# Equilibrium in 3 dimensions

1. Oct 6, 2012

### mrcheeses

1. The problem statement, all variables and given/known data
A 100kg mass is supended by 3 ropes. one rope is attached at a point 1mxˆ + 1myˆ, one is attached at 1mxˆ - 1myˆ and one is attached at -4mxˆ. The three ropes all connect at -1mzˆ, at which point the mass is attached. What is the tension T in the rope attached at -4mxˆ?

2. Relevant equations
Fnet=0
Fg=mg

3. The attempt at a solution
I have no idea how to do this. Do I need to find the angles in between each rope?

2. Oct 6, 2012

### voko

You should represent the tension of each rope vectorially. Which is not hard, as you are given the coordinates of each rope's endpoints, and the rope is a straight line between the endpoints.

3. Oct 6, 2012

### shutdo

If you bother with the angle and different planes, you could, but it is more convenient to solve this with vectors.
First, you need to set up vector equations for the 4 forces involved.
Since you can work out the direction of each Force vectors, the magnitudes are the 3 unknowns.
Then, all of the Force vectors add up to a null vector. In other words, forces in each direction (i,j,k) add up to 0.
And by then you are left with 3 equations for 3 unknowns.