What is the component of x axis along y axis and vise versa
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Alright. It's been long that I studied trigonometry and did Laws of Motion and Free Body Diagrams, and I was decent good at them, but somehow I am having trouble in understanding the following.
Note : I will try to understand the problem statement as well as I can without the use of figures and appropriate notations since I dont know how to use them. But if it is somehow unclear, please let me know.
I get that in an XY plane, if I have a straight line-segment y=x from (0,0) to (1,1) then it means that the component of that line is 1 unit along X axis and 1 unit along Y axis. i.e.
The length of line segment between (0,0) and (1,1) is 2–√. Now
Along X axis, value = Length⋅cos(θ) and with θ=45, we get value along X=1. Similarly, we get value along Y = Length⋅sin(θ)=1.
I understand the above concept.
Now, if I extend the same concept to Forces.
Free Body Diagram of a body on an inclined plane.
Referring to the above image, the force in the X direction is mgsin30 and in the Y is mgcos30.
As I understand, the above force is mgsin(30) along X is because of the following
Force = m⋅g. Mass is going to be the same in each direction so take that out. g is basically, distance (displacement) divided by time square. Now time is going to be the same in each direction so we can take that out too. This leaves us with
Force is proportional to Displacement(Distance). Now this is going to be different in different dimensions, that is why we derive the component along X and Y for distance. Hence the cos(30) and sin(30) that we see is because of the distance in the Force.
Firstly, am I correct in my understanding of the above?
Now, let's say our force was defined as.
F = (distance)(distance) instead of the usual MassAcceleration.
In this case, if I were to figure out the Force along X and Y, then my
F along X = F.sin(30).sin(30) instead of F.sin(30). F along Y = F.cos(30).cos(30) instead of F.cos(30). Right?