Components of a Plane of Separation Problem

[LCSphysicist]

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.

 

[Delta2]

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.

 

[LCSphysicist]

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.

 

[Delta2]

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.

 

[Delta2]

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.