Solving Relativity Homework: Mass & Speed

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Homework Help Overview

The problem involves two objects of mass m1, where one object is moving towards the other with speed u, and after a collision, they stick together and move as one mass with speed v. The discussion centers around determining the resulting mass and final speed after the collision, within the context of relativistic physics.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the conservation of energy and momentum in the context of an inelastic collision. There is a question about whether the second object is at rest, which influences the conservation equations. Some participants explore the implications of energy dissipation during the collision.

Discussion Status

Participants are actively engaging with the problem, considering different aspects of conservation laws. Guidance has been offered regarding the need for two equations to solve for the unknowns, but there is no explicit consensus on the correct approach or interpretation of the problem.

Contextual Notes

One participant asserts that there is no energy loss during the collision, which may affect the assumptions being made about energy conservation. The status of the second object's motion is also a point of clarification that remains unresolved.

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Homework Statement



We have two objects of mass m1. The first object is moving towards the second and has speed u. After they collide, they stick together and move as one mass with speed v.
Now what is the resulting mass and what is v?


Homework Equations






The Attempt at a Solution



I used that the energy is conserved and the equation E^{2}=(mc^{2})^{2}+(pc)^{2}

But I don't get the correct answer
 
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Is the second object at rest? Regardless of the answer to this question, you need to conserve momentum. This is an inelastic collision and unless you can account for the energy that is dissipated as heat during the collision, you cannot conserve energy.
 
the second one is at rest, and there is no energy loss.
 
OK, if there is no energy loss, then total relativistic energy is conserved. You need to say with an equation that

Energy before = Energy after

and with another equation that conserves momentum:

Momentum before = Momentum after

This will give you two equations and you have two unknowns, the final velocity and the final mass.
 

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