Finding the Coordinates of Point A in a Force Equilibrium System

[Nivlac2425]

Homework Statement

The system is in equilibrium. What are the coordinates of point A?
(see attached image)

Homework Equations

ƩF_y = 0
ƩF_x = 0

The Attempt at a Solution

The sum of forces in the x and y directions is zero since the system is in equilibrium. At point A, I also know that there is a weight W directed downwards, and each of the two tensions in the ropes T are equal in magnitude.

I was told that this "proof" problem required consideration of the distance between the weight on the left and its pulley (call it ε), and also the two angles (α and β) between each of the two ropes at point A with the horizontal.

Although I was given these hints, I still can't figure out where to start in the problem. Can anyone help me out here? Thanks!

 

[azizlwl]

Actually all the tension of the strings are equal.
Using these values, you can find the angles by resolving the components.

 

[SammyS]

Homework Statement

The system is in equilibrium. What are the coordinates of point A?
(see attached image)

Homework Equations

ƩF_y = 0
ƩF_x = 0

The Attempt at a Solution

The sum of forces in the x and y directions is zero since the system is in equilibrium. At point A, I also know that there is a weight W directed downwards, and each of the two tensions in the ropes T are equal in magnitude.

I was told that this "proof" problem required consideration of the distance between the weight on the left and its pulley (call it ε), and also the two angles (α and β) between each of the two ropes at point A with the horizontal.

Although I was given these hints, I still can't figure out where to start in the problem. Can anyone help me out here? Thanks!

What is the tension in each of the three ropes ?

 

[Nivlac2425]

What is the tension in each of the three ropes ?

I believe the tensions are equal and they are all equal to W

 

[SammyS]

I believe the tensions are equal and they are all equal to W

Correct.

What does that tell you about the angles made by the three ropes at point A ?

 

[Nivlac2425]

Correct.

What does that tell you about the angles made by the three ropes at point A ?

So if I resolve the tensions into their components, and realize that the sum of forces in x and y are both equal to zero, I get the following relations:

sin(α) + sin(β) = 1

cos(α)=cos(β)

This tells me that the angles must be equal, and that α = β = 30°

And since: tan(α) = (h+y)/(b-x) and tan(β) = y/x,

I get x = (1/2)[b - hcot(30°)] and y = (1/2)[btan(30°) - h]

Is this the correct way to think about the problem?