Analyzing Forces in a Three-String Knot

[CaptainSFS]

Homework Statement

Three strings, in the horizontal plane, meet in a knot and are pulled with three forces such that the knot is held stationary. The tension in string 1 is T1 = 2.9 N. The angle between strings 1 and 2 is q12 = 130° and the angle between strings 1 and 3 is q13 = 120° with string 3 below string 1 as shown.

Homework Equations

F=ma

The Attempt at a Solution

I am unsure. I tried finding two equations with two unknowns and then tried solving for one, but I no idea what to do. my free body diagrams aren't helping either. Could someone explain how my FBD would look or at least explain what equations I should have come up with? Thanks for any help.

 

[LowlyPion]

Homework Statement

Three strings, in the horizontal plane, meet in a knot and are pulled with three forces such that the knot is held stationary. The tension in string 1 is T1 = 2.9 N. The angle between strings 1 and 2 is q12 = 130° and the angle between strings 1 and 3 is q13 = 120° with string 3 below string 1 as shown.
I am unsure. I tried finding two equations with two unknowns and then tried solving for one, but I no idea what to do. my free body diagrams aren't helping either. Could someone explain how my FBD would look or at least explain what equations I should have come up with? Thanks for any help.

The key phrase is the "knot is held stationary". That means that the net forces are = 0. It also means that the sum of the component forces in each direction is also 0 or it would move along that direction.

Now you can choose any coordinate system, but being lazy I like to choose at least one axis that makes things easier. Since the angles are given in terms of the relationship with T1, that would be my choice for x-axis.

Now develop equations for T1_x and T2_x and their angles and T3_x and since there is no Y component of T1 then another equation expressing T1_y and T2_y as a function of their angles.

2 equations. 2 unknowns. You don't need any more than that.

 

[CaptainSFS]

hey thanks! I worked out the rest of it just fine. :)