Friction problem of a block sandwiched between 2 surfaces

[vcl0124]

I don't know how to post a picture so I tried my best to describe my question in words.

X is horizontal, Y is vertical and there is no gravity effect.

There is a block is sandwiched by 2 surfaces (top surface and bottom surface). Both surfaces are fixed in X direction and the bottom surface is also fixed in Y direction. There is a downward force N pushing the top surface. The static friction coefficient between block and 2 surfaces are different (let's say u1, u2 and u1<u2). If I pull the block with a X direction force F. My understanding is I need F>N(u1+u2) to make the block start moving. For F<N(u1+u2), there will be static friction (F1 and F2) to cancel F and keep the block static. So my question is F1 and F2 will be in 1:1 ratio (F1 reach the static friction threshold first) or they will be in u1:u2 ratio (F1 and F2 reached the static friction threshold together)?

Looking forward to an answer. Thanks a lot!

 

[Baluncore]

Welcome to PF.

We are looking forward to an annotated diagram.
There is an "attach files" button below the edit area, that will load a .jpg file.

 

[vcl0124]

Does this help?

 

[Baluncore]

So my question is F1 and F2 will be in 1:1 ratio (F1 reach the static friction threshold first) or they will be in u1:u2 ratio (F1 and F2 reached the static friction threshold together)?

One surface will slip first, but the other will immediately come into play, so it will appear to be coincident.
The friction force, needed to move the block, will be; F = N * ( u1 + u2 ) .

 

[vcl0124]

One surface will slip first, but the other will immediately come into play, so it will appear to be coincident.
The friction force, needed to move the block, will be; F = N * ( u1 + u2 ) .

Thanks a lot! Let me assume some numbers to verify whether I understand you answer correctly. Assume N=1, u1=0.3 and u2=0.5. So the F1 and F2 vs F will be like A plot not B plot. Is it what you mean?

 

[Baluncore]

The CoF is not relevant, until something slips.
The block will settle, clamped symmetrically between the two surfaces, presumably with the same force from each surface.
Diagram A is more realistic.

 

[A.T.]

Thanks a lot! Let me assume some numbers to verify whether I understand you answer correctly. Assume N=1, u1=0.3 and u2=0.5. So the F1 and F2 vs F will be like A plot not B plot. Is it what you mean?View attachment 348569

The problem is statically indeterminate:
https://en.wikipedia.org/wiki/Statically_indeterminate

Note that you also need to satisfy moment equilibrium. So if the static friction forces were different, the normal forces on the block would have to redistribute to counter that. This could lead to edge loading, and the assumptions about the friction coefficient might not be valid anymore.