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Physics Riddle: The Plane on a Conveyor Belt |
 I'd like to pose a riddle which has gained alot of notoriety on the Internet, particular in the Physics world. Even Physics teachers can't seem to agree on this.
The riddle is:
If a plane is sitting on a conveyor belt, and the belt will always move in the opposite direction of the plane, at the same speed, if the pilot throttles forward, does the plane have the ability to take off?
Now, before you answer, consider a couple of things first:
A plane is not a car.
A plane requires forward movement in order to generate lift. With that said, do not make any assumptions about the plane's forward movement (or lack of movement).
Assume the conveyor belt can be as long as a runway.
Assume the wheels are strong enough to spin at any speed without breaking.
Assume there are no snakes on this plane
Assume the wheels are free-spinning and are not locked/braked in any way.
So, what do you think?
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http://blogs.starwars.com/hangover_boy/17 |
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YoshiYoda
"No Slotting, No Disintegration, No Accidents." - "Not Even a Good Slap?"
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date Posted: Jul 18, 2006 7:55 AM
I have a feeling it couldn't. It needs the forward motion, and if the conveyor belt is moving at the same speed, then it wouldn't get anywhere fast. If you would try to lift off while driving, without moving, it seems like you would go strait up, stall, and fall a few feet back down to the conveyor belt. But, then this may be a trick question.
If a plane is sitting
at the same speed
It seems that this would mean neither are moving, but this is most likely incorrect.
Perhaps this is a vertical take-off plane, in which case it could ride the conveyor belt to the end of the runway while beginning to lift off vertically.
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Padawan Binks
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date Posted: Jul 18, 2006 8:07 AM
Actually it's not so hard of a riddle, fact of the matter is that the plane doesn't need only forward movement to take off, it needs air moving over the wings at a certain speed (takeoff speed). It doesn't matter how fast a plane is moving for take off, all that matters is how the air is moving over the wings for takeoff. Really what you'd need is a converyer belt to build the plane up to its takeoff speed then use a fan to accelerate air over it so that it lifted off and immediatly began moving forward at takeoff speed, though I'm not even sure that would work.
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YoshiYoda
"No Slotting, No Disintegration, No Accidents." - "Not Even a Good Slap?"
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date Posted: Jul 18, 2006 8:08 AM
(continued)
And that way, they would have to be moving at the same speed, because the plane is riding the conveyor belt.
Oh, and a question, what timeframe is this plane from? 1942, or modern day? Because if it had a prop., then it might be able to inch its way up to speed. This is definetly a hard one.
Maybe, the wheels aren't the one doing anything, it's the thrust. The thrust from the plane may allow it to lift off, because the wheels just guide the plane, and don't have engines. But it still may not be able to escape if they are going at the same speed... Hmm.. 
You can delete the two comments above this one, and then I will only have two comments. 
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Darth Rex0
So be it....
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date Posted: Jul 18, 2006 9:22 AM
I saw this on the discussion boards and my brain hurt there too.
I would say no. The relative air speed (very important for a plane) would be zero. Not near enough to generate lift.
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Sol Kassar
Ramblings from the Detention Center (Startled)
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date Posted: Jul 18, 2006 9:38 AM
I read some of the thread and there's alot of techno-babble in there. Bottom line is the conveyor belt is moving in the opposite direction, and the plane is still stationary, regardless of the wheels spinning, the plane is not lifting off. The conveyor belt is counteracting against and, in a way, eliminating all that is needed for the plane to take off.
the belt moves in the opposite direction of the plane
This line alone implies that the plane is also moving. But if the belt is counteracting the tires of the plane, the motion of the plane is negated, leaving just the wheels spinning in place, kinda like stuck in mud.
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Hangover Boy
Captain's Log, supplemental...
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date Posted: Jul 18, 2006 9:51 AM
Okay, you guys are thinking, that's good, but you're making an assumption. You're assuming the plane remains stationary (I didn't mean to imply that in my question, so I've edited it).
If the pilot throttles forward, will the plane take off?
