Plane on a coneyor belt
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Brain storming session ?? Fellows !
On the same level: a small monkey is climbing a rope, which other side around a pulley, is attached to a stone having exactly the same weight than the monkey ( ouf it's not so easy to explain )
the pulley is supposed to be perfect, the rope's weight very light.
question : does the stone lift up when the monkey climbs up ?
MALAISE
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hold on, im not willing to let the other one go, as it seems to be still wrong. Plot-paris, you were so close with your skateboard example, but I'm wondering if you read my skateboard example earlier?
So Pav's on his skateboard. As soon as the conveyor moves backwards, he goes with it. But if he grabs on to the rail with his hand, he hold still. No matter how fast the conveyor goes, he holds still. All he has to do is pull forward with his arms to go forward. This forward motion will then make the conveyor go faster, which makes his wheels spin faster, but it doesn't make him hold stationary. His arms are pulling him forward, and they are not controlled by the ground. The conveyor doesn't make him lose hold with his hands. He can still pull himself forward.
So a plane sits on the conveyor and it moves backwards, so it grabs on to the air which is sitting still. It pulls itself forward through the air. Even though the conveyor begins to spin faster, and the wheeels spin faster, they do not keep the plane from moving forward. I'm sorry, they just don't. You can't assume that a conveyor can go infintely fast, and then argue that you have to take in to account friction on the wheels. If you go with one perfect case scenario, then you go with all.
Why this doesnt work for a car.
Pav is back on his skateboard, but this time there are no handrails. Its just him kicking his foot on the ground propelling him forward. Now the conveyor can keep him from moving forwards, because he has no other means of propulsion. he is only moving by exerting force directly on the ground below him, which is moving.
And so a car would be the same. A converoy belt will keep it in place, because it only moves by pushing on the ground. A plane doesn't move by doing anything to the ground, it pulls itself through the air. Its wheels will spin as fast as needed to stay fixed to the aircraft.
Are we getting there yet?
Chris
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I agree with Chris.
It's not a good idea to start introducing real world problems of overheating etc into a theoretical argument. In any case, why apply mechanical failure only to the plane?...it's the conveyor that really has to do the work. If anything is going to burn out it's the conveyor motor.In the second scenario:
The plane moves forward at 10 mph. The conveyor attempts to counteract this by moving backward at 10 mph. However, the plane will still move forward at 10 mph...I'm sorry, it just will.
However, its wheels are now spinning at 20 mph. The conveyor adjusts its speed to 20 mph...now spinning the wheels at 30 mph, (assuming no acceleration on the part of the aircraft). So the conveyor matches that at 30 mph, spinning the wheels at 40 mph; and so on up to light speed.I think it's clear that even if the aircraft only travels at a constant speed...however small...not even accelerating...then, if the feedback to the conveyor is instant, the conveyor will instantly accelerate to a phenomenal speed. You have a looping function (conveyor speed = conveyor speed + 10mph) that has everything to do with the conveyor and next to nothing to do with the aircraft. In effect, you'll pull the tablecloth from under the plane....and it won't move back with it any more than the china on the table does.
Therefore, the plane will just move forward pretty much as normal. Or I guess you could say that the small amount of resistance in the wheel bearings would be equivalent to it taxiing slightly uphill. If it chose to accelerate rather than just taxi there would be nothing to stop it getting airborne.
Any idea that the conveyor will somehow transport the plane backwards is largely fallacious. There will be some degree of that, but nothing like as much as most people intuitively suspect.
I suggest taking a piece of paper out of the printer, resting it on the table, then standing a roll of Sellotape on top and pulling the paper backwards. You'll find that the Sellotape is not nearly as willing to travel back with the paper as you might imagine.
It might...if you pull the paper extremely slowly...but we aren't talking slow, we're talking a plane accelerating to takeoff speed. -
but Chris, you are allways completely disregarding the friction. and that is the important thing.
the FRICTIONAL RESISTANCE is the only thing, that can work against the plane's forward thrust.
surely we both agree, that if the brakes of the wheels were locked, the plane would be transported backwards. see the native frictional resistance of a wheel as a tiny brake-effect.
and you don't need to have the conveyor spin with indefinite speed. if we asume that only 1/1000 of the conveyor's backwards movement is transferred into heat-energy, meaning that this amount of energy in form of movement was transferred to the plane, then the conveyor simply has to spin one thousand times faster than the plane.
simply try it out. sit onto a bicycle and hold onto a car that is driving forward. you will need energy to holt onto the car. part of this energy is lost by wind resistance, part of it by keeping your ballance - and part of it by the friction of the wheels!
