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Plane

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Because regardless of whether it is taking off on wheels from a runway, skis from snow or a hull type design from water, the engines exert a force in the air to propel it forwards. What the wheels are doing is irrelevant.
So how does it initially get forward along the ground before it gets to take-off speed?
 
This is where your assumptions completely break down, and probably why the OP is very clever.

The wheels on an airplane have zero effect on anything. They just react to a planes movement. But, you somehow thing that a consequence of the wheels moving is that they propel the plane forwards. So, you are thinking that the effect of the wheels turning in the forward momentum of the plane. Therefore, you assume the OP means:

"the conveyor belt is programmed to match the speed of the PLANE in the opposite direction, perfectly counteracting it's movement through air"

Clearly the OP does not say that, because it would be impossible to achieve. The spinning of the wheels on an airplane has no impact on it's speed, regardless of how quickly or what direction they go in
I don't get why you think anyone who disagrees with you must be stupid. We all know that the wheels are undriven, like casters on a sofa.

The wheels are attached to the plane.
If the wheels aren't rotating the conveyor isn't moving, the plane isn't moving.
If the wheels are rotating such that their surface is moving at 500mph then the conveyer is moving at 500mph to perfectly match them. The plane isn't moving.

It works whatever the speed and whatever external horizontal force is applied to the plane.

But the external horizontal force (jet engine) is the only force being applied to the plane.

But the plane can only move if the wheels move.

But the wheel rotation is annulled by the belt perfectly opposing it.

It's a chicken/egg paradox.
 
OK, so your answer is you don't understand the meaning of the word "counteracting" in the question, that's one of the main ways the puzzle gets people debating. "Counteracting" is not stopping the wheels from turning, it is cancelling out the effect of them turning, which is what treadmills do. If Crow was as vociferous as you I would question him again, I think I already did, but he isn't so I'm asking you.

I'll stress again that I'm not saying whether this plane can or can't take off, but I'm questioning your vehemence and logic saying that it definitely can. Normally when the engines apply the thrust, the wheels allow the thrust to move the plane forward, then when the plane is at speed the airflow gives the lift. But as the conveyor belt is always "counteracting" the roll/role of the wheels, how does the plane get the lift?
If the conveyor is moving and the wheels are moving then they will both be moving at the same speed - that is their relative change of contact point will always be the same.
The only way for this not to happen is if there is some slipping/skidding going on. We are assuming that this is not happening.

I hope you can accept that it takes little power from the engines for the plane to remain stationary when the conveyor is moving at say 10mph.
If the speed of the conveyor is increased to 50mph, the engines do not need to increase power to remain stationary - the wheels spin faster - made to do so by the conveyor.
If the speed of the conveyor is increased to 500mph - still no increase in power of the engines - plane remains stationary.

Then - and this is the big change in perception - engines power up and the plane moves forward. There is no resisting power or force to stop the plane moving forwards.
The faster the conveyor goes the faster the wheels spin. They are always "perfectly matched" which is perhaps a better wording than counteracting.

The wheels are not "acting" they are passively responding to the surface beneath them. The conveyor is acting, but offers no more resistance to the engines that a static runway does.
Just need to overcome that tiny bit of inertia/friction/whatever and away the plane goes.
 
If the conveyor is moving and the wheels are moving then they will both be moving at the same speed - that is their relative change of contact point will always be the same.
The only way for this not to happen is if there is some slipping/skidding going on. We are assuming that this is not happening.

I hope you can accept that it takes little power from the engines for the plane to remain stationary when the conveyor is moving at say 10mph.
If the speed of the conveyor is increased to 50mph, the engines do not need to increase power to remain stationary - the wheels spin faster - made to do so by the conveyor.
If the speed of the conveyor is increased to 500mph - still no increase in power of the engines - plane remains stationary.

Then - and this is the big change in perception - engines power up and the plane moves forward. There is no resisting power or force to stop the plane moving forwards.
The faster the conveyor goes the faster the wheels spin. They are always "perfectly matched" which is perhaps a better wording than counteracting.

The wheels are not "acting" they are passively responding to the surface beneath them. The conveyor is acting, but offers no more resistance to the engines that a static runway does.
Just need to overcome that tiny bit of inertia/friction/whatever and away the plane goes.
Which breaks the one rule of the puzzle.
If the wheels are allowed to skid on the belt it's not really a puzzle.
 
