Point of application of resultant force from bound vector forces

However, to answer your question, yes, it is possible to calculate the point of application or line of action of the resultant force. This can be done by finding the sum of all the forces and then using the concept of moments to find the point where the resultant force can be applied. In summary, for two or multiple free vectors, the resultant vector can be easily determined using the head-tail rule. However, for bound vectors, the point of application matters and can be calculated using the concept of moments.
  • #1
fog37
1,568
108
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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  • #2
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.
 

1. What is the point of application of the resultant force from bound vector forces?

The point of application of the resultant force from bound vector forces is the single point where the combined effect of all the bound vector forces is concentrated. This is the point where the resultant force would act if it were a single force.

2. How is the point of application of resultant force determined?

The point of application of resultant force is determined by finding the vector sum of all the bound vector forces, taking into account their magnitude, direction, and line of action. The point of application can be calculated using mathematical equations or by graphical methods such as the head-to-tail method.

3. Can the point of application of resultant force change?

Yes, the point of application of resultant force can change depending on the magnitude and direction of the bound vector forces. If the bound vector forces are balanced, the point of application will remain the same. However, if the bound vector forces are unbalanced, the point of application will shift towards the direction of the stronger force.

4. Why is it important to know the point of application of resultant force?

Knowing the point of application of resultant force is important in understanding the overall effect of the bound vector forces on an object. It helps in determining the stability, equilibrium, and movement of the object. It is also crucial in engineering and design, as it allows for the proper placement and distribution of forces to ensure structural integrity.

5. Can the point of application of resultant force be outside of the object?

Yes, the point of application of resultant force can be outside of the object. This is often the case when dealing with distributed forces, where the resultant force acts at a different point than the object's center of mass. In such cases, the object may rotate or experience a net torque due to the offset point of application.

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