# Change in the direction of motion of the particle

• TheDispStud

#### TheDispStud

New poster has been reminded to show their work on schoolwork problems
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.

## Answers and Replies

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.

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 :-)

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!

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.