Then - and this is the big change in perception - engines power up and the plane moves forward. There is no resisting power or force to stop the plane moving forwards.
Incorrect according to the scenario:

"THE BELT IS PROGRAMMED TO MATCH THE SPEED OF THE PLANE'S WHEELS IN THE OPPOSITE DIRECTION, PERFECTLY COUNTERACTING THEIR ROTATION"
If the belt always counteracts the rolling of the wheels, the plane can't move forward can it.
 
We are assuming the wheels are passive. We are also assuming there is a pilot in the plane, trying to take off as a pilot would normally take off.

You’re changing the parameters of the original question

Well since the original question says 'imagine a plane'... it kinda means its an imaginary plane

An imaginary plane can do whatever the chuff you imagine it can do. It can have an imaginary pilot but he may be a harbour pilot and as much as he tries he knows sod all about flying planes. It can even have passive aggressive wheels that don't behave as regular wheels would

The imaginary plane can remain still and the (also imaginary) conveyor belt can take off instead and do loops :p
 
Again you've created assumptions that aren't based on what's written.
No, I have never said that the wheels actively move the plane forward. The wheels simply allow the plane to move forward as a reaction to the thrust of the engines, I think we all knew that when we reached about 8 years old.

Your thoughts on what I assume are incorrect, I do not think anything in the puzzle means "counteracts it's movement through the air", that is obviously silly, how would a conveyor belt on the ground affect a plane in the air?

The query is, how can a plane take off if the conveyor belt means it is not actually moving along the ground when the engines are providing thrust? If the plane is not moving in relation to the ground, can it take off without the normal lift from the air that comes from moving at speed?

The wheels don't really allow the plane to move forward at all, because if the plane was resting on it's fuselage and the engines were engaged, it will move forwards. Wouldn't be comfortable, but it would clearly move forwards. Maybe your opinion is indeed based on something you learnt when you were 8 years old, but have you learnt anything since then?

Your last line makes no sense. I don't know why you are asking the question, because you are fully aware that it has been discussed at length on this thread by myself and others. How simple do you need it spelt out, or is your automatic response to ignore anything someone posts because it goes against your thoughts, and you just continually ask the same question? Maybe I can do it especially for you, as I'm a nice enough person. The engines provide thrust, the plane IS moving forwards. It IS moving in relation to the air around it and it will generate lift once it gets to the required take off speed.
 
Your last line makes no sense. I don't know why you are asking the question, because you are fully aware that it has been discussed at length on this thread by myself and others. How simple do you need it spelt out, or is your automatic response to ignore anything someone posts because it goes against your thoughts, and you just continually ask the same question? Maybe I can do it especially for you, as I'm a nice enough person. The engines provide thrust, the plane IS moving forwards. It IS moving in relation to the air around it and it will generate lift once it gets to the required take off speed.
Lol.

We're trying to establish if you understand the whole point of the conveyor belt and it's becoming very obvious that you don't.

The plane ISN'T moving in relation to the fixed ground, that's the whole point of the question because the belt counteracts the wheels which normally allow the plane to move forward.

So basically, your whole premise that the plane will take off is based on the fact that you are either ignoring the biggest part of the puzzle, ie the plane is on a conveyor belt, or you don't understand the question.

The plane never gets to normal take off speed, that's the whole point.
 
I don't get why you think anyone who disagrees with you must be stupid. We all know that the wheels are undriven, like casters on a sofa.

The wheels are attached to the plane.
If the wheels aren't rotating the conveyor isn't moving, the plane isn't moving.
If the wheels are rotating such that their surface is moving at 500mph then the conveyer is moving at 500mph to perfectly match them. The plane isn't moving.

It works whatever the speed and whatever external horizontal force is applied to the plane.

But the external horizontal force (jet engine) is the only force being applied to the plane.

But the plane can only move if the wheels move.

But the wheel rotation is annulled by the belt perfectly opposing it.

It's a chicken/egg paradox.
All of that I have already agreed with.

To anyone that has assumed that the conveyor belt runs against the planes desired movement, at same speed as wheels, the paradox is there. It is impossible. The wheels can only move if the plane moves forwards, and if the ground beneath then runs backwards it speeds the wheels up even more. It is why the meme gets so many comments, because if a car was used and the question was simply about forward motion, the answer would be obvious. It is why they use the plane, because many automatically assume it operates like a conventional treadmill.

The wheels rotation will be perfectly neutralised if the conveyor belt runs at the same speed as the plane. Which is why Crow's explanation fits the OP the best
 
All of that I have already agreed with.

