Plane on a conveyor belt

Handsome_Chris

viz said:

0 mpHandsome_Chris said:

@viz, wouldn't the wheel at surface contact with the belt be doing 0 mph?

0mph relative to each other, ie matched, but spinning very quickly none the less - infinitely fast in fact! And the plane's wheels will go at a larger infinity speed than the conveyor.

No

The tangential speed of the wheel at any speed of the plane is 0 mph.  The Conveyor belt is then going 0 mph in the other direction.

as the plane picks up speed the tangential speed of the wheel on contact with the conveyor belt is 0 mph. Therefore teh conveyor belt matches that 0 mph by going at 0mph.

The plane picks up more speed.  The tangential speed of the wheel on contact with the conveyor belt is 0 mph. Therefore the conveyor belt matches that 0 mph by going at 0mph.

@Viz, thank you for bringing tangential speed into it.  It has made it even easier to sort out.

Handsome_Chris

PS - The plane takes off.

doogz84

viz said:

doogz84 said:

viz said:

doogz84 said:

The trickiest part of the problem is how does the conveyor belt know what speed to move at?!

It knows it needs to ramp up to infinity as soon as it hears the engines firing up. 

I disagree. But the question could be phrased better, which is the only problem.

I believe the question was supposed to propose a problem whereby the conveyor belt rotates at a speed equal to, but opposite in direction to, the wheels if the aircraft was taking off as normal, on a normal take off run.

What you're suggesting is that if the wheel starts rotating at 1mph, the conveyor is going 1mph in the opposite direction, therefore the wheel is actually doing 2mph, so the conveyor must to 2mph, meaning the wheel is now doing 4mph and so on, instantly to infinity.

I don't think that's what the question was meaning to ask.

That's not what I mean. I mean that regardless of how fast the conveyor moves backwards, it still cannot provide any counter force to the thrust of the jets, so they will automatically spin up to infinity to match the wheels (whose inclination will be to rotate forwards, and which in turn will have to acccelerate to be faster than the belt). 

I've read your reply and it seems to be exactly what you mean, you're just phrasing it differently?

You're stating the belt will speed up to infinity to match the wheels. So the wheels are travelling at infinity. Why? Our aircraft has only just started rolling, it's doing 10mph airspeed, why are the wheels spinning infinitely fast?

viz

No, tangential speed is an absolute figure - a 1m diameter tyre fixed in absolute position, spinning at 60rpm has a tangential speed of 3.14m/s. It doesn't mean the speed relative to the belt, which is, as you rightly say, 0 - because there is no slippage in this thing. 

Handsome_Chris

@Viz, I'm glad that you agree with common sense.  

You can't argue with maths.

viz

doogz84 said:

viz said:

doogz84 said:

viz said:

doogz84 said:

The trickiest part of the problem is how does the conveyor belt know what speed to move at?!

It knows it needs to ramp up to infinity as soon as it hears the engines firing up. 

I disagree. But the question could be phrased better, which is the only problem.

I believe the question was supposed to propose a problem whereby the conveyor belt rotates at a speed equal to, but opposite in direction to, the wheels if the aircraft was taking off as normal, on a normal take off run.

What you're suggesting is that if the wheel starts rotating at 1mph, the conveyor is going 1mph in the opposite direction, therefore the wheel is actually doing 2mph, so the conveyor must to 2mph, meaning the wheel is now doing 4mph and so on, instantly to infinity.

I don't think that's what the question was meaning to ask.

That's not what I mean. I mean that regardless of how fast the conveyor moves backwards, it still cannot provide any counter force to the thrust of the jets, so they will automatically spin up to infinity to match the wheels (whose inclination will be to rotate forwards, and which in turn will have to acccelerate to be faster than the belt). 

I've read your reply and it seems to be exactly what you mean, you're just phrasing it differently?

You're stating the belt will speed up to infinity to match the wheels. So the wheels are travelling at infinity. Why? Our aircraft has only just started rolling, it's doing 10mph airspeed, why are the wheels spinning infinitely fast?

Assuming frictionless bearings:

At rest, the plane isn't moving. As soon as it inches forward (well, millimetres forward), and its wheel starts to turn, the conveyor switches on and starts going backwards. From that INSTANT, both speed up instantaneously to infinity, because the aeroplane wants to move forwards and the conveyor is trying to keep it in position. But because it cannot succeed in that task (because it doesn't provide backwards force, and the plane WILL move forwards), it spins to infinity, as do the plane wheels, but the plane wheels reach infinity plus 300mph (which on the one hand equals infinity, and on the other is larger than infinity - hence it's a paradox). 

Handsome_Chris

viz said:

doogz84 said:

viz said:

doogz84 said:

viz said:

doogz84 said:

The trickiest part of the problem is how does the conveyor belt know what speed to move at?!

It knows it needs to ramp up to infinity as soon as it hears the engines firing up. 

I disagree. But the question could be phrased better, which is the only problem.

I believe the question was supposed to propose a problem whereby the conveyor belt rotates at a speed equal to, but opposite in direction to, the wheels if the aircraft was taking off as normal, on a normal take off run.

What you're suggesting is that if the wheel starts rotating at 1mph, the conveyor is going 1mph in the opposite direction, therefore the wheel is actually doing 2mph, so the conveyor must to 2mph, meaning the wheel is now doing 4mph and so on, instantly to infinity.

I don't think that's what the question was meaning to ask.

That's not what I mean. I mean that regardless of how fast the conveyor moves backwards, it still cannot provide any counter force to the thrust of the jets, so they will automatically spin up to infinity to match the wheels (whose inclination will be to rotate forwards, and which in turn will have to acccelerate to be faster than the belt). 

