What is the correct calculation for total kinetic energy after the collision?

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SUMMARY

The discussion centers on calculating the total kinetic energy after a collision involving two particles, one with a mass of 1 MeV/c² and kinetic energy of 2 MeV, and another stationary particle with a mass of 2 MeV/c². The key points include the conservation of momentum and energy equations, specifically p_0=(m_1'+m_2')vγ and E_0=(m_1'+m_2')c²γ. The participant successfully solved for the speed and total energy of the first particle, but encountered difficulties in determining the total kinetic energy after the collision.

PREREQUISITES
  • Understanding of relativistic momentum and energy conservation principles
  • Familiarity with the concepts of mass-energy equivalence (E=mc²)
  • Knowledge of Lorentz factor (γ) in relativistic physics
  • Basic algebraic manipulation skills for solving equations
NEXT STEPS
  • Study the derivation and application of the Lorentz factor (γ) in collisions
  • Learn how to apply conservation laws in relativistic collisions
  • Explore examples of inelastic collisions in relativistic physics
  • Investigate the relationship between kinetic energy and momentum in particle physics
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Students and educators in physics, particularly those focusing on relativistic mechanics and collision theory, will benefit from this discussion.

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Homework Statement


••• A particle of mass 1 MeV/c2 and kinetic
energy 2 MeV collides with a stationary particle of mass
2 MeV/c2. After the collision, the particles stick together. Find
(a) the speed of the first particle before the collision, (b) the
total energy of the first particle before the collision, (c) the ini-
tial total momentum of the system, (d) the total kinetic energy
after the collision, and (e) the mass of the system after the
collision.

I could do (a,b) and (c).

My doubts are on (d).
I know momentum must be conserved.
So,

[tex]p_0=(m_1'+m_2')v\gamma[/tex]

Total energy must be conserved too:

[tex]E_0=(m_1'+m_2')c^2\gamma[/tex]


If I work out these too expressions, I don't find the correct value. :smile:

What am I doing wrong.

Homework Equations





The Attempt at a Solution

 
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Show more work.
What did you do when you worked these out?
 
I solved for m1'+m2'. And substituted.
 

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