To anyone that has assumed that the conveyor belt runs against the planes desired movement, at same speed as wheels, the paradox is there. It is impossible.
No it's not, it's the whole point of the puzzle.
The wheels can only move if the plane moves forwards, and if the ground beneath then runs backwards it speeds the wheels up even more.
Not true. The belt is programmed to move at the same speed as the wheels to counteract what they normally do, ie allow the plane to move forward.
It is why the meme gets so many comments, because if a car was used and the question was simply about forward motion, the answer would be obvious.
Not at all, why would there be a question about whether a car would fly or not?
It is why they use the plane, because many automatically assume it operates like a conventional treadmill.
Nobody assumes, they just read and understand the puzzle, the treadmill "counteracts" the movement of the wheels, so the plane doesn't move in relation to fixed objects.
The wheels rotation will be perfectly neutralised if the conveyor belt runs at the same speed as the plane. Which is why Crow's explanation fits the OP the best
Not at all. Crow says the treadmill will move in the forward direction which most people disagree with. That is not "counteracting".
 
Lol.

We're trying to establish if you understand the whole point of the conveyor belt and it's becoming very obvious that you don't.

The plane ISN'T moving in relation to the fixed ground, that's the whole point of the question because the belt counteracts the wheels which normally allow the plane to move forward.

So basically, your whole premise that the plane will take off is based on the fact that you are either ignoring the biggest part of the puzzle, ie the plane is on a conveyor belt, or you don't understand the question.

The plane never gets to normal take off speed, that's the whole point.
Look, I've explained it. You will never ever get it. That is fine. As I've said, the wheels don't allow the plane to move forwards, but again you have chosen to ignore that point along with everything else I've said

Your arguments are all over the place, and I sense you are simply posting to have an argument, rather than actually knowing anything, or deliberately not caring. In post 408 you said:

"You cannot claim to be right on this, none of us can because the conundrum is worded to be deliberately misleading"

And yet in post I'm replying to, you are now back to giving us what you think is the definitive answer.

So, here is another paradox: How can one have a sensible logical debate with another person who has no logic?
 
That's why it's a paradox. Even theoretically it can't work the way you describe. Whatever the plane is doing, the movement of the conveyer belt cancels out any rotation of the wheels. Assuming the conveyor belt and wheel bearings are indestructible, the plane either topples forwards or breaks free of its landing gear.
You are simply disregarding the laws of motion. I'll ask once more where is the required opposing force coming from to counter the thrust of the engines.
 
You are simply disregarding the laws of motion. I'll ask once more where is the required opposing force coming from to counter the thrust of the engines.
Question for you in order that we might all understand each other a bit better maybe...

Can you give us a very simple picture of how you see the plane taking off?
Is it like normal, ie it accelerates forward and eventually takes off when it gets up to speed, or does it just go from being on the conveyor to being in the air?
Thanks.
 
Question for you in order that we might all understand each other a bit better maybe...

Can you give us a very simple picture of how you see the plane taking off?
Is it like normal, ie it accelerates forward and eventually takes off when it gets up to speed, or does it just go from being on the conveyor to being in the air?
Thanks.
It takes off as normal.

Now you explain how it's circumvents newtons 2nd law.
 
Incorrect according to the scenario:

"THE BELT IS PROGRAMMED TO MATCH THE SPEED OF THE PLANE'S WHEELS IN THE OPPOSITE DIRECTION, PERFECTLY COUNTERACTING THEIR ROTATION"
If the belt always counteracts the rolling of the wheels, the plane can't move forward can it.
It can and it does.

There is nothing to counteract the force/power of the engines.
The wheels and the surface beneath them are perfectly matched - no slippage - just as in a normal take off on a normal runway.
Whatever speed the conveyor goes - only a small amount of power is needed to keep the plane stationary - more power and the plane moves forwards.

You mentioned earlier today a sprinter who runs on to a conveyer being slowed down. Yes, this would happen.
But it would not happen if the sprinter was on free spinning wheels and he was powered by a jet-pack.
As he mounts the conveyor he is not slowed. They conveyor can not counteract the jet-pack.

Lets say a plane is on a normal runway and would reach take off speed of 180mph after 1,000 yards.
After 400 yards the plane has reached 100mph and is still accelerating, but the rest of the runway is a conveyor running at 250mph against travel of the plane.
What happens?
 
It takes off as normal.
So you're saying that the plane travels several hundred metres down the runway then hits a certain speed then angles up into the air.