Now, you guys are comparing speeds, however, in order for an object to accelerate, it must have a positive net FORCE. Equal speeds does not always mean equal Forces.
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ywingempress
Shroud of the Dark Side
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date Posted: Jul 18, 2006 9:52 AM
I'd say no. Like Padawan Binks said, it's the air moving around the wings that generates lift. It has nothing to do with how fast the wheels are spinning. That's assuming the air is relatively static though - if the air above the conveyor belt was moving at the same speed and direction as the conveyor belt, it'd be a different story.
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ywingempress
Shroud of the Dark Side
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date Posted: Jul 18, 2006 9:56 AM
Ok, but the question says the plane and conveyor belt are travelling the same speed, albeit in opposite directions. Obviously the plane is accelerating, so does the conveyor belt accelerate as well? If not - well, they're no longer going the same speed and it's likely the plane would take off eventually.
This is a neat question. 
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Darth Rex0
So be it....
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date Posted: Jul 18, 2006 9:58 AM
Okay, I think I'm starting to get this. The fact that the planes use of force (the engines) is not related to contact with the ground (like a car) the fact that the belt is moving is not relevant. The ground moving only means the wheels will spin faster.
I have no idea if that makes sense.
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The Dark Moose
Moose Poodoo
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date Posted: Jul 18, 2006 10:15 AM
If the pilot throttles forward, will the plane take off?
If he throttles forward and it creates enough forward motion to move the plane through the stationary air to create lift, yes - but that has nothing to do with the conveyor belt. The only instance the conveyor belt's speed affects the aircraft's lift is if the conveyor is moving with the plane "stationary" on the conveyor track (moving at the same speed as the conveyor, in other words) with enough speed opposite airspeed to create lift.
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The Dark Moose
Moose Poodoo
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date Posted: Jul 18, 2006 10:15 AM
Replace the conveyor belt with an aircraft carrier deck and you get the same scenario. The aircraft carrier deck can be moving with or opposite the direction the plane is facing. The plane can be catapulted by steam to lift speeds (sort of like a very fast conveyor belt.) Or, if somehow the carrier deck was moving at say 125 mph, it could achieve lift. But that's only because the air over the wings is being moved at 125 (for instance) mph.
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The Dark Moose
Moose Poodoo
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date Posted: Jul 18, 2006 10:20 AM
However if the carrier was suddenly moving at 125mph indpendant of the airplane (let's say someone loaded the carrier into a giant slingshot that launched it over the surface of the water incredible speed) the airplane on the deck would do one of three things - due to inertia, the carrier deck would shoot out from underneath it, and it would fall in the ocean (like the tablecloth trick) - unlikely; or, it would remain stationary on the deck due to friction. Or, if facing the right direction into 125 mph winds relative to the plane, it could take off. But without power, it falls into the ocean. Basically, that just means it was blown off the carrier.
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The Dark Moose
Moose Poodoo
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date Posted: Jul 18, 2006 10:22 AM
Long and short of it - the effect that causes the plane to become airborne is not its speed relative to the surface its sitting on - it is the speed of the airplane's wings through the air around it. Given the right speed and density of air relative to the wings, the plane can become airborne. Whether it stays airborne or not is dependant on if it is powered flight, or simply a "leaf on the wind".
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Hangover Boy
Captain's Log, supplemental...
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date Posted: Jul 18, 2006 12:33 PM
Okay, I think I'm starting to get this. The fact that the planes use of force (the engines) is not related to contact with the ground (like a car) the fact that the belt is moving is not relevant. The ground moving only means the wheels will spin faster.
I have no idea if that makes sense
You, my friend are right.
Many people assume the conveyor belt is somehow "counteracting" the speed of the plane...but why? What force is keeping the plane from moving forward?
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Sol Kassar
Ramblings from the Detention Center (Startled)
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date Posted: Jul 18, 2006 1:15 PM
What force is keeping the plane from moving forward?
Like I said, kinda like mud. The faster you spin your wheels, the faster you sink into the mud.
