Force Resultant is equal to the sum of the components -- why?

  • #1

Main Question or Discussion Point

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?
 

Answers and Replies

  • #2
berkeman
Mentor
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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?
Why not? What else would they be equal to?
 
  • #3
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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?
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.
 
  • #4
Tom.G
Science Advisor
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upload_2018-9-19_18-13-19.jpeg


If one more person was added to the right end of the rope, which side would win?
 

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Pulling or pushing ?
 
  • #6
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?
It follows from one of the axioms of Classical mech.: the Principle of Superposition
 

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