Mechanics of Couples: How to Counteract Rotational Forces in a System?

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Discussion Overview

The discussion revolves around the mechanics of couples and how to counteract rotational forces in a system, specifically in the context of a homework problem involving a force and a couple. Participants explore the concepts of statically equivalent force systems and the implications of force direction and magnitude.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • One participant presents a homework problem involving a force F1 and its replacement by a force F2 and a couple C, seeking help on how to approach the problem.
  • Another participant emphasizes the need to clarify what has been attempted and where the confusion lies to provide effective assistance.
  • Some participants discuss the nature of a couple, noting that it consists of two forces acting in opposite directions, but express confusion about replacing a single force with a couple and another force.
  • There is a suggestion that the second force F2 should be parallel to the original force F1, rather than opposite, which leads to further confusion for one participant.
  • A hint is provided indicating that adding a force and an equal and opposite force can lead to a clearer understanding of the system.
  • One participant uses an analogy involving pushing a heavy object to illustrate the concept of torque and the need to counteract rotational effects when applying force at a different point.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the replacement of forces and the concept of couples. There is no consensus on how to proceed with the problem, and confusion persists among some participants about the correct approach.

Contextual Notes

Participants have not fully resolved the mathematical steps required to determine the magnitude and direction of force F2 or the characteristics of the couple C. The discussion reflects a range of assumptions and interpretations regarding the mechanics involved.

sean777
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Homework Statement


The question reads:
F1 is 120kn at A. B is located 300mm from A. f1 is inclined at 40 degrees to the x axis. Force one may be replaced by a statically equicilant force system consisting of a single force f2 and a couple c. Let force f2 pass through b


It asks you to
B) determine the plane, magnitude and direction and inclination of force f2
C) determine the plane of the couple c, it's sense of rotation and the magnitude of it's resultant

No idea where to start with this. Help would be greatly appreciated
 

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welcome to pf!

hi sean777! welcome to pf! :wink:

show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
I understand that a couple is made of 2 forces acting in opposite directions but how to replace this force with a couple and another force is what is confusing me.
 
well, forget the couple for the moment …

what do you think the magnitude and the direction of the second force are?​
 
I imagine it would be 120kn to the left inclined at 40 degrees to the x-axis with the line of action passing through B
 
sean777 said:
I imagine it would be 120kn to the left inclined at 40 degrees to the x-axis with the line of action passing through B

ah, no …

it should be parallel to the original force (down and to the right), not opposite to it

ok, now subtract the orignal force from that to get the couple :wink:
 
tiny-tim said:
ah, no …

it should be parallel to the original force (down and to the right), not opposite to it

ok, now subtract the orignal force from that to get the couple :wink:

And now I'm completely confused and don't know what to do
 
The hint is: you have to add a force to the system, and then add to it an equal and opposite force. You then have three forces. You're neally there.
 
Imagine a heavy steel bridge strut lying in the middle of the welding factory floor. To slide it out of the way, you push against it. But unless you push at the exact right spot, not only will it slide along the floor, but it will also rotate. But it might happen that this optimum spot to push against (point A) is just where the paint hasn't dried yet. So you move along a bit and push with the same force[/color][/color] (i.e., same magnitude & direction) but where the paint is safely dry (point B). This gets the beam moving all right, but to stop it rotating you have to arrange for someone to exert a torque to cancel the turning movement you are now causing. How to counteract the torque you are causing by pushing at point B instead of point A? How to describe what must be done to cancel it out? One way is to express it as a pair of forces about point B.
 
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