The distance between two telephone poles is 58.0 m. When a 1.00-kg bird lands on the telephone wire midway between the poles, the wire sags 0.240 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 draw a free-body diagram of the bird, follow these steps:
1. Draw a dot to represent the bird.
2. Draw a straight line from the dot in a vertical direction to represent the weight of the bird acting downwards.
3. Label this downward arrow "W" for weight and write the value of the weight below the arrow. In this case, the weight is the mass of the bird multiplied by the acceleration due to gravity (9.8 m/s^2).
To calculate the tension produced by the bird in the wire, follow these steps:
1. Divide the sag distance of 0.240 m by 2 to find the vertical distance between the bird and the midpoint of the wire. This will help us find the vertical component of tension.
Vertical distance = 0.240 m / 2 = 0.120 m
2. Use the Pythagorean theorem to find the tension in the wire. The horizontal component of tension is equal to half the horizontal distance between the poles (58.0 m / 2 = 29.0 m).
Tension^2 = (Vertical distance)^2 + (Horizontal distance)^2
Tension^2 = (0.120 m)^2 + (29.0 m)^2
3. Take the square root of both sides to find the tension:
Tension = √[(0.120 m)^2 + (29.0 m)^2]
Calculating this value will give you the tension that the bird produces in the wire.
Note: Remember to perform the necessary calculations to find the exact value of the tension.
To determine the tension produced by the bird on the wire, we first need to draw a free-body diagram of the bird. Here are the steps to draw the free-body diagram:
1. Draw a dot in the center of the paper to represent the bird.
2. Draw an arrow pointing downwards from the dot to represent the weight force acting on the bird. The weight force can be calculated using the formula Fw = m * g, where m is the mass of the bird and g is the acceleration due to gravity (approximately 9.8 m/s^2).
3. Draw two arrows pointing upwards and outwards from the dot to represent the tension forces acting on the bird from both sides. Since the bird is in equilibrium, these tension forces must be equal and opposite.
4. Label the downward arrow as "Fw" for the weight force and label the upward arrows as "T" for the tension forces.
Now that we have the free-body diagram, we can calculate the tension produced by the bird in the wire. The tension force can be found using the formula T = (m * g) + Fd, where Fd is the force of deflection caused by the sag in the wire.
Given:
Distance between two telephone poles, d = 58.0 m
Weight of the bird, m = 1.00 kg
Deflection due to the bird's weight, h = 0.240 m
Acceleration due to gravity, g = 9.8 m/s^2
First, we need to determine the force of deflection, Fd. Since the bird's weight causes the wire to sag, the force of deflection can be calculated using the formula Fd = m * g * h.
Fd = 1.00 kg * 9.8 m/s^2 * 0.240 m
Fd = 2.352 N
Now we can calculate the tension force, T:
T = (m * g) + Fd
T = (1.00 kg * 9.8 m/s^2) + 2.352 N
T = 19.6 N + 2.352 N
T = 21.952 N
Therefore, the tension produced by the bird in the wire is approximately 21.952 N.