How can tension be the same along all points in a rope?

In summary: The tension in the rope farthest from a pole is lower, and so is the tension in the wire.In summary, the tension in the wire when a 1.00-kg bird lands midway between two telephone poles that are 50.0 m apart is 613 N. However, if the bird lands closer to one of the poles, the tension on each side of the wire will be different due to the difference in angles. This is because the horizontal components of the tensions must cancel, leading to different magnitudes. This can be seen in extreme cases where a weight hangs vertically from a wire mounted to a pole and the wire is connected to another pole, resulting in different tensions on each side of the wire.
  • #1
FisherDude
23
0
Consider the following problem: 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. How much tension does the bird produce in the wire? Ignore the weight of the wire.


The tension is 613 N. But what if the bird didn't land midway, but instead, for example, somewhere closer to one of the poles? Wouldnt the tension in each side of the wire (relative to the bird) be a different number than the tension in the other side? (since it seems that the angle between one side of the wire and the horizontal would differ for both sides in this case) So how can the tension be the same? Unless the tension in each side would be the same no matter where the bird landed..

Thanks in advance.
 
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  • #2
Take an extreme case. A weight hangs vertically from a wire mounted to a pole, and the wire also continues on to be connected to another pole. Here it's clear that the tension between the two parts of the wire is not the same.
 
  • #3
rcgldr said:
Take an extreme case. A weight hangs vertically from a wire mounted to a pole, and the wire also continues on to be connected to another pole. Here it's clear that the tension between the two parts of the wire is not the same.

agreed.
So
The tension is 613 N. But what if the bird didn't land midway, but instead, for example, somewhere closer to one of the poles? Wouldnt the tension in each side of the wire (relative to the bird) be a different number than the tension in the other side?
yes I think that's right.
 
  • #4
Since the horizontal components of the tensions must cancel, the magnitude will be different ilf the angles are different. You are right.
 
  • #5
pam said:
Since the horizontal components of the tensions must cancel, the magnitude will be different ilf the angles are different. You are right.

That's it exactly.
.'. The tension in the rope closest to a pole carries most of the vertical weight, and so has a higher tension.
 

1. How is tension defined in a rope?

Tension in a rope is the pulling force exerted by the rope on any object or point that it is attached to. It is a result of the internal forces within the rope, specifically the stretching and compression of its individual fibers.

2. Can tension be the same at all points in a rope?

Yes, tension can be the same at all points in a rope as long as the rope is under a uniform load and there are no external forces acting on it. This is known as the principle of transmissibility, which states that a force can be moved along its line of action without changing its effect.

3. How does tension remain constant in a rope?

Tension remains constant in a rope because the individual fibers within the rope are in equilibrium, meaning that the forces acting on each fiber are balanced. This results in a uniform distribution of tension throughout the rope.

4. Are there any factors that can affect the uniformity of tension in a rope?

Yes, there are factors that can affect the uniformity of tension in a rope, such as variations in the rope's diameter, material, or construction. External forces, such as friction or wind, can also disrupt the uniform distribution of tension in a rope.

5. How can tension be calculated at different points in a rope?

Tension can be calculated at different points in a rope by using the principle of equilibrium, which states that the sum of all forces acting on an object must equal zero. By considering the forces acting on different sections of the rope, the tension at each point can be determined.

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