# 3-D equilibrium

1. Sep 20, 2009

### MechTech

1. Collars A & B are connected by a 525-mm long wire and can slide freely on frictionless rods. If force P= (341 N)j is applied to collar A determine the tension of the wire when y=155mm and the magnitude of force Q(which is along the z axis) to maintain equilibrium

2. Relevant equations
$$\Sigma$$F=0

$$\overline{v}$$=$$\sqrt{vx^2+vy^2+vz^2}$$

3. The attempt at a solution

I was given y was 155mm and x=200mm and found the z value of the wire to be 460mm. I then created a unit vector for the wire and came up with these equilibrium formulas:

$$\Sigma$$Fx=$$200/525$$Tab=0 (Something is wrong here)

$$\Sigma$$Fy=$$-155/525$$Tab=-341N

$$\Sigma$$Fz=Q+$$460/525$$Tab=0

Now I'm stuck....can anyone lead me in the right direction?

2. Sep 21, 2015

### deuel18

Think about Newton's 3rd Law of Motion - action and reaction. So you know that a force P acting on point A will make it move up and also create tension on T(ab). However, you know also that T(ab) must have three components of xyz. The problem is that point A can only move at y axis, but to satisfy equilibrium, there must be a hidden force opposite of T(ab) in which it will make the sum of the forces on x and z zero.