Change in the direction of motion of the particle

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Homework Help Overview

The problem involves a particle of mass m transitioning between two half-spaces with different potential energies, U1 and U2, and seeks to determine the change in the direction of motion of the particle. The context is rooted in Analytical Mechanics and relates to concepts such as the Hamilton variational principle and potential energy changes.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relevance of the Hamilton variational principle and draw parallels to the refraction of light. There are inquiries about the theoretical framework and how it applies to the problem at hand.

Discussion Status

The discussion is ongoing, with participants expressing uncertainty about the application of their theoretical knowledge to the problem. Some have suggested ideas related to refraction and Hamilton's principle, but there is no clear consensus or resolution yet.

Contextual Notes

Participants have indicated a lack of clarity regarding the problem's solution and have noted their prior study of the relevant theories without being able to connect them to the current question.

TheDispStud
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Homework Statement
A particle of mass m moving with velocity v1, leaves a half-space in which the potential is a constant U1 and enters the other half-space, where the potential energy is a different constant U2.
Relevant Equations
Determine the change in the direction of motion of the particle.
Unfortunately, I have no idea about a possible solution.
 
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TheDispStud said:
Homework Statement:: A particle of mass m moving with velocity v1, leaves a half-space in which the potential is a constant U1 and enters the other half-space, where the potential energy is a different constant U2.
Relevant Equations:: Determine the change in the direction of motion of the particle.

Unfortunately, I have no idea about a possible solution.
In which context did this question come up? Have you studied the variational principle?
 
Yes, we discussed about the Hamilton variational principle.
 
TheDispStud said:
Yes, we discussed about the Hamilton variational principle.
Does this question look similar to the refraction of light?
 
This is an exercise of Analytical Mechanics :-)
 
TheDispStud said:
This is an exercise of Analytical Mechanics :-)
What would Hamilton say in this case?
 
I really have no idea :(.. I mean I studied the theory but i do not see how to solve this problem!
 
TheDispStud said:
I really have no idea :(.. I mean I studied the theory but i do not see how to solve this problem!
I've given you two ideas: refraction and Hamilton's principle. It's up to you to show us something based on those ideas.
 

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