I solved it using my know units and it didn't match. Now I see why...I messed up the m² under the radical.

My answer is slightly different, so I'll go back and change it. (0.995 vs. 0.993)

Thanks for the help.

And thanks for pointing out the super/subscript buttons. I never saw those and didn't like using LaTeX in the middle of a sentence just for that.