Unable to understand how these two forces are equal

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    Forces Torque
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Discussion Overview

The discussion revolves around understanding the conditions for static equilibrium of an object, specifically addressing the relationship between normal forces (N1 and N2), a horizontal force (f), and the weight (W) of the object. Participants explore the justification for equating these forces and the implications of their application at different positions on the object.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about how N1=f and N2=W can be proven, questioning the validity of comparing vertical and horizontal forces applied at different positions on the object.
  • Another participant asserts that the object is in static equilibrium, implying that all forces and moments must cancel each other out, but does not clarify how this leads to the specific relationships between the forces.
  • A participant reiterates the importance of balancing forces and moments, acknowledging the vector sum of forces but still questioning the direct comparison of forces applied at different locations.
  • One suggestion is made to relocate all forces to the center of mass of the object to simplify the analysis, although this raises questions about the validity of such an approach.
  • Another participant confirms that relocating forces to the center of mass is permissible when analyzing translational equilibrium, stating that the distances of external forces to the center of mass are irrelevant for static equilibrium conditions.

Areas of Agreement / Disagreement

Participants generally agree on the concept of static equilibrium and the need for forces and moments to balance, but there is disagreement and confusion regarding the justification for equating the forces N1, N2, f, and W, particularly in relation to their application points on the object.

Contextual Notes

Participants express uncertainty about the implications of relocating forces and the conditions under which such an analysis is valid, indicating a need for further clarification on the concepts of static equilibrium and force application.

tbn032
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In the solution given in the above image, I am unable to understand and prove why N1=f and N2=W. I have tried balancing the torque on different point but still unable to prove. Explain how N1=f and N2=W can be proved.
The justification for N1=f and N2=W which I have so far read is that it is just balancing the vertical force with vertical force and the horizontal force with horizontal force which are being applied on the object since the object is at equilibrium. My confusion with that is that the vertical and horizontal forces are being applied at different position of the object, how can they be directly compared so that the ladder is in equilibrium.
 
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The object is solid and strong enough to transfer these forces from one end to the other.
The object is in static equilibrium; therefore, all the forces and moments created by them must be cancelling each other.
All the reactive forces and moments counteract the force of the weight and any moment that it induces.

Without those being present, the weight force will acelerate the object downwards, without inducing any rotation.
Imagining that it could be possible, without the weight force, those reactive forces will move and rotate the object in diferent directions.
 
Lnewqban said:
The object is solid and strong enough to transfer these forces from one end to the other.
The object is in static equilibrium; therefore, all the forces and moments created by them must be cancelling each other.
All the reactive forces and moments counteract the force of the weight and any moment that it induces.
Since the object is at equilibrium, I understand that the vector sum N1+N2+W+f=0 and the vector sum of torque generated by these forces =0.but I do not understand how can the vertical forces be compared directly with vertical forces and horizontal force directly compared with horizontal force resulting in N1=f and N2=W even after they are being applied at different position.
 
Since the balance of moments is not confusing to you, just relocate all those forces to the center of mass of the object.
The actual location of each of those forces is only important for the moment it induces.
 
Lnewqban said:
jus relocate all those forces to the center of mass of the object.
Is relocation of forces which being applied at different position of the object to the center of mass of thr object which is at equilibrium allowed?if it is allowed, can you explain the concept behind it.
 
tbn032 said:
Is relocation of forces which being applied at different position of the object to the center of mass of thr object which is at equilibrium allowed?if it is allowed, can you explain the concept behind it.
Yes, you may do that when you are analyzing translational equilibrium only.
For this first equilibrium condition for the static equilibrium (no translational acceleration) of a rigid body, the distances of the external forces to the center of mass are irrelevant.

Please, see:
https://courses.lumenlearning.com/s...apter/12-1-conditions-for-static-equilibrium/

https://courses.lumenlearning.com/suny-osuniversityphysics/chapter/9-6-center-of-mass/
 
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