Electrical power is transmitted across long distances through cables strung from one support to another. The wires are usually made of many smaller wires wrapped into a flexible bundle. For example one similar to the image below has 7 steel wires making a strong inner core, and 26 aluminum wires around it to make a cable 29mm in diameter (over 1 inch). It has a mass of 1.63 kg/m and can sustain a load of 699,000 N safely without risk of failure.  When lines are strung from one support to another, their enormous mass creates a tension in the cable that exerts a gravitational pull on its supports. 

Suppose such a cable is strung between poles spaced 1200 meters apart across a rural landscape. The cable is allowed to sag, following a natural curve called a catenary, increasing its length negligibly compared to the distance between the poles, while potentially lowering the cable to nearly contacting the ground at midpoint.

Consider a cable tension of 230,000 N that results in a sag of about 10 meters at the middle of the cable over this 1200 meter span. The sag would add only 1% to the length of the cable.

1. Explain this statement

The vertical sag relative to a support point equals cable weight per unit length times the distance to the low point squared divided by twice the horizontal tension.

2. If a small mass compared to the total cable mass were added to the middle of the cable, how would this affect the tension in the cable?

Answer rating: 100% (QA)

1 The statement explains how the vertical sag of the cable is r... View the full answer