Parallelogram Rule for combining forces (moments)

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SUMMARY

The discussion centers on the Parallelogram Rule for combining forces in two dimensions, specifically addressing the conditions under which resultant forces act through a point of intersection, denoted as point X. It is established that at point X, no moment is generated by the two forces since their lines of action are aligned at 0 degrees. The conversation raises a critical question regarding the assumption that any force passing through point X at a specific angle and magnitude can be considered a resultant force, seeking clarification on the necessity of a proof for this assertion.

PREREQUISITES
  • Understanding of vector forces and their representation in two dimensions.
  • Familiarity with the concept of moments and their relation to force vectors.
  • Knowledge of the Parallelogram Rule in mechanics.
  • Basic principles of static equilibrium in physics.
NEXT STEPS
  • Research the mathematical proof of the Parallelogram Rule for combining forces.
  • Explore the implications of resultant forces in static equilibrium scenarios.
  • Study the graphical representation of forces and moments in two-dimensional mechanics.
  • Investigate the applications of the Parallelogram Rule in engineering and physics problems.
USEFUL FOR

Students of physics, mechanical engineers, and anyone studying mechanics who seeks a deeper understanding of force combinations and their resultant implications.

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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