# Homework Help: Relativistic and non-relativisitic kinetic energy

1. Dec 3, 2009

### lola2000

1. The problem statement, all variables and given/known data
at what speed does the expression for relativistic kinetic energy vary from the non-relativistic expression by 5%?

2. Relevant equations
Relativistic kinetic energy K=(gamma-1)mc^2
Non-relativistic kinetic energy K=0.5mv^2

3. The attempt at a solution
I'm not sure how to attempt this!
Should I be finding the difference? ie K(relativistic)-K(non-relativistic)=0.05??

2. Dec 3, 2009

### gabbagabbahey

Hi lola2000, welcome to PF!

Close, you should be finding the relative difference |Krel-Knon-rel|/Knon-rel=0.05 .... make sense?

3. Dec 3, 2009

### lola2000

I see, that makes sense.

But when I do this I get
0.05 = [(gamma-1)mc^2 - 0.5mc^2] / 0.5mv^2
which simplifies to
0.6mv^2 = (gamma-1)mc^2
0.6v^2/c^2 +1 = gamma

which is really nasty to solve! Is there a trick I have missed?

4. Dec 3, 2009

### gabbagabbahey

I assume this is a typo?

Really?

5. Dec 4, 2009

### lola2000

You are right!
That was a typo - it should have been -0.5mv^2

But I am still stuck with the algebra

I have 0.525v^2/c^2 = gamma - 1

How do I rearrange this??

It is not simplifying!

6. Dec 4, 2009

### nrqed

I did not check the previous steps so I cannot guarantee this is the correct equation. But assuming it is, you just need to add 1 to both sides (to have gamma isolated). Then square both sides and rename $$v^2/c^2 = X$$ . Then you will have a quadratic equation for X. Solve, keep only the positive root. That will be $$v^2/c^2$$. Then the answer is the square root of X.