Can I treat blocks as a single axis of rotation?

[Femme_physics]

Can I treat "blocks" as a single axis of rotation?

http://img171.imageshack.us/img171/2245/blockthingy.jpg


Basically those A and B wooden blocks are pressed against two hardened steel plates through the tension of the bolt. My question, can I treat these blocks as a single point? For instance, If I do sum of all moment on A, can I ignore Fsa (on both sides) and Na (on both sides), saying their arm is zero because it's considered a single point?

 

[I like Serena]

Hi Fp!

What do you mean by treating these blocks as single points?You can ignore Fsa (on both sides) and Na (on both sides), because those forces cancel each other out.This means that on any sum of forces, Fsa would be added and Na would be subtracted, so the net result would be zero.

And it means that on any sum of moments, Fsa times distance would be added and Na times the same distance would be subtracted, so the net result would be zero.

 

[Femme_physics]

Well, I just glimpsed at the solution manual which appears to contradict what you're saying. I tried taking a webcam pic of the solution:

http://img339.imageshack.us/img339/3710/this1o.jpg

http://img52.imageshack.us/img52/5167/this2f.jpg

See what I mean?

They did sigma Mb = 0 ; 0.225 NA - 0.135Fc = 0
Na = 300 [N]

So no forces cancel each other out!

 

[I like Serena]

I can see I was a bit hasty in saying those forces cancel out. :shy:

If you do a moment sum for the entire system, the Na forces cancel each other out.
If you do a moment sum on block A, the Na forces cancel each other out.
If you do a moment sum on the left plate, you have only one Na force, so indeed it is not canceled.Back to your question, that I understand a little better now.

The Na and Fsa forces act on a surface, but they can be treated as acting on a point in the middle of that surface.
(Actually that point should be in the middle of where the surfaces "touch", and not in the middle of the block.)

For your moment sum you can choose this same point, meaning the Na distances to this point are indeed zero. But one of the Fsa forces will have a distance of zero, while the other one does not.

 

[Femme_physics]

If you do a moment sum on the left plate, you have only one Na force, so indeed it is not canceled.

It's kinda weird! I didn't know it was possible! You can just take a shape, and only look at one plate of it? I thought we always look at the entire shape! It's not a truss, it's not a frame, what gave us the right to isolate a part of this object and only look at its left plate?

 

[I like Serena]

It's kinda weird! I didn't know it was possible! You can just take a shape, and only look at one plate of it? I thought we always look at the entire shape! It's not a truss, it's not a frame, what gave us the right to isolate a part of this object and only look at its left plate?

You can always look at as little a part of a body that you want.
However, in practice it's not very useful to look at only a part of a specific rigid body, so that is why Statics was invented, to treat rigid bodies as complete entities.

Do note that in a later course, you'll probably be learning that what you thought was a "rigid" body, is not rigid after all, but it can bend, shear and break.
The body is then treated as a lot of very small bodies that are connected.

If different rigid bodies can rotate or shift relative to each other, that must be considered and they must be treated separately, so you should draw an FBD for it.

Looking only at the left plate is no different than looking at a single body in a system that is connected by joints.

 

[Femme_physics]

Looking only at the left plate is no different than looking at a single body in a system that is connected by joints.

Ah, gotcha, brilliant

It's hard to grasp that you need to isolate one part to get the answer in this exercise. But I'm glad this method has been approved by you

Also, I saw some of hibbeler mechanics of material, and we actually had some basic stuff in calculating shear/bend/break stuff, but only 1 or 2 exercises that were promised not to be on the final test. So, unsure whether how deep we'll delve into the calculations of it, though I hope we will!

Thanks