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?
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?