A harmless little riddle

I think the point of the riddle is to incite these discussions, where people inject their own assumptions and then logically deduce what would happen. I think it has probably made people think about the problem a lot more closely than they normally would, and that's a good thing.

Yay! wow left! Great job, to all those who contributed to exterminating a troll.

My only regret is that he never found out the correct answer...

cgaites wrote:

First, off I do not believe this is a valid interpretation of the riddle because in order to the conditions of the riddle to be satisfied at all times one would have to assume both a treadmill and airplane engines capable of infinite acceleration

hi all wrote:

Well, if the plane is to remain stationary, the treadmill must provide an acceleration equal to (F_(engines)*I/r^2), as argh... has posted. Which means that the treadmill will soon become relativistic, making the treadmill shrink, eventually so much that the plane falls off the treadmill and starts to roll. By that time, though, most of the air on the planet will have been flung into far space, the rubber surfaces in question would have vaporized, and the material of the treadmill surface would have contorted as it rapidly accelerates around the corners.

These ideas are ridiculous. Why do you have to travel at the speed of light or need infinite accelerations to keep an airplane stationary (relative to the ground) on a moving treadmill? The treadmill exerts a finite frictional force on the airplane, and the wheels have finite moments of inertia. Just get the treadmill going and turn the jets on "low" setting, and you have a stationary airplane on a moving treadmill.

P.S. I am not saying that the plane will not take off (because it will). I'm just pointing out the flaws in these responses.

If you remember Newton's First Law, objects in motion stay in motion. This is why if you turn the treadmill on a constant speed and turn the jet engines on, the plane will undergo constant acceleration.

In order for the treadmill to counter the force of the engines (say a constant force), the treadmill needs to exert a force on the wheels. This is precisely the force that causes the wheels to accelerate, since the force also acts as a torque. But if the wheels accelerate, the treadmill must accelerate, too.

So the treadmill can stop the plane only by constantly accelerating at a rate of a=F_{engines}*I/r^2, where I is the moment of inertia of the wheels. You can see how after some time the treadmill will be moving quite fast, even relativistically fast. This might take a few centuries, but still...

oh man wrote:

These ideas are ridiculous. Why do you have to travel at the speed of light or need infinite accelerations to keep an airplane stationary (relative to the ground) on a moving treadmill? The treadmill exerts a finite frictional force on the airplane, and the wheels have finite moments of inertia. Just get the treadmill going and turn the jets on "low" setting, and you have a stationary airplane on a moving treadmill.

P.S. I am not saying that the plane will not take off (because it will). I'm just pointing out the flaws in these responses.

Hey man I agree with you. I started out trying to explain just what you said, but after the fifteenth time I shifted my tactic to trying to explain the flaw in the opposing arguement - hence the whole treadmill at the speed of light thing.

You would have to accelerate the treadmill at some astronomical rate to over come the trust of normal airplane the engines since the friction forces at the wheels are so much less than the thrust force produced by the engines. The rate at which you would have to accelerate the treadmill to stop the plane is proportional to the thrust produced by the engines and the moment of inertia of the wheels. If you were going to say the plane will never fly you would need to keep increasing this rate of acceleration as the amount of thrust increases. Since the engines are arbitrarily and infinitely powerful in the riddle, in order for the plane to never fly the treadmill would have to be capable of infinite acceleration. Therefore it is ridiculous to say that the treadmill is capable of preventing the plane from flying and to interpert the riddle to mean that the treadmill prevents the plane from moving relative to a stationary observer off to the side of the treadmill.

C'mon people, keep this going. We can make 1000.

Sorry, wow can make 1000.

hello wrote:

If you remember Newton's First Law, objects in motion stay in motion. This is why if you turn the treadmill on a constant speed and turn the jet engines on, the plane will undergo constant acceleration.

Yes, but that constant acceleration can just as well be zero as long as you choose the correct thrust for the engines to produce.

I do remember newton's first law, and it has nothing to do with your point about constant acceleration.

in that case, i'm confused about what your point is. in your first post, you said that if treadmill is on (meaning running at a constant velocity?) and the plane's jets are on a "low" setting, then the plane won't accelerate. this is incorrect-if the treadmill is running at a constant velocity, then the planes engines need to be off (consider the frame of reference of the treadmill, which is now an inertial frame).

the constant acceleration will be zero only if the engines are completely off. this is the application of newton's first: if you consider the frame of reference of the moving treadmill, the plane will stay moving at exactly the same speed when its engines are off.

hello wrote:

in that case, i'm confused about what your point is. in your first post, you said that if treadmill is on (meaning running at a constant velocity?) and the plane's jets are on a "low" setting, then the plane won't accelerate. this is incorrect-if the treadmill is running at a constant velocity, then the planes engines need to be off (consider the frame of reference of the treadmill, which is now an inertial frame).

the constant acceleration will be zero only if the engines are completely off. this is the application of newton's first: if you consider the frame of reference of the moving treadmill, the plane will stay moving at exactly the same speed when its engines are off.

