Parallelogram Rule for combining forces (moments)

AI Thread Summary
When two forces act on an object, their lines can be projected to find a point of intersection, X, where no moment is created due to the forces being aligned. The resultant force, which combines the two forces, must also pass through point X and adhere to specific angle constraints. The discussion raises a question about the assumption made in mechanics literature that any force passing through X at a defined angle and magnitude can be considered the resultant force. This assumption lacks a formal proof, leading to uncertainty about its validity. While such proof may not be necessary for exams, the desire for clarity and understanding of foundational principles is emphasized.
HuaYongLi
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(2 dimensions.)
Given 2 forces acting on an object (not modeled as particle), you can project their lines so that you can find a point of intersection - X.
On this point of intersection exists no moment caused by the 2 forces since the line action makes 0 degrees with the forces. It follows that any resultant force representing the 2 forces must project through this point X also.
Combining this with the knowledge of the angle of a resultant force, you can find that any resultant force must be on a certain line. (This is the result of constraints of the resultant's angle and the fact it has go through a point X.)
This is basically how my Mechanics book explains the parallelogram rule.
I see that a resultant force must project through X and be at a certain angle.
What I don't get is that the book seems to assume that any force projecting through X and at certain angle and magnitude can be the resultant force.
Is there a proof of this?
 
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Are you ever going to need a proof of this obscurity?
 
No, not for any exams in the future. But I don't like assumptions, I'm OK if the assumption if fundamental or it can't be explained with my current knowledge.
 
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