I think I found a flaw in vector combination theory

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Discussion Overview

The discussion revolves around the validity of conventional vector combination theory, particularly in the context of graphical vector addition and its applicability to scenarios involving opposing vector components. Participants explore the implications of vector addition in various physical contexts, including force analysis and internal force equilibrium.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant argues that conventional vector addition neglects portions of vectors when they have opposite-facing components, suggesting that the theory is only valid for parallel vectors.
  • Another participant dismisses the initial claim, asserting that the conventional method of vector addition is sound.
  • A different participant supports the initial claim by stating that the graphical representation provided is accurate, but questions the application of vector addition in the context of internal forces and deformation physics.
  • One participant emphasizes that while conventional vector addition works on a macro scale, it may not adequately represent internal forces in certain physical scenarios, such as finite element analysis (FEA).
  • Another participant counters that the conventional method of vector addition is the only logical approach, criticizing the suggestion that the order of addition could yield different results.

Areas of Agreement / Disagreement

Participants express disagreement regarding the validity of conventional vector combination theory. Some support the critique of the theory, while others defend the conventional approach as sound and necessary.

Contextual Notes

The discussion highlights limitations in the applicability of conventional vector addition, particularly in specific physical contexts like internal force equilibrium and deformation physics, but does not resolve these limitations or assumptions.

BreezyLeaf
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I've seen it often taught that the combination of two vectors is their graphical sum, but I think that there is a problem with this, in that if the vectors have opposite-facing components, then there are portions of the vectors completely neglected by the calculation. The idea seems to only be valid for parallel vectors, a case so narrow-in-applicability as to often be irrelevant.

Here's what I think is flawed about conventional vector combinations:

attachment.php?attachmentid=72400&stc=1&d=1408836408.jpg


Please let me know your impression. Thank you.
 

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"I think I found a flaw in vector combination theory"

No you didn't
 
Your second set of drawings shows perfectly well why your theory is flawed. You are correct up to that point then you wander off into lala land.

Your "preposterous" drawing is exactly right.
 
Think FEA not motion...

phinds said:
Your "preposterous" drawing is exactly right.

I know that that is the conventional assumption, but it's on a macro scale.
Assuming the vectors are forces, the 'preposterous' vector might be a theory in the sum force on the tendency of a piece as a system. But in terms of internal-force-equilibrium, the vectors are much different than just the assumed sum. While the assumption might work well in terms of continuum physics, in the realm of deformation-physics, it seems completely inadequate.

Let's take a ball for example: If there are 10-'forceunit' pushing up on the ball, and 10-'forceunit' pushing down. The vector would assume there is 0-'forceunit' on the ball. Preposterous, because in terms of FEA, Volume-Physics and rigidity, the ball has to withstand a lump input of '20' and the vector assumptions says '0'.
 
BreezyLeaf said:
I know that that is the conventional assumption, but it's on a macro scale.
It is not a "conventional assumption", it is the only way to add vectors that makes any sense.

If you add -1 and 1, the result is -1+1=1+(-1)=0, but you suggest that the result should be -2 or +2, depending on the order in which you add them (!). Sorry, that makes absolutely no sense.
 

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