Change in the direction of motion of the particle

[TheDispStud]

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.

 

[PeroK]

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?

 

[TheDispStud]

Yes, we discussed about the Hamilton variational principle.

 

[PeroK]

Yes, we discussed about the Hamilton variational principle.

Does this question look similar to the refraction of light?

 

[TheDispStud]

This is an exercise of Analytical Mechanics :-)

 

[PeroK]

This is an exercise of Analytical Mechanics :-)

What would Hamilton say in this case?

 

[TheDispStud]

I really have no idea :(.. I mean I studied the theory but i do not see how to solve this problem!

 

[PeroK]

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.