Plane on a conveyor belt

Handsome_Chris

viz said:

I wasn't wishing to be rude. 

The puzzle states that the conveyor matches the wheels. 

Yes it does.

viz said:

We have discussed that this means the backwards velocity of the belt matches the tangential velocity of the wheels. 

It may have been discussed, but not explicitly stated in the question.  It is something that some people have taken for granted that is the meaning.

viz said:

That implies that the plane is not moving. But as I have explained in the trolley and rope analogy, even the conveyor won't provide any counter force even at an infinite spinning speed, so that's why it's a paradox. The question implies the plane doesn't move, but it also implies that it will. 

It doesn't imply it so much as serves to lead one down a rabbit hole if one presumes certain things..

As @Emp_Fab said "It's absolutely not a paradox."  He is a walking continent of common sense.

CabbageCat

Handsome_Chris said:

viz said:

I wasn't wishing to be rude. 

The puzzle states that the conveyor matches the wheels. 

Yes it does.

viz said:

We have discussed that this means the backwards velocity of the belt matches the tangential velocity of the wheels. 

It may have been discussed, but not explicitly stated in the question.  It is something that some people have taken for granted that is the meaning.

viz said:

That implies that the plane is not moving. But as I have explained in the trolley and rope analogy, even the conveyor won't provide any counter force even at an infinite spinning speed, so that's why it's a paradox. The question implies the plane doesn't move, but it also implies that it will. 

It doesn't imply it so much as serves to lead one down a rabbit hole if one presumes certain things..

As @Emp_Fab said "It's absolutely not a paradox."  He is a walking continent of common sense.

Your interpretation of the question is such that the word "wheels" need not exist in it at all. If it didn't then there would be no discussion here. All the people you are arguing with here have decided that "wheels" means something. The "speed of the wheels" does not mean the same as the speed of the plane, it's the speed that the wheels are turning.

This is how I have interpreted it and I hope that you can understand why. 

I can understand that, if "speed of the wheels" does mean "speed of the plane" then I completely agree that it will take off. Do you agree that if "speed of the wheels" means "speed that the wheels are turning" then the plane will not take off for the reasons discussed over the past 5000 pages?

Axe_meister

But it does not matter if we have wheels or skids. No matter what the motion of the belt the aircraft will take off.
The wheels are not driven they are free wheeling.
All the wheels do is hold the aircraft up they having nothing to do with forward motion other than reduce friction

CabbageCat

Axe_meister said:

But it does not matter if we have wheels or skids. No matter what the motion of the belt the aircraft will take off.
The wheels are not driven they are free wheeling.
All the wheels do is hold the aircraft up they having nothing to do with forward motion other than reduce friction

For the umpty-third time....if your plane is going fast enough to take off then it must be going faster than the belt. Right? So let's speed up the belt. Ooh. Still, the plane has to go forwards so speed up the wheels...etc...etc...etc. Plane moves 0mm, wheels spin a zillion rpm. Melty wheels.

Maynehead

Axe_meister said:

But it does not matter if we have wheels or skids. No matter what the motion of the belt the aircraft will take off.
The wheels are not driven they are free wheeling.
All the wheels do is hold the aircraft up they having nothing to do with forward motion other than reduce friction

Here's where I answered that earlier: http://www.thefretboard.co.uk/discussion/comment/1245753/#Comment_1245753

And also here: http://www.thefretboard.co.uk/discussion/comment/1247677/#Comment_1247677

Maynehead

CabbageCat said:

Axe_meister said:

But it does not matter if we have wheels or skids. No matter what the motion of the belt the aircraft will take off.
The wheels are not driven they are free wheeling.
All the wheels do is hold the aircraft up they having nothing to do with forward motion other than reduce friction

For the umpty-third time....if your plane is going fast enough to take off then it must be going faster than the belt. Right? So let's speed up the belt. Ooh. Still, the plane has to go forwards so speed up the wheels...etc...etc...etc. Plane moves 0mm, wheels spin a zillion rpm. Melty wheels.

My god, I just realised that your avatar really is a cabbage cat! Awesome!

Handsome_Chris

CabbageCat said:

Handsome_Chris said:

viz said:

I wasn't wishing to be rude. 

The puzzle states that the conveyor matches the wheels. 

Yes it does.

viz said:

We have discussed that this means the backwards velocity of the belt matches the tangential velocity of the wheels. 

It may have been discussed, but not explicitly stated in the question.  It is something that some people have taken for granted that is the meaning.

viz said:

That implies that the plane is not moving. But as I have explained in the trolley and rope analogy, even the conveyor won't provide any counter force even at an infinite spinning speed, so that's why it's a paradox. The question implies the plane doesn't move, but it also implies that it will. 

It doesn't imply it so much as serves to lead one down a rabbit hole if one presumes certain things..

As @Emp_Fab said "It's absolutely not a paradox."  He is a walking continent of common sense.

