Static friction(Impending motion)

[aerograce]

Homework Statement

A 100 kg block rests as shown in Figure on a wedge of negligible weight. Knowing that
the coefficient of static friction is 0.25 at all surfaces of contact, determine: (g = 9.81 m/s2)
a) the angle θ (degree) for which sliding is impending and
b) compute the corresponding value of the normal force (N) exerted on the block by the vertical wall.

Homework Equations

F=μN; ψ=arctanμ

The Attempt at a Solution

This solution is given by my professor, as attached below.

My doubt is:
Why we can make an assumption that all the contact surfaces are in the condition of impending? It can happen that only the wedge is in the impending motion while others may haven't reached their maximum static friction yet. Thank you so much for your help and message me if you cannot get what I mean, I will try to elaborate more. Thank you!

 

[NihalSh]

Why we can make an assumption that all the contact surfaces are in the condition of impending? It can happen that only the wedge is in the impending motion while others may haven't reached their maximum static friction yet. Thank you so much for your help and message me if you cannot get what I mean, I will try to elaborate more. Thank you!

It should be clear by geometry that if one body moves then the other has to move as well. Just imagine what will happen if the wedge moves slight but the upper body stays put. clearly the normal force from the wall/wedge will disappear and the upper body will tend to fall due to gravity. so when the wedge is just about to move, the upper body is just about to fall (but not free-fall). so both the bodies will have the tendency to move simultaneously.

I hope that helps.