# Resolution of Forces

I have been thinking about the logic of resolution of a main force into its component forces. Up to my stage i have just come across with the 2-dimension force which take x-axis and y-axis as their basis. So if they take y and x axis as the basis for the components of a single force, supposedly a force that acts perpendicularly to the horizontal x-axis or vertical y-axis should have no vertical components or horizontal components respectively.
Yet, while explaining the objects on an inclined plane with only its vertically downwards gravitational force(weight), people tends to resolve the only force which acts perpendicularly to the x-axis into 2 component forces, one of which acts parallel to the inclined plane while the other acts perpendicular to the inclined plane.Note that if we again resolve the 2 forces above into x-components and y-components, we find that these 2 forces have their x-components opposing each other and consequently cancel out ache other! it seems like logically these x-components originally are NOT EXISTED !! instead , we resolve them out and meanwhile they impart effects on the object as Action ! Mathematically, let's say we have a quantity 5. We say
5 = 10 - 5 , note that the quantity is never existed let's alone imparting any effects on the surrounding! the things we have now is only The 5! That's it. But why can we resolve in this way?? Maybe there is some misconception . Or is it because the force is actually an INTERACTION with the surrounding objects that will dependently affects the other objects in contact?? If it is true, meaning the force can be resolved in infinite ways as in figure 3. could somebody explain clearly for me?? Thanks you very much.

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10=5+5 or 1+9 or 15-5 or 1+2+2+5 or 1+2+2+3+2 ...........
Or 10=1+9=1+(6+3)
Likewise any vector can be resolved to any number of vectors.
Or a vector can be the sum of any number of vectors.

sophiecentaur
Gold Member
2020 Award
This thread deals with just the same question and it may be best to confine the discussion in just one thread or someone could miss some of the contributions.

Yes sir. Sorry because i faced problem in uploading photo as attachment. So there is a need for me to create another thread.

sophiecentaur