Ant on a rubber rope

[AlexGTV]

From the wiki article of the same name:

"An ant starts to crawl along a taut rubber rope 1 km long at a speed of 1 cm per second (relative to the rubber it is crawling on). At the same time, the rope starts to stretch by 1 km per second (so that after 1 second it is 2 km long, after 2 seconds it is 3 km long, etc). Will the ant ever reach the end of the rope?"

It is easy to picture, but can you give a definite answer?

Vote and then check below.

The answer in the link:
http://en.wikipedia.org/wiki/Ant_on_a_rubber_rope

 

[DG_Silva]

Yes, because although the position that the ant is in relation to the overall is closer to the start point than the end point, at some time physics has to cut in and the rope cannot extend any further without snapping, and it's at that point when the ant will reach the end (eventually). Given a philosophical answer, and an infinitely extending rope, then no, it will never reach the end.

 

[AlexGTV]

^Half-right.

 

[DG_Silva]

Hmmm, I read the article after I answered. I cannot understand how the ant can move along an ever expanding rope when the ending position is further away in a constant extension. Is there a simpler way of explaining it without resorting to vast amounts of algebra?

 

[AlexGTV]

^I'm in your position as well, though I believe I will "get" it eventually. You could ask similarly, will the car with a lower top speed ever catch the faster one?

 

[Seismica]

Does the stretching happen instantaneously at 1 second intervals, or is it at a constant rate?

Because the way I imagine it, the 1cm that the ant is travelling on would be stretched by the same factor as the overall length so the 1cm distance would change according to it's relation to the overall length of the rope. Also the length of rope behind the ant would also be stretched by the same factor.

e.g. A cm is 1/100000 of km, so if the rope stretches to 2km the ant will have travelled 1/100000 of 2km which is 2cm relative to it's starting point, and again for 3km, 4km etc. always travelling 0.001% of the overall length per second.

I like to think of it as similar to walking on a conveyor belt, or a treadmill. On a treadmill you are travelling but remain at the same point. On a conveyor belt (like those in airports) you may take a stride that is 0.5m long, but you will have actually travelled further depending on the speed of the conveyorbelt.

From my quick analysis, it would take 100,000 seconds for the ant to reach the end of the rope (I think).

*EDIT: Missed a zero out, there isn't 10,000 cm to a km... mind fart, I should really know this stuff by now seen as i'm studying engineering.

 

[Villain]

The ant is moving with the rope. It'll get there eventually.

 

[Rockettd]

The further the ant walks.. the more rope will be behind it.

 

[Cowboys965]

I say yes.

You should've said "What speed does the train leave for Chicago at?"

 

[DG_Silva]

From what I can see, as you extend the rope, the ant's position moves with it. So the idea is it will take 1x100(cm)x1000(m)^1,000s to reach the end. That would be a very rough estimate, as the article extends it further.

 

[nick09]

Well considering that 1km is 100000cm, it would take the ant to travel 1km in 27.77~ hours. Just from my simple maths, if I were the ant and if I knew that, I would not even attempt to climb the rope. In the first second the distance will double and will effectively double the time. If the rope never broke or stopped stretching then yes the ant would never reach the end.

Never been a fan of advanced math so you could take my comment like a pinch of salt.

 

[Lizard]

If the ant is dead center of the rope or behind the center point then surely it can't get to the end.

 

[MatskiMonk]

You are not given enough information to give a definative answer, therefore the question is pointless.

Given the assumptions the question implies, then no, taking out assumptions, then yes, easily.

 

[PeterJB]

Their is no addition of matter to the rope, it has simply stretched. This stretching aids the ant in it's passage. The initial speed is 1 cm per second relative to the rope, but since the rope starts stretching this 1 cm distance is stretched proportionally, so yes, it will reach the end.

 

[AOS-]

Wasn't too hard to figure out.

 

[W3H5]

Want a mind 🤬?

According to some law of physics, I forget which I read it years ago, a train leaves Chicago at 12:33, on it's journey the train reaches 40mph. OK enough about the train.

A fly is flying in the opposite direction as train. The train and the fly collide. Who wins? The train, of course. But for the fly to be going in an opposite direction to the train, hit the train and the travel back the way it came it must have to have stopped completely, for however short a period. If the fly stopped, the train must have too. Thus, a fly can stop a train.

Boggled? Took me a while to get my head around. Good thought experiment, though.

 

[TB]

A fly is flying in the opposite direction as train. The train and the fly collide. Who wins? The train, of course. But for the fly to be going in an opposite direction to the train, hit the train and the travel back the way it came it must have to have stopped completely, for however short a period. If the fly stopped, the train must have too. Thus, a fly can stop a train.

The train may have slowed down (and when I say slowed down I mean by an infinitesimally small amount) but there is no way it stopped. It's simply a matter of mass. A multi-ton train, or a one ton car, for that matter, isn't going to react in the slightest to a 10 milligram fly.

 

[W3H5]

For the fly to begin travelling back the way it came it must have stopped. Therefore the train must have stopped for however minute amount of time for the fly to be going in the opposite direction.

EDIT: I'll try to find the obscure part of an obscure physics law that contains this information if I can. I'm sure it must be online and currently, I imagine, is still at theory level.

 

[Seismica]

Want a mind 🤬?

