Static Equilibrium Rope Problem

[Miss Figgy]

Homework Statement

Three ropes are tied together. One of your friends pulls on a rope with 3.0 units of force and another pulls on a second rope with 5.0 units of force. Friend Two is 120 degrees to the left of Friend One (where Friend One's vector is on the positive x-axis).

Homework Equations

How hard must you pull on the third rope to keep the knot from moving? And In what direction must you pull on the third rope to keep the knot from moving (counterclockwise from the left direction)?

The Attempt at a Solution

T(1)=3 N
T(2)=5 N
T(3)=? N

T(1)= 0 degrees
T(2)= 120 degrees
T(3)= ? degrees

HELP!

 

[alphysicist]

Hi Miss Figgy,

Homework Statement

Three ropes are tied together. One of your friends pulls on a rope with 3.0 units of force and another pulls on a second rope with 5.0 units of force. Friend Two is 120 degrees to the left of Friend One (where Friend One's vector is on the positive x-axis).

Homework Equations

How hard must you pull on the third rope to keep the knot from moving? And In what direction must you pull on the third rope to keep the knot from moving (counterclockwise from the left direction)?

The Attempt at a Solution

T(1)=3 N
T(2)=5 N
T(3)=? N

T(1)= 0 degrees
T(2)= 120 degrees
T(3)= ? degrees

HELP!

Have you drawn a force diagram for this problem? What equations do you get from it?