9. (a) Conservation of energy gives
Q = K
2
+
K
3
=
E
1
–
E
2
–
E
3
where
E
refers here to the
rest
energies (
mc
2
) instead of the total energies of the particles.
Writing this as
K
2
+
E
2
–
E
1
= –(
K
3
+
E
3
) and squaring both sides yields
KK
EK
E
E
E
E
E
2
2
22
21
1
2
2
3
2
33
3
2
2
+−+
−
=
++
b
g
.
Next, conservation of linear momentum (in a reference frame where particle 1 was at rest)
gives

p
2
 = 
p
3
 (which implies (
p
2
c
)
2
= (
p
3
c
)
2
). Therefore, Eq. 3754 leads to
E
E
2
2
3
2
+=
+
which we subtract from the above expression to obtain
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 Fall '10
 TimothyBolton
 Conservation Of Energy, Energy, Mass, General Relativity, Special Relativity, k2, Noether's theorem, Invariant mass

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