Yeah, but you're assuming there is no internal friction in the wheels, which there most certainly is. Like, for example, if you have your skateboard sitting on a treadmill going a constant speed and you let go of the skateboard, it will slowly drift off the back of the treadmill because the internal resistance of the wheels will slow them and so the skateboard will fall off the back. Same thing with the plane.

You need a very small force from the engines to keep the plane on the treadmill at a constant speed.

Since the internal resistance, moment of inertia of the wheels, max force of the engines, and rate of acceleration of the treadmill are all undefined variables in the riddle, they could be anything and it could be either quite easy for the treadmill's acceleration to counteract the force of the engines, or it could be impossible. It just depends on what values you choose.

hello wrote:

i'm confused

agreed

The only question here should be what the speed of the plane is relative to. Nothing else matters. If it's relative to the rest of the earth, yes it can take off if the speed is high enough.

Again, the real question is if a tree falls in a forest and then springs back up as a joke, do the squirrels freak out?

Went for a run tonight and asked a buddy about it. He explained it well and now I get it; the plane will fly. I had posted before it wouldn't. It was posted already but the speed of the plane relative to the ground has to do with the thrust generated and not the speed of the wheels. Unlike a car on treadmill, the wheel speed doesn't matter.

The skateboard being pulled is actually a good way of envisioning it.

no! don't slow down! 1000 posts in sight!

well, good this turned out better than I thought...

the answer:

No it will not fly...you friggn' retards. You people who think it can b/c of what you think I meant are completely gay. It will never fly while it is on a treadmill.

from the person who asked the question...case closed.....and i'm like 99.9% sure wow. has downsyndrome.

Exactly...the whole point of this riddle is to catch people off guard at first, and then, after 30 seconds or so of explanation and/or though, realise that the plane doesn't act like a car, and that the treadmill is a red herring and is irrelevant to something which moves itself by thrusting itself through air instead of driving its wheels.It's not supposed to be 40 pages of idiocy.

mandingo wrote:Went for a run tonight and asked a buddy about it. He explained it well and now I get it; the plane will fly. I had posted before it wouldn't. It was posted already but the speed of the plane relative to the ground has to do with the thrust generated and not the speed of the wheels. Unlike a car on treadmill, the wheel speed doesn't matter.

the riddler wrote:

well, good this turned out better than I thought...

the answer:

No it will not fly...you friggn' retards. You people who think it can b/c of what you think I meant are completely gay. It will never fly while it is on a treadmill.

from the person who asked the question...case closed.....and i'm like 99.9% sure wow. has downsyndrome.

Well I registered my username and this crap won't be happening again.

the magic breath of life wrote:

the riddler wrote:

well, good this turned out better than I thought...

the answer:

No it will not fly...you friggn' retards. You people who think it can b/c of what you think I meant are completely gay. It will never fly while it is on a treadmill.

from the person who asked the question...case closed.....and i'm like 99.9% sure wow. has downsyndrome.

Well I registered my username and this crap won't be happening again.

...what?

I switched too, (although that happened way back on page 25 or so). Theoretically it is true, the plane shouldn't be able to fly IF the treadmill is keeping it from moving forward relative to the ground, as the question words it. However the forces involved would have to be extremely large to keep the plane from advancing forward, and in actuality the plane would ultimately easily overcome the treadmill's resistance.

At the very first moment that the plane starts its engine and the treadmill starts moving, it is truly the case as worded in the question- that the thrust of the plane's jets or propellers can be successfully countered by the treadmill- however, this is only at the very lowest of power levels, since the resistance to movement offered by the friction of the wheels and treadmill is very small. The only way I can think of that you could possibly keep the plane from flying in the scenario given, is that if it was so heavily loaded, that its gross weight was just below the limit where it could have normally lifted off the ground, but the added friction of the treadmill prevented it from doing so. But in any case, the plane should be able to accelerate and move forward (if it is not overloaded and could normally fly).

Make that page 34 where I switched: http://www.letsrun.com/forum/flat_read.php?board=1&thread=1161075&id=1455985#1455985