Special Relativity: Conservation of Energy + Momentum?

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Homework Help Overview

The discussion revolves around the conservation of energy and momentum in the context of special relativity, particularly focusing on the behavior of particles during decay processes. Participants are examining the relationships between energy, momentum, and velocity vectors in relativistic scenarios.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants are questioning the treatment of velocity components and their implications for momentum conservation. There is a focus on the necessity of distinguishing between different vector directions and the implications of gamma factors in relativistic equations.

Discussion Status

The discussion is exploring various interpretations of momentum conservation in both x and y directions, with some participants suggesting the need for momentum balances and questioning the equality of gamma factors before and after decay. There is an acknowledgment of the initial conditions affecting the final momentum calculations.

Contextual Notes

Participants note that the total momentum in the y direction is zero initially, which may influence the analysis of the system. There is also mention of constraints related to the mass of final particles being less than that of the original particle, which is relevant to the discussion of energy and momentum conservation.

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Homework Statement



6qb2oh.png


Homework Equations


Energy of a moving particle = γmc^2
Momentum of a moving particle = γmv


The Attempt at a Solution


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I feel like there is something wrong here...I know I'm supposed to find the VERTICAL component of velocity, but can the total velocity really be the same?
 
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Velocity and momentum are vectors. The picture clearly shows that those vectors have different directions. You cannot denote them both by the same symbol ##v## and treat them as equal.
 
Besides, the gamma factors before and after decay are not equal.
 
You need to write the momentum balances in the x- and y- directions, and also for the time components. Note that the sum of the masses of the final particles is less than the original particle. This will come into play in the time component balance.
 
There is supposed to be conservation of momentum in both x and y direction. The total momentum in y is zero, as it has no initial component in the y-axis.
 

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