What is the speed of the centre of momentum frame in terms of c?

AI Thread Summary
The discussion focuses on determining the speed of the center of momentum frame (S') for two colliding particles, one moving at 0.802c and the other at rest in frame S. Participants explore how to apply Lorentz transformations and the four-momentum vector to find the necessary conditions for the total momentum to be zero. The equation for transforming velocities, v = (u + v')/(1 + uv'/c²), is suggested as a method to relate the speeds in different frames. There is also a mention of needing to establish the value of gamma (γ) in the Lorentz transformation to ensure momenta are equal in magnitude but opposite in sign. Understanding these concepts is essential for solving the problem effectively.
abanana
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Homework Statement


A particle with mass m has speed 0.802c relative to inertial frame S. The particle collides with an identical particle at rest relative to frame S. Relative to S and in terms of c, what is the speed of a frame S' in which the total momentum of these particles is zero? This frame is called the centre of momentum frame.

Homework Equations

The Attempt at a Solution


If particle 2 is at rest in the S frame, then in the S' frame particle 2 must have the same velocity as the S' frame relative to the S frame, but I'm not sure how to apply this.
 
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Do you know how to form the four-momentum vector for a massive particle in one spatial dimension, and how to write Lorentz transformations as matrices? In this case the vector has effectively only two components and the transformations are 2x2 matrices. You will find help here: http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/vec4.html

You just have to form an equation for the value of ##\gamma## in the Lorentz transformation that makes the momenta equal in magnitude but opposite in sign.
 
abanana said:

Homework Statement


A particle with mass m has speed 0.802c relative to inertial frame S. The particle collides with an identical particle at rest relative to frame S. Relative to S and in terms of c, what is the speed of a frame S' in which the total momentum of these particles is zero? This frame is called the centre of momentum frame.

Homework Equations

The Attempt at a Solution


If particle 2 is at rest in the S frame, then in the S' frame particle 2 must have the same velocity as the S' frame relative to the S frame, but I'm not sure how to apply this.

Do you know how to transform velocities from one frame to another?
 
@PeroK are you referring to using the equation
v = (u + v')/(1 + uv'/c2)
 
abanana said:
@PeroK are you referring to using the equation
v = (u + v')/(1 + uv'/c2)

Yes, you can use that equation. I assume you haven't covered energy-momentum transformations yet? If not, then the above formula is the way to go.
 
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