Radio Tower

The radio antenna for station WEML sits on a nearby hill for better transmission. The support cables have been pre-tensioned to keep the antenna stable, which causes a known force on the antenna. In addition, a storm with high winds is adding a significant lateral load on the antenna. The storm could cause problems because the cable anchors were not placed to provide maximum support.

What is known:

• The locations of the cable anchors on the ground (in reference to point O) are
       A(x,y,z) = (66.5 m, -86.5 m, 0 m)
       B(x,y,z) = (-26.3 m, -86.5 m, -63.0 m)
       C(x,y,z) = (-68.0 m, -86.5 m, 42.8 m)
  
• The wind exerts a 1 kN force, F_wind, on the antenna in the negative z direction, F_wind.
  
• The antenna experiences a 5.2 kN compression force, F_tower, due to the pre-tensioning in the cables.
  
• The cables will fail at tensions greater than 4 kN.

Will any of the cables break due to the force of the wind on the antenna?

• Use Cartesian coordinates to define cable forces.
  
• Apply the equilibrium equations to solve for the cable tensions. (This will involve 3 equations and 3 unknowns.)
  
• Remember, cables experience only tension forces.