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

Tags:
1. Sep 19, 2018

### Bassel AbdulSabour

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. Sep 19, 2018

### Staff: Mentor

Why not? What else would they be equal to?

3. Sep 19, 2018

### Staff: Mentor

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. Sep 19, 2018

### Tom.G

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

5. Oct 1, 2018

### hmmm27

Pulling or pushing ?

6. Oct 10, 2018

### wrobel

It follows from one of the axioms of Classical mech.: the Principle of Superposition