Finding an Equivalent Couple for the Forces in the Figure

In summary, the conversation discusses a homework question asking to replace a couple shown in a figure with an equivalent couple acting at points A and B. The student is unsure of what the question is asking for and provides a possible solution, but questions the validity of the 6 marks assigned to the question. The expert suggests having a pair of opposite parallel forces through A and B with the same Fd to solve the question. However, the expert also notes that the question may be poorly worded and drawn.
  • #1
mehsham
1
0

Homework Statement



The forces shown in the Figure below form a couple. Replace the couple shown with an equivalent couple acting at points A and B. Please see figure

Homework Equations



Couple force moment equation is M = Fd (take only one of the two force vectors and distance between them)

The Attempt at a Solution



Actually, I don't understand what they want. I was just going to do M = 15 lb x(12in) but this question is for 6 marks so I'm definitely missing something. Please advice if you know what this question means.

Thank you,
Faisal Shibli
 

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  • #2
Welcome to PF!

Hi Faisal! Welcome to PF! :smile:
mehsham said:
The forces shown in the Figure below form a couple. Replace the couple shown with an equivalent couple acting at points A and B. Please see figure
…
… this question is for 6 marks so I'm definitely missing something. Please advice if you know what this question means.

The 6 marks do seem strange. :confused:

The question seems to be asking for a pair of opposite parallel forces through A and B …

which could be at any angle …

with the same Fd.
 
  • #3
Looks to me like a badly worded and badly drawn question. My response was to have a couple at A and B with forces perpendicular to AB. I wonder if I would have passed.
 

Related to Finding an Equivalent Couple for the Forces in the Figure

1. What is an equivalent couple for the forces in the figure?

An equivalent couple for the forces in the figure is a pair of forces that have the same magnitude, direction, and line of action as the original forces, but act in opposite directions and have equal distance from the axis of rotation.

2. Why is finding an equivalent couple important?

Finding an equivalent couple is important because it allows us to simplify the analysis of a system by replacing multiple forces with just one couple. This helps in understanding the overall effect of the forces on the system and makes calculations easier.

3. How do you determine the magnitude of the equivalent couple?

The magnitude of the equivalent couple can be determined by finding the sum of the moments of the original forces about any point on the axis of rotation. This sum will be equal to the magnitude of the equivalent couple.

4. Can an equivalent couple be used to replace any set of forces?

No, an equivalent couple can only be used to replace a set of forces that have equal and opposite forces acting at the same line of action. If the forces do not meet these criteria, then an equivalent couple cannot be found.

5. Is the equivalent couple the only way to represent a set of forces?

No, an equivalent couple is not the only way to represent a set of forces. Other methods, such as vector addition or decomposition, can also be used to represent a set of forces. However, an equivalent couple is a useful tool for simplifying the analysis of a system.

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