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. Determine the tension when
(b) θ=5° and
(c) θ=0.5°. Assume that each half of the line is straight.

Answer 1

The tension in the line can be calculated using the equation T = mg/2sinθ. The tension when θ is 5° is 0.027 N and when θ is 0.5° is 0.130 N.

Step-by-step explanation:

To calculate the tension in the line, we can use the equation T = mg/2sinθ, where T is the tension, m is the mass of the bird, g is the acceleration due to gravity, and θ is the angle between the line and the horizontal.

Using this equation, we can determine the tension when θ is 5° and when θ is 0.5°. Plugging in the given values, we get T = (0.026 kg)(9.8 m/s^2)/(2sin(5°)) = 0.027 N for θ = 5°, and T = (0.026 kg)(9.8 m/s^2)/(2sin(0.5°)) = 0.130 N for θ = 0.5°.