Solving the Problem: Calculating the Tension in a Sagging Wire

In summary, the problem involves finding the tension produced by a bird landing on a telephone wire that sags 0.203 m between two poles 50.5 m apart. The solution involves using the length of the hypotenuse, the weight of the bird, and the angle of the sag to calculate the tension. The correct answer is 1708.35 N.
  • #1
Freeze
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Ok this is the problem

The distance between two telephone poles is 50.5 m. When a 1.40 kg bird lands on the telephone wire midway between the poles, the wire sags 0.203 m. How much tension does the bird produce in the wire?

This is what I did

I divided 50.5/2 = 25.25m (to get length of one leg)
The other leg is = .203 m

So, Length of Hypotenuse = 25.2508

Weight of the bird = (9.81 * 1.40) = 13.734 N


Now to solve the problem I did the following


(Weight of the bird/ the distance of the wire sagged) * the hypotenuse

To get the tension


so, the tension is = 1708.35 N

But this is not the right answer, so can anyone tell me what I am doing wrong?
 
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  • #3
Yep got it.. I don't know why I was ignoring the angles.

Thx.
 

What is the problem of calculating the tension in a sagging wire?

The problem of calculating the tension in a sagging wire is a common issue in engineering and physics. It involves determining the amount of force or tension that is exerted on a wire that is suspended between two points and sagging due to its weight or external forces.

What factors affect the tension in a sagging wire?

The tension in a sagging wire is affected by several factors, including the weight of the wire itself, the distance between the two supporting points, the angle of sag, and any external forces acting on the wire.

How do you calculate the tension in a sagging wire?

To calculate the tension in a sagging wire, you can use the formula T = (wL^2)/8S, where T is the tension, w is the weight of the wire per unit length, L is the distance between the two supporting points, and S is the sag distance (half of the sag depth).

What is the significance of calculating the tension in a sagging wire?

Calculating the tension in a sagging wire is crucial for ensuring the safety and stability of structures such as bridges, power lines, and suspension cables. It also helps in determining the appropriate materials and design for such structures.

Are there any limitations to calculating the tension in a sagging wire?

Yes, there are some limitations to calculating the tension in a sagging wire. The formula mentioned earlier is an idealized equation and does not take into account factors such as wind, temperature, and vibrations, which can affect the actual tension in a real-world scenario. Additionally, the weight and distribution of the wire may not be uniform, which can also impact the accuracy of the calculation.

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