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173. Problem 21.53 (RHK) A particle of mass m travelling at a relativistic speed
makes a completely inelastic collision with an identical particle that is
initially at rest. We have to find (a) the speed of the resulting single
particle and (b) its mass. We will express our answers in terms of the
Lorentz factor
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of the
incident particle.|
Solution: Click For PDF Version (a) Let the mass of the particles be m. Let the speed of the incident particle be v. The Lorentz factor
We note
Initial momentum of the two particles one of which is at rest is
The initial total energy of the two particle system is
Let the mass of the two-particle system after the inelastic collision be M and its speed be V. The momentum of the system after the inelastic collision will be
The energy of the system after the inelastic collision will be
From conservation of energy, we have
From conservation of momentum, we have
(b) And,
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is
defined as
.
