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
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,
Fwind, on the antenna in the negative z direction,
The antenna experiences a 5.2 kN compression force, Ftower, 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.)