The distance between two telephone poles is 50.0 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. How much tension does the bird produce in the wire? Ignore the weight of the wire.
What do I do now?
Look at the triangle formed with the wire and the horizontal, and the bird vertical.
At the bird, the force down is 1/2 mg (we are doing only one side, due to symettry). The other force is tension, along the wire.
Looks like sinSag=1/2 mg/tension and...
tanSag= .2/50
use the second dto find angle Sag, and the first to solve for tension.
how much tension the birdroduce in the wire?
To determine the tension the bird produces in the wire, you first need to draw a free-body diagram of the bird. Here's a step-by-step guide on how to do it:
1. Start by drawing a dot or a small circle to represent the bird.
2. Draw an arrow going downward from the dot to represent the weight of the bird. Label it "mg" where "m" is the mass of the bird (1.00 kg) and "g" is the acceleration due to gravity (usually taken to be 9.8 m/s^2).
3. Draw two arrows going upward and away from the dot to represent the tension in the wire. Label both arrows as "T".
Now, to determine the tension the bird produces in the wire, you need to consider the vertical equilibrium. Since the bird is in equilibrium, the sum of the vertical forces must be zero. In other words:
T + T - mg = 0
Since the bird is in the middle of the wire, each tension force is half of the total tension in the wire. Therefore:
2T - mg = 0
Simplifying the equation:
2T = mg
T = mg/2
Plug in the values:
T = (1.00 kg)(9.8 m/s^2)/2
Evaluate the expression to find the tension produced by the bird in the wire.
To determine the tension in the wire produced by the bird, we need to analyze the forces acting on the bird when it lands on the wire. Here's what you can do step by step:
1. Draw a free-body diagram: Begin by drawing a diagram showing the bird as a dot in the center, representing its position on the wire. Label the downward force of gravity acting on the bird with its weight, which is the mass (1.00 kg) times the acceleration due to gravity (9.8 m/s^2). Also, label the upward force exerted by the wire and the downward force of gravity acting on the bird.
2. Calculate the weight of the bird: Multiply its mass (1.00 kg) by the acceleration due to gravity (9.8 m/s^2) to find its weight.
3. Determine the upward force exerted by the wire: In a situation where the bird is at rest, the upward force exerted by the wire is equal in magnitude and opposite in direction to the downward force of gravity acting on the bird. Therefore, this force can be calculated as the weight of the bird.
4. Calculate the tension in the wire: Since the wire sags 0.200 m, forming a triangle with the bird at the center, the vertical component of the tension force equals the weight of the bird (upward force). The horizontal components of the tension forces on either side will balance each other out, resulting in no net horizontal force. Thus, the tension in the wire can be found by calculating the vertical component of the tension force.
5. Use trigonometry: The vertical component of the tension (tension_force_vertical) can be determined using trigonometry. The sag of the wire (0.200 m) forms a right triangle with the horizontal distance from the bird to either pole (25.0 m).
- The tangent of the angle (θ) between the wire and the horizontal can be found as tangent(θ) = sag / half_distance.
- Use the inverse tangent function (arctan) to find the angle.
- Finally, use the angle and the weight of the bird as inputs to the equation: tension_force_vertical = weight * cosine(θ) to calculate the vertical component of the tension force.
6. Calculate the tension in the wire: Now that you have the vertical component of the tension force (tension_force_vertical), multiply it by 2 to account for both sides of the wire. The tension in the wire can be found by taking the absolute value of this result.
Following these steps should help you determine the tension produced by the bird in the wire.