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

  1. Sep 19, 2018 #1
    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?
  2. jcsd
  3. Sep 19, 2018 #2


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    Why not? What else would they be equal to?
  4. Sep 19, 2018 #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.
  5. Sep 19, 2018 #4


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    If one more person was added to the right end of the rope, which side would win?
  6. Oct 1, 2018 #5
    Pulling or pushing ?
  7. Oct 10, 2018 #6
    It follows from one of the axioms of Classical mech.: the Principle of Superposition
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