How can we prove that the forces acting on a body can form a closed-up

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Discussion Overview

The discussion revolves around the question of how to prove that the forces acting on a body can form a closed polygon, particularly in the context of equilibrium in physics. It explores theoretical aspects of force vectors and their relationships in equilibrium scenarios.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant suggests that if the forces do not form a closed polygon, there would be a resultant force, implying that equilibrium requires the forces to sum to zero.
  • Another participant points out that in cases with no forces or only two forces, the object could still be in equilibrium, but the force vectors would not form a polygon.
  • A different perspective is offered regarding the two forces case, where it is described as moving along a line and back along the same line, indicating a different conceptualization of equilibrium.
  • It is noted that the sum of the force vectors must equal a zero vector for an object to be in equilibrium, emphasizing the importance of vector addition in this context.

Areas of Agreement / Disagreement

Participants express differing views on the conditions under which forces can be considered to form a closed polygon, indicating that multiple competing perspectives remain without a clear consensus.

Contextual Notes

The discussion does not resolve the implications of having no forces or only two forces on the formation of a closed polygon, leaving assumptions about vector relationships and equilibrium conditions open to interpretation.

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How can we prove that the forces acting on a body can form a closed-up polygon?
 
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If they didn't, then there would be a resultant force. The magnitude of the resultant is zero only if the other forces form a closed polygon. The condition for equilibrium is, of course, no net force
 


If there are no forces or only two forces on the object then that object could be in equilibrium but the force vectors can't be connected to form a polygon.
 


Well you could think of the two forces case as going along a line and back along the same line.

The idea to remember is that the sum of the force vectors is a zero vector for the object in equilibrium.
 

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