# Change in the direction of motion of the particle

• TheDispStud
In summary, the conversation discusses a problem involving a particle of mass m moving with velocity v1, leaving one half-space with a constant potential U1 and entering another half-space with a different constant potential U2. The objective is to determine the change in the direction of motion of the particle. The participants mention the context of the question, the Hamilton variational principle, and the potential similarity to the refraction of light. One participant expresses uncertainty about how to approach the problem despite having studied the theory. The other participant offers two ideas, refraction and Hamilton's principle, for potential solutions.
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.

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.

## 1. How does a change in the direction of motion of a particle occur?

A change in the direction of motion of a particle can occur due to a force acting on the particle, such as gravity or a collision with another object. This force causes the particle to accelerate in a different direction, resulting in a change in its motion.

## 2. Can a particle change direction without any external force?

No, according to Newton's first law of motion, an object at rest or in motion will remain in its state of motion unless acted upon by an external force. Therefore, a particle cannot change direction without an external force acting on it.

## 3. How does the mass of a particle affect its change in direction?

The mass of a particle does not directly affect its change in direction. However, a particle with a larger mass will require a greater force to change its direction compared to a particle with a smaller mass.

## 4. What is the difference between a change in direction and a change in velocity?

A change in direction refers to a change in the path or trajectory of a particle, while a change in velocity refers to a change in the speed or magnitude of the particle's motion. A change in direction can occur without a change in velocity if the speed remains constant, and vice versa.

## 5. How does friction affect a particle's change in direction?

Friction is a force that opposes motion and can cause a change in direction for a particle. For example, if a particle is moving on a surface with friction, the frictional force will act in the opposite direction of the particle's motion, causing it to change direction or slow down.

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