# Statics: System in equilibrium - determine height (h)

1. Mar 14, 2012

### gate13

1. The problem statement, all variables and given/known data

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. I have attached (in pdf) the problem's context and the free body diagram I have drawn.

The data we are give are as follows:
r = 0.575 m, a=1.05 m, W=4.905 N, Wc = 4.905 N

2. Relevant equations

We are asked to find h.

3. The attempt at a solution

What I have so far is as follows:

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

Td cos(θ) - Tccos(α) = 0 (along x-axis: $\rightarrow$)
Td sin(θ) + Tcsin(α) - W= 0 (along y-axis: $\uparrow$)

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.

Ans so using the sine law, I obtained:
$\frac{sin180-α-θ}{a}$ = $\frac{sin(α)}{r}$

But when I try solving the system with the values, I get:
α=90, θ=88.17 and Td = -1* 10-81

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.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

#### Attached Files:

• ###### context_fbd.pdf
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2. Mar 14, 2012

### tiny-tim

hi gate13!

show us how you got those figures

3. Mar 14, 2012

### gate13

Hello tiny-tim,

First of all, I wish to thank you for taking time to answer my question. The values I listed above were obtained using a TI Voyage 200 calculator. What I entered (in the calclulator) was the following:
solve(Td*cos(theta)-Tc*cos(alpha)=0 and Td*sin(theta)+Tc*sin(alpha)-W = 0 and r*(180-alpha-theta) = a*sin(apha), {alpha, theta, Td})
I just realized I should be entering:
solve(Td*cos(theta)-Tc*cos(alpha)=0 and Td*sin(theta)+Tc*sin(alpha)-W = 0 and r*sin(180-alpha-theta) = a*sin(apha), {alpha, theta, Td}).
Upon correcting this, I obtained:
Td = 5.06 N, alpha = 27.99 degrees, theta = 31.00 degrees.

Once more I wish to thank you for your help ( and I feel a bit embarassed with respect to my mistake).