Question

A bird alights on a stretched telegraph wire. Does this change the tension in the wire? If so, by an amount less than, equal to, or greater than the weight of the bird?

Answer 1

A bird alights on a stretched telegraph wire. Does this change the tension in the wire? If so, by an amount less than, equal to, or greater than the weight of the bird?

Solution:

Real life photo ;)

Schematic sketch.

Wire deflects under birds weight:

According to the second Newton's law:

$$m \vec {g} + \overrightarrow {T _ {1}} + \overrightarrow {T _ {2}} = m * \vec {a}$$

As there is only one wire:

$$\left| \overrightarrow {T _ {1}} \right| = \left| \overrightarrow {T _ {2}} \right| = T$$

Bird doesn't move:

$$a = 0;$$

Thus:

$$m * g = T * \cos \alpha + T * \cos \alpha$$ $$T = \frac {m g}{2 \cos \alpha}$$

As $\alpha$ is small thus:

$$\alpha \rightarrow 0 \Rightarrow \cos \alpha \rightarrow 1$$

So:

$$T \approx \frac {m g}{2}$$

Answer: The tension in the wire changes by an amount less than the weight of the bird.