Replace with equivalent force-couple system?

In summary, the conversation is about replacing forces with equivalent force-couple systems, where the force is represented by a vector and the couple is represented by the cross product of the position vector and the force vector. The attached picture shows two examples of this concept being applied.
  • #1
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Replace with equivalent force-couple system??

My book has one page on this and I do not understand what they want...

Please see attached picture for problems..

First one, left side, says replace the 5KN force with an equivalent force-couple system at O.

and

The second one says to replace the 500N force with a equivalent force-couple system at B.

Thanks a lot
 

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  • #2


I think what you want is C = rXF where r is the vector from the point in interest to the point where the force acts and F is the applied force vector.

C = r_x*F_y - r_y*F_x

See, "What is a couple?"

In

http://plus.maths.org/content/unspinning-boomerang
 

What is a force-couple system?

A force-couple system is a combination of forces and moments that act on an object. It consists of two or more forces that are parallel to each other and have the same line of action, along with a moment that is perpendicular to the plane containing the forces.

Why is it important to replace a force-couple system with an equivalent one?

Replacing a force-couple system with an equivalent one is important because it simplifies the analysis of a system. It allows us to treat the forces and moments acting on an object as a single resultant force and a single resultant moment, making calculations and predictions easier.

How do you determine if two force-couple systems are equivalent?

Two force-couple systems are considered equivalent if they produce the same external effects on an object, such as the same translational and rotational motion. This can be determined by comparing the resultant forces and moments of the two systems.

Can any force-couple system be replaced with an equivalent one?

Yes, any force-couple system can be replaced with an equivalent one. This is because the laws of physics, specifically the principle of transmissibility, state that the external effects of a system are independent of where the forces are applied. Therefore, the same external effects can be achieved with different force-couple configurations.

What are some applications of replacing a force-couple system with an equivalent one?

One common application of replacing a force-couple system is in the design and analysis of structures, such as buildings and bridges. By simplifying the forces and moments acting on a structure, engineers can determine the stability and safety of the structure more easily. It is also commonly used in the field of mechanics to analyze the motion and equilibrium of objects.

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