Answer to Question #125962 in Physics for Mwansa Kunda

Question

A bird has a mass of 26 g and perches in the middle of a stretched telephone line. (a) Show that the tension in the line can be calculated using the equation T=mg/2sinθ. 

Answer 1

The free-body diagram is shown on the figure:

As far as the bird doesn't move, its acceleration $a = 0$. Thus, writingg the second Newton's law in a projection on the vertical axis, obtain:

$$mg - T\sin\theta - T\sin \theta = 0\\ mg = 2T\sin\theta\\ T = \dfrac{mg}{2\sin\theta}$$

QED