Plane on a conveyor belt

ICBM

No, the question specifically does not preclude the plane moving - you're reading more into it than is required to solve the problem. It simply says the speed of the conveyor must match the speed of the wheels, in the opposite direction - but since the speed of the conveyor is irrelevant to whether the plane moves forward or not, it can still be discounted even if in the thought experiment, it becomes infinite.

As Emp has now said, it's purely a question of the forces on the plane.

Sporky

ICBM said:

the speed of the conveyor is irrelevant to whether the plane moves forward or not

No it isn't.

Forget pre-GCSE physics for a moment and read the question. The conveyor exactly matches the speed of the wheels, moving in the opposite direction. That means that no matter how fast the wheels turn the plane cannot move forwards (or backwards for that matter).

Given that the plane is resting on its wheels, how can it move forwards if the conveyor moves backwards just as fast as the wheels turn?

By your and Emp's argument, the plane engines start, the plane moves forward and therefore its wheels are turning faster than the conveyor. It can't move forwards without the wheels moving faster than the conveyor. At which point you've violated the constraint set out in the original question.

Yet again, it's a paradox.

Drew_TNBD

Rocker said:

Impossible for the plane to take off and fly.  It is the air movement over and under the wing that provides the lift  and the engine that provides the forward movement to cause the air movement over and under the wing.

In my naivety I thought everyone knew why aeroplanes fly.  Seems I was wrong.

Belt go on.
Plane go back.
Plane engine go on.
Plane go forward.
Perception is that plane isn't moving.
But plane is moving.
Vroom vroom.
Plane takes off.

Sambostar

Engines suck in air,
Wheels roll,
conveyor starts,
Plane accelerates on it's wheels
Conveyor accelerates to counteract the forward motion
No airspeed achieved
Plane sits still.

monquixote

I think much of the disagreement that occurs is as a result of the fact that there are more than two possible answers to the question. As well as "Yes the plane will take off" and "No it won't" there is a third answer which is: "The question is invalid" (Sometimes called "Mu").

Starting from a realistic plane and conveyor belt the answer is "Mu" because no such conveyor belt could be built so the question is invalid.

Adding in the assumption that this is a "magic" conveyor with omnipotent control systems and infinite torque then the answer becomes "No" because the plane and the conveyor would instantly be destroyed. This is unsatisfactory so you have to add in the assumption that the plane and conveyor are indestructible.

Adding in the plane and conveyor being indestructible. The plane would take off, but this would cause the speed of the plane to exceed that of the conveyor so in this case the answer is "Mu" because the question is invalid.

If you add in the assumption that the wheel bearings are capable of generating sufficient friction to dissipate all of the energy of the conveyor and the jet then the sensible conclusion is that the wheels would lose traction with the belt and the plane might potentially skid and be able to take off without invalidating the experiment. 

If you add in the assumption that the wheels are infinitely tractable then you can potentially conclude that the plane might reach some kind of equilibrium and consider the answer to be "no", but I think there are two other possibilities:

• The engines and the moving conveyor belt would entrain so much air that the plane would get lift while remaining stationary.
• Twice the output of a 747 being dissipated through a wheel bearing would generate an enormous amount of heat sufficient to heat the air to the point where the resulting expansion and updraft would lift the plane off the ground.  

Paul_C

http://www.airplaneonatreadmill.com/2008/01/airplane-on-treadmill.html

ICBM

Sporky said:

ICBM said:

the speed of the conveyor is irrelevant to whether the plane moves forward or not

No it isn't.

Forget pre-GCSE physics for a moment and read the question. The conveyor exactly matches the speed of the wheels, moving in the opposite direction. That means that no matter how fast the wheels turn the plane cannot move forwards (or backwards for that matter).

Given that the plane is resting on its wheels, how can it move forwards if the conveyor moves backwards just as fast as the wheels turn?

By your and Emp's argument, the plane engines start, the plane moves forward and therefore its wheels are turning faster than the conveyor. It can't move forwards without the wheels moving faster than the conveyor. At which point you've violated the constraint set out in the original question.

Yet again, it's a paradox.

No it isn't. It's simply a problem with an infinite parameter - ie can only be a thought experiment.

Forget the insults for a minute and ask yourself if the plane can move forward if the conveyor is moving at any finite speed independent of the plane. If the answer is yes (which it is) then it can move if the speed of the conveyor is dictated by the speed of the plane as well.

