Help with energy momentum relation.

[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?

 

[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).

 

[randombill]

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).

Sure,

I http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html" that (pc)² = (mc²)² - (m_o²c⁴)



So would this be correct?

E = ((m_oc²)² + (mc²)² - (m_o²c⁴))^1/2

 

[jtbell]

So would this be correct?

E = ((m_oc²)² + (mc²)² - (m_o²c⁴))^1/2

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?

 

[jfy4]

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

 

[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" 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!