Momentum Analysis in Rest Frame Decay of Particle with Mass M

AI Thread Summary
In the decay of a particle with mass M into two particles with masses ma and mb, the discussion centers on the conservation of momentum in the center of mass reference frame. The two resulting particles will move in opposite directions, conserving momentum, but their momenta will not necessarily be equal due to their differing masses. The center of mass reference frame is crucial for understanding this decay process, as it simplifies the analysis. While the concept of equal momentum might seem reminiscent of Newtonian mechanics, relativistic effects must be considered at high velocities. Overall, the principles of momentum conservation remain applicable, though they require careful application of relativistic equations.
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Homework Statement


A particle with mass M at rest decays into two particles with masses ma=0.15M and mb=0.65M .
i) Discuss the relative directions and magnitudes of the momenta of these two particles in the centre of mass reference frame.

Homework Equations

The Attempt at a Solution


What's the centre of mass reference frame?! Isn't there really only one relevant frame here?

As for the relative directions - just in opposite directions, by conservation of momentum? And with the same magnitude of momentum? Although them having the same magnitude of momentum seems weird, because that would be just like Newtonian mechanics, and using that never seems to work anymore ;)
 
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whatisreality said:
What's the centre of mass reference frame
Use the definition ! For one particle (your initial situation) it is really easy and quite intuitive !
As for the relative directions - just in opposite directions, by conservation of momentum? And with the same magnitude of momentum? Although them having the same magnitude of momentum seems weird, because that would be just like Newtonian mechanics, and using that never seems to work anymore.
Yes, yes, and: never say never again! :smile: Newton always :rolleyes: works in the nonrelativistic limit. It's just that with high velocities you have to use the right relationships for velocity-momentum, kinetic-total energy etc.
 
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