Plane on a conveyor belt

hywelg

Sporky said:

hywelg said

That's where logic left you.

 How can the conveyor slow the aircraft down?  It can only influence the rotation of the wheels.

How many times now have I explained that it is a paradox?

Yes, no conveyor can slow the plane down. However, the question states that the conveyor matches the speed of the wheels, but in the opposite direction.Thus the setup of the scenario precludes the plane's wheels, and thus the plane, from moving.

However, this is clearly impossible. The scenario is impossible because it prevents the plane from moving via a method which could not, in the real world, prevent the plane from moving.

Paradox.

No its not a paradox. All that happens is that the wheels speed over the conveyor is twice the speed of the wheels over the ground.

What you are confusing is relative velocity and absolute velocity (in earthly terms, ignore extraterrestrial considerations), speed over the conveyor and actual speed. The OP states the conveyor matches the speed of the wheels in the opposite direction. The 'speed of the wheels' can mean only one thing, the forward velocity of the wheel in relation to a static point, ie the ground. It is perfectly possible for the wheels to be rotating such that the peripheral speed is twice the forward velocity. In this scenario velocity implied by the wheel rotational speed ≠ absolute velocity.

If you take a toy car and whizz its wheels by hand does the wheel have velocity whilst held by you? No. If you sum all the peripheral velocities of the rotating wheel at all points on the circumference the result will be zero. So the speed of the tyre at the point of contact with the tyre will equal the speed of the conveyor. The speed of the tyre at the periphery at a point diametrically opposed to the contact point with the conveyor will be -(speed of conveyor). When considering what the 'speed of the wheel' means it has to mean the speed of the axis in relation to the ground. Therefore the speed of the wheel = the speed of the aircraft = -( speed of the conveyor).

It not a paradox. Go back to first principles. Apply mathematics and physics and you'll see its perfectly possible for the plane to take off, indeed the existence of the moving conveyor will be little hindrance to the plane taking off. All that will hinder it is the extra rolling friction from having the wheel rotate at twice the speed they would  ordinarily be doing.

Sporky

Drew_TNBD said:

Sporky said:

Drew_TNBD said:

13 pages...

This is why none of you are musicians.

Logical fallacy on the grounds of a faulty premise.

Did you leave your sense of humour at church this morning?

I am sorry that my joke went over your head.

It seemed apt in a thread about logic.

Drew_TNBD

Sporky said:

Drew_TNBD said:

Sporky said:

Drew_TNBD said:

13 pages...

This is why none of you are musicians.

Logical fallacy on the grounds of a faulty premise.

Did you leave your sense of humour at church this morning?

I am sorry that my joke went over your head.

It seemed apt in a thread about logic.

Ahhh.

I need more coffee.

Handsome_Chris

You are all mad. The conveyor belt does not move. It is fixed to the ground.  I'm surprised all you brainiacs on here did not notice that.  

Sporky

Drew_TNBD said:

Sporky said:

Drew_TNBD said:

Sporky said:

Drew_TNBD said:

13 pages...

This is why none of you are musicians.

Logical fallacy on the grounds of a faulty premise.

Did you leave your sense of humour at church this morning?

I am sorry that my joke went over your head.

It seemed apt in a thread about logic.

Ahhh.

I need more coffee.

To be fair, it wasn't terribly funny and should have been supplemented with a smiley.

Sporky

hywelg said:

The 'speed of the wheels' can mean only one thing

That is patently not correct. Between us we've come up with at least two things it could mean.

sinbaadi

hywelg said:

Sporky said:

hywelg said

That's where logic left you.

 How can the conveyor slow the aircraft down?  It can only influence the rotation of the wheels.

How many times now have I explained that it is a paradox?

Yes, no conveyor can slow the plane down. However, the question states that the conveyor matches the speed of the wheels, but in the opposite direction.Thus the setup of the scenario precludes the plane's wheels, and thus the plane, from moving.

However, this is clearly impossible. The scenario is impossible because it prevents the plane from moving via a method which could not, in the real world, prevent the plane from moving.

Paradox.

No its not a paradox. All that happens is that the wheels speed over the conveyor is twice the speed of the wheels over the ground.

What you are confusing is relative velocity and absolute velocity (in earthly terms, ignore extraterrestrial considerations), speed over the conveyor and actual speed. The OP states the conveyor matches the speed of the wheels in the opposite direction. The 'speed of the wheels' can mean only one thing, the forward velocity of the wheel in relation to a static point, ie the ground. It is perfectly possible for the wheels to be rotating such that the peripheral speed is twice the forward velocity. In this scenario velocity implied by the wheel rotational speed ≠ absolute velocity.

If you take a toy car and whizz its wheels by hand does the wheel have velocity whilst held by you? No. If you sum all the peripheral velocities of the rotating wheel at all points on the circumference the result will be zero. So the speed of the tyre at the point of contact with the tyre will equal the speed of the conveyor. The speed of the tyre at the periphery at a point diametrically opposed to the contact point with the conveyor will be -(speed of conveyor). When considering what the 'speed of the wheel' means it has to mean the speed of the axis in relation to the ground. Therefore the speed of the wheel = the speed of the aircraft = -( speed of the conveyor).

It not a paradox. Go back to first principles. Apply mathematics and physics and you'll see its perfectly possible for the plane to take off, indeed the existence of the moving conveyor will be little hindrance to the plane taking off. All that will hinder it is the extra rolling friction from having the wheel rotate at twice the speed they would  ordinarily be doing.