FRICTION, FRICTION, FRICTION!!!
if you find a wheel that does not have a frictional resistance, give me a shout and henceforth I will cycle to work
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jakob, i reckon you need to get a skateboard and go down to the gym, after your TV show with pav, of course.
Alan, you cant just disregard wheels spinning infinitely fast, if one part of the system doesnt work then the system as a whole cant work.
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True Remus, but considering practicalities like that brings the whole argument crashing down, because the bearings on the conveyor motor would fail long before those on the aircraft wheels...they are carrying a much heavier load with a massive amount of torque. There is virtually no torque on the aircraft wheels...they're essentially freewheeling. If the conveyor motor fails, the plane takes off....end of argument. My point was that you can't start contemplating actual shortcoming of the plane's mechanics while allowing the conveyor mechanism to have unlimited magical powers.
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Its not a shortcoming in the physicalities though, its a problem with the theoretical physics/mathematics behind the problem.
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Any volunteer to make the model in Sketchup Physics and see what happens?
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There isn't any problem with the physics/mathematics behind the problem. The physics say that the plane will take off. The calculations really aren't that difficult. It's the seemingly persistent...and entirely intuitive...notion that the conveyor will have any significant effect on the plane that's the problem.
The friction would be F=uR, where F= friction force, u is friction coefficient, and R= weight. The friction is constant (other than the plane getting lighter as it approaches takeoff speed); therefore the speed of the conveyor is totally irrelevant....nowhere does its velocty (v) appear in the frictional calculation.
This frictional force is not great. There are YouTube videos of people pulling Lear jets with their teeth. They are overcoming not only the friction, but also the inertia.
If the speed of the conveyor is irrelevant...and it is...it doesn't matter whether it's matching the speed of the plane or the rotational speed of the wheels. It's irrelevant in both cases.
As long as the forward thrust of the plane is greater than the friction (not exactly difficult) it will accelerate and take off as normal. It wouldn't surprise me to discover that a fighter jet could take off even with its brakes on. All it has to do is burn rubber for a few seconds. In such a case, of course, the conveyor would be stationary as the wheels wouldn't be rotating at all.
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I was refering to the fact that for the wheels to be moving forward they must spin infinitely fast+the speed of the plane.
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For any matter to reach an infinite speed would require all the energy in the Universe.
Perhaps the second part of the question ought to have asked whether such a model was possible at all rather than asking something more specific like whether or not the plane could take off. If the model isn't valid then whether the plane can take off or not ceases to have any meaning -
But the model does work (to an extent) and the plane cant take off.
Th reasoning: if the plane has any forward velocity this sets the wheels off in to a cycle whereby the wheels keep rotating faster and faster forever, this is impossible so the plane cant have a forward velocity.
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@alan fraser said:
As long as the forward thrust of the plane is greater than the friction (not exactly difficult) it will accelerate and take off as normal.
but the question was what happens, if the conveyor prevents exactly this. and for this question is theoretical we can asume that the conveyor can keep up to the speed (we could create a huge one with incredible speed after all).
is it right, if we say:
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theoretically the conveyor could stop the plane from taking off, because there is no windpressure on it's wings to take off
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practically the speed of the conveyor necessary to stop the plane from moving forward is impossible to reach with todays technology
(I think that is a satisfying solution, because it shows, that we all where right - only approaching the problem from differend ends.
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i like this response, it's clear, concise, correct, and most importantly has a reference to chuck norris.
pav
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Fair point about the conveyor spinning infinitely fast, although the wheels would then be doing the same speed as the conveyor belt, and as theyre going in opposite directions that means no forward velocity.
As for practicalaties, i dont think theres a lot of point discussing them in this situation.
EDIT: to sum up my argument, whatever speed the wheels on the plane are rotating at is exactly matched by the conveyor belt, so the plane cant have a forward velocity as then the the infinite cycle starts. Even if we then follow this through both the speed of the wheel and the speed of the conveyor belt tend to infinity, and so are the same once more, thus no take off.