The conveyor belt is moving, according to the riddle - at the same speed. Throttling forward would engage the engines and cause the plane to move faster, but the belt is matching the speed. In order for the plane to take off, wouldn't the surface underneath need to be stationary?
You need air under the wings for the plane to lift, but you don't have that when the belt is moving at the same speed but the plane is still.
Now if this were occuring in a wind tunnel, then that's different...
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Darth Rex0
So be it....
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date Posted: Jul 18, 2006 1:51 PM
wouldn't the surface underneath need to be stationary?
I don't think so. If the force moving the object forward required friction with the surface than yes, but not in this case. The plane is creating its own relative air speed because the engines don't require friction with the surface, they operate independently.
Picture a car in one of those things designed to test top speeds. You know where the drive-train wheels sit in a thing that lets the wheels sping freely? You only put the wheels that make the car go forward in that device. Which wheels would you sit in the device with an airplane? None, because the wheels don't create the speed.
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Hangover Boy
Captain's Log, supplemental...
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date Posted: Jul 18, 2006 2:36 PM
Like I said, kinda like mud. The faster you spin your wheels, the faster you sink into the mud.
You're comparing it to a car on a treadmill...a car uses friction with the ground to propel itself forward.
The plane interacts with the air, not the ground, therefore the ground would have no effect on it.
Put a car on ice. the wheels will spin, and spin, and not go anywhere. Put put a plane on ice, and the jets will thrust it forward as if on skiis.
The reason planes dont take off in icy weather is because the plane still needs the wheels to stop once the brakes are applied.
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Master_Skywalker54
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date Posted: Jul 18, 2006 7:53 PM
i remember going to an airport on a field trip a couple years ago and theres like 5 things a plane needs to take off i cant remeber all of em but i know lift and drag were 2 of them and those would not be happening on a plane on a treadmill i think but i dont know it depends if the force is involved
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Darth Daffy Duck
Dagobah Deleted Scene Babble
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date Posted: Jul 18, 2006 8:13 PM
What about those planes that take off by going straight up?
I thought I'd throw that into the mix.
I understand the spirit of the question. Lets just build a scale model and do it!
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gencrs
Technical Manuals from The GFFA
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date Posted: Jul 18, 2006 8:16 PM
That really hurts my brain. I didn't do too well in physics. Interesting to read the answers that are posted here and at the link that Rex provided. (Thanks Rex.)
I have to go back to work now.
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Rustar Landos
Chronicals of a Madman
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date Posted: Jul 18, 2006 8:33 PM
If the plane is not moving forward in the sense that it is not changing it's geographical position, it will therefor not be able to generate any air resistance, being the key factor to generate lift. Therefor, the answer is no. The plane cannot take off, assuming that the plane and conveyor belt will always be travelling the same speed(reciprocals can be a b****) No actual forward movement, no air resistance, no lift, no take off.
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Rustar Landos
Chronicals of a Madman
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date Posted: Jul 18, 2006 8:42 PM
As stated earlier, in the Cecil Adams link, the plane moves forward by having the turbine/propeller spin, displacing the air, moving it forwards. But the problem is, since the plane isn't already in the air, it uses the wheels to facilitate movement, the same way a car does. If one wants to get technical, the engine of the car moves it, the wheels are just there to smooth out friction, and add it when braking. Since the plane is on the ground, it abides by the rules of ground movement.
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Rustar Landos
Chronicals of a Madman
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date Posted: Jul 18, 2006 8:42 PM
cont. Not to say that the turbine will generate air resistance to the wings. But the resistance will be so minor, that it will not have nearly enough force to generate lift by itself. It pushes the plane forward on the ground, and uses the drag generated to lift off. Unfortuatly, since we dont live in space, we cannot apply any old force and move somewhere. Gravity wins in this situation.
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cbern
Omega Squad's 5th member
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date Posted: Jul 19, 2006 5:02 AM
good riddle
i really have no idea, but i would say no the plan couldn't take off
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DarthSolidus/Bob
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date Posted: Jul 19, 2006 5:11 AM
I think the simplest way to find the answer is to actually try it out... Or maybe not...?
