# Kinetic energy, special relativity

1. Aug 21, 2010

### fluidistic

1. The problem statement, all variables and given/known data

Calculate the kinetic energy of an electron whose momentum is 2MeV/c.

2. Relevant equations
$$P=\gamma m_0 v =mv$$.
$$E_K=(m-m_0)c^2$$.

3. The attempt at a solution
I'm told that $$\gamma m_0 v=\frac{2MeV}{c}$$.
If only I had the mass at rest of the electron (it isn't given in the problem), I could calculate its velocity with the first formula I gave. Then I could calculate its mass (not its rest mass, its apparent mass or whatever it's called). And then I could apply the third formula and this would solve the problem. Am I right?
So, should I look for the electron's rest mass in some book? Is there a missing data, or can I solve the problem without this info?

2. Aug 21, 2010

### aq1q

You can do that. But you shouldn't have to look anything up. Do you know the relationship between $$\lambda$$ (the lorentz factor) and v? if so, solve for the rest mass. Similarly, you can find the relationship between $$m$$ and $$m_0$$. I hope that helps!

Last edited: Aug 21, 2010
3. Aug 21, 2010

### fluidistic

I appreciate very much your help.
What I know is $$\gamma =\frac{1}{\sqrt {1-\frac{v^2}{c^2}}}$$. I don't know how to solve for the rest mass since v is unknown. I get $$m_0=\frac{P}{v}\sqrt {1-\frac{v^2}{c^2}}$$ where P and c are known but not v...

4. Aug 21, 2010

### aq1q

ahh what was i thinking. you're right! you need to look up the rest mass. I'm really sorry, at a quick glance I thought this was just algebra.

5. Aug 22, 2010

### fluidistic

Ok thanks for your help. Problem solved!

6. Aug 22, 2010

great!