I'm going to stop here because you are still intentionally putting more constraints on the problem than are in the original question.

Sporky

@monquixote - that, right there, is probably about as good a summing up as we're likely to get.

Drew_TNBD

monquixote said:

I think much of the disagreement that occurs is as a result of the fact that there are more than two possible answers to the question. As well as "Yes the plane will take off" and "No it won't" there is a third answer which is: "The question is invalid" (Sometimes called "Mu").

Starting from a realistic plane and conveyor belt the answer is "Mu" because no such conveyor belt could be built so the question is invalid.

Adding in the assumption that this is a "magic" conveyor with omnipotent control systems and infinite torque then the answer becomes "No" because the plane and the conveyor would instantly be destroyed. This is unsatisfactory so you have to add in the assumption that the plane and conveyor are indestructible.

Adding in the plane and conveyor being indestructible. The plane would take off, but this would cause the speed of the plane to exceed that of the conveyor so in this case the answer is "Mu" because the question is invalid.

If you add in the assumption that the wheel bearings are capable of generating sufficient friction to dissipate all of the energy of the conveyor and the jet then the sensible conclusion is that the wheels would lose traction with the belt and the plane might potentially skid and be able to take off without invalidating the experiment. 

If you add in the assumption that the wheels are infinitely tractable then you can potentially conclude that the plane might reach some kind of equilibrium and consider the answer to be "no", but I think there are two other possibilities:

• The engines and the moving conveyor belt would entrain so much air that the plane would get lift while remaining stationary.
• Twice the output of a 747 being dissipated through a wheel bearing would generate an enormous amount of heat sufficient to heat the air to the point where the resulting expansion and updraft would lift the plane off the ground.  

It should also be noted that both the conveyor belt and plane identify as attack helicopters.

hywelg

Sporky said:

ICBM said:

the speed of the conveyor is irrelevant to whether the plane moves forward or not

No it isn't.

Forget pre-GCSE physics for a moment and read the question. The conveyor exactly matches the speed of the wheels, moving in the opposite direction. That means that no matter how fast the wheels turn the plane cannot move forwards (or backwards for that matter).

Given that the plane is resting on its wheels, how can it move forwards if the conveyor moves backwards just as fast as the wheels turn?

By your and Emp's argument, the plane engines start, the plane moves forward and therefore its wheels are turning faster than the conveyor. It can't move forwards without the wheels moving faster than the conveyor. At which point you've violated the constraint set out in the original question.

Yet again, it's a paradox.

Wrong wrong wrong......

You are confusing the movement of the wheels relative to the ground and relative to the conveyor.

The movement of the plane is not governed by the rotation of its wheels, since neither are they driven nor are they braked. Therefore they are free to rotate at any rotational velocity without impacting AT ALL on the aircraft. The moment thrust is applied forward momentum is achieved (once frixtion is overcome, but I think we are agreed this is a frictionless scenario). The conveyor is utterly incapable of countering that thrust since the wheels are free to rotate.

So the plane moves at 1mph, Thus its wheels are moving at 1mph relative to the ground, and therefore the conveyor moves at -1mph. So both the aircraft and the wheels are moving at 1mph relative to the ground, but relative to the conveyor the aircraft and wheels are moving at 2mph. At 150mph (approximate take off speed) the conveyor will be moving at -150mph and thus the wheels speed over the conveyor will be 300mph, at which point the aircraft lifts off and the wheels stop rotating.....

A5D5E5

I suspect the continuing argument is because people have different interpretations of what "wheel speed" means.

If you consider it to be the speed that the axel is moving relative to the ground then there is no problem.  The plane moves forward when it turns its engines on and its wheels spin twice as fast as if it was on a normal runway.

If you mean there is a system monitoring the speed of the plan and it somehow adjusts the treadmill speed to spin backward as fast as the plane is going forward then you have a system that can't exist in the real world - as many people have already said, the conveyor would accelerate up to infinity.  This is world that the question inhabits (or at least tempts you to inhabit).

If you struggle to visualise why this is the case, imagine that rather than jet engines, the plane is powered by a very strong rope attached to the front of the plane and a very powerful winch.  When the winch is turned on does anyone really doubt that the plane will move forwards?   The jet engines and the rope & winch are exactly analogous - they simply provide thrust from a source which is not connected to the conveyor.

