Free body diagram of a compressed board between two boards

[Romain Nzebele]

Hello everyone. I find the following problem confusing.

A board sandwiched between two boards in the figure below weighs 95.5N. If friction exists between the middle and the compressing boards, draw the free body diagram of the middle board.

Below I attached the diagram found in the solution manual but I don't agree with it. Since the middle board is compressed by 2 boards, I believe the diagram should include two forces pointing toward the middle board in addition to the normal forces. Can someone explain to me why the solution manual omitted them? I will appreciate it very much.

 

[Chestermiller]

Please show us your version of the free body disgram.

 

[Romain Nzebele]

Hello, here is the body diagram I believe is correct. In my drawing Ff represents the force of friction, F represents the compression force, N represents the normal force, and Fg represents the weight of the middle board.

 

[Chestermiller]

What makes you think that N and F are separate and distinct entities? Why isn't the normal force N just the compression force F?

 

[Romain Nzebele]

The normal force results from the compression force. If there was no compression force, there will be no normal force. Since we have two boards compressing the middle block, it seems correct to me to represent these forces. Although I understand that the normal force and the compression force are equal in magnitude in this example.

 

[Chestermiller]

The normal force results from the compression force. If there was no compression force, there will be no normal force. Since we have two boards compressing the middle block, it seems correct to me to represent these forces. Although I understand that the normal force and the compression force are equal in magnitude in this example.

There is only one force. You can call it a compression force or you can call it a normal force, but either way, there is only one. They are one and the same thing.

 

[Romain Nzebele]

Okay, thank you for the feedback. I appreciate it.

 

[Chestermiller]

Okay, thank you for the feedback. I appreciate it.

My pleasure. By the way, Welcome to Physics Forums!