What Forces Balance a Knot Pulled by Three Different Ropes?

[mjunderhill]

The figure shows three ropes tied together in a knot. 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. These two ropes are being pulled 120 degrees apart.


How hard must you pull on the third rope to keep the knot from moving?

In what direction must you pull on the third rope to keep the knot from moving?


I assumed the vectors formed a right triangle and the 5.0 force was the hypotenuse, so the third rope would require 4.0 units of force.

 

[Quincy]

Why did you assume the vectors formed a right triangle? They're 90 degrees apart.
Break up the vectors into X & Y components first.

 

[rl.bhat]

The figure shows three ropes tied together in a knot. 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. These two ropes are being pulled 120 degrees apart.How hard must you pull on the third rope to keep the knot from moving?

In what direction must you pull on the third rope to keep the knot from moving?I assumed the vectors formed a right triangle and the 5.0 force was the hypotenuse, so the third rope would require 4.0 units of force.

welcome to PF.
Since angle between the ropes is 120^o, vectors do not form a right triangle.
If two vectors and angle between them are given, what is the relevant equation to find the magnitude and direction of the resultant vector?