Conservation of relativistic energy

[stepheng123]

A particle of rest mass m_0 disintegrates into two particles of rest masses m_1 and m_2.
Use conservation of relativistic energy and relativistic 3-momentum to find the energies E1 and E2 of the particles in the rest fram of the original particle.

Relevant equations:
E0 = E1 + E2
p0 = p1+ p2

?

 

[cupid.callin]

A particle of rest mass m_0 disintegrates into two particles of rest masses m_1 and m_2.
Use conservation of relativistic energy and relativistic 3-momentum to find the energies E1 and E2 of the particles in the rest fram of the original particle.

Relevant equations:
E0 = E1 + E2
p0 = p1+ p2

?

put values in p0 = p1+ p2

you will have m1v1 = m2v2

 

[stepheng123]

you will have m1v1 = m2v2

Would it not be m1v1 = -m2v2 as p0 = 0 ?
And how would this lead to me obtaining the energies of the particles?

 

[cupid.callin]

no ... v1 will be opposit to v2

so m_o(0) = m1v1-m2v2 => m1v1 = m2v2

but i don't think that Eo = E1 + E2 will be valid ... if by E you mean mechanical energy

 

[vela]

Stick with E's and p's instead of using velocities. So far you have

$$\begin{align*} E_0 &= E_1 + E_2 \\ 0 &= p_1 + p_2 \end{align*}$$

What equations do you have relating energy, momentum, and mass?

 

[stepheng123]

What equations do you have relating energy, momentum, and mass?

I have E$$^{2}$$ = p$$^{2}$$c$$^{2}$$ + m$$^{2}$$c$$^{4}$$

I need E1 and E2 in terms of c, m0, m1 and m2..

 

[vela]

Good. Since p₀=0, you know E₀=m₀c², and you can multiply the second equation by c, which leaves you with

$$\begin{align*} m_0c^2 &= E_1 + E_2 \\ 0 &= p_1c + p_2c \end{align*}$$

You're going to want to square the equations, subtract the second from the first, and use the relation you have to replace combinations of E² and (pc)² with (mc²)². The trick is to first arrange the equations so that the cross term you get from squaring conveniently let's you solve for one of the energies.