Cue PH brainiacs - logic puzzle!
Discussion
There's one other possible way to produce the conditions claimed for this experiment, and that relies on the inertia of the wheels. If you take a simplified view of wheels acting like frictionless supports, you can accelerate the conveyor belt and it won't have any effect on the plane. But in practice the wheels have finite rotational inertia, and as you accelerate the belt backwards it will pull the wheels back slightly. In theory, as long as you keep sufficient acceleration on the belt you can keep applying a backwards load on the wheels to oppose the thrust from the engines.
I'm not saying this is the 'right' answer to the puzzle, IMO the assertion that the conveyor belt can prevent the plane from moving forwards is utter b*llocks so the answer is that there is no answer because the situation that is described cannot occur.
I'm not saying this is the 'right' answer to the puzzle, IMO the assertion that the conveyor belt can prevent the plane from moving forwards is utter b*llocks so the answer is that there is no answer because the situation that is described cannot occur.
GreenV8S said:
There's one other possible way to produce the conditions claimed for this experiment, and that relies on the inertia of the wheels. If you take a simplified view of wheels acting like frictionless supports, you can accelerate the conveyor belt and it won't have any effect on the plane. But in practice the wheels have finite rotational inertia, and as you accelerate the belt backwards it will pull the wheels back slightly. In theory, as long as you keep sufficient acceleration on the belt you can keep applying a backwards load on the wheels to oppose the thrust from the engines.
I'm not saying this is the 'right' answer to the puzzle, IMO the assertion that the conveyor belt can prevent the plane from moving forwards is utter b*llocks so the answer is that there is no answer because the situation that is described cannot occur.
Its much easier than that. You don't have to explain why the plane stays still. The problem definition says the conveyor moves backards at the same speed the plane moves forwards. You don't have to reason why it should or should not according to physics, friction, thrust or hyperspatial interactive chocolate, it is defined to stay still.
Does nobody understand the concept of a theoretical problem?
Size Nine Elm said:
Its much easier than that. You don't have to explain why the plane stays still. The problem definition says the conveyor moves backards at the same speed the plane moves forwards. You don't have to reason why it should or should not according to physics, friction, thrust or hyperspatial interactive chocolate, it is defined to stay still.
Does nobody understand the concept of a theoretical problem?
Actually, as far as I remember it the original problem statement was quite ambiguous about how fast the conveyor belt was moving and in which direction, which I think is why people have been guessing at how the stated scenario could be achieved using effects that require arbitrarily high belt speeds. I think I do understand the concept of a theoritical problem, and as I understand it these problems ignore practicality and discuss things that could happen in theory.
You seem to be saying that an aircraft on a conveyor belt with engines pushing it forwards is prevented from moving forward because the belt is moving backwards. The fact that the belt is moving backwards does not prevent the plane from moving forwards, so the situation you're describing cannot occur unless there is some other factor that you have not described, or you are carrying out the experiment in a universe which doesn't obey the same laws of physics as our one. Saying that it is a theoretical poblem does not mean you can ignore the laws og physics, it just means you can ignore practical constraints.
I can't beleive this aeroplane debate has gone on so long 
It really is a badly worded problem and as such it's a pointless one. The opposing force to the thrust of the engines is NOT the floor/belt it's the air and hence the belt is utterly irrelevant. The plane of course would take off.
It really is a badly worded problem and as such it's a pointless one. The opposing force to the thrust of the engines is NOT the floor/belt it's the air and hence the belt is utterly irrelevant. The plane of course would take off.
GreenV8S said:That was my understanding of the problem.
You seem to be saying that an aircraft on a conveyor belt with engines pushing it forwards is prevented from moving forward because the belt is moving backwards.
GreenV8S said:Hmmm. Well, obviously that's going to make a fundamental difference to the solution, because at the end of the day it all boils down to whether the aircraft achieves airspeed and hence lift. My arguments thus far have been based on the assumption that there was no net forward motion. If that proves to be flawed then so are my arguments.
The fact that the belt is moving backwards does not prevent the plane from moving forwards, so the situation you're describing cannot occur unless there is some other factor that you have not described
carrera2 said:
I can't beleive this aeroplane debate has gone on so long
It really is a badly worded problem and as such it's a pointless one. The opposing force to the thrust of the engines is NOT the floor/belt it's the air and hence the belt is utterly irrelevant. The plane of course would take off.