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Darth Necriloth
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date Posted: Jul 19, 2006 5:34 AM
It is a witty puzzle.
The plane would not be able to take off because it would have to go twice as fast as normal to lift off the conveyer belt and get enough lift to fly. (or however fast it needed to go to clear the conveyer belt, depends on the speed of the belt)
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darthbaker613
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date Posted: Jul 19, 2006 6:04 AM
I have yet to take physics, but I am pretty confident that it wouldnt work. i guess it would depend on the plane. If you had one that was powerful enough, it could have the throttle forward for a few minutes until it had so much force it could blast offf like a rocket.
heres a good one, if a plane was sitting on a conveyor belt, and moved the plane forward at the same speed a plane normally needs to take off, and the pilot didnt move the throttle at all, could it take off?
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yodaz1127
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date Posted: Jul 19, 2006 6:10 AM
I have two questions:
1) What does this have to do with Star Wars?
2) Why is this debate still going on after Padawan Binks posted what seems to me to be the correct answer.
Note: I assume that the belt is always moving at the same speed as the plane (the original post only says that it has the "ability" to do so).
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Hangover Boy
Captain's Log, supplemental...
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date Posted: Jul 19, 2006 6:11 AM
Alot of you keep making the same assumption. You cannot compare it to a car, because a car uses it's wheels for propulsion. A car's thrust is friction...and it is being counteracted by the friction applied by the conveyor belt.
A plane is entirely different. I dont know how many people here have taken Physics, but I will mention a fundamental physics concept that is used to solve this riddle.
In order for an object to move forward, it must have a net force. That means that the force needed to push an object forward, must be greater than the force pushing it backward.
(cont)
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Hangover Boy
Captain's Log, supplemental...
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date Posted: Jul 19, 2006 6:12 AM
(cont)
In the case of an airplane on a standard runway, its Thrust must be greater than both Air Resistance and the Friction from the tires on the ground. Since planes take off every day, we know that to be the case.
Now, put the plane on a treadmill, what changes? Thrust certainly doesn't change, because the pilot controls the throttle and can make thrust the same. Air resistance certainly doesn't change, because it's dependent on the plane's motion. What about Friction? Frictional Force is found with this equation:
F = uN, where u is the coefficent if friction (a constant), and N is the weight of the plane (also a constant).
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Hangover Boy
Captain's Log, supplemental...
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date Posted: Jul 19, 2006 6:17 AM
That must mean, that Friction is a constant as well. Assume the plane weighs 1000 pounds, and let's assume the coefficent of friction is .37. Then, put the plane on a runway. The Frictional Force caused by the plane is:
F = .37 * 1000 = 370 Newtons.
Now, put the plane on a giant treadmill. What is the Frictional Force caused now? The weight of the plane doesn't change, therefore:
F = .37 * 1000 = 370 Newtons. Friction is the same in both cases.
So, if Thrust, Air Resistance, and Friction are all the same in both cases, the plane will have no problem rocketing forward on the treadmill, just as it does on the ground. The only difference, is that the wheels are spinning twice as fast as normal.
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Hangover Boy
Captain's Log, supplemental...
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date Posted: Jul 19, 2006 6:23 AM
In order for the plane to move forward, Thrust must be greater than friction plus air resistance, or T > A + F.
On a runway, this is the case every day when planes take off, so T > A + F holds true.
On a giant treadmill, there is no force (except friction) which keeps the plane from moving forward. I've shown that Friction is the same in both cases, and that the thrust from the engines is easily capable of breaking that force and rocketing forward. So, the equation still holds true, T > A + F.
In short, just because the treadmill moves at the same speed as the plane, doesn't mean it is applying sufficient force to counteract the thrust provided by the engines.
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Jedi Master Darth Aglor
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date Posted: Jul 19, 2006 6:26 AM
Many people assume the conveyor belt is somehow "counteracting" the speed of the plane...but why? What force is keeping the plane from moving forward?
What's keeping the plane from moving forward? The question is easy to answer. If God himself wishes for the plane to stay on the ground, he will.
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Hangover Boy
Captain's Log, supplemental...
