The distance between two telephone poles is 59.0 m. When a 1.00 kg bird lands on the telephone wire midway between the poles, the wire sags 0.200 m. draw a free-body diagram of the bird. (do this on paper. your instructor may ask you to turn in this work.) how much tension does the bird produce in the wire/ ignore the weight of the wire
To determine the tension produced by the bird on the wire, we can analyze the forces acting on the bird using a free-body diagram. Here is how you can draw the free-body diagram on paper:
1. Draw a dot to represent the bird in the center of the wire.
2. Draw a downward vector labeled "Weight" to represent the gravitational force acting on the bird. The magnitude of the weight can be calculated using the mass of the bird (1.00 kg) and the acceleration due to gravity (9.8 m/s^2).
3. Draw two upward vectors, each labeled "Tension," to represent the tension forces acting on either side of the bird. These tensions are pulling the wire upwards. Note that since the wire sags, the tensions will be greater than the weight of the bird.
4. Connect the "Weight" vector to the dot representing the bird with a straight line.
5. Connect the two "Tension" vectors to the dot representing the bird with angled lines, indicating that the tensions are acting upwards.
Now that you have drawn the free-body diagram, you can calculate the tension in the wire using the given information. Since the wire sags 0.200 m, the distance between the bird and each telephone pole is half of that, which is 0.100 m.
The wire is in equilibrium, meaning the sum of forces in the vertical direction must be zero. Based on this, the tension forces on both sides of the bird must balance the bird's weight. Therefore, the tension produced by the bird in the wire is equal to the weight of the bird.
So, to calculate the tension, multiply the mass of the bird by the acceleration due to gravity:
Tension = mass of the bird * acceleration due to gravity
Tension = 1.00 kg * 9.8 m/s^2
Tension = 9.8 N
The bird produces a tension of 9.8 N in the wire.
Note: Make sure to write and label all the vectors and calculations clearly on your paper.
To draw a free-body diagram of the bird and calculate the tension it produces in the wire, you need to consider the forces acting on the bird.
Free-body diagram:
1. Draw a dot to represent the bird.
2. Draw an arrow upwards from the dot to represent the force exerted by the wire on the bird (tension).
3. Draw an arrow downwards from the dot to represent the weight of the bird.
Now, to calculate the tension in the wire:
We know that the wire sags 0.200 m when the bird lands on it, which means that the wire is displaced downward by that distance. This displacement creates an additional force acting upwards on the bird due to the tension in the wire.
Given:
Distance between the telephone poles (L) = 59.0 m
Mass of the bird (m) = 1.00 kg
Wire sag (h) = 0.200 m
Additional force (F) due to the sagged wire = ?
To calculate the additional force exerted by the wire, we can consider the sagged wire as a right-angled triangle, with the distance between the bird and one of the poles forming the base and the sag (0.200 m) forming the height.
Using Pythagoras' theorem, we can find the length (d) of the hypotenuse:
d² = (L/2)² + h²
d² = (59.0/2)² + (0.200)²
d ≈ 29.5 m
Now, we can calculate the additional force F exerted by the wire using the formula:
F = (m * g * h) / (d/2)
F = (1.00 kg * 9.8 m/s² * 0.200 m) / (29.5 m/2)
F ≈ 0.067 N
Therefore, the tension produced by the bird in the wire is approximately 0.067 N.