If you take "speed of the wheels" to mean "speed of the axles" then you actually mean "speed of the plane", which would have been a much simpler and explanatory way to write that, so I don't think your meaning is correct and certainly not obvious.

Maynehead

Ok to answer a couple of the clarification questions...

The way I personally understand it is that the wheel's speed is taken to mean the TANGENTIAL speed of the wheel. I.e. the linear speed of a point on the outer edge of the wheel. In practical terms, assuming no skidding, this is the speed of the whole plane relative to the belt surface.

E.g. all of the following results in a "wheel speed" of 10m/s:

The plane is moving forward at 10m/s on a stationary belt.
The plane moves forwards (in space) at 5m/s and the belt moves backwards at 5m/s.
The plane is stationary (in space) and the belt moves backwards at 10m/s.

*Quiz question: out of the three scenarios above, which is the only scenario that satisfy the premise of the question?

The logic behind my assumption is that the question refers specifically to the speed of the WHEELS, and not the speed of the plane, and this specificity leads me to infer that the speed referred to is a property based on the rotational speed of the wheel rather than the speed of the plane relative to a static observer located off the conveyor.

As for which direction the belt is moving, my personal understanding is that the surface of the belt is moving from the head of the plane towards the tail of the plane. I.e. against the direction of travel.

Handsome_Chris

Sussed it.

If the plane and its associated wheels are moving forward at 200 mph , the conveyer belt is moving at 200 mph in the other direction. All that is happening is the wheels are rototating at a twice the normal speed.

The plane takes off! 

All you self proclaimed experts out there who thought that the plane could not take off, shame on you:  do you believe the earth is flat? 

Emp_Fab

Well, I'm happy with my understanding of it.  It all works with Newton's laws, it's absolutely not a paradox.  Thinking it is is just a get-out from working out what's actually going on.  Nothing runs at the speed of infinity and it can be implemented in reality without the universe collapsing to a singularity.  Right, what's next ?  How much wood could a woodchuck chuck if a woodchuck could chuck wood?

Sambostar

42

Drew_TNBD

Sambostar said:

42

The number of voices you hear in your head?

Sporky

Handsome_Chris said:

Sussed it.

If the plane and its associated wheels are moving forward at 200 mph , the conveyer belt is moving at 200 mph in the other direction. All that is happening is the wheels are rototating at a twice the normal speed.

So you're saying the wheels are turning at 400mph? But the conveyor matches the speed of the wheels, so it must be going at 400mph too, but then the wheels must be going at 800mph and so on and so forth.

If they'd just said "the plane" instead of "the wheels" then it'd be very simple.

hywelg

Let's look at it another way. 

A conveyor has rollers underneath it. When the conveyor is moving at 10mph how fast are the rollers moving?

Answer, they are not moving, the are held fixed by the frame that holds them.  They are rotating. This is not the same as motion. 

sinbaadi

So if someone says a wheel is "moving" (not that that is a particularly elegant way of saying it) at 100mph, you presumably do not conclude that it is rotating or spinning at 100mph.  Certainly open-minded of you, but I think most people would make that fair assumption.

I could say that the conveyor is not moving any more than the checkouts at tesco move.    

But what I will say is:  LET IT DIE!

Maynehead

hywelg said:

Let's look at it another way. 

A conveyor has rollers underneath it. When the conveyor is moving at 10mph how fast are the rollers moving?

Answer, they are not moving, the are held fixed by the frame that holds them.  They are rotating. This is not the same as motion. 

Not quite correct. A correct answer could be either:

Not moving relative to an observer in the same inertial frame of reference as the framework of the conveyor belt.

or

10mph relative to an observer in the same inertial frame of reference as the surface of the belt.

You assume the former, whilst I assume the latter, due to the fact that only the latter frame of reference is directly referenced and derivable from the premises of the question. The former is purely created from your imagination of how the conveyor is constructed, and is not provable from the information contained in the question.

Handsome_Chris

Sporky said:

Handsome_Chris said:

Sussed it.

If the plane and its associated wheels are moving forward at 200 mph , the conveyer belt is moving at 200 mph in the other direction. All that is happening is the wheels are rototating at a twice the normal speed.

So you're saying the wheels are turning at 400mph? But the conveyor matches the speed of the wheels, so it must be going at 400mph too, but then the wheels must be going at 800mph and so on and so forth.

If they'd just said "the plane" instead of "the wheels" then it'd be very simple.

No I am agreement with the original question that the conveyor belt is matching the speed of the wheels. I do not know how the conveyor belt is matching the speed as I would believe that is would be anchored to the ground; however I'm working to the impossible constraints of the question. 

RocknRollDave

Have we factored in the inevitable delay due to industrial action by the baggage handlers' union?

Sporky

hywelg said:

Answer, they are not moving, the are held fixed by the frame that holds them.  They are rotating. This is not the same as motion. 

Rotation is a kind of motion.

I agree that if the question means the axles of the wheels then the plane can take off (assuming the wheels can survive rotating twice as fast as they normally do at takeoff, which I think they can).

But if that was the intention, it'd be simpler and clearer to say "the plane". Surely it is specific about the wheels for a reason.

Sporky

You may all be pleased to hear that I'm off on holiday this week.

By car, not plane.