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Originally posted by Nedd
No. The second a tension gradient exists within a cable, it snaps. Reductio ad absurdum, your reasoning is flawed.
To be clear, you can have all the tension gradients you want laterally. We were talking about longtiudinal gradients, of which there are none.
The longitudinal tension gradient does exist even without transversal components…
- Connect a rope to a wall
- A first guy comes and pulls it, now the tension in the rope between the wall and the guy has a certain value, the rope behind the guy just lies on the floor.
- A second guy takes the loose part of the rope and pulls it right behind the other guy, now the tension in the rope between the wall and the first guy is equal to the force both guys pull with; between the first and the second guy it’s equal to the force of the second guy only.
A longitudinal tension gradient in all its beauty!
Theoretically, you can let the distance between the guys shrink to almost zero just as the difference between (did I say “between”?) their strength.
Then you got a smooth function, without gaps or values that suddenly jump up or down.
Walking along the rope we see the tension increasing as we are approaching the wall and passing the guys that are pulling. With each step we reach a higher tension value and a new tension gradient starts at our feet and points all the way down through the rope right to the point where it meets the wall. BTW, the rope will not snap just due to its existance.
memento mentioned another example of a longitudinal tension gradient earlier. A long rope hanging from the sky with (or without) a weight at its end. Each section has to carry the weight of the part under it, so the tension increases as we’re coming near the sky.