But it can't, because to do so, it would have to move faster forwards than the belt was moving backwards.
If you hypothesize in this manner, you have abandoned the original problem scenario for one of your own construction.
It's funny what your mind will do to you in the early hours of the morning when you're suffering from fitful sleep, because a solution popped into my head in the night that changes my position on this debate a bit.
We've talked about frames of reference, speed relative to it surroundings (ie. GPS position), speed relative to conveyor belt, etc.
We have all agreed that the only way for the plane to take off is if it achieves sufficient airflow over its wings to generate lift, and the only way for that to happen is if it moves relative to its GPS position.
Thus far I have been arguing that if the plane moves forward by distance d, regardless of motive force, and the belt moves the plane backwards by an equal distance d then there is no net movement and thus no lift. I believe this assumption may be flawed.
What I beleive may instead happen is that the aircrafts propellors or jet engine extert a backward force F on the surrounding air and by F=ma cause an acceleration in the forward direction, which will correspond to a movement of distance d in the forward direction.
The conveyor, sensing the forward motion of the aircraft, travels a corresponding distance d backwards. As a result, the wheels of the aircraft rotate n=d/C times (where d is the distance moved and C is the circumference of the wheels). How much of that movement is translated into a force on the aircraft in a direction opposite to its direction of travel is the key to the outcome of this problem. If even some of the conveyor belt's movement d is accounted for by the wheels rotating rather than being transferred to a movement of the aircraft, then the aircraft will move forward by a non-zero distance that is less than d. Over time t then a speed of s=d/t will be achieved and s will eventually be sufficient for take-off, albeit with the wheels spinning much, much faster than normal.
Yes, I know that's what joust said. Do you have any idea what a smug bastard he's going to be when he reads this?
So basically, the question is insufficiently defined as it does not define the characteristics of the wheels. It is only if they have almost infinitely high traction and extremely high rolling resistance that they could translate all of that movement d into a force F of equal (but opposite) magntitude to the force that was imparted by the aircraft's propulsion.
Do you have any idea what Humble Pie tastes like at 8.45am on a Sunday morning?
>> Edited by JonRB on Sunday 11th December 08:48
We've talked about frames of reference, speed relative to it surroundings (ie. GPS position), speed relative to conveyor belt, etc.
We have all agreed that the only way for the plane to take off is if it achieves sufficient airflow over its wings to generate lift, and the only way for that to happen is if it moves relative to its GPS position.
Thus far I have been arguing that if the plane moves forward by distance d, regardless of motive force, and the belt moves the plane backwards by an equal distance d then there is no net movement and thus no lift. I believe this assumption may be flawed.
What I beleive may instead happen is that the aircrafts propellors or jet engine extert a backward force F on the surrounding air and by F=ma cause an acceleration in the forward direction, which will correspond to a movement of distance d in the forward direction.
The conveyor, sensing the forward motion of the aircraft, travels a corresponding distance d backwards. As a result, the wheels of the aircraft rotate n=d/C times (where d is the distance moved and C is the circumference of the wheels). How much of that movement is translated into a force on the aircraft in a direction opposite to its direction of travel is the key to the outcome of this problem. If even some of the conveyor belt's movement d is accounted for by the wheels rotating rather than being transferred to a movement of the aircraft, then the aircraft will move forward by a non-zero distance that is less than d. Over time t then a speed of s=d/t will be achieved and s will eventually be sufficient for take-off, albeit with the wheels spinning much, much faster than normal.
Yes, I know that's what joust said. Do you have any idea what a smug bastard he's going to be when he reads this?
So basically, the question is insufficiently defined as it does not define the characteristics of the wheels. It is only if they have almost infinitely high traction and extremely high rolling resistance that they could translate all of that movement d into a force F of equal (but opposite) magntitude to the force that was imparted by the aircraft's propulsion.
Do you have any idea what Humble Pie tastes like at 8.45am on a Sunday morning?
>> Edited by JonRB on Sunday 11th December 08:48
Cristo montado en bicicleta!
