Point of application of resultant force from bound vector forces

AI Thread Summary
Determining the resultant force from bound vector forces requires understanding the point of application, as opposed to free vectors where the head-tail rule can be applied easily. In the case of bound vectors, the resultant force's location is calculated relative to a fixed point by summing the products of each force and its respective position. The discussion highlights the complexity of calculating the resultant force when multiple forces are applied at different points on an object. Clarification on the definitions of free and bound vectors is sought, indicating a need for deeper understanding of these concepts. The conversation emphasizes the importance of considering the point of application in force calculations.
fog37
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Hello Forum,

in the case of two or multiple free vectors, it is easy to determine graphically (head-tail rule) the resultant vector (magnitude and direction). The resultant vector is also a free vector.
A free vector is actually an infinite number of vectors with the same magnitude and direction but different points of application (equivalence class)

In the case of bound vectors, the point of application matters. For example, if an object has two different forces applied at different points on the extended object. How do we calculate the point of application or the line of action of the resultant force which is the sum of the two applied forces?

Is it possible?
thanks,
fog37
 
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You calculate the location of the resultant R relative to some fixed point x such that:

Rx = ∑Fixi

I don't really understand your definitions of free and bound vectors as I have never heard those terms before.
 
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