How can I draw the resultant force of the couple M, F1 and F2?

In summary, the conversation discusses how to express the resultant force R in terms of F1, F2, r, s, and α. The problem involves finding the sum of forces and moments acting on a rigid body in equilibrium. The resulting force of F1 and F2 is R = F1 + F2, but in order to sum these forces, they must be resolved into horizontal and vertical components. The final expression for R is R = F1 + F2 cos(α) + F2 sin(α). However, the individual components must be calculated correctly in order to get the correct magnitude for R.
  • #1
FabledIntg
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I'm supposed to express the reultant force R of M, F1 and F2 in terms of F1, F2, r, s and α. But I need to know how to draw R first. How can one do this?

Does the couple create a force uppwards from O? Can I move F_1 and F_2 also to the origin and combine the forces?

Here is the image:

qygwsn.png
 

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  • #2
What is the exact statement of the problem?
 
  • #3
Hi,

Problem: Express the resultant force in terms of F1, F2, r, t and α.
 
  • #4
So you are aware that, for a rigid body to be in equilibrium, the sum of the forces and of the moments acting on the body must each be zero, right? The moment M does not contribute an external force.
 
  • #5
Yes I understand that, and I've tried the answer 0, but is still says it's wrong answer.

However, if the moment doesn't contribute an external force, shouldn't the resulting force of F1 and F2 be just R = F1 + F2? I don't understand How I'm supposed to express a resulting force with all those variables. I've tried similar triangles and all sorts of trig identities.
 
  • #6
FabledIntg said:
Yes I understand that, and I've tried the answer 0, but is still says it's wrong answer.

However, if the moment doesn't contribute an external force, shouldn't the resulting force of F1 and F2 be just R = F1 + F2? I don't understand How I'm supposed to express a resulting force with all those variables. I've tried similar triangles and all sorts of trig identities.
Vectorially, R = F1+ F2. But, to sum these forces, you need to resolve them into horizontal and vertical components, and then add the components. R has a component in the horizontal direction and a component in the vertical direction. If you have tried to do this, please show us what you have done.
 
  • #7
Ok, but as I understand, F1 can't be divided into vertical/horixontal components since it's already pointing straigt downwards, so it has only one vertical component. For F2 I get

F2y = F2 cos(α)
F2x = F2 sin(α)

So I get R = F1 + F2y + F2x = F1 + F2 cos(α) + F2 sin(α).

Still wrong. Keep in mind that it's not nesseccary to use ALL the variables above in order to express R.
 
  • #8
This is not done correctly. You seem to lack the knowledge of how to get the components of R and then to determine its magnitude. Have you been taught how to do this kind of thing in your course?
 

Related to How can I draw the resultant force of the couple M, F1 and F2?

1. How do I determine the direction of the resultant force of a couple?

To determine the direction of the resultant force of a couple, you will need to draw a free body diagram and apply the principle of moments. The direction of the resultant force will be perpendicular to the plane of rotation and will follow the right-hand rule.

2. What is the magnitude of the resultant force of a couple?

The magnitude of the resultant force of a couple is equal to the product of the distance between the two forces and the magnitude of one of the forces, also known as the moment arm. This can be calculated using the formula M = Fd, where M is the moment, F is the force, and d is the distance between the two forces.

3. How do I draw the resultant force of a couple on a diagram?

To draw the resultant force of a couple on a diagram, you will need to draw an arrow representing the direction of the force and label it with the magnitude of the force. The arrow should be drawn perpendicular to the plane of rotation and should follow the right-hand rule.

4. What is the difference between a couple and a single force?

A couple consists of two equal and opposite forces that act on a rigid body but do not have a net force or translation effect. This means that a couple only causes a rotational effect on a body. In contrast, a single force has both a magnitude and direction, and can cause both translation and rotational effects on a body.

5. Can the magnitude of the resultant force of a couple ever be zero?

Yes, the magnitude of the resultant force of a couple can be zero if the two forces are equal in magnitude and act at the same distance from the axis of rotation. This means that the two forces will cancel each other out, resulting in no net force or moment on the body.

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