Tension on a String

[epena]

I'm trying to figure out the sag of a wire hanging between two objects. If I string a wire between two structures and tension the wire 5000 lbs in the horizontal direction, I can estimate the shape of the wire to be parabolic and use the equation: Sag = (W*L^2)/(8*T), where W=Weight of wire, L=Span between two supports, and T=Horizontal Tension to calculate the sag. If now I add a much heavier wire to the first wire, how can I arrive at the new Sag and Tension for the two wire combination? I am assuming the same temperature for both installations (60 degrees F). The first wire is .65 lbs/ft; the second wire is 7.8 lbs/ft. I am trying to solve the problem without neglecting the initial wire's weight.

 

[Mentz114]

Have a look at this

http://mathworld.wolfram.com/Catenary.html

If two different wires hang in the same curve they must be joined along their length, so you can pretend it's one wire with the average density (?)