Your interpretation of the question is such that the word "wheels" need not exist in it at all. If it didn't then there would be no discussion here. All the people you are arguing with here have decided that "wheels" means something. The "speed of the wheels" does not mean the same as the speed of the plane, it's the speed that the wheels are turning.

This is how I have interpreted it and I hope that you can understand why. 

I can understand that, if "speed of the wheels" does mean "speed of the plane" then I completely agree that it will take off. Do you agree that if "speed of the wheels" means "speed that the wheels are turning" then the plane will not take off for the reasons discussed over the past 5000 pages?

My interpretation does nothing to discount the wheels.  I know what wheels are.  They almost an everyday object where I live. 

@CabbageCat , by your own admission you like to presuppose that the "speed of the wheels" means "speed that the wheels are turning".  I have read the question a number of times and I really can't see where is says anything about "rotational this" or "turning that".  Please point that out to me.

Are you asking me to agree to the answer you have provided to question you have created?  Yeah I'm sure that I can do that, however, can we finish answering this one first.

CabbageCat

Handsome_Chris said:

@CabbageCat , by your own admission you like to presuppose that the "speed of the wheels" means "speed that the wheels are turning".  I have read the question a number of times and I really can't see where is says anything about "rotational this" or "turning that".  Please point that out to me.

I 100% accept that. But the speed of the wheels has to be a specific part of the wheel relative to something and the question doesn't specify which. You have chosen the middle of the wheel relative to the ground. I have chosen the option that seems most logical to me. "Wheel speed" generally means the rotational speed so that's what I went with. Indeed, I didn't consider for a page or two that anyone would consider it to be otherwise. 

If you had made the same assumption as me would you have reached the same conclusion?

DiscoStu

@Handsome_Chris I understand what you are trying to get at, but we are arguing different points based on interpretation of the word 'speed'. 
It isn't specified in the question but the wheels' speed can be measured in mph (if there is forward motion) or rpm. You seem to be taking it as mph whereas I read it as rpm.

Whatever rpm the plane's wheels are doing the belt matches it and there can't be any forward motion no matter how much thrust is applied. The wheels would HAVE to turn faster than the belt if the plane is to move and they can't.

Looking at your argument that it is the mph that is matched: if the plane is moving forward at 1mph via thrust, the wheels will also be moving forward at this speed as they are attached to the plane. The belt also moves at 1mph the other way and they cancel each other out. The plane must be producing the thrust required to move at 2mph on solid ground to outrun the belt by 1mph. But every time the plane increases thrust to up its mph, the belt speeds up to match that mph and the plane needs more and more thrust to try to beat the belt. To reach 180 mph through the air the plane would need to be effectively producing 360mph to outrun the -180mph effect of the belt and I don't think it could build that kind of gap as each time it pushes harder the belt drags harder.

If measured as rpm, the wheel speed and belt speed are always equal and the plane can't move.

A5D5E5

DiscoStu said:

@Handsome_Chris I understand what you are trying to get at, but we are arguing different points based on interpretation of the word 'speed'. 
It isn't specified in the question but the wheels' speed can be measured in mph (if there is forward motion) or rpm. You seem to be taking it as mph whereas I read it as rpm.

Whatever rpm the plane's wheels are doing the belt matches it and there can't be any forward motion no matter how much thrust is applied. The wheels would HAVE to turn faster than the belt if the plane is to move and they can't.

Looking at your argument that it is the mph that is matched: if the plane is moving forward at 1mph via thrust, the wheels will also be moving forward at this speed as they are attached to the plane. The belt also moves at 1mph the other way and they cancel each other out. The plane must be producing the thrust required to move at 2mph on solid ground to outrun the belt by 1mph. But every time the plane increases thrust to up its mph, the belt speeds up to match that mph and the plane needs more and more thrust to try to beat the belt. To reach 180 mph through the air the plane would need to be effectively producing 360mph to outrun the -180mph effect of the belt and I don't think it could build that kind of gap as each time it pushes harder the belt drags harder.

If measured as rpm, the wheel speed and belt speed are always equal and the plane can't move.

Rpm will differ other than by chance as the conveyor belt is a lot bigger than the planes wheels.

CabbageCat

A5D5E5 said:

DiscoStu said:

@Handsome_Chris I understand what you are trying to get at, but we are arguing different points based on interpretation of the word 'speed'. 
It isn't specified in the question but the wheels' speed can be measured in mph (if there is forward motion) or rpm. You seem to be taking it as mph whereas I read it as rpm.

Whatever rpm the plane's wheels are doing the belt matches it and there can't be any forward motion no matter how much thrust is applied. The wheels would HAVE to turn faster than the belt if the plane is to move and they can't.

Looking at your argument that it is the mph that is matched: if the plane is moving forward at 1mph via thrust, the wheels will also be moving forward at this speed as they are attached to the plane. The belt also moves at 1mph the other way and they cancel each other out. The plane must be producing the thrust required to move at 2mph on solid ground to outrun the belt by 1mph. But every time the plane increases thrust to up its mph, the belt speeds up to match that mph and the plane needs more and more thrust to try to beat the belt. To reach 180 mph through the air the plane would need to be effectively producing 360mph to outrun the -180mph effect of the belt and I don't think it could build that kind of gap as each time it pushes harder the belt drags harder.

