Kinetic energy, special relativity

[fluidistic]

Homework Statement

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

Homework Equations

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

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?

 

[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!

 

[fluidistic]

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!

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...

 

[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.

 

[fluidistic]

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.

Ok thanks for your help. Problem solved!

 

[aq1q]

Ok thanks for your help. Problem solved!

great!