To find the reaction in a system at a ring

In summary, the conversation discusses finding the reaction forces for a system, including using a diagram and equations to determine the values. It is concluded that the reaction force R must be perpendicular to CB and that R = w/2. The discussion also mentions using the fact that the ring is smooth to further deduce the direction of the reaction force.
  • #1
gnits
137
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Homework Statement
To find the reaction in a system at a ring
Relevant Equations
moments
Could I ask for a hint as to where to go next with this question please?

leanQ.png

I've done this first part, to find the reaction on the wall. Here's my diagram:

lean.png

I've labelled the internal forces at B in red.

In green I've shown the reaction at the ring.

So I need to find sqrt(Rx^2 + Ry^2) = R.

So I need to find Rx and Ry in order to calculate R.

For the whole system:

Vertically: R_C + Ry = 3w
Horizontally: R_A + Rx = F

For BA only:

Vertically Y = w
Horizontally: R_A = X
Moments about B gives: R_A * a sin(30) = w * (a/2) * cos(30) which yields R_A = sqrt(3)*W/2 as required.

Now that we know R_A, for whole system:

Taking moments about C leads to: sqrt(3)*Rx + Ry = w

Not sure how to proceed.

If I take moments about C for BC only, this leads to the same equation sqrt(3)*Rx + Ry = w

If I take moments about D for BC only this yields: R_C - sqrt(3)*F = w/2

All my answers above are consistent with the book answer, but I can't see how to proceed.

Book answers is: R = sqrt(Rx^2 + Ry^2) = w/2

So, I am trying to find Rx and Ry in order to calculate R.

Thanks for any pointers.
 
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  • #2
The ring is smooth. Can you deduce from this anything about the direction of the reaction force ## \vec R##?
 
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  • #3
Yes, of course, thank you. The reaction force R must be perpendicular to CB, and so using my already derived formula sqrt(3)*Rx + Ry = W and replacing Rx with R cos(30) and Ry with R sin(30) I find that R = w/2 as required. Thank you very much indeed.
 
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Related to To find the reaction in a system at a ring

1. What is a reaction in a system at a ring?

A reaction in a system at a ring refers to the changes that occur in a system when a ring structure is present. This can include changes in the chemical composition, physical properties, or behavior of the system.

2. How do you determine the reaction in a system at a ring?

The reaction in a system at a ring can be determined through various analytical techniques such as spectroscopy, chromatography, or mass spectrometry. These methods allow scientists to identify and quantify the changes in the system caused by the ring structure.

3. What factors can affect the reaction in a system at a ring?

There are several factors that can influence the reaction in a system at a ring, including the type and size of the ring, the nature of the surrounding environment, and the presence of other molecules or ions that can interact with the ring.

4. Why is it important to study the reaction in a system at a ring?

Studying the reaction in a system at a ring can provide valuable insights into the behavior and properties of different chemical systems. This knowledge can be applied in various fields such as drug development, materials science, and environmental research.

5. Can the reaction in a system at a ring be controlled or manipulated?

Yes, the reaction in a system at a ring can be controlled or manipulated by altering the conditions of the system, such as temperature, pressure, or pH. Additionally, the introduction of specific molecules or ions can also influence the reaction in a desired way.

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