consider a head on elastic collision of a bullet of rest mass M with a stationary target of rest mass m.(adsbygoogle = window.adsbygoogle || []).push({});

prove that the post-collision gamma factor of the bullet cannot exceed (m^2+M^2)/(2mM)

im given as a hint to prove that if P,P' are the pre and post 4 momentum of the bullet and Q,Q' are of the target, then in the CM frame (P'-Q)^2>=0

well i understand how from the hint i get the answer, but how to arrive at this, i mean the momentum is conserved, i.e: P'+Q'=P+Q

so by interchanging we get:

P'-Q=P-Q'

now in the cm, we must have: (P'-Q)^2-(P-Q')^2=(M+m)^2c^2

but i don't quite see why this is correct, i mean

P=(E/c,p)

Q=(mc,0)

P'=(E'/c,p')

Q'=(E''/c,p'')

where in the cm we have: p'=-p''

so (cause the 3 momentum there is zero) (P'-Q)^2=(E'/c)^2+(mc)^2-2*E'*m

(P-Q')^2=(E/c)^2+(E''/c)^2-2EE''/c^2

here's where im stuck, can anyone help?

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

Dismiss Notice

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!

# Homework Help: Centre of mass (in relativity).

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