MHB Free Body Diagram Explained: Why is Right FBD Upward?

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The discussion focuses on understanding free body diagrams (FBDs) and their components, particularly why one member's FBD includes an upward force. This upward force is explained through Newton's third law, which states that forces act in equal and opposite pairs. Participants clarify that for vertical forces, if one force is directed downward, the opposing force must be upward. Additionally, a question arises regarding the number of unknown forces in the diagrams, leading to the clarification that given coefficients of friction can reduce the number of unknowns. Overall, the conversation emphasizes the principles of force interactions and their representation in FBDs.
Drain Brain
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Can you explain why the free body diagram of each members are as shown? I kind of understand why the FBD of the member on the left is drawn as shown. But the FBD on the right is confusing, Why does it have a component in Y (upward) direction?
thanks!
 

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Drain Brain said:
Can you explain why the free body diagram of each members are as shown? I kind of understand why the FBD of the member on the left is drawn as shown. But the FBD on the right is confusing, Why does it have a component in Y (upward) direction?
thanks!

Hi Drain Brain!

It's Newton's 3rd law: whenever a body pushes against another body, that body pushes back with an equal and opposite force.
For the horizontal forces that should be intuitive.
For the vertical forces we pick one down, meaning the other must be up.
 
I like Serena said:
Hi Drain Brain!

It's Newton's 3rd law: whenever a body pushes against another body, that body pushes back with an equal and opposite force.
For the horizontal forces that should be intuitive.
For the vertical forces we pick one down, meaning the other must be up.

Hi I Like Serena! Now I understand!

There's another thing I want to ask, my book says that there are 3 unknown forces on each member, but I see 4 unknowns. Can you tell me why that is?
 
Drain Brain said:
Hi I Like Serena! Now I understand!

Good!

There's another thing I want to ask, my book says that there are 3 unknown forces on each member, but I see 4 unknowns. Can you tell me why that is?

They're probably jumping a bit ahead.
Since the coefficients of friction are given, that gives us the extra equation $F_A=\mu_A N_A$, effectively eliminating $F_A$ as an unknown.
 
I like Serena said:
Good!
They're probably jumping a bit ahead.
Since the coefficients of friction are given, that gives us the extra equation $F_A=\mu_A N_A$, effectively eliminating $F_A$ as an unknown.

Do you mean to say that the 3 unknown forces my book is referring to are the components bx, by and the normal force Na?
 
Drain Brain said:
Do you mean to say that the 3 unknown forces my book is referring to are the components bx, by and the normal force Na?

That's what I expect yes.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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