The distance between two telephone poles is 31 m. When a 1.54kg bird lands on the telephone wire midway between the poles, the wire sags 0.165 m. The acceleration of gravity is 9.8 m/s^2. How much tension in the wire does the bird produce? Ignore the weight of the wire.
Tan A = Y/X = 0.165/(31/2) = 0.01065.
A = 0.61 Degrees = B = Angle the wire makes with the hor.
-T2*Cos 0.61 + T1*Cos 0.61 = 0.
T1*Cos 0.61 = T2*Cos 0.61.
T1 = T2.
T2*sin 0.61 + T1*sin 0.61 = M*g.
Replace T2 with T1:
T1*sin 0.61 + T1*sin 0.61 = 1.54*9.8
2*T1*sin 0.61 = 15.1 N.
0.02129T1 = 15.1
T1 = 709 N. = T2.
15
To find the tension in the wire produced by the bird, we can use the concept of equilibrium. Since the wire sags when the bird lands on it, the tension forces in both sides of the wire (acting upwards) must balance the downward force due to the weight of the bird.
Let's break down the problem:
1. Determine the weight of the bird:
The weight of an object can be calculated using the formula: weight = mass × acceleration due to gravity.
Given that the mass of the bird is 1.54 kg and the acceleration due to gravity is 9.8 m/s², we can calculate the weight:
Weight of the bird = 1.54 kg × 9.8 m/s² = 15.092 N (rounded to three decimal places).
2. Calculate the total sag in the wire:
The sag in the wire can be determined by measuring the vertical distance between the lowest point of the wire and the straight line connecting the tops of the two poles. The total sag is given as 0.165 m.
3. Determine the distance from the point where the bird is sitting to each pole:
Since the bird is sitting midway between the poles, the distance from the bird to each pole is half of the total distance between the poles: 31 m / 2 = 15.5 m.
4. Calculate the angle of sag:
The angle of sag (θ) can be determined using the formula: θ = arcsin(sag / distance), where sag is the total sag and distance is the distance from the bird to each pole.
θ = arcsin(0.165 m / 15.5 m) ≈ 0.0639 radians (rounded to four decimal places).
5. Determine the total vertical component of tension:
The total vertical component of tension can be found using the formula: Tension × sin(θ) = weight of the bird. Here, Tension refers to the tension in each side of the wire.
Thus, Tension = weight of the bird / sin(θ).
Tension = 15.092 N / sin(0.0639) ≈ 293.925 N (rounded to three decimal places).
Therefore, the tension in the wire produced by the bird is approximately 293.925 N.