Fishing line strength

[CJJ]

@Xema

As I understand it, we’re talking about a single string connecting two masses - your hand on one end and the weight on the other. So it looks symmetrical to me, and the only thing that will make the string’s tension non-uniform is the mass of the string itself - which can certainly oscillate a bit, but looks to be small enough that it can safely be ignored.

The string tension will be non-uniform for the brief time it takes to transmit force from the jerk of the hand to the object to be moved. Tension is related directly to a stretching of the string.

Imagine the string were a slightly-stretched Slinky. In jerking at one end, you pull the first coil of the slinky toward you. The second coil remains briefly in place because of inertia, but then is pulled along by the tension you introduced at the first coil. The second coil similarly drags the third, and so on down the line.

It is important to note that the motion of the coils is not instantaneous; they follow in succession based on the elasticity of the Slinky. To an observer standing alongside the Slinky, tension will appear to move down the Slinky like a wave (I foolishly called this a transverse wave in my original response; this is actually a longitudinal wave). Over time, this wave will eventually distribute across the entire length of the slinky, and all the coils will again be stretched out an equal amount.

The key point is that during this first jerk, if done quickly enough, the wave will reach the other end and reflect before the object to which the rope/slinky is attached will have moved. For that moment when the wave is reflecting, the original plus the reflection will be folded atop one another at the end attached to the object. They’re additive, and so up to double the force of the original jerk is present at that end.

That demo is a bit different - it includes a hand, two masses, and three strings.

Bad choice of demo; chalk it up to hasty Googling. My point in citing it was to show that the inertia of an object has a (brief) effect on the distribution of tension in a connected string if it is quickly jerked vs. slowly pulled. Unfortunately I didn’t make that clear, and so was misleading again. Sorry :smack:

On reflection, the best practical demonstration of the principle I have so far failed to explain is in the way we tear a toilet-paper roll. When the roll is large, there is sufficient inertia such that when you unroll, say, a two-foot length, a quick jerk at the end will cause the paper to tear at the perforation closest to the roll (rather than, say, in the middle). Now, this doesn’t usually work when the roll is nearly gone; there’s not enough inertia in the nearly-used roll to avoid it reacting quickly to the jerk, and you end up with a bathroom floor full of paper.

[Xema]

@CJJ*

Imagine the string were a slightly-stretched Slinky. In jerking at one end, you pull the first coil of the slinky toward you. The second coil remains briefly in place because of inertia, but then is pulled along by the tension you introduced at the first coil. The second coil similarly drags the third, and so on down the line.

This is correct. But a Slinky is quite massive and “stretchy” (i.e. a small force produces a large elongation). In the case of fishing line, both the mass and the elongation with force are very much lower. Thus my contention that they can pretty much be ignored when analysing the matter of breaking strength.

On reflection, the best practical demonstration of the principle I have so far failed to explain is in the way we tear a toilet-paper roll. When the roll is large, there is sufficient inertia such that when you unroll, say, a two-foot length, a quick jerk at the end will cause the paper to tear at the perforation closest to the roll (rather than, say, in the middle).

I agree that this is a better example. But I find that there is no tendance for the paper to separate near to the roll: indeed, in a dozen tries, the separation always happened away from the roll.

[CJJ]

I agree that this is a better example. But I find that there is no tendance for the paper to separate near to the roll: indeed, in a dozen tries, the separation always happened away from the roll.

We have really hijacked this thread, and to the OP I apologize; if there is a way to move these posts into a whole new thread someone please let me know, as I think the question now–though not the original poster’s–is of somewhat general interest.

I did the same experiments last evening on a lengthy visit to la salle de bain. The general experiment was to unroll five squares worth of paper from the roll (underhand, if it makes a difference), tug, and see where the damn thing breaks (I expected it to break at one of the five perforations in the unrolled length, since they’re obviously the weak points in the paper; it would be foolish to expect unperforated paper near the roll to tear first).

In 10 attempts, I got results similar to Xema’s. In four cases, the perforation nearest the roll broke. In three other cases, the perforation nearest my hand broke, two saw the length of TP broken in two places (nearest the roll and at one of the perforations in the middle), and one broke in the middle as the roll unraveled in a scene I’m sure is familiar to everyone. Hardly conclusive I’ll agree.

However, I noticed during the tugs my roll would “give” slightly on the dowel (when it didn’t spin maniacally out of control), so I repeated the experiment and used my other hand to hold the roll in place as I tugged. I also took care to keep the fifth perforation close to the roll without touching the rolled paper. After a couple false starts, I was able to get the length to break at the perforation nearest the roll in 10 consecutive trials (had to change rolls mid-way).

The force of the tug seemed to be a factor; too hard and it broke near the hand, too soft and it wouldn’t break at all. It wasn’t difficult to achieve the right amount of force, but it wasn’t automatic either. Once I “got it”, I was able to break it rather regularly without holding the roll until the roll became too small to resist spinning (did this to limit the possibility I was subconciously introducing tension with my hand on the roll). Adults wishing to feel a sense of pride they haven’t felt in the bathroom since potty training are welcome to duplicate the experience.

I further confirmed the effect by pulling gradually on the unrolled piece, rather than tugging quickly. In these cases breaks would occur at any one of the five exposed perforations (I didn’t keep track of these, but it seemed pretty random).

I’ll also note that I took care to tug along a line perpendicular to the axis of the roll, thinking at the time pulling at an angle might favor the perforation nearest the roll because the length is shearing against the roll, but frankly I’m not sure if this is true–another experiment to pass the time as I pass–well, I’ll leave that to you imagination.

So besides a TP’ed bathroom floor, I conclude the following: A strong-enough tug on the end of a length of TP will cause the length to break at the perforation nearest the roll under sufficiently controlled conditions; (1) the perforation has to be near the roll itself, (2) the roll either has to have sufficient inertia to avoid moving because of the tug, or must be held in place. I surmise the effect is as I described above; the reflected tension–introduced by the tug propagating down the unrolled portion–“folding over” and nearly doubling at the end attached to the roll.

If anyone has a better theory, I’ll happily discuss, but you’ll have to explain to my wife what I’m doing with all the toilet paper…she’s a little worried:-)

[Gary_Robson]

@CJJ*

I would assume in many cases the fish is lifted out of the water by the line

Sure, if you’re catching five-pound trout. If you’re out in the ocean catching marlins, you don’t lift them by the line. You gaff or harpoon them when you get them up close to the boat.

[David_Simmons]

@InvisibleWombat

Sure, if you’re catching five-pound trout. If you’re out in the ocean catching marlins, you don’t lift them by the line. You gaff or harpoon them when you get them up close to the boat.

This line of discussion started with my post about the fish weighing nothing in water. I posted that to clear the air in advance about fish and the strength of fishing line. Unless you have encountered the phenomenon you would be flabbergasted at the number of people who are mystified by the fact that you can catch a 10 lb. fish on 6 lb. line.