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

[FisherDude]

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.

 

[goeat]

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.

 

[YellowTaxi]

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.

 

[pam]

Since the horizontal components of the tensions must cancel, the magnitude will be different ilf the angles are different. You are right.

 

[YellowTaxi]

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.