So you either pick a system which is based in the real world and the plane takes off.  Or you pick one which can't exist in the real world and it doesn't.  The resolution to this is just the ambiguity in the question and the fact that people become so entrenched in their own opinions.

Sporky

ICBM said:

Forget the insults for a minute

What, the time you said I didn't understand basic physics? OK. Soon as you apologise for that I'll forget it, though frankly it takes more than that to upset me.

ICBM said:

you are still intentionally putting more constraints on the problem than are in the original question.

No, I simply restated the exact constraint in the original question. The conveyor moves backwards at the exact same speed that the wheels move forwards. That's written right there.

Thus the wheels cannot change their position relative to the conveyor.

monquixote

hywelg said:

Wrong wrong wrong......

You are confusing the movement of the wheels relative to the ground and relative to the conveyor.

The movement of the plane is not governed by the rotation of its wheels, since neither are they driven nor are they braked. Therefore they are free to rotate at any rotational velocity without impacting AT ALL on the aircraft. The moment thrust is applied forward momentum is achieved (once frixtion is overcome, but I think we are agreed this is a frictionless scenario).

If it's frictionless then the plane will take off without the wheels turning at all, but that's a bit silly.

Sporky

hywelg said:

So the plane moves at 1mph, Thus its wheels are moving at 1mph relative to the ground, and therefore the conveyor moves at -1mph. So both the aircraft and the wheels are moving at 1mph relative to the ground, but relative to the conveyor the aircraft and wheels are moving at 2mph. At 150mph (approximate take off speed) the conveyor will be moving at -150mph and thus the wheels speed over the conveyor will be 300mph, at which point the aircraft lifts off and the wheels stop rotating.....

You're breaking the constraint that the conveyor moves backwards at the same speed that the wheels move forwards - you're only letting it move at half the speed.

As soon as you move away from the original question, you're not answering the original question, and you might as well answer any question you like.

Sporky

hywelg said:

The movement of the plane is not governed by the rotation of its wheels

Have you ever watched a plane take off? I can assure you that the wheels do rotate. If they didn't there'd be a horrible screeching noise and a lot of friction and then the tyres would burst or the landing gear would snap.

If the movement of planes on the ground wasn't governed by their wheels then planes wouldn't have wheels.

Drew_TNBD

Sporky said:

hywelg said:

The movement of the plane is not governed by the rotation of its wheels

Have you ever watched a plane take off? I can assure you that the wheels do rotate. If they didn't there'd be a horrible screeching noise and a lot of friction and then the tyres would burst or the landing gear would snap.

If the movement of planes on the ground wasn't governed by their wheels then planes wouldn't have wheels.

He meant to say the flight of the plane is not governed by the rotation of its wheels.

Nomad

What is the 'opposite direction' in this context? If the plane is on a normal runway and facing to the left, and if we followed the wheels with our eyes, they would rotate anti-clockwise - the top of the wheel would move left, and the bottom of the wheel (on the tarmac) would move right.

If we add in the conveyor, how does it move? Is the idea that it counteracts the rotation of the wheels? If so, would that mean that the conveyor moves to the left to counteract the right-moving bottom of the wheel that it's in contact with?

sinbaadi

The instant you move the axle of the wheel forwards, it means the wheel MUST have broken the rule of the experiment.  The wheel and belt are 1:1 as dictated by the rule.  Imagine a plane fixed to a an inverted belt sitting on an identical belt and both belts MUST turn at the EXACT same rate.  

There is no way for the aircraft to take off without breaking that rule, in fact, it can't even move an inch.

Paul_C

Emp_Fab

Sporky said:

Emp_Fab said:

FORGET THE DAMN WHEELS !!!  They, and the conveyor belt are mental distractions !

So you're rejecting the question that's actually posed, and instead substituting your own. Which is why you and ICBM keep getting the answer wrong - you reject a constraint that fundamentally changes the puzzle.

@Sporky  The question, as posed, is not the same wording as used in all of the other instances of the 'Plane on a conveyor belt' conundrum I've seen whilst searching the web.  In all the other examples, it's the plane's speed that is matched by the conveyor, not the plane's wheels.  I'm working on the assumption that we are trying to solve the conundrum as posted elsewhere, and not the misquoted version used here.  However - I can't (yet) see any difference between them.  Could you clarify what the constraint is that you feel challenges the puzzle ?

Edit: hold on - I've just seen your post above...  brb.