Can someone kindly explain why we use Fn and not Mg to determine x & y component

Question

Can someone kindly explain why we use Fn and not Mg to determine x & y components and also what the Fapplied tells us?

Any advice will be greatly appreciated!

Problem 4.55 A small block of mass m rests on the sloping side of a triangular block of mass M which itself rests on a horizontal table as shown in the figure (Figure 1). Part A Assuming all surfaces are frictionless, determine the magnitude of the force vector F that must be applied to M so that m remains in a fixed position relative to M (that is, m doesn?t move on the incline). [Hint Take x and y axes horizontal and vertical.] Express your answer in terms of the given quantities and appropriate constants.

Explanation / Answer

for m

alog the plane
m*g*sintheta = m*a*costheta

a = g*tantheta

F = (M+m)*g*tan theta)

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