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date Posted: Jul 19, 2006 6:36 AM
On a car, however, since thrust is actually provided by Friction, it is a constant as well. So, on a moving treadmill, the friction provided by the wheels is the same as the friction provided by the treadmill, so the car moves nowhere.
Just because a bird flies east at 10 mph, above a bird flying west at 10mph, does not mean their speeds cancel each other out.
Ultimately, the only force that could possibly hold the plane back is friction from the wheels on the treadmill. That is entirely dependent on the plane's weight, and not how fast either object is moving, thus never changes.
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Tigerith_Kenobi_02
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date Posted: Jul 19, 2006 6:45 AM
This is a very complacated question. The plane needs a forward Net Force to take off. Fnet = Ffoward - Fbackward. Ffoward = mass X acceleration. The mass of the plane won't change no matter what so the changing factor would have to be accelration. A = change in velocity / time. Time also doesnt change and unless the conveyor belt changes speed to match the plane at all times the change in velocity will also stay the same as normal. So the accelration won't change and neither will the foward force.
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Tigerith_Kenobi_02
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date Posted: Jul 19, 2006 6:46 AM
The backward force should be (as Hangover Boy stated) Friction and Air Resistance. Air Resistance is dependant on the plane's foward motion and Friction = mu X the Normal Force. Mu is a constant and in this case the normal Force is the weight of the plane (not the mass, the weight). So the plane should still take off.
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bluejedi32
The Force Is All Around Us
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date Posted: Jul 19, 2006 6:46 AM
Yes the plane would take off. Very good question. And great idea. Now if all airports just had conveyor belts we wouldn't need runways and we could save a lot more space on something else instead of a long runway. We could use that space to make more schools or something more important like a Krispy Kreme.
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Hangover Boy
Captain's Log, supplemental...
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date Posted: Jul 19, 2006 7:21 AM
Yes the plane would take off. Very good question. And great idea. Now if all airports just had conveyor belts we wouldn't need runways and we could save a lot more space on something else instead of a long runway
"yes" is the correct answer, however not for that reason 
The plane will always need forward motion in the absence of wind. If a conveyor belt were used, it would still need to be as long as a runway in order for the plane to take off. If you were standing off to the side, watching, and if you didn't notice the conveyor belt, everything would look exactly the same as a normal take off, except the wheels would spin twice as fast.
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Tras111
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date Posted: Jul 19, 2006 7:57 AM
The answer is indeed yes. i havn't taken physics yet. But it is easy to solve if you think about planes and try and visualize an experiment. For those of you that get blown away by technical terminology and mathmatic equations think of it this way. we know planes have wheels, but power does not go to the wheels but rather to the turbines in jet engines. When a plane throttles forward the turbines turn pulling air in and ejecting it out the back with enough force to propel the plane forward. so as stated wheels are not necessary for forward motion, they only help reduce friction and provide enough room so the plane can safely tilt for takeoff and landing.
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Tras111
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date Posted: Jul 19, 2006 7:58 AM
(cont.) Now take a toy plane or car and turn on a treadmill. hold the toy on the treadmill and it goes nowhere. This is what happens when a car drives on a conveyer belt the opposing motion negates any propulsion that could be garnered from the friction between tire and belt. The car goes nowhere. Now change the focus of propulsion to something other than the wheels. You can do this by simply pushing forward regardles of whether or not the belt is at top spead the fact remains that the toy will still move forward. Yor muscles pushing forward act in the same manner as the air passing through the turbines. So long as the air is being forced fast enough to move the plane on a stationary surface it will move, conveyor or no.
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Sol Kassar
Ramblings from the Detention Center (Startled)
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date Posted: Jul 19, 2006 8:19 AM
You cannot compare it to a car, because a car uses it's wheels for propulsion.
So the engine plays no part? Isn't the engine of a car comparable to the engine of a plane? Both used to propel? If you put the car on the belt, it's not going anywhere. Just like the plane. Wheels spinning in place, with the conveyor belt spinning in opposite direction, matching speeds and canceling out what's needed to move.
just because the treadmill moves at the same speed as the plane, doesn't mean it is applying sufficient force to counteract the thrust provided by the engines.
