Plane on a conveyor belt

Handsome_Chris

DiscoStu said:

If the rollers driving the conveyor belt are the same size as the wheels on the plane then...

Yeah, but that isn't the question is it?  

Next.

DiscoStu

You have misinterpreted the question Chris. But you are Handsome!

Handsome_Chris

holnrew said:

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

I can see from the statement that the conveyor belt is rotating so that the surface facing the aircraft is moving at exactly the same speed, but in the opposite direct.

DiscoStu said:

You have misinterpreted the question Chris. But you are Handsome!

You, @DiscoStu , have misinterpreted the question. But you are Disco!

Ravenous

I've got a plane that would look good on that conveyor. A woodworking plane!

Wouldn't fly but boy, it would be smooth.

Handsome_Chris

Ravenous said:

I've got a plane that would look good on that conveyor. A woodworking plane!

Wouldn't fly but boy, it would be smooth.

Would it be as smooth as jazz?

Maynehead

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. 

I can see from the statement that the conveyor belt is rotating so that the surface facing the aircraft is moving at exactly the same speed, but in the opposite direct.

I interpret wheel speed to mean that:

If the wheel had a circumference of 1m, and it is rotating at 1 revolution per second, then the wheel speed = 1m/s, because that is how fast the wheel would be travelling relative to the surface it is rolling on.

I interpret the belt speed to mean that:

The speed of the surface of the belt, travelling in the opposite direction. E.g. if you drew a black dot on the top of the belt in the picture above, it would be moving towards the right, at the same rate as the wheel speed, which in the above example would be 1m/s.

If both the wheel speed and belt speed according to the above interpretation are 1m/s, then the plane would be stationary relative to an observer standing on the "ground to which the conveyor system is fixed to" for sake of argument.

DiscoStu

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. 

I can see from the statement that the conveyor belt is rotating so that the surface facing the aircraft is moving at exactly the same speed, but in the opposite direct.

DiscoStu said:

You have misinterpreted the question Chris. But you are Handsome!

You, @DiscoStu , have misinterpreted the question. But you are Disco!

Moving at exactly the same speed. The plane's wheels dictate the speed of the conveyor belt so it doesn't matter what size the belt's roller wheels are. If the belt wheels are larger they will turn at a lower rpm to the plane wheels and if they are smaller they will turn at a higher rpm. 

viz

Maynehead 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. 

I can see from the statement that the conveyor belt is rotating so that the surface facing the aircraft is moving at exactly the same speed, but in the opposite direct.

I interpret wheel speed to mean that:

If the wheel had a circumference of 1m, and it is rotating at 1 revolution per second, then the wheel speed = 1m/s, because that is how fast the wheel would be travelling relative to the surface it is rolling on.

I interpret the belt speed to mean that:

The speed of the surface of the belt, travelling in the opposite direction. E.g. if you drew a black dot on the top of the belt in the picture above, it would be moving towards the right, at the same rate as the wheel speed, which in the above example would be 1m/s.

If both the wheel speed and belt speed according to the above interpretation are 1m/s, then the plane would be stationary relative to an observer standing on the "ground to which the conveyor system is fixed to" for sake of argument.

^ yes, the linear velocity of the conveyor belt is equal to the tangential velocity of the plane wheels (or tries to be). 

doogz84

This confuses me.

As soon as you realise that the wheels aren't what provides drive/thrust, you realise their speed is irrelevant theoretically, until we talk about melting wheel bearings or overheating tyres, that sort of thing.

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

Handsome_Chris

viz said:

Maynehead said:

Handsome_Chris said:

holnrew said:

^ yes, the linear velocity of the conveyor belt is equal to the tangential velocity of the plane wheels (or tries to be). 

But @Viz, where does it say that in the question?

viz

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. 

Handsome_Chris

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

viz

Handsome_Chris said:

viz said:

Maynehead said:

Handsome_Chris said:

holnrew said:

^ yes, the linear velocity of the conveyor belt is equal to the tangential velocity of the plane wheels (or tries to be). 

But @Viz, where does it say that in the question?

It says the speeds must match, and as the only speeds that have the same units are tangential and linear, they must be the matches. I suppose it could be the rpms of the plane's and conveyor's wheels, but seeing as it specifically mentions the conveyor belt, not the conveyor wheels, it must be that. 

CabbageCat

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.

DiscoStu

Handsome_Chris said:

viz said:

Maynehead said:

Handsome_Chris said:

holnrew said:

^ yes, the linear velocity of the conveyor belt is equal to the tangential velocity of the plane wheels (or tries to be). 

But @Viz, where does it say that in the question?

In the bit where it says 'The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction'.
Imagine the bicycle roller in my earlier vid but put a belt on it over its rollers to make it a conveyor belt, as the bike wheels turn faster the belt instantly turns faster in the opposite direction regardless of the size of the wheels and rollers or the length of the belt.
The bike/plane wheels drive the belt, the belt doesn't drive the wheels.
Action and opposite reaction.

viz

Handsome_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.

Handsome_Chris

viz said:

Handsome_Chris said:

viz said:

Maynehead said:

Handsome_Chris said:

holnrew said:

^ yes, the linear velocity of the conveyor belt is equal to the tangential velocity of the plane wheels (or tries to be). 

But @Viz, where does it say that in the question?

It says the speeds must match, and as the only speeds that have the same units are tangential and linear, they must be the matches. I suppose it could be the rpms of the plane's and conveyor's wheels, but seeing as it specifically mentions the conveyor belt, not the conveyor wheels, it must be that. 

@viz , why must it be so?

Handsome_Chris

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?

doogz84

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.

viz

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).