If measured as rpm, the wheel speed and belt speed are always equal and the plane can't move.

Rpm will differ other than by chance as the conveyor belt is a lot bigger than the planes wheels.

I assume Stu means the wheel speed as a function of rpm (revs * circumference). Of course the conveyor won't match the rpm of the wheels or the 747 would fly off the back of the belt in an instant. 

DiscoStu

Actually you're right as the belt's drive wheels would need to be an identical diameter to the plane's (and this is not specified) for it to be an rpm match, as I myself started earlier on! D'oh!

Still, two freewheels of different diameters will have surfaces moving at the same mph if those surfaces are touching, though they could have different rpm. 

Maynehead

Handsome_Chris said:

My interpretation does nothing to discount the wheels.  I know what wheels are.  They almost an everyday object where I live. 

@CabbageCat , by your own admission you like to presuppose that the "speed of the wheels" means "speed that the wheels are turning".  I have read the question a number of times and I really can't see where is says anything about "rotational this" or "turning that".  Please point that out to me.

Are you asking me to agree to the answer you have provided to question you have created?  Yeah I'm sure that I can do that, however, can we finish answering this one first.

Your interpretation relies on the velocity of the centre of rotation of the wheel, and hence the plane itself. This is all well and good until we ask the question, "the velocity relative to what?"

As you should understand from the theory of relativity, velocity is not absolute, but relative to an observer situated in an inertial frame of reference. What is the frame of reference for the observer in your interpretation?

The belt's framework and machinery?
The surface of Earth?
The centre of the Sun?
The centre of Alpha Ursae Minoris?

The fact is, the question does not specify anything about this third imaginary frame of reference on which your velocity values are based, and any attempts to create one is simply making it up from figments of your own imagination.

There are only two frames of reference described by the question: the wheel (which transitively includes the plane) and the belt. My own interpretation of the term "wheel speed" is based purely and exclusively on these two frames of reference, and any speeds/velocities mentioned are fully derivable from the relationships between them.

In the situation where there are two possible interpretations; one of them built on only the information provided by the question, and the other based on elements sourced from an imaginary environment that our brains have constructed, to augment the the basic elements that we have been provided with; I choose the former simple, concise and well defined interpretation.

Handsome_Chris

Maynehead said:

Handsome_Chris said:

My interpretation does nothing to discount the wheels.  I know what wheels are.  They almost an everyday object where I live. 

@CabbageCat , by your own admission you like to presuppose that the "speed of the wheels" means "speed that the wheels are turning".  I have read the question a number of times and I really can't see where is says anything about "rotational this" or "turning that".  Please point that out to me.

Are you asking me to agree to the answer you have provided to question you have created?  Yeah I'm sure that I can do that, however, can we finish answering this one first.

Your interpretation relies on the velocity of the centre of rotation of the wheel, and hence the plane itself. This is all well and good until we ask the question, "the velocity relative to what?"

As you should understand from the theory of relativity, velocity is not absolute, but relative to an observer situated in an inertial frame of reference. What is the frame of reference for the observer in your interpretation?

The belt's framework and machinery?
The surface of Earth?
The centre of the Sun?
The centre of Alpha Ursae Minori?

The fact is, the question does not specify anything about this third imaginary frame of reference on which your velocity values are based, and any attempts to create one is simply making it up from figments of your own imagination.

There are only two frames of reference described by the question: the wheel (which transitively includes the plane) and the belt. My own interpretation of the term "wheel speed" is based purely and exclusively on these two frames of reference, and any speeds/velocities mentioned are fully derivable from the relationships between them.

In the situation where there are two possible interpretations; one of them built on only the information provided by the question, and the other based on elements sourced from an imaginary environment that our brains have constructed to augment the the basic elements that we have been provided with, I choose the former simple, concise and well defined interpretation.

TL:DR 

@Maynehead tries to blur the issues rather than admit he is wrong.

No need to apologise mate, we are all good.

Maynehead

Woohoo, our suspicions are confirmed!

Gassage

Has anyone posted this on pprune.org?

Ravenous

Gassage said:

Has anyone posted this on pprune.org?

Yes, you guessed right, someone has - over ten years ago 

Seems to have run for 50 pages there, which doesn't bode well for here...

http://www.pprune.org/jet-blast/200511-conveyor-belt-airplane.html

Sambostar

Stick it on Mumsnet, it won't even make two pages.

BigMonka

Sambostar said:

Stick it on Mumsnet, it won't even make two pages.

"I took my dearest little daughter on a plane once with my dearest husband whilst we flying to go have some Centre Parc times. Am I being unreasonable to be embarrassed when hubby asked the air stewardess for a penis beaker?"

Handsome_Chris

I though that's said "Am I being unreasonable to be embarrassed when hubby asked the air stewardess for a penis breaker?"