# annoying relativity

• Feb 13th 2006, 01:37 PM
dented42
annoying relativity
I am having problems with an equation involving relativity, but my question is directly math related currently the equation is in the form of e=mc^2(blah blah blah), but I need it in the form e=mv^2(blah blah blah).

the current equation is "E=mc^2((1/(sqrt(1-v^2/c^2)))-1"

what I really need is the answer, but I would love to know the steps taken.
• Feb 13th 2006, 02:53 PM
ThePerfectHacker
Quote:

Originally Posted by dented42
I am having problems with an equation involving relativity, but my question is directly math related currently the equation is in the form of e=mc^2(blah blah blah), but I need it in the form e=mv^2(blah blah blah).

the current equation is "E=mc^2((1/(sqrt(1-v^2/c^2)))-1"

what I really need is the answer, but I would love to know the steps taken.

I do not understand you want to solve for $v$?
• Feb 13th 2006, 05:02 PM
topsquark
Quote:

Originally Posted by dented42
I am having problems with an equation involving relativity, but my question is directly math related currently the equation is in the form of e=mc^2(blah blah blah), but I need it in the form e=mv^2(blah blah blah).

the current equation is "E=mc^2((1/(sqrt(1-v^2/c^2)))-1"

What you want to do is expand the gamma function ( $\gamma=1/\sqrt{1-v^2/c^2}$) in a Taylor series about v=0. So $E = mc^2(1+1/1!*\gamma'(v=0)+1/2!*\gamma''(v=0)+...)$. You should get $E=mc^2(1+1/2*v^2/c^2+3/8*v^4/c^4+...)$.