According to some law of physics, I forget which I read it years ago, a train leaves Chicago at 12:33, on it's journey the train reaches 40mph. OK enough about the train.

A fly is flying in the opposite direction as train. The train and the fly collide. Who wins? The train, of course. But for the fly to be going in an opposite direction to the train, hit the train and the travel back the way it came it must have to have stopped completely, for however short a period. If the fly stopped, the train must have too. Thus, a fly can stop a train.

Boggled? Took me a while to get my head around. Good thought experiment, though.

Incorrect, the fly is only deemed to have stopped when it changed direction, because the velocity will have changed from positive to negative and will have been zero at the point at which it changed direction (Though the same can't be said for the internal organs of the fly, which will have kept going).

As the train did not change direction it didn't stop.

 

[W3H5]

At the point when the train connects with the fly and it becomes zero and has stopped, for it to stop so must the train.

 

[ROAD_DOGG33J]

Impossible since the train would have to be at 0mph and then accelerate back to speed in that brief amount of time.

 

[wfooshee]

Fly had an infinitesimal moment of being "stopped" although not in the state of being an intact fly, because its direction of travel was reversed. Was going east, now going west, there had to be a zero moment between there somewhere.

The train did not change direction. It may have been slowed by a factor calculated out into the 10^10^10th decimal place, but it did NOT stop.

As for the ant on the rope, the way I read that article, the ant reaches the end, but not until an amount of time passes that makes the age of the Universe look like nanoseconds.

 

[Cowboys965]

For the fly to begin travelling back the way it came it must have stopped. Therefore the train must have stopped for however minute amount of time for the fly to be going in the opposite direction.

EDIT: I'll try to find the obscure part of an obscure physics law that contains this information if I can. I'm sure it must be online and currently, I imagine, is still at theory level.

But the train didn't go in the opposite direction than it was headed like the Fly did.

 

[Seismica]

At the point when the train connects with the fly and it becomes zero and has stopped, for it to stop so must the train.

Well not really, the point at which the fly stops the train decelerates by the same force required to stop the fly, which isn't enough to stop the train.

The fly doesn't really stop, it's velocity won't be 0 for any measurable length of time.

But if you think about it, for it to be stopped fully it's acceleration also needs to be 0 (At the same point that v=0), which it isn't, because there is rapid negative acceleration (or deceleration) in the direction the train is moving. So the fly is never stopped.

 

[PeterJB]

At the point when the train connects with the fly and it becomes zero and has stopped, for it to stop so must the train.

They would have to exert equal resultant force on one another for them to both stop completely. The train has a far higher mass and velocity then the fly, so it exerts a considerably higher force on the fly than the fly does in the train. The fly goes to zero very briefly when changing direction, but the fly wouldn't affect the velocity of the train in the slightest.

 

[spunwicked]

Come on, we all know trains can't fly

 

[Syntax error]

For the fly to begin travelling back the way it came it must have stopped. Therefore the train must have stopped for however minute amount of time for the fly to be going in the opposite direction.

EDIT: I'll try to find the obscure part of an obscure physics law that contains this information if I can. I'm sure it must be online and currently, I imagine, is still at theory level.

Newton's third law states that "for every action there is an equal and opposite reaction". This means that the force required to stop the fly's speed at impact will also be applied to the train however it's such a small amount of force that gravity and wind resistance would be more effective at stopping the train than the fly.

 

[kennylmao]

My answer is no, because, as the length of the rope increases, the distance the ant travels per second doesn't increase.

You're just increasing the length the rope, not the speed of the ant.

Their is no addition of matter to the rope, it has simply stretched. This stretching aids the ant in it's passage. The initial speed is 1 cm per second relative to the rope, but since the rope starts stretching this 1 cm distance is stretched proportionally, so yes, it will reach the end.

Not trying to pick you out from all the other replies and attack you specifically but I seem to understand your point best.

Which is why I am going to start an argument.

But logic(my logic at least) does not give the ant increased speed as the String is stretched. The ant itself is not stretched as the string is stretched. Thus, the body length of the ant does not increase. The length of the legs of the ant does not increase so I don't know how would the speed of the ant increase. (I think I should stop since I'm talking about ant's legs now )

Great question that is, and has got me thinking.

If you minus 10% from any number and continue to do the same(to minus 10%) for the result of the initial action, would the result eventually be 0(zero)?

What do you think? DISCUSS!

 

[Bram Turismo]

From what I can see, as you extend the rope, the ant's position moves with it. So the idea is it will take 1x100(cm)x1000(m)^1,000s to reach the end. That would be a very rough estimate, as the article extends it further.

This depends on where you place the stretching point on the rope. The ant is moving with the rope if the rope is being held at its starting point. But if one assumes the midpoint of the rope along its length is the starting point, then the ant will actually be removed further from the endpoint of the rope in comparison to when the rope is not stretched.

If the rope is held in its middle, I think it's all a question of how long the rope can be extended until it snaps. Also don't forget ants have a certain lifetime. If one assumes the rope can be stretched indefinitely or not, one also has to assume how long an ant lives.

 

[dhandeh]

It's certainly gets you thinking, which is the point. But to get the correct answer, you will need to know about the variables, where the rope is stretching, how etc.

Also what about Dec?