system
Given the following post, respond as if you're commenting on Reddit:
human
Is the weight of a line distributed throughout the line, or is it "felt" at every point along the line?

Imagine a length of monofilament fishing line (which for these purposes we'll assume is uniform and undamaged in any way) that is suspended vertically.  Now let's assume that it's a reallllllly long length, long enough that the total weight of the length surpasses the line's rated breaking strength.  This would be hundreds of thousands of feet in practice, I don't know if it factors into the question or not.

Say the line is 100,000 feet long and it is expected to break with 10 lbs of (force? load? tension?), and the whole 100,000 foot length weighs 20 lbs.

My primary question is: **will the line break?**

More generally what I'm wondering is how the 10 lbs is distributed along the line.  Will the line break at the point where the weight of the line below exceeds 10 pounds?  Will it break at a random spot?  Will it not break at all because the 20 lbs is distributed evenly along the entire length of the line?

Is the answer different if there's a significant weight tied to the end of the line, say a 1 lbs weight or a 9 lbs weight or a 11 lbs weight.

I don't even know the vocabulary to go search for info on this.  By the way, this is not a practical problem, this is just idle curiosity.
gpt
At a theoretical steady-state, the tension in the line at any location is equal to the weight of all the line below that location. So, the entire upper half of the line is overloaded, and liable to break at any location in that half. In other words, it can't actually reach that theoretical steady-state, it's an impossible condition.

Where would it actually break? Because we can't be in steady-state, let's say we did the experiment by laying the line out horizontally, clamping it between two 100,000 foot long flat surfaces, then turned the clamps upright and released them at t=0. The line would sag slightly as it stretched under the effects of gravity, the tension increasing everywhere. It wouldn't increase linearly with time, nor would it increase linearly with position on the line, but what is true is that the tension would always be higher at any point in the line than every point below it. So the tension would be highest at the top, and that's where it would break, once it had sagged enough to exceed 10 lbs of tension at the very top.