What is the tension on the wire due to a bird?

Question

If 100m of telephone wire is suspended between two poles separated by 95m and a pelican (m=5kg) lands midway along the wire, what is the tension in the wire due to the bird?

I'm having trouble setting this one up. My book does not give very many tension examples so unfortunately I do not have any models to go by.

Answer 1

First, figure out how far the wire will dip below the horizontal, by using the Pythagorean. It's √ ( (50)² - (47.5)² ) = 15.6125. Now, there's a tension force up each wire away from the bird, as well as a downward force by the bird's weight, and they all balance each other out. Imagine that the 2 equal tension vector forces on the wires make a rhombus, and the vertical diagonal of the rhombus equals the vector force of the bird, or 5 kg. What does one of the tension forces equal to? A little bit of geometry will get you:

(15.6125 / 50) = ( (1/2) 5 kg / T )

where T is the vector tension force along one of the wires. It works out to:

T = 8 kg, almost exactly.

What a lot of people get confused about is that tension in a wire is represented by two equal tension vector forces, but the level of the tension in the wire is NOT the sum of them, but just one of them. If you stand on the ground exerting a force of 150 pounds on it, and the ground pushes back with 150 pounds force, so that you're not falling anywhere, that does not mean that there's 300 pounds of force anywhere. It's still 150 pounds force.

Answer 2

its hard