Calculating CM Velocity in a Two-Particle System

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Homework Help Overview

The discussion revolves around calculating the center of mass (CM) velocity in a two-particle system, where one particle is moving at a relativistic speed and the other is at rest. Participants are exploring the implications of relativistic energy and momentum on the system's CM frame.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to calculate the energy and momentum of each particle and is uncertain about the correct CM velocity, with conflicting suggestions from others. Some participants question the definition of the center of mass in a relativistic context and propose the "zero momentum" frame as a relevant concept.

Discussion Status

The discussion is ongoing, with participants exploring the definitions and calculations related to the CM velocity. Some guidance has been offered regarding the total momentum in the CM frame being zero, but there is no explicit consensus on the correct velocity values or the next steps to find the resultant velocities.

Contextual Notes

There is uncertainty regarding the correct value for the CM velocity, with participants suggesting different outcomes (2c/5 or c/2). The original poster is seeking clarification on how to proceed with the calculations in the CM frame.

Tonyt88
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So I have this problem:
A mass m travels to the right at 4c/5, and another mass m is at rest.

They ask fro the energy and momentum of each particle, so I have:

Energy of traveling: 5/3 mc^2

Energy of rest: mc^2

Momentum of traveling: 4mc/3

Momentum of rest: 0

Then they ask for the velocity of the CM of the system:

Which I have 2c/5, but then some people are telling me c/2.

But anyway, I have to solve for the velocities of the particles in the CM frame, so how I do go from there.
 
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What is the definition of the center of mass for a relativistic system of point particles...?

Daniel.
 
1/M (x1m1 + x2m2) ?
 
It should be the "zero momentum" frame.
 
Then I really don't know what to say, but I would like to know, if you have the value for the velocity at the CM (which I think is either 2c/5 or c/2), how do I go from there to solve for the resultant velocities?
 
You just need the CM's velocity. You've been hinted that in the CM frame the total momentum of the particles is zero.

Daniel.
 

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