The plane does not takeoff as there is no airspeed. You are using flawed logic as per the following example:
The Hare and the Tortoise have a Race:
Tortoise has the traditional head start.
When the hare gets to where the tortoise was (call this T), the tort will have moved some way ahead (T+n)
When the hare gets to this new place (T+n), the tort will have moved a tiny bit further ahead and is now at (T+n+n/y). And so on. Whenever the big-eared thing catches the shelly thing, the latter will have moved a teeny weeny bit further ahead. Ergo, the hare can never overtake the tortoise.
The plane does not takeoff as there is no airspeed. You are using flawed logic as per the following example:
The Hare and the Tortoise have a Race:
Tortoise has the traditional head start.
When the hare gets to where the tortoise was (call this T), the tort will have moved some way ahead (T+n)
When the hare gets to this new place (T+n), the tort will have moved a tiny bit further ahead and is now at (T+n+n/y). And so on. Whenever the big-eared thing catches the shelly thing, the latter will have moved a teeny weeny bit further ahead. Ergo, the hare can never overtake the tortoise.
Size Nine Elm said:As I said about 5 pages before
Its much easier than that. You don't have to explain why the plane stays still. The problem definition says the conveyor moves backards at the same speed the plane moves forwards. You don't have to reason why it should or should not according to physics, friction, thrust or hyperspatial interactive chocolate, it is defined to stay still.
Does nobody understand the concept of a theoretical problem?
the real answer is that "the question can never happen". QED, MCP, MIDG.
J
JonRB said:Not smug Jon, just glad you got there in the end. It's a great problem, and flawed from a theory to practice basis.
Yes, I know that's what joust said. Do you have any idea what a smug bastard he's going to be when he reads this?
Do you have any idea what Humble Pie tastes like at 8.45am on a Sunday morning?
One slight thing, the force isn't produced "against" the air by the engines. Jet engines work by simple newotonian mechanics (his third law). For every force there is an equal and opposite force.
Jet engines work by ejecting mass (the combined fuel and air mixture) out of the rear of the engine, and accelerate that mass. Simple f=ma gives you the amount of force being generated by taking a small amount of fuel (say 1 gramme per second) and accelerating it due to the exposive force and sending it out the rear. That f then has an equal and opposite f going the other way, and that is what "pushes" the engine forward, which hence "drags" the plane along with it.
www.ueet.nasa.gov/Engines101.html
Consequently, the ground is irrelevant as the force that propels the plane forward has nothing to do with the ground or even the air around it as the plane is "deattached" from the ground by the wheels (theoretically, if there was no air behind the plane, i.e. the plane carried it's own air supply and was in a vacuum, the plane would still move forward. This is how rockets work in space - there is nothing to "push" against in space, but because of the way a jet engine works, it doesn't matter...)
There is a slight drag effect due to the frictional loss in the bearings of the wheels, but it is so small compared to the thrust of a jet engine that you could never overcome even the smallest of jet engines.
In summary, the question is flawed as it doesn't specify enough detail, but if you take it at face value you get the answer you just came to.
J
Size Nine Elm said:Actually, I seem to recall that the problem stated that the conveyor belt's speed automatically matched the forward speed of the aircraft, which is a fairly wooly statement.
Its much easier than that. You don't have to explain why the plane stays still. The problem definition says the conveyor moves backards at the same speed the plane moves forwards. You don't have to reason why it should or should not according to physics, friction, thrust or hyperspatial interactive chocolate, it is defined to stay still.
I can actually see both sides of the argument now, and my conclusion is that the question is insuffiently defined.
joust said:Yes, I realise that. I was being imprecise in my definitions - I actually meant in the frame of reference of the surroundings (excluding conveyor).
One slight thing, the force isn't produced "against" the air by the engines. Jet engines work by simple newotonian mechanics (his third law). For every force there is an equal and opposite force.
JonRB said:
Actually, I seem to recall that the problem stated that the conveyor belt's speed automatically matched the forward speed of the aircraft, which is a fairly wooly statement.
The issue is then the definition of the word 'matched'. If this implies a reactive behaviour, then the plane has to change speed, and position, before the conveyor reacts, and there is an interval in which the plane is not at rest.