I've read your reply and it seems to be exactly what you mean, you're just phrasing it differently?

You're stating the belt will speed up to infinity to match the wheels. So the wheels are travelling at infinity. Why? Our aircraft has only just started rolling, it's doing 10mph airspeed, why are the wheels spinning infinitely fast?

Assuming frictionless bearings:

At rest, the plane isn't moving. As soon as it inches forward (well, millimetres forward), and its wheel starts to turn, the conveyor switches on and starts going backwards. From that INSTANT, both speed up instantaneously to infinity

No they don't.  You're making stuff up now.

doogz84

Which is exactly what I explained, but you said that's not what you meant?

I don't think that is the purpose or point of the thought experiment though, the question is slightly open to interpretation, but I don't believe that's how it was meant to be perceived.

viz

doogz84 said:

Which is exactly what I explained, but you said that's not what you meant?

I don't think that is the purpose or point of the thought experiment though, the question is slightly open to interpretation, but I don't believe that's how it was meant to be perceived.

Not quite because your point was that when the wheel is at 1mph and the conveyor is 1mph, that's 2mph relatively. Actually it's 0 (because they are matched). 

CabbageCat

Handsome_Chris said:

CabbageCat said:

Handsome_Chris said:

holnrew said:

I am interpreting that the wheels are moving at the same speed as the rest the plane it is attached to. 

A couple of others have done that as well. I think that the more usual interpretation is that the surface or the conveyor is moving at the same speed as the surface of the wheel.

But @CabbageCat at which point on the surface of the wheel are you taking that speed?  Is it the part where the wheel touches the conveyor belt?

That is itself up to interpretation. I think most people her have gone for the scalar speed of any bit of the wheel relative to the middle. Someone here, can't remember who, definitely went for the top bit relative to the ground since they felt that the skidding speed should be taken into account when determining the conveyor speed. Personally I want the wheel to blow up and cause a fireball so I prefer to allow skidding.

doogz84

viz said:

doogz84 said:

Which is exactly what I explained, but you said that's not what you meant?

I don't think that is the purpose or point of the thought experiment though, the question is slightly open to interpretation, but I don't believe that's how it was meant to be perceived.

Not quite because your point was that when the wheel is at 1mph and the conveyor is 1mph, that's 2mph relatively. Actually it's 0 (because they are matched). 

But opposite in direction. I was explaining the reasoning for the speed tending to infinity. 

Do you agree that it isn't really the point of the experiment though?

doogz84

If the wheel rotates at 1mph, and the conveyor matches it, what speed is the tread of the tyre travelling at relative to the surface it's rotating on?

viz

doogz84 said:

viz said:

doogz84 said:

Which is exactly what I explained, but you said that's not what you meant?

I don't think that is the purpose or point of the thought experiment though, the question is slightly open to interpretation, but I don't believe that's how it was meant to be perceived.

Not quite because your point was that when the wheel is at 1mph and the conveyor is 1mph, that's 2mph relatively. Actually it's 0 (because they are matched). 

But opposite in direction. I was explaining the reasoning for the speed tending to infinity. 

Do you agree that it isn't really the point of the experiment though?

Well, not really because I think the fascinating thing about this question is exactly what would happen. And the answer is, in the no friction model, the system would reach paradoxically infinite speeds and there is no satisfactory solution. In real life with friction in the plane wheels, they system would speed up immediately until the forward thrust was equal and opposite to the resistance in the wheels. Then either that would be steady state (for a time), or the wheels would melt and the definition of "matched speed" would no longer apply and the plane would scrape itself down the conveyor and take off as though someone had taken the handbrake off. 

Handsome_Chris

I am loving this thread.  It's interesting to see how entrenched (blinkered?) in their belief of what is right.

As for me, I'm siding against the flat earth/conspiracy theorist argument that the plane doesn't fly.

@Holnrew, are you happy now?

CabbageCat

doogz84 said:

If the wheel rotates at 1mph, and the conveyor matches it, what speed is the tread of the tyre travelling at relative to the surface it's rotating on?

Bottom: 0mph
Middle: 1mph
Top: 2mph

Handsome_Chris

doogz84 said:

If the wheel rotates at 1mph, and the conveyor matches it, what speed is the tread of the tyre travelling at relative to the surface it's rotating on?

Do you mean that the wheel rotates at 1 rpm?

viz

I'm not entrenched, just thinking hard about it.

The no-friction trolley example is excellent. Think about what would happen if you pushed hard, but the conveyor matched the wheels, backwards. Would you be able to push it forwards? Theoretically no. The conveyor would speed up to prevent the trolley moving. But then what would you be feeling as you tried to push it? Resistive force, presumably, if it wasn't budging. But what causes that resistive force? Nothing is there to resist it. So it moves forwards? But it can't because the conveyor goes faster. The more you carry on pushing, the more the trolley stays put and the conveyor goes faster. But we know there is NO resistive force being applied, so the trolley WILL go forwards, but we also know the conveyor matches the trolley. So the conveyor has to move at infinity, so do the trolley wheels, but a little bit faster infinity than the conveyor. 

Handsome_Chris

Yeah, but @viz , why are you choosing to think of it that way?  

viz

Because it's a good comparison, don't you think? Same as the idea of pulling the plane with a rope. The belt will spin up to infinity before the plane moves (in the no-friction model), and it would have to be instantaneous, because the plane would actually move forwards (almost) immediately too. Well that's one outcome of the paradox - the other is that it can't move because the infinities are the same. 

Handsome_Chris

But, @viz, do you believe there is a paradox, or do you choose to think there is one?