- #1
Bassel AbdulSabour
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Why are the resultant's X and Y components of two forces equal the sum of the X and Y components of the two forces?
Force Resultant is equal to the sum of the components -- why?
- Context: High School
- Thread starter Bassel AbdulSabour
- Start date
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Discussion Overview
The discussion centers around the question of why the resultant's X and Y components of two forces are equal to the sum of the X and Y components of those forces. It touches on theoretical aspects of vector addition and principles in classical mechanics.
Discussion Character
- Technical explanation, Conceptual clarification, Debate/contested
Main Points Raised
- Some participants assert that the equality of the resultant's components follows from the addition laws of a vector space, suggesting a mathematical basis for the claim.
- Others reference the geometric interpretation of vector addition, indicating that the visual representation of vectors supports this equality.
- A participant mentions the Principle of Superposition as a foundational axiom in classical mechanics that underpins this relationship.
- There is a question posed about the implications of adding another force, indicating a potential shift in the dynamics of the system, though it does not directly address the original question.
- Another participant questions the nature of the forces involved, asking whether they pertain to pulling or pushing, which introduces ambiguity into the discussion.
Areas of Agreement / Disagreement
Participants express varying perspectives on the foundational principles behind the equality of the components, with some agreeing on the mathematical and geometric interpretations while others introduce different considerations. The discussion remains unresolved regarding the implications of additional forces and the nature of the forces in question.
Contextual Notes
Some assumptions about the nature of forces and the context of their application are not explicitly stated, which may affect the interpretations of the principles discussed.
- #2
berkeman
Admin
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Why not? What else would they be equal to?Bassel AbdulSabour said:
- #3
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Because these are the addition laws of a vector space: ##\begin{bmatrix}u_x\\u_y\end{bmatrix}+\begin{bmatrix}v_x\\v_y\end{bmatrix}=\begin{bmatrix}(u+v)_x\\(u+v)_y\end{bmatrix}\,.## This coincides with the geometric vector addition of arrows. But whatever you take as a definition, they should yield the same result.Bassel AbdulSabour said:
- #4
Tom.G
Science Advisor
Gold Member
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- #5
hmmm27
Gold Member
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Pulling or pushing ?
- #6
wrobel
Science Advisor
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It follows from one of the axioms of Classical mech.: the Principle of SuperpositionBassel AbdulSabour said:
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