Answer:
A) N = W cos θ , B) fr = W sin θ, C) N = W cos θ
Explanation:
To find the required expressions, let's make a free body diagram of the block, see attached.
In the problem of inclined plane the reference system used the x axis is parallel to the plane and the y axis is perpendicular
In this reference system the only force that we must decompose is the body weight F_w = W) for this we use trigonometry
Note that the angle of the plane is equal to the angle between the axis and the weight, therefore
sin θ = [tex]W_{x}[/tex] / W
cos θ = [tex]W_{y}[/tex] / W
[tex]W_{x}[/tex] = W sin θ
[tex]W_{y}[/tex] = W cos θ
B) Let us write Newton's second law for each axis, in this case as the block is still the acceleration is zero
X axis
fr - [tex]W_{x}[/tex] = 0
fr = W sin θ
A) Y Axis
N - [tex]W_{y}[/tex] = 0
N = W cos θ
C) N = W cos θ