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!
EDIT:
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), there would be about 10.5 hours between you pulling the string and the bell ringing on the other side.
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.
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.
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.
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.
How dense is it? A string that long would have a lot of mass, which you’d have to overcome to accelerate the string to a speed that would ring a bell.
This raises another important question: what sort of bell? A taut string attached to a clapper isn’t going to do much; you release the string and it won’t hit the other side. Unless it’s one of those bells where the bell also pivots the other direction when you pull the clapper.
Or is it a bicycle bell where the act of pulling the lever rings the bell?
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.
