Okay.
So we’ve got an entirely flat surface that also happens to be the exact same length as the earth’s surface.
If you had one continuous piece of string that went from one end of that flat surface to the other, and on one end there was attached a bell… would you be able to ring the bell by pulling on the other end of string?
I did some numbers because it sounded fun.
Earth’s diameter is 41.804 million feet. I’m not sure if you meant that or Earth’s circumference when you said “Earth’s surface”, but I figure either one is gonna get us a really big number.
The first result I can find for string comes in a pack that weighs 2.89oz and contains 328 feet of string.
Using that as our standard, you would need 127,452 packs of string (assuming you find a way to perfectly attach them without wasting any length on knots).
127,452 * (2.89 / 16) = 23,021 lbs of string total.
So if we ignore the string stretching, compressing, or breaking, you’d only need to be able to pull 11ish tons of string to ring the bell!
Just for fun: Assuming the motion of the string travels at the speed of sound (I have no idea if it actually would, it just sounds right)
It is true in principle. But the speed of sound is different, depending on the material. For that string we can assume it to be roughly 10 times faster than in the air.
would be about 10.5 hours between you pulling the string and the bell ringing
~ 1 hour then.
Wouldn’t the motion of the string move at the speed of the pull!? Assuming no compression.
Assuming no compression
Compression and expansion is real. The first part of the string moves with your hand, at the same speed as your hand moves. But then it takes some time until further parts of the string - or the final part of the string - even start with their motion. Ok? And here we were talking about how fast this “beginning of the motion” travels forward through the string. That’s the speed of sound.
Okay, but what if there is no compression or expansion? What if it’s a rigid string already stretched out just enough to be expanded completely but not enough to move the bell? Or maybe a thin wire of the same weight?
Okay, but what if there is no compression or expansion?
That means, the speed of sound is infinite in your material. It doesn’t happen in this world.
Physics. The force you place on that string will effect the far end only at a rate no sooner than the speed of sound thru said medium.
The speed of sound in metal is about 17000 feet per second. Of materials on earth it has some of the fastest rates of transfer. But if you had a metal rod 17000 feet long and pushed one end a foot, the other end wouldn’t move a foot till a second later. It will compress.
Interestingly a neutron star has material that is so densely compacted that the speed of sound thru that material is approaching that of the speed of light.
need to be able to pull 11ish tons of string to ring the bell
But the weight of the string isn’t the force you need to pull.
Why not? If I try to pull a toy car alomg using a big thick rope, the weight of the rope is relevant, not just the weight of the toy car.
Why not?
When you want to lift it up vertically, then the force that you need is exactly the same as the weight.
But when you push or pull it forward on a surface, you need a different force.
Push a golf ball on the table: you need very small force, much less than it’s weight. Suck the same golf ball through a garden hose: you need much more force.
You want to look up “coefficient of friction” in your books.
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The force of friction is dependent on its weight (or more specifically the force of normal) but not only its weight
It kind of is. That is still 11 tons of mass. To ring a bell, you need to create some velocity on the striker. Pull a 11 ton mass in a frictionless environment will result in an extremely slow rate of acceleration. But in the spirit of the post, I suspect they are not considering how hard they are ringing the bell.
You are technically right though. Even blowing on a string long enough and you could accelerate it up to speeds approaching that of light. Providing there is no friction.
Why would you use packs of string? Just leave the manufacturing machine running and don’t cut it into packs.
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Is the string a massless, frictionless, magic physics string that doesn’t stretch? Yes, you can ring the bell.
Normal real-world string? Probably not.
It depends what the string is made of. When you tug on one end of the string, you create waves that travel the length of the string at the speed of sound. The speed of sound depends on the medium, so if the speed of sound in the material that the string is made of is 50mph for example, then the wave generated by pulling the string will propagate at that speed until it reaches the other end.
The other consideration is the weight of the string. If you go to tug on one end of the string, but the rest of the string weighs thousands of pounds, then you probably won’t be able to tug it.
I couldn’t, no. But I’m very lazy and, as you said, it’s all the way over there
A string that long that doesn’t sag to the ground or break is already physically unlikely, but assuming it exists it would probably stretch enough to compensate for the movement. So I’d say no, unless you had a perfectly rigid string.
Yeah I should have emphasized that the string is perfectly taught, has no slack, isn’t affected by things like the wind and can’t break.
What about gravity and friction though? Because as it stands now, if the string was in a frictionless environment and was unaffected by gravity, then yes, you’d be able to ring the bell. However, the friction between the string and the earth over that kind of distance would require more pull strength than the string itself would be able to handle without breaking, unless it was made of some crazy strong material like some kind of nanocarbon alloy or something like that.
This truly is the string theory the people deserve
Sorry that we don’t all have string factories at our beck and call…
Since we’re doing strings around the Earth, here’s the simplest, most unintuitive fact in geometry:
Say you have a string wrapped taut around the planet (purely spherical), like a belt. You want to raise that string up so that it’s one meter above ground all the way around the planet. How much more string do you need?
I’ll give you a hint. You don’t need to know the radius of the Earth to know the answer.
c = pi x dSo, to increase d by 2 meters (cause
d = 2 x r), that’s 2 X pi, or 6.28 meters for string?Correct.
To really emphasize it, the same amount of extra string would be needed if it was instead wrapped around a small marble at first and the diameter expanded by the same amount.
So I’m bad at math. Can you explain why we’ve decided to multiply pi by 2? Is there an articulable reason or is it just a rule?
c+x= pi * (d+2) in this case, right? So where did that multiply pi by 2 come from?
Distribute the pi on the right side of your equality, and replace c with pi*d:
c+x = pi*(d+2)
pid+x = pid + pi*2
x = pi*2
To generalize for an height h,
x = pi2h
Edit: I did some weird markup, but won’t be fixing it
Oh, I see now. I missed some pretty basic math there with that distribution. That makes sense now, thank you!
Good question. Many good answers. Put them aside and you still got a string made of multiple fibers that rub against each other. I’d guess that after a few hundred yards (depending on the string), the energy of your pull would be turned into heat by internal friction alone.
No one has really answered you so here you go. Yes you would be able to. It’s not instant though because information and energy cannot break the speed limit of the universe (speed of light). So essentially you’d pull the string and a few seconds later the bell would ring. Extend the string to the sun and it would take 8ish minutes for the bell to ring.
Speed of light is a lower limit but it would actually be the speed of sound in the material of the string that matters, so likely much slower than C
The speed of light is so much faster than the speed of sound, and that’s why sometimes you think someone is bright at first until you hear them talk.
:-)
