Understanding Velocity Vector Components in a Gas Molecule Bouncing Back?

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Discussion Overview

The discussion revolves around the decomposition of a velocity vector into its x, y, and z components, particularly in the context of a gas molecule bouncing off a y-z plane. Participants explore the mechanics of vector resolution in three dimensions and the behavior of velocity components during collisions.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant asks how the velocity vector can be broken into components and why only the x component changes after bouncing off a y-z plane.
  • Another participant explains that when bouncing off a vertical wall (y-z plane), only the component normal to the plane reverses, while the other components remain unchanged.
  • There is a discussion about the ability to resolve vectors into components in three dimensions, with some participants affirming that all vectors can be resolved into three linearly independent components.
  • One participant expresses familiarity with resolving vectors only in two dimensions, prompting clarification that three-dimensional resolution is also possible.
  • Participants discuss the implications of vectors that lie in two dimensions and how components are affected when a vector extends out of the plane of interest.
  • Clarifications are made regarding how to determine the components of a vector by dropping normals to the coordinate axes from the tip of the vector.

Areas of Agreement / Disagreement

Participants generally agree on the mechanics of vector resolution and the behavior of components during a bounce, but there are varying levels of understanding regarding the application of these concepts in two versus three dimensions.

Contextual Notes

Some participants express uncertainty about resolving vectors that are not fully represented in three-dimensional space, indicating potential limitations in understanding how components relate when visualizing vectors in different planes.

gracy
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can someone help me .In this video from 2.00 to 3.00 how the velocity vector drawn with red color can be broken into x-y-z components and why after bouncing back only x component of velocity changed and y ,z components remained same?
 
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gracy said:
can someone help me .In this video from 2.00 to 3.00 how the velocity vector drawn with red color can be broken into x-y-z components and why after bouncing back only x component of velocity changed and y ,z components remained same?

It's bouncing off a y-z plane. Just bounce a ball off a vertical wall, and see which components reverse and which components remain the same. Only the component normal to the plane reverses.

Chet
 
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Chestermiller said:
It's bouncing off a y-z plane. Just bounce a ball off a vertical wall, and see which components reverse and which components remain the same. Only the component normal to the plane reverses.

Chet
how the velocity vector drawn with red color can be broken into x-y-z components ?
Chestermiller said:
It's bouncing off a y-z plane.
how you came to know that?
 
gracy said:
how the velocity vector drawn with red color can be broken into x-y-z components ?
You can always resolve a vector into components.

how you came to know that?
You can see in the figure that the wall that it bounces off is parallel to the y-z plane.

Chet
 
Chestermiller said:
You can always resolve a vector into components.
i know how to resolve vectors but only in 2 dimensions.
 
gracy said:
i know how to resolve vectors but only in 2 dimensions.
Well, it can be done in 3 dimensions too.

Chet
 
Chestermiller said:
Well, it can be done in 3 dimensions too.

Chet
can all vectors be resolved in 3 dimensions?
 
gracy said:
can all vectors be resolved in 3 dimensions?
Yes. In 3D space, all vectors can be resolved into combinations of 3 linearly independent components.

Chet
 
Chestermiller said:
Yes. In 3D space, all vectors can be resolved into combinations of 3 linearly independent components.

Chet
but only vectors which are in 3d ,for example this kind of vector (in the image below) can only be resolved in 2d i.e only with two perpendicular component.right?
images?q=tbn:ANd9GcSKd7xZd5V-4P4sk36mIENHU_m4sYE0QL5Pm8pa6md9cAnq5Z6j.jpg
 
  • #10
gracy said:
but only vectors which are in 3d ,for example this kind of vector (in the image below) can only be resolved in 2d i.e only with two perpendicular component.right?
images?q=tbn:ANd9GcSKd7xZd5V-4P4sk36mIENHU_m4sYE0QL5Pm8pa6md9cAnq5Z6j.jpg
All that means is that the component out of the paper is zero.

Chet
 
  • #11
Chestermiller said:
All that means is that the component out of the paper is zero.

Chet
ok if any vector is coming out of page ,what it's x component would be?i can only imagine it in y z plane.
 
  • #12
gracy said:
ok if any vector is coming out of page ,what it's x component would be?i can only imagine it in y z plane.
If the vector is through the origin, then you drop a normal from its tip to each of the three coordinate axes to get its x, y, and z components.

Chet
 
  • #13
Chestermiller said:
its tip
From Tip of vector which has to be resolved?
 
  • #14
gracy said:
From Tip of vector which has to be resolved?
Yes.
 

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