How to Find the Speed of Particles from a Decay Event?

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SUMMARY

The discussion focuses on calculating the total energy and speed of decay particles from a parent particle of mass M = 7m. The decay results in two particles, each of mass m, moving in opposite directions along the y-axis. The total energy is determined to be (3.15x10^17 * m) Joules. The participants emphasize the importance of manipulating the equations E = mc² and \(\frac{u}{c} = \frac{pc}{E}\) to derive the speed of each particle without substituting numerical values for c.

PREREQUISITES
  • Understanding of relativistic energy equations, specifically E = mc²
  • Familiarity with momentum and its relation to velocity
  • Knowledge of particle decay processes in physics
  • Basic grasp of the concept of rest mass
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  • Learn how to apply conservation of energy and momentum in decay events
  • Explore advanced topics in relativistic kinematics
  • Investigate the implications of mass-energy equivalence in practical scenarios
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This discussion is beneficial for physics students, educators, and anyone interested in particle physics and decay processes, particularly those studying relativistic effects and energy conservation in particle interactions.

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Homework Statement


A particle of mass M = 7m decays into two particles of mass m - one travels in the '+y' direction, the other in the -y' direction.
In the rest frame of M, find the total energy(in terms of m) and the speed of each m.

Homework Equations



E = mc2

[tex]\frac{u}{c}[/tex] = [tex]\frac{pc}{E}[/tex]

The Attempt at a Solution



I figured out the mass of each of the small particles is half of the rest energy of the parent particle and it came out to be (3.15x10^17 * m)Joules. I just don't know how to manipulate the equations to find the speed of each m...?
 
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Welcome to the forum.
Your results will be more easier to understand if you don't insert values for c. Just keep c^2. standing there. There is no need for actual numbers as your are not given m anyway.
Your first relation can be written in a more explicit way relating total energy, rest mass and momentum.
Once you have the momentum you then can relate it to the velocity using your second.
 

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