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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?
Why not? What else would they be equal to?Bassel AbdulSabour said: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.Bassel AbdulSabour said: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 SuperpositionBassel AbdulSabour said: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?
The force resultant is the net or overall force acting on an object, taking into account both magnitude and direction.
This is based on the principle of vector addition, where forces acting on an object can be broken down into their individual components. The sum of these components in each direction results in the total force acting on the object.
The direction of the force resultant is determined by the direction of the individual components. If the components are acting in the same direction, the force resultant will also act in that direction. If the components are acting in opposite directions, the force resultant will act somewhere in between.
Yes, as long as the components are acting on the same object and in the same direction. If the components are acting on different objects or in different directions, the force resultant will not necessarily be equal to the sum of the components.
No, the force resultant can never be greater than the sum of the components. This is because the force resultant takes into account both magnitude and direction, and the sum of the components already includes the magnitude of each individual force.