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

[FabledIntg]

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:

 

[Chestermiller]

What is the exact statement of the problem?

 

[FabledIntg]

Hi,

Problem: Express the resultant force in terms of F1, F2, r, t and α.

 

[Chestermiller]

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.

 

[FabledIntg]

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.

 

[Chestermiller]

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.

 

[FabledIntg]

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

F_2y = F₂ cos(α)
F_2x = F₂ sin(α)

So I get R = F₁ + F_2y + F_2x = 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.

 

[Chestermiller]

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?