Plane on a conveyor belt

monquixote

Maynehead said:

menamestom said:

Sporky said:

In that sense it reminds me of a puzzle in my dear old mum's university alumni newsletter, which I'd read before. Basically your doctor gives you two lots of pills, which are identical in appearance. You must take one of each each day or you'll die. Don't take them? Die. Take more than one of either? Die. You go on holiday the next day to a really remote place, and on arriving (your transport having departed) you discover that the containers broke and the pills spilled out into your suitcase. They look identical and have the same mass, size, smell, blah blah blah. The cottage you're staying in has a pestle and mortar and some very accurate scales.You're not being picked up again for a fortnight and can't ontact the outside world. How do you make it out alive?

There's a classic answer, and there's the obviously correct answer

Weigh one pill.  Grind the lot, mix it all up.  Weigh an amount of powder which is twice the weight of the single pill.  Then consume that amount daily.  Hopefully the total amount is enough to last 2 weeks.  Then question the wisdom of going to a really remote place with a life threatening illness. 

This heavily relies on the assumption that each bottle contained an equal amount of pills.

If you don't I'm not sure there is a solution.

prh777

fretmeister said:

No.

No airflow over the wings. No Bernoulli effect. No lift.

Correct but the bernoulli effect can only occur due to the kutta condition.  digging deep there....

Maynehead

monquixote said:

Maynehead said:

This heavily relies on the assumption that each bottle contained an equal amount of pills.

If you don't I'm not sure there is a solution.

O RLY?

You don't need to make that assumption, you chose to. 

If you decide to go with that set of assumptions then you are asking how to mix two equal sets of pills which is an obvious and boring question.

I kid, I KID!

littlegreenman

Both points of view are of course correct.

In the idealistic world where the plane never actually moves forwards on the hypothetical runway and remains static then lift can't be achieved and the plane stays put. This of course assumes a perfect rolling runway no longer than the plane itself and perfect rolling stock.

In the real world the plane will always outrun the rolling runway, which is presumably of finite length and the plane lurches forwards and crashes as it reaches the end of said hypothetical runway and falls off the end nose first. Or takes off if it's long enough. An airplane length runway does not exist for the purposes of this question.

I like real runways and solid ground, those journeys have always worked out for me, at least so far!

monquixote

Maynehead said:

monquixote said:

Maynehead said:

This heavily relies on the assumption that each bottle contained an equal amount of pills.

If you don't I'm not sure there is a solution.

O RLY?

You don't need to make that assumption, you chose to. 

If you decide to go with that set of assumptions then you are asking how to mix two equal sets of pills which is an obvious and boring question.

I kid, I KID!

There might be a solution I just don't know what it is

dtr

CabbageCat said:

monquixote said:

Maynehead said:

monquixote said:

Maynehead said:

If by that you mean it always maintains traction with the belt surface then yes, that is one of the many assumptions.

Ofcourse you can circumvent the problem completely by appying the brakes and powering through the locked up wheels with the sheer force of the engines and take off that way, with the wheels, and therefore the belt, never turning; but that would not be in the spirit of the question

Where does it say you have to make that assumption?

It does seem a bit silly.

So you are assuming that all of the retarding force on the plane is coming from the friction in the wheel bearings?

I agree that this is one of the more critical assumptions we need to make, because it directly affects outcome of the core question, which is: "Can a wheel translate in space if it is rolling on a surface that matched its velocity exactly and instantaneously?".

The answer to which could be: "Depends if the wheel can slide along the surface.".

So to make the question better and more concise we need to add the clause: "Given that there is perfect traction between the wheel and the surface.".

In which case the answer would be "No.".

You don't need to, you choose to. 

If you decide to go with that set of assumptions then you are asking what do equal and opposite forces do which is an obvious and boring question.

I dunno, I think it's quite an interesting question. Sorry everyone who doesn't like this thread. I think it's great.

