Compression Forces: Solve Homework Statement on P4.77 w/ Friction 0.663

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The problem involves calculating the compression forces acting on a center board weighing 95.5N, sandwiched between two other boards, with a coefficient of friction of 0.663. The friction forces must balance the weight of the board, leading to the equation 2F = 95.5N, resulting in F = 47.8N. The normal force, calculated as 72.1N, is essential for determining the compression forces, as it is the force exerted perpendicular to the surfaces in contact. The confusion arises from the distinction between vertical friction forces and horizontal normal forces, with the latter being considered as the compression forces in this scenario. Understanding that the normal forces act horizontally due to the vertical orientation of the surfaces clarifies the relationship between these forces.
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Homework Statement


The board sandwiched between the other two boards in Figure P4.77 weighs 95.5N. If the coefficient of friction between the boards is 0.663, what must be the magnitude of the compression forces (assumed to be horizontal) acting on both sides of the center board to keep it from slipping?

https://www.physicsforums.com/attachment.php?attachmentid=7118&d=1149969727


Homework Equations


fs< or = usn
F=ma


The Attempt at a Solution



So far, I've figured out that the friction forces must cancel out the weight of the board so I did:

2F=95.5 N
F=47.8N
and from that I figured out the normal force is 72.1 N:
47.8 N < or = 0.663n
72.1 N < or = normal force

I can't figure out how to solve for the compression forces. I assume there are two (one on each side), but I haven't a clue what my next step would be to solving it. Any input would be greatly appreciated.
 
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The normal force is the compression force.
 
Can you explain why though? The normal force is a vertical force, whereas it asked me for compression forces which it told me to assume were horizontal.
 
The normal force is perpendicular (normal) to the surfaces. Since the surfaces are vertical, the normal forces are horizontal in this case.

The friction force is vertical; the normal force is horizontal.
 

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