Components of a Plane of Separation Problem

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Homework Help Overview

The discussion revolves around a problem involving the components of a plane of separation, particularly focusing on the conservation of velocity components in relation to forces and potential energy. The subject area includes concepts from classical mechanics and potential energy fields.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the idea that the component of velocity parallel to the plane of separation is conserved due to the absence of forces acting in that direction. There is questioning about the nature of the field assumed in the problem, with some suggesting that the problem may be limited to fields perpendicular to the plane.

Discussion Status

Participants are actively discussing the implications of the forces acting on the particle and the nature of the potential energy in relation to the plane of separation. There is a recognition of differing interpretations regarding the fields that could influence the particle's motion.

Contextual Notes

Some participants note that the problem may assume a specific type of field, which could affect the conservation of velocity components. There is also mention of a negative sign in the force equation, indicating a need for careful consideration of the direction of forces and potential energy changes.

LCSphysicist
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Homework Statement
Be a particle with mass M and velocity v1 in a space with potential energy U1, it passes from this space to another with potential energy U2. What is the final direction of motion?
Relevant Equations
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I have no idea how to solve this problem. The solution says that the component parallel to the plane of separation is conserved, i am not sure why. Seems to me that in the problem was assumed a special field, but not a generic field.
 
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I can't be fully rigorous here but i think the particle will experience a force upon it and this force will be towards the direction of change of the potential energy, i.e perpendicular to the plane of separation. (because it is ##\vec{F}=\nabla U##.)

Hence the component parallel to the plane of separation has no forces , so this component of the velocity is conserved.
 
Delta2 said:
I can't be fully rigorous here but i think the particle will experience a force upon it and this force will be towards the direction of change of the potential energy, i.e perpendicular to the plane of separation. (because it is ##\vec{F}=\nabla U##.)

Hence the component parallel to the plane of separation has no forces , so this component of the velocity is conserved.
OBS: There is a negative sign, ##\vec{F}=-\nabla U##
But see, i think you agree with me there is fields that can produce a force parallel to the plane of separation. Seems the question is imagining a field perpendicular to the plane.
 
LCSphysicist said:
But see, i think you agree with me there is fields that can produce a force parallel to the plane of separation.
If there is such field, then the potential energy wouldn't be constant ##U_1## in one space and ##U_2## in the other space, the potential energy will also vary along the direction parallel to the plane of separation.
 
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LCSphysicist said:
Seems the question is imagining a field perpendicular to the plane.
This field is a consequence that the potential energy varies (from U_1 to U_2) in the direction perpendicular to the plane of separation.
 

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