Hi(adsbygoogle = window.adsbygoogle || []).push({});

I checked this problem many times but I didn't end up with the result wanted.

Assume that a particle of rest mass [tex]m_0[/tex], (relativistic) energy [tex]e_0[/tex] and (relativistic) momentum [tex]p_0[/tex] is moving in a straight line. This particle suddenly hits a stationary particle with rest mass [tex]M_0[/tex] ahead and they both get involved in an elastic collision. As a result of the collision, the second particle gains momentum [tex]P[/tex] and energy [tex]E[/tex] and the first one keeps moving with a new momentum, [tex]p[/tex], while its energy is now [tex]e.[/tex]

In the Newtonian limit, using the conservation laws of energy and momentum we can get

[tex]P=\frac{2p_0M_0}{M_0+m_0},[/tex]

[tex]p=\frac{p_0(m_0-M_0)}{M_0+m_0}.[/tex]

But in the relativistic case, the two conservation laws get really sloppy and complicated, though it is claimed that, for example,

[tex]P=\frac{2p_0M_0(e_0+M_0c^2)}{2M_0e_0+m^2_0c^2+M^{2}_0c^2}.[/tex]

How can we obtain this expression? Is this even correct?

Thanks in advance

AB

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# An elastic collision

**Physics Forums | Science Articles, Homework Help, Discussion**