A bird rests at the centre of a thin rope suspended between two poles 0.5 m apart. The rope sags 2 cm under the bird's weight, and the tension in each side is 5 N. What is the mass of this bird?
A)200 g
B)100 g
C)50 g
D)25 g

Question

Quizplus · Accepted Answer

The mass of the bird can be found using the equilibrium of forces. The vertical component of the tension forces balances the weight of the bird. Since the rope sags symmetrically, we can consider one half of the rope to form a right triangle, with the sag (2 cm = 0.02 m) as the height and half the distance between the poles (0.25 m) as the base. The tension (T = 5 N) is the hypotenuse. The vertical component of the tension (T_y) is T*sin(θ), where θ is the angle between the tension and the horizontal. Using the small angle approximation, sin(θ) ≈ opposite/adjacent = 0.02/0.25. Thus, T_y = T*(0.02/0.25) for one side, and since there are two sides, the total vertical force is 2*T_y. Setting this equal to the weight of the bird (mg), we get mg = 2*T*(0.02/0.25). Given T = 5 N, and g = 9.8 m/s^2, solving for m gives m ≈ 0.1 kg or 100 g.

A Bird Rests at the Centre of a Thin Rope