But the scenario says that is impossible because as the engines thrust the plane forward over the wheels, the conveyor belt is programmed to "counteract" (neutralise/offset) them, hence the wheels are just spinning and therefore the plane does not move as normal.

Newton's 2nd law looks pretty complicated, but if you're happy to summarise it for dummies and then say how this over-rides the conveyor I'm happy to read your explanation.

"Newton’s second law is a quantitative description of the changes that a force can produce on the motion of a body. It states that the time rate of change of the momentum of a body is equal in both magnitude and direction to the force imposed on it. The momentum of a body is equal to the product of its mass and its velocity. Momentum, like velocity, is a vector quantity, having both magnitude and direction. A force applied to a body can change the magnitude of the momentum or its direction or both. Newton’s second law is one of the most important in all of physics. For a body whose mass m is constant, it can be written in the form F = ma, where F (force) and a (acceleration) are both vector quantities. If a body has a net force acting on it, it is accelerated in accordance with the equation. Conversely, if a body is not accelerated, there is no net force acting on it."
 
It can and it does.

There is nothing to counteract the force/power of the engines.
The wheels and the surface beneath them are perfectly matched - no slippage - just as in a normal take off on a normal runway.
Whatever speed the conveyor goes - only a small amount of power is needed to keep the plane stationary - more power and the plane moves forwards.

You mentioned earlier today a sprinter who runs on to a conveyer being slowed down. Yes, this would happen.
But it would not happen if the sprinter was on free spinning wheels and he was powered by a jet-pack.
As he mounts the conveyor he is not slowed. They conveyor can not counteract the jet-pack.

Lets say a plane is on a normal runway and would reach take off speed of 180mph after 1,000 yards.
After 400 yards the plane has reached 100mph and is still accelerating, but the rest of the runway is a conveyor running at 250mph against travel of the plane.
What happens?
You're getting the scenario round the wrong way in some of your examples, the plane does not respond to the conveyor, the conveyor is programmed to respond and counteract/neutralise/offset the movement of the wheels. The movement of the wheels as we all agree is a direct result of the force of the engines pushing, nobody disputes that.

Let me ask you a question:
If the engines provide enough thrust to force the wheels to move one 360 degree rotation forward, but the conveyor is programmed to respond in an exact equal amount to counteract that, how far has the plane travelled in relation to a fixed point next to it?
 
So you're saying that the plane travels several hundred metres down the runway then hits a certain speed then angles up into the air.

But the scenario says that is impossible because as the engines thrust the plane forward over the wheels, the conveyor belt is programmed to "counteract" (neutralise/offset) them, hence the wheels are just spinning and therefore the plane does not move as normal.

Newton's 2nd law looks pretty complicated, but if you're happy to summarise it for dummies and then say how this over-rides the conveyor I'm happy to read your explanation.

"Newton’s second law is a quantitative description of the changes that a force can produce on the motion of a body. It states that the time rate of change of the momentum of a body is equal in both magnitude and direction to the force imposed on it. The momentum of a body is equal to the product of its mass and its velocity. Momentum, like velocity, is a vector quantity, having both magnitude and direction. A force applied to a body can change the magnitude of the momentum or its direction or both. Newton’s second law is one of the most important in all of physics. For a body whose mass m is constant, it can be written in the form F = ma, where F (force) and a (acceleration) are both vector quantities. If a body has a net force acting on it, it is accelerated in accordance with the equation. Conversely, if a body is not accelerated, there is no net force acting on it."
My apologies, it's the 3rd law.
For every action etc
To counter the thrust of the engines you need an opposing force.
This is basic science, neither the wheels or the conveyor are providing this , so where does it come from ?
The wheels of the plane can only move as a direct consequence of the forward push of the engine thrust, they have no power of there own.
You've made the basic error of thinking it's like a car, where the wheels turn and push themselves along the floor.
Not the case with a plane, it's push itself against the air.
 
You're getting the scenario round the wrong way in some of your examples, the plane does not respond to the conveyor, the conveyor is programmed to respond and counteract/neutralise/offset the movement of the wheels. The movement of the wheels as we all agree is a direct result of the force of the engines pushing, nobody disputes that.

Let me ask you a question:
If the engines provide enough thrust to force the wheels to move one 360 degree rotation forward, but the conveyor is programmed to respond in an exact equal amount to counteract that, how far has the plane travelled in relation to a fixed point next to it?
What's the diameter of the wheel?
 
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