- #1

gate13

- 4

- 0

## Homework Statement

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

## Homework Equations

We are asked to find h.

## 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:

T

_{d}cos(θ) - T

_{c}cos(α) = 0 (along x-axis: [itex]\rightarrow[/itex])

T

_{d}sin(θ) + T

_{c}sin(α) - W= 0 (along y-axis: [itex]\uparrow[/itex])

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:

[itex]\frac{sin180-α-θ}{a}[/itex] = [itex]\frac{sin(α)}{r}[/itex]

But when I try solving the system with the values, I get:

α=90, θ=88.17 and T

_{d}= -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.