If it is predictive and absolute, then the conveyor's speed always matches that of the plane and no takeoff is possible.
So it boil down to the unspecified latency in the word 'matched'.
BTW, Jon, I htink your humble pie is incorrect - it is possible that the plane could achieve a takeoff speed in a differential manner, but it will be for insufficient time for a takeoff - unless the latency is indeed of the order of numbers of seconds.
ETA: With a bit of lateral thinking, there are other ways in which the plane could achieve takeoff without breaking the constraints of the problem, e.g the windspeed reaches 180mph headwind. Plane takes off at zero groundspeed.
(Other solution removed on the grounds of taste).
>> Edited by Size Nine Elm on Sunday 11th December 11:17
carrera2 said:
I can't beleive this aeroplane debate has gone on so long
It really is a badly worded problem and as such it's a pointless one. The opposing force to the thrust of the engines is NOT the floor/belt it's the air and hence the belt is utterly irrelevant. The plane of course would take off.
?? i really dont see where you come to the conclusion that the plane would take off?
the only thing that matters is the amount of air passing over and under the wings. the wings give lift. the engine propel the plane through the air so that the air moves over the wings which in turn creates lift.
so the wheels and engines when the plane is on a conveyor belt have nothing to do with it. you HAVE to measure the speed of the air going over the wings. which in this scenario there would be zero airspeed so the wings are going to give no lift.
Size Nine Elm said:
If it is predictive and absolute, then the conveyor's speed always matches that of the plane and no takeoff is possible.
So it boil down to the unspecified latency in the word 'matched'.
I think you're repeating the original mistake, which is to assume that by moving backwards, the conveyor belt can somehow prevent the plane from moving forwards. The only way it could do this is by applying a backwards force on the plane, and if you think that is the case you need to explain how it achieves this.
GreenV8S said:Yes, that's the conclusion I came to during my screaming U-turn. The conveyor belt will certainly interact with the wheels, but it is unclear how that is then translated into movement on the aircraft. Same concept as the "whipping the tablecloth away whilst leaving the crockery (relatively) intact" trick.
I think you're repeating the original mistake, which is to assume that by moving backwards, the conveyor belt can somehow prevent the plane from moving forwards. The only way it could do this is by applying a backwards force on the plane, and if you think that is the case you need to explain how it achieves this.
JonRB said:
I think you're repeating the original mistake, which is to assume that by moving backwards, the conveyor belt can somehow prevent the plane from moving forwards. The only way it could do this is by applying a backwards force on the plane, and if you think that is the case you need to explain how it achieves this.
Just think of the rollerblades and rope example.....
Size Nine Elm said:Sorry. Assuming the wheels did actually produce maximum theoretical drag (of which of course most will be the drag of the rubber on the surface which is many many times more than the drag due to the bearings), to stop even the very first jet engine ever made the conveyer belt would have to be going back at somewhere arond 5 times the speed of light.
If it is predictive and absolute, then the conveyor's speed always matches that of the plane and no takeoff is possible.
The question is therefore impossible to replicate in real life. Also, even if you could defy the laws of physcis in making the conveyer go backwards quick enough to produce enough drag, any modern jet engine would require a converyer going backwards at around 100 times the speed of light to stop it.
Ergo the plane, as described, will take off.
J
JonRB said:
I think you're repeating the original mistake, which is to assume that by moving backwards, the conveyor belt can somehow prevent the plane from moving forwards. The only way it could do this is by applying a backwards force on the plane, and if you think that is the case you need to explain how it achieves this.
Nope. As I said sometime earlier, if the conveyor is defined to move backwards at the same speed the plane moves forwards, I don't have to provide any reason whatsoever, except to state that it is a precondition of any proposed solution to the problem as stated that this is true.
So any proposed solution which inludes any instant at which the plane is moving at a different speed forwards to the conveyor moving backwards is not a solution to this problem - merely a statement that planes can, in fact, sometimes take off.
If you really want a reason, then perhaps the plane has been fitted with square wheels and the brakes are locked on, or there's a huge chain attached to the rear of the plane stopping it moving forwards... I don't really care, its just not moving forwards at a different speed to the conveyor moving backwards.
And it won't take off.
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