Direction of forces on a uniform catilever

[Sunwoo Bae]

Homework Statement

shown in the text

Relevant Equations

none

The following is my work:

The following is the answer given:

While I took FA as the pivot point, the answer seem to have taken FB as the pivot point, and got negative value for FB.
As the result, the answer seems to have used the tensile strength for FA and compressive strength for FB (opposite of what I did).
In this case, how do you know which pivot I should take and whether FA or FB should get a negative value?

Thank you for your help!

 

[haruspex]

While I took FA as the pivot point, the answer seem to have taken FB as the pivot point, and got negative value for FB.

I think you mean the answer text got a negative value for FA.
It shouldn’t matter which point you take moments about, you should get the same answer. Indeed, you do seem to have the same answers for the forces.
Your error is in deducing which is compressive and which tensile. A positive (upward) force from the support means the support is under compression.

 

[Sunwoo Bae]

I think you mean the answer text got a negative value for FA.
It shouldn’t matter which point you take moments about, you should get the same answer. Indeed, you do seem to have the same answers for the forces.
Your error is in deducing which is compressive and which tensile. A positive (upward) force from the support means the support is under compression.

Can you explain why a positive force from the support means the support is under compression? I thought the tensile stress is the one in which materials are subjected to stretching, and the compressive stress is the one that forces act inwardly on the object.

If the positive value indicates compression, then what would be the corresponding downward force in the system?
Thank you!

 

[Sunwoo Bae]

I think you mean the answer text got a negative value for FA.
It shouldn’t matter which point you take moments about, you should get the same answer. Indeed, you do seem to have the same answers for the forces.
Your error is in deducing which is compressive and which tensile. A positive (upward) force from the support means the support is under compression.

And I'm quite confused because this is the part of the explanation in the answer sheet (the photo I attached above).
The way I understood from this explanation is that point A is under tension because FA is directed upward, and point B is under compression because FB is directe downwards.

 

[haruspex]

View attachment 283737
And I'm quite confused because this is the part of the explanation in the answer sheet (the photo I attached above).
The way I understood from this explanation is that point A is under tension because FA is directed upward, and point B is under compression because FB is directe downwards.

You seem to be confusing the force the support applies to the cantilever with the force the cantilever exerts on the support. Action and reaction are equal and opposite.
FB acts upwards (positive) on the cantilever, which means the cantilever is pressing down on support B, putting it in compression.
FA acts downwards (negative) on the cantilever, which means the cantilever is pulling up on support A, putting it in tension.

 

[Sunwoo Bae]

You seem to be confusing the force the support applies to the cantilever with the force the cantilever exerts on the support. Action and reaction are equal and opposite.
FB acts upwards (positive) on the cantilever, which means the cantilever is pressing down on support B, putting it in compression.
FA acts downwards (negative) on the cantilever, which means the cantilever is pulling up on support A, putting it in tension.

Thank you for helping me out. That cleared up my confusion!