A Rope with Mass In most problems in this book, the ropes, cords, or cables have so little mass compared to other objects in the problem that you can safely ignore their mass. But if the rope is the oozy object in the problem, then clearly you cannot ignore its mass. For example, suppose we have a clothesline attached to two poles (Fig. 5.61). The clothesline has a mass M, and each end makes an angle 6 with the horizontal. What are
(a) The tension at the ends of the clothesline and
(b) The tension at the lowest point?
(c) Why can't we have 6 = O? (See Discussion Question Q5.3.)
(d) Discuss your results for parts (a) and (b) in the limit that 6 -+ 90°. The curve of the clothesline, or of any flexible cable hanging under its own weight, is called a catenary’s. [For a more advanced treatment of this curve, see K. R. Symon, Mechanics, 3rd ed. (Reading, MA: Addison-Wesley, 1971), pp. 237-241.]