Finding Minimum Friction for Static Wedge: A Free Body Analysis Approach

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To determine the minimum coefficient of friction (μ) required for a static wedge to remain stationary, a free body analysis is essential. The discussion emphasizes identifying all forces acting on the wedge, including tension forces F1 and F2. It clarifies that the wedge has mass M and a smooth surface, indicating no friction between the wedge and block M1. Participants suggest conducting a thorough analysis of the forces and accelerations while assuming the wedge is stationary. The goal is to accurately calculate the forces exerted by tension on the wedge to find the necessary friction coefficient.
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Homework Statement


Find the minimum μ required between wedge M and ground so that it stays static.


Homework Equations



I already found the equations for accelerations and tension (when μ is big).
Do I need them?

The Attempt at a Solution


I would like to know whether I found all the forces acting on the wedge. (see attachment)
Which component should I use for the green arrow force?
NB the red forces act on the wedge
 

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Is the wedge massless? Is there friction between the wedge and M1?
 
no, wedge has mas M, and its surface it's smooth.
 
F1 and F2 are the tension, yes?
 
I think so.
 
Go through the usual free body analysis on the two blocks (assuming the wedge is stationary) to find the acceleration and the tension. Then figure out the forces the tension applies to the wedge.
 

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