Even with the super-assumption model there are some layers to it. If the force of the jets are what makes the plane move and the plane moving is what makes the wheels turn and the wheels turning are making the conveyor move and the conveyor moving is what keeps the plane still then there is no movement so the wheels wouldn't have turned in the first place but the jets are still firing and the plane is still stationary (ery?). I know I've repeated that a couple of times now but it amuses me to think of it. It's a lot more fun than irrepressible force vs immovable object. 

The flaw in your argument is the phrase "and the conveyor moving is what keeps the plane still".  There isn't any way for a moving conveyor to keep a plane still.  You're assuming the existence of a mechanism that doesn't exist - sure, you're being invited to do so by the way a question is phrased, but doing so is an error.  You're basically saying "yes, but MAGIC!" and the moment you do that, you've bounced totally outside the sphere of it being a question about physics or maths because... MAGIC!

The jet engine provides forward thrust by acting against the surrounding air, agreed?

The plane doesn't need wheels.  Seaplanes don't have wheels.  All the plane needs is insufficient friction to counteract the effect of the jets pushing air.  This can be achieved by a freewheeling wheel, the relevant part of which is the friction at the axle and wheel bearings, or skis on ice or a hull on water, etc, agreed?

The plane is resting on a conveyor belt that can move forwards or backwards at any speed, agreed?

If you set the conveyor belt to "slow"... much slower than a plane can move, the jets would thrust against the air, and the plane would move in the air, and reach take off speed because it's moving through the air, and it wouldn't matter that the wheels were on a slow moving conveyor, agreed?

If you set the conveyor belt to "fast"... much faster than a plane can move, the jets would thrust against the air, and while the freewheeling wheels would be spinning backwards like all buggery, the plane would still move forwards through the air and reach take off speed, and it wouldn't matter that the wheels were on a fast moving conveyor, agreed?

Is there a speed somewhere in between "slow" and "fast" that would magically stop the jets moving the plane forwards through the air?  Of course there bloody isn't!  If the speed of the conveyor was set manually, there would be no speed you could set it that could possibly prevent the plane taking off.

(facepalm) "and the conveyor moving is what keeps the plane still"  (/facepalm)

CabbageCat

Emp_Fab said:

It appears that only a few of you have read my explanation ;-)

Emp_Fab said:

You know what..... @ICBM is right....  the plane would take off !!!   The humble pie is ready for us all to eat !!!

The little drawing in the original post is misleading - it implies a little conveyor belt (just bear this in mind for the moment).

The reason we're all saying the plane wouldn't fly is because we're all assuming the plane remains stationary relative to the ground (and the surrounding air).  The plane doesn't remain stationary - it moves along the (very long) conveyor belt and takes off exactly the same as if it were on a tarmac runway.

Why does it move ?  Because the forward thrust from a plane is generated by its engines against the surrounding air.  The surrounding air has no 'knowledge' of the existence of the conveyor belt.  If the forward thrust was applied through the plane's wheels instead, then yes, the plane would remain stationary and wouldn't take off.  However, a plane with powered wheels is useless - it's just a car with wings.  The reason any plane moves is because of the force it applies against the surrounding air.  What is going on beneath the wheels is irrelevant (unless the brakes are applied).  Discounting the minor effect of friction in the wheel bearings, the wheels have no role to play in any of this other than to keep the plane from hitting the ground.  The ground / conveyor belt could be moving sideways for all it matters (presuming the wheels were on castors !).  The only force that has any relevance here is the thrust of the engines against the surrounding air - which is what makes the plane move forward, regardless of the ground beneath it.

Of course, in the OP's post, it's a tiny conveyor belt, in which case, the plane would just fall off the end.

Sporky said:

The plane cannot achieve any forward motion, because the premise is that the conveyor moves at the same speed as the wheels but in the opposite direction. It doesn't matter that the plane isn't propelled by its wheels.

