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Problem 4.10i : Broadcast pole, 3-D

( this is Problem 3.6h revisited , now using vector algebra )

In order to cover a wider area broadcast antennas are often mounted on high slender poles. The one shown in the figure to the left is supported by guide wires, AB, AC, and AD. These guide wires are pretensed so that even under high-wind conditions, when the pole is leaning over to one side, all guide wires remain taut and do not flap in the wind.

The three shown wires exert forces onto the pole at point A. The resultant of these three forces is supposed to have a magnitude of 30 kN (so that the pole beneath does not break) and is supposed to be pointing vertically downwards ( in my minus y direction ).
Determine the forces each of the three wires is exerting on the pole (so that one can find the necessary diameter of the cables).

Use vector algebra ( location vectors, section 4.7, and unit vectors, section 4.5 ) to solve this problem.

My solution

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Zig Herzog,

Last modified : Thu Jun 19, 1997