Expert: Dr. Abdulaziz Jarkas - 10/17/2006

Question
I have a taut steel cable tied to 2 trees 100 feet apart. A 200 lb weight is suspended in the middle. What is the force (tension?) exerted on each tree? Is it different if there is a sag in the cable? What equation can I use to solve this question?

Answer
Dear Eric,

If we assume an angle of 45 deg., and the total weight (200 lbs) is equally supported by both trees, i.e. 100 lbs/tree, then we simply resolve the components of the resultant into the tension and compression forces as 0.707, i.e. sin and cos 45 deg., x 100 lbs or 70.7 lbs per tree.

It all depends on the angle between the cable and the trees, thus, whether there is a sag in the cable or not, we need such angle to resolve the force into its vert. and horiz. components.

Hope this helps!

Dr. Jarkas