@Sporky The plane will achieve forward motion because the thrust is against the air, not the conveyor.  The plane will push against the air and move forward.  What the conveyor is doing underneath the wheels is irrelevant - the only thing the conveyor movement has any effect on is the rotational speed of the wheels.  You have to assume that friction in the wheel bearings plays no part in this.  Picture a huge mass sitting on frictionless wheels that is sitting on a conveyor belt.  When the belt moves, the huge mass is going to stay put, because there is no force being applied to it.  Do you agree so far ?  Now, if you accept that moving the ground underneath a huge mass with frictionless wheels doesn't move the mass, then you have to accept that if you apply a force to the mass, such as from jet engines bolted onto it, the mass will move - because it now has a force applied to it.  The plane is the huge mass and its engines are the force applied.  The rest of it is a mental distraction.

This has been dealt with many times many pages ago. The conveyor is pulling at the wheels. If the plane is moving forwards (without skidding as per monquixote's situation) then the wheels are moving faster than the conveyor which breaches the terms of the scenario. The source of the impetus is what is irrelevant.

menamestom

Wouldn't the pills just shoot off the back of the conveyor belt? Youd'd die, but not due to taking the wrong pill, but the friction of the conveyor belt (assuming the pestle and mortar would not counteract that friction).

Maynehead

menamestom said:

Wouldn't the pills just shoot off the back of the conveyor belt? Youd'd die, but not due to taking the wrong pill, but the friction of the conveyor belt (assuming the pestle and mortar would not counteract that friction).

Yes but the real question is will the scales take off?

Maynehead

monquixote said:

Maynehead said:

monquixote said:

Maynehead said:

This heavily relies on the assumption that each bottle contained an equal amount of pills.

If you don't I'm not sure there is a solution.

O RLY?

You don't need to make that assumption, you chose to. 

If you decide to go with that set of assumptions then you are asking how to mix two equal sets of pills which is an obvious and boring question.

I kid, I KID!

There might be a solution I just don't know what it is

Well if there is then it's beyond me...

Which nicely draws a parallel with the (m*****f**king) plane question. The context of the pill puzzle could be viewed as to imply the equality of each type of pill at the start, because, otherwise, the presence of the pestle and mortar, and the scales would be irrelevant, as you would probably die regardless (unless you were very, very lucky).

Similarly, in the plane question, the existence of the conveyor belt, and the fact that the relation between the speed of the conveyor belt and the plane's wheels is so explicitly constrained, could be viewed as to imply the lack of any sliding between the two surfaces; as otherwise you may as well be asking if a plane can take off on ice, or take off with its brakes on, which is a much simpler question.

DiscoStu

The dress is blue and black. End of.

paul_c2

holnrew said:

Looking at it another way....the plane takes off....this is what occurs

1) We start with everything stationary (wheels, conveyor belt, plane, etc)
2) The engines are started and develop a little bit of thrust.
3) This pushes the plane forwards a bit
4) Look at the conveyor belt. Look at its underside - it doesn't have any supports, the underside of the belt is flat on the ground!!!!
5) Due to 3, the top of the conveyor belt remains with the plane while the underside remains on the ground. but in a catterpillar-track-vehicle style, the whole system (conveyor belt and plane) move forwards at half the rate of the top side of the conveyor belt.
6) Due to the magic properties of the conveyor belt, because its turning forwards, the wheels of the plane start spinning backwards. Because it always matches the speeds, the plane remains in the middle of the conveyor belt throughout (until it takes off)
7) The wheels will be spinning at twice the air speed, backwards, as the plane & conveyor belt accelerates.
8) This may overheat the tyres but because of the slow rate of them heating up, an overspeed can occur for short periods. Let us assume the tyres of the plane remain intact and keep working, albeit warmer than usual
9) at take off speed, the pilot pulls back the stick, rotates the plane and the angle of attack increases to generate more lift so the plane lifts off clear of the conveyor belt. The pilot dabs the brakes (as one does, when one takes off and before retracting the wheels, the magic conveyor belt senses this and stops too (otherwise it will carry on down the runway and plough into the outfield).

