Help with energy momentum relation.

1. Jul 20, 2011

randombill

Hi,

I needed to derive a few equations using relativistic kinematics and I needed help with this simple equation.

Basically I need to write the p^2c^2 part in terms of mass and c, in other words, what is p equal to without E being in the equation?

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2. Jul 20, 2011

timthereaper

p=m0*v/Sqrt[1-v^2/c^2], m0 is the rest mass.

For anything more, you'll have to let us know where you're trying to get to (i.e. the equations you want to derive).

3. Jul 20, 2011

randombill

Sure,

I http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html" [Broken] that (pc)2 = (mc2)2 - (mo2c4)

So would this be correct?

E = ((moc2)2 + (mc2)2 - (mo2c4))1/2

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4. Jul 20, 2011

Staff: Mentor

Yes, but it doesn't say anything really new. The first and last terms in that equation cancel. After you do that, what do you have left?

5. Jul 20, 2011

jfy4

$$E=\gamma m_0c^2$$
and
$$(pc)^2=E^2-(m_0 c^2)^2$$
Make the appropriate substitution.

6. Jul 20, 2011

randombill

Thanks for the help thus far. The page I'm looking at is http://teachers.web.cern.ch/teachers/archiv/hst2002/bubblech/mbitu/applications_of_special_relativi.htm" [Broken] and I'm trying to derive the general equation for an elastic collision. So far I have the following solved, please check my math. It's a little blurry, sorry!

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