752
Chapter 6 | Applications of Integration
Applications One physical application of hyperbolic functions involves hanging cables. If a cable of uniform density is suspended between two supports without any load other than its own weight, the cable forms a curve called a catenary . High-voltage power lines, chains hanging between two posts, and strands of a spider’s web all form catenaries. The following figure shows chains hanging from a row of posts.
Figure 6.83 Chains between these posts take the shape of a catenary. (credit: modification of work by OKFoundryCompany, Flickr)
Hyperbolic functions can be used to model catenaries. Specifically, functions of the form y = a cosh( x / a ) are catenaries. Figure 6.84 shows the graph of y =2cosh( x /2).
This OpenStax book is available for free at http://cnx.org/content/col11964/1.12
Made with FlippingBook - professional solution for displaying marketing and sales documents online