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

[Bassel AbdulSabour]

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?

 

[berkeman]

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?

 

[fresh_42]

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.

 

[Tom.G]

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

 

[hmmm27]

Pulling or pushing ?

 

[wrobel]

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