So the plane will eventually surpass the belt and take off?
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Hangover Boy
Captain's Log, supplemental...
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date Posted: Jul 19, 2006 8:23 AM
Tras111, that is a perfect explanation, thank you.
You can't compare this to a car on a treadmill, because the forces involved are fundamentally different.
A car relies on friction to move, a plane does not. Plane only needs air...what its wheels are doing, or what the ground is doing, is irrelevent and don't affect a plane's forward motion.
The only way a plane stops is by cutting the engines (thereby eliminating the thrust), and letting the friction between the wheels and the ground stop the plane. But when there is enough thrust, friction would be overcome.
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Hangover Boy
Captain's Log, supplemental...
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date Posted: Jul 19, 2006 8:28 AM
So the engine plays no part? Isn't the engine of a car comparable to the engine of a plane? Both used to propel?
Yes, and no.
Both have engines, but both work in completely different ways.
The engine of a plane propels air, causing it to move regardless of what it's wheels are doing.
The engine of a car spins the wheels, causing friction on the ground to propel itself forward.
it's Friction vs. expelled air. One is applied on the ground, which is why it can be negated by a treadmill, and the other is applied in the air, therefore, can never be negated by a treadmill.
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Hangover Boy
Captain's Log, supplemental...
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date Posted: Jul 19, 2006 8:30 AM
So the plane will eventually surpass the belt and take off?
Once the thrust of the engines breaks the frictional force caused by the wheels (which is the same on a conveyor as it is on a runway), yes.
The plane will move forward, gaining airflow, and lifting off.
So, it will take the same amount of time, and the same amount of effort on the plane's part in both scenarios. The moving conveyor makes no difference. it does not increase friction, and it doesn't counteract anything.
It's similar to putting skiis or skates on a plane and letting it take off on ice. the engines would cause the plane to glide over the ice. But a car would spin and spin and go nowhere.
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Tras111
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date Posted: Jul 19, 2006 9:05 AM
the only time a car might be comparable to a plane's engine is if it were jet propelled like the bat mobile. In that instance it is the energy being forces out of the rear of the vehicle that is diplacing air with enough force to move the vehicle forward so it wouldn't matter if the wheels were locked up. It would still move forward, but at a slower speed and possibly....most likely.....a good bit of damage to the car.
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cbern
Omega Squad's 5th member
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date Posted: Jul 19, 2006 9:22 AM
wow, hangoverboy
good job solving it, that was really neat
thanks
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Sol Kassar
Ramblings from the Detention Center (Startled)
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date Posted: Jul 19, 2006 9:28 AM
Once the thrust of the engines breaks the frictional force caused by the wheels (which is the same on a conveyor as it is on a runway), yes.
The plane will move forward, gaining airflow, and lifting off.
So, it will take the same amount of time, and the same amount of effort on the plane's part in both scenarios. The moving conveyor makes no difference. it does not increase friction, and it doesn't counteract anything.
OK, I think I get it now. I had to understand that the engines would actually make the plane overcome the belt, regardless of it matching speeds, and this would move the plane, gain more momentum, causing wind and lift the plane. Am I close?
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Hangover Boy
Captain's Log, supplemental...
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date Posted: Jul 19, 2006 11:04 AM
OK, I think I get it now. I had to understand that the engines would actually make the plane overcome the belt, regardless of it matching speeds, and this would move the plane, gain more momentum, causing wind and lift the plane. Am I close?
That's pretty much exactly it. And this is why the riddle is tricky. The riddle tricks the reader into assuming that because the two objects are moving at the same speed, then the forces associated with them must also be equal, therefore cancel each other out.
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Hangover Boy
Captain's Log, supplemental...
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date Posted: Jul 19, 2006 11:05 AM
(cont)
But the thrust of a plane engine is HUGE in comparison to the friction on the ground. Also, realize that a moving conveyor causes the plane to use no more energy, effort, or time than if it were sitting on solid ground, because the frictional forces at play are identical.
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