Nomad

(Haven't read all of the thread.)

For those that think the wheels need to rotate to drive the plane forward, such that the conveyor prevents this, could you please explain how a seaplane works?

Do they have propellers at the backs of the floats?

Sambostar

holnrew

The picture of the plane is on a small treadmill, but it does say in the writing that the conveyor is as wide and as long as a runway.

Garthy

http://i50.photobucket.com/albums/f312/UP_M5/firstflight2-1.jpg

ICBM

DiscoStu said:

The seaplane is being held to the trailer by gravity and friction.

Its engines may well be helping it stay on the trailer but it is the car pulling the trailer which is making air pass over the plane's wings, creating the crucial lift it needs to take off.

No, still wrong.

The only purpose of the car is to keep the trailer under the plane. The plane is accelerating itself, not being pulled by the car.

Yes, at the beginning there's the plane's weight causing friction too, but as the plane gets closer to flying speed it decreases, to the point where just before takeoff where lift is equal to weight it falls to zero. If the car was pulling the plane then, the plane would slide off the back of the trailer. If it hadn't reached its own full flying speed it would then stall and fall onto the runway… so it's critical that that doesn't happen.

You'll see that the blocks on the trailer are at the *front*, not the back - they're to stop the plane moving forward and hitting the car if the pilot and the driver don't manage to match their speeds properly.

JohnnyPlectrum

I had reasonable success with a small child using this answer…

The 747 pilot has control of thrust and braking but cannot increase wheel speed.
The treadmill ‘operator’ can increase and decrease treadmill speed to match the 747 wheel speed.
 
To fly the 747 needs speed relative to the ground.
 
If we assume no friction other than that between the tyre and the treadmill the following can be easily visualised:
 
At the start of the experiment everything is at zero, the 747 can’t increase wheel speed and if the treadmill increases its speed the 747 wheels will simply rotate and the plane will remain stationary.
The treadmill can then happily accelerate and decelerate and the 747 wheels will match the speed – there will be no movement of the plane relative to the ground.
 
If the pilot then applies any thrust the 747 will move forward relative to the ground with the treadmill and wheels going whatever speed the treadmill chooses. The treadmill cannot arrest the forward movement of the aircraft therefore it flies.
 
The problem is that for the 747 to have forward motion it must have a higher wheel speed than the treadmill speed thus failing to address the brief, however, as the treadmill has no effect on the retardation of the 747 then it can take off if it wants to.

For the 747 to remain stationary relative to the ground requires the pilot’s intervention, not the treadmill’s, which is at odds with the plane’s desire to take off.

Therefore it's actually a question that can't be answered and is designed simply to clog up the internet.

CabbageCat

ICBM said:

DiscoStu said:

The seaplane is being held to the trailer by gravity and friction.

Its engines may well be helping it stay on the trailer but it is the car pulling the trailer which is making air pass over the plane's wings, creating the crucial lift it needs to take off.

No, still wrong.

The only purpose of the car is to keep the trailer under the plane. The plane is accelerating itself, not being pulled by the car.

Yes, at the beginning there's the plane's weight causing friction too, but as the plane gets closer to flying speed it decreases, to the point where just before takeoff where lift is equal to weight it falls to zero. If the car was pulling the plane then, the plane would slide off the back of the trailer. If it hadn't reached its own full flying speed it would then stall and fall onto the runway… so it's critical that that doesn't happen.

You'll see that the blocks on the trailer are at the *front*, not the back - they're to stop the plane moving forward and hitting the car if the pilot and the driver don't manage to match their speeds properly.

It's still a rubbish illustration of the original question. If the truck was significantly longer and driving in the opposite direction it would be much better.

Sambostar

If the women of your dreams was standing at a bus stop with your best mate who saved your life and they both needed a lift but you could only carry one passenger in your car, who would you offer a lift to or what would you do?