Good day to all, I have been given a problem in statics, ore specifically a syst

Question

Good day to all,

I have been given a problem in statics, ore specifically a system that is in equilibrium, but a system I am having some trouble with. The problem's context and the free body diagram I have drawn are as follows:

The data we are give are as follows:

r = 0.575 m, a=1.05 m, W=4.905 N, Wc = 4.905 N

We are asked to find h.

What I have so far is as follows:

Using the fact that the hoop is in equilibrium, I obtained the two equations:

We know W and Tc and so we have two equations with three unknowns so far. Then I thought of using the problem's geometry to obtain a third equation.

And so using the sine law, I obtained:

which I am quite certain are wrong.

I can,t seem to pinoint the third equation to help solve the problem. Any help would be greatly appreciated.

Thank you.

Explanation / Answer

Friend
Your equations are all correct. Looks like you are making a calculation mistake somewhere.
Your third equation can be simplified to Sin(+)=(a/r)*Sin.

Further, multiplying your first equation by Sin and second equation by Cos and then subtracting these resulting two equations and simplifying, we get SinCos + CosSin = Cos. Hence, Sin(+) = Sin(90-) which yields that +=90-. Therefore, =(90-)/2.

Putting this in the simplified third equation shown above we get, Sin((90+)/2) = 1.826 Sin (After putting values of a and r.)

Now, this can be solved graphically or by some other means to yield =28 degrees.

Therefore, =31 degrees. and Td = 5.05 N.

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