Can I treat blocks as a single axis of rotation?

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Discussion Overview

The discussion revolves around the treatment of two wooden blocks (A and B) pressed against steel plates under tension from a bolt, specifically whether these blocks can be treated as a single point for the purpose of calculating moments and forces. The scope includes theoretical considerations of mechanics and statics.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions if the blocks can be treated as a single point, suggesting that the forces acting on them might cancel out when summing moments.
  • Another participant argues that the forces do cancel out in certain moment sums, but acknowledges that this is not universally applicable across all calculations.
  • A later reply indicates that while the Na forces can cancel out in some contexts, they do not in others, particularly when considering the left plate alone.
  • There is a discussion about the validity of isolating parts of a rigid body for analysis, with some participants expressing confusion about this approach.
  • One participant mentions that in practice, treating a rigid body as a whole is more common, but acknowledges that in certain cases, isolating parts can be necessary.
  • Another participant reflects on their learning experience, noting that they have encountered concepts of shear and bending but are uncertain about their depth in future studies.

Areas of Agreement / Disagreement

Participants express differing views on whether forces can be ignored in certain calculations, and there is no consensus on the best approach to treat the blocks in this scenario. The discussion remains unresolved regarding the treatment of the blocks as a single point.

Contextual Notes

There are limitations in the assumptions made about the forces and moments, as well as the definitions of rigid bodies and their interactions. The discussion highlights the complexity of analyzing systems with multiple components.

Femme_physics
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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?
 
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Hi Fp! :smile:

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.
 
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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. :smile:

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.
 


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?
 


Femme_physics said:
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.
 


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 :smile:

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 :smile:

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 :wink:
 

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