Help with determining other mass of a relativistic collision

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SUMMARY

The discussion focuses on a relativistic collision problem involving two objects with masses of 3.000 u and 4.000 u, moving at velocities of 0.8c and 0.6c, respectively. After the collision, one object has a mass of 6.000 u and is at rest, while the mass of the second object needs to be determined. The conservation of energy and momentum principles are essential for solving this problem, leading to the equations \(\gamma m_1 c^2 + \gamma m_2 c^2 = \gamma m_3 c^2 + \gamma m_4 c^2\) and the need to calculate the corresponding gamma factors for each mass. The discussion emphasizes the importance of applying both conservation laws to find the unknown mass.

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  • Understanding of relativistic physics concepts, specifically mass-energy equivalence.
  • Familiarity with the conservation of momentum and energy principles.
  • Knowledge of gamma factor calculations in special relativity.
  • Ability to solve algebraic equations involving multiple variables.
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  • Study the derivation and application of the gamma factor in relativistic equations.
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dgresch
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Homework Statement


A 3.000 u (1 u = 931.5 MeV/c2) object moving to the right through a laboratory at
0.8c collides with a 4.000 u object moving to the left through the laboratory at
0.6c. Afterward there are two objects, one of which is a 6.000 u object at rest.
Determine the mass of the other object

Homework Equations


CONSERVATION OF ENERGY
[itex]\gamma[/itex]m1c2+[itex]\gamma[/itex]m2c2=[itex]\gamma[/itex]m3c2+[itex]\gamma[/itex]m4c2

The Attempt at a Solution


Each gamma is different because of different speeds but for the purpose of time management and the fact that past this I don't know what to do, I left them as gamma.
[itex]\gamma[/itex]2794.5Mev+[itex]\gamma[/itex]3726MeV=5589Mev+[itex]\gamma[/itex]m4c2

Am I supposed to assume both objects are at rest? Doesn't seem like that would be the case because the other object would just be 1u. Any thoughts anyone?
 
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You will also need to apply conservation of momentum. Together with conservation of energy, you will have two equations for the two unknowns [itex]\gamma_4, m_4[/itex].
 

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