Replace with equivalent force-couple system?

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The discussion focuses on the concept of replacing a force with an equivalent force-couple system at specific points in a mechanical problem. The first problem involves replacing a 5 kN force with a force-couple system at point O, while the second requires replacing a 500 N force at point B. The key formula mentioned is C = r × F, where r is the vector from the point of interest to the force application point, and F is the applied force vector. The discussion also references the need to understand what constitutes a couple in mechanics. This information is crucial for solving the problems effectively.
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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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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
 
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