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inelastic relativistic collision
A particle of mass
m
, moving at speed
v
= 4
c
/5, collides inelastically with a similar
particle at rest.
(a) What is the speed
v
C
of the composite particle?
(b) What is its mass
m
C
?
Solution by Rudy Arthur:
Call the moving particle ‘M’, and the particle at rest ‘R’ (the composite particle is defined
to be ‘C’).
The momentum of the moving particle is
M
2
2
4
3
1
mv
p
v
c
==
−
m
c
M
2
.
(
1
)
And, the square of its energy is
M
22
2
()
E
mc
p c
=+
.
(
2
)
The energy of the particle at rest is
R
2
E
mc
=
.
(
3
)
The square of the energy of the composite particle
is
CC
C
2
(
2
)
E
mc
pc
.
(
4
)
By conservation of energy:
, or squaring and rearranging,
MR
EEE
+=
C
2
C
M
R
2
E
EEEE
=−−
(
5
)
Substituting (2) and (4) into (5):
( )
C
C
M
2
2
2(
)
(
)
2
(
)
(
)
E
Em
c
p
c
m
c
p
c
−+
By conservation of momentum,
CM
p
p
=
, so this reduces to
C
)
2
(
)
E
c
m
c
=−
Squaring again:
(
C
2
2 2
4(
)
2
(
EE
m
c
)
)
(
6
)
Substituting from (2) and (3) into (6) and expanding on the right,
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 Fall '10
 Guna

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