can somebody site me an example of practical application of resolution of forces?

Answer 1

Imagine the trusses making up the structure of a bridge or a tall building or any structure that has to hold up a great deal of weight. Those trusses ("two-force members") are either in tension or compression. The materials that make up each truss will only be able to hold a certain amount of weight before breaking. It is important to know how much force they will be required to hold in order to pick the appropriate truss. We do that by resolving the weight of the structure along two dimensions (horizontal and vertical, for example) and then distribute that weight appropriately on the trusses. We know how to distribute the weight based on the angles that the trusses make with the horizontal and vertical axes. Once we have distributed the weight in these two perpendicular directions to each truss, we can then calculate the total amount of force directed along the truss. This tells us how much force the truss needs to support and thus gives us an idea on what material should be used.

On top of this, some trusses in a building may add nothing to the support. After doing this analysis, we may want to remove this "0-force members."

Some structures can replace rigid trusses with cables that can only support tension; these cables are simply loose and contribute nothing to the structure when in compression. If the building will never be in a configuration that will put these cables in tension, the cables can be removed. Otherwise, the cable material/type should be chosen so that it can withstand the tension load. The total tension directed along the cable comes from the resolution of forces.

Resolving forces into orthogonal directions is fundamental to static analysis (and design) of structures. More generally, resolving things into orthogonal components is fundamental to analysis (and design) of many things.

In fact, the RF frequency spectrum is simply the resolution of light into uncountably many orthogonal directions (i.e., frequencies).

Similarly, position and momentum are two orthogonal directions of quatum mechanical wave functions, and that's why a particle's wave function can never be resolved into a single position and momentum at the same time. Saying that you know a particle's position and momentum with absolute certainty is like saying that something is traveling 100% north and 100% east at the same time. It just doesn't make sense.