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yup, Alan is still right on this. Its that simple. Theortically and practically, the plane still takes off.
Remus, ask yourself this: "Where does a car get foraward motion from?" and next "Where does a plane get forward motion from?"
Plot-Paris, the theortical part of you situation is wrong, because a plane doesn't need pressure on its wings to move forward. I thought it did earlier in this thread, but see now that is wrong. It moves forward by sucking air through its propller/turbine. It does not need any lift whatsoever under its wing to move forward. So the engines alone are capable of pushing it forward through the air. Therefore it doesnt matter what the wheels are doing, they just spin. The plane only moves in relation to the air around it, even when its on the ground. That is a very important phrase.
Chris
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@ Remus. No. Acceleration to infinity is impossible. That means that the entire model is invalid, it does not mean that the plane can't take off. You could just as easily argue that the travelator can't accelerate to infinity, therefore the plane CAN take off.
The wheels could only spin infinitely fast if the conveyor was also travelling infinitely fast. In practice the wheels wouldn't spin infinitely fast...they'd go as fast as they could, then they'd skid, adding a slight extra friction, but nothing that amounted to anything serious.@ plot-paris. No. For the umteenth time, the speed of the conveyor is irrelevent. The conveyor can only exert a small amount of reverse force in the form of friction on the plane. This is equivalent to (depending on the size of the plane) between 1 manpower and a couple of horsepower. It is also constant whatever the speed of the conveyor. Admittedly, more work will be done as the conveyor accelerates and the wheels spin faster. However, all that extra energy will be supplied by the conveyor, not deducted from the plane's thrust. It is the conveyor that is making the wheels spin faster than they would ordinarily need to. That work energy is rotational, not directional; it has no effect on the forward motion of the plane.
The plane, on the other hand has its full forward thrust available. It will move forward through the air nearly as normal. Where are you getting this no wind pressure from?
Are you really saying that a man with a rope tied around the tail of a plane can stop it taking off by pulling backwards? Chuck Norris could, of course. -
of course we all know, that chuck norris would never do that, because he enjoys us mortals struggling with this problem
ok. we all agree with the fact, that the plane has to move forward to take off, right (because it needs to move foreward to get air pressure under it's wings). of course we all know as well, that to achieve this foreward movement, the plane doesn't need this upward lift (that is merely a result of the forward movement).
so our whole difference lies in the question, if the conveyor, moving backwards, can transfer any energy in form of motion through the wheels to the plane.
you say that the wheels do not have the option to transfer this energy to the plane whatsoever.
and I completely disagree with that. let me tell you again, why:if you place pav's skate board on the treadmill again and switch it on, it will be transported backwards and fall off.
to prevent this, you hold your finger against the board - it stays stationary
if you remove your finger, the board will move backwards and fall off!that demonstrates, that energy was necessary to keep the board in place.
the kinetic energy was transferred from the treadmill, through the wheels, to the board due to the frictional resistance - thereby was transformed to heat-energy in the wheels.
if you speed up the treadmill, the tyres will heat up quicker, than with low speed. at the same time you need slightly more energy to keep the board in place on the treadmill.
and that demonstrates, that increasing the speed of the conveyor increases the kinetic energy transferred to the plane - therefore the theoretical possiblility to prevent the forward-movement of the plane is proven!
ps: nice argumentation with infinity, remus. would never have thought to take it thus far
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Ok, i think ive come up with a neat mathematical way of explaing this.
First, the question states that the conveyor belt will always match the speed of the wheel, so if we call wheel speed 'x' and conveyor speed 'y':
x=y
For the plane to take off it must have forward velocity of say 100 mph, this can be expressed as:
y+100
if we take to be any speed the conveyor had before the forward velocity.
so at the moment of take off:
x=y+100
Looking back at our first equation
x=y
and
x=y+100
cannot both be true at the same time.
EDIT: i realised a flaw in the original argument, and changed it.
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I am afraid, this is not correct, for you assume that the entire speed of the conveyor (Y) will be transferred to the plane, which is not correct.
we had to introduce the variable of the frictional resistance (f). so the objective speed of the plane (OS) would be (the speed the plane normally would travel is hence called SuS (for Subjective Speed)):
OS = SuS - Y*f
[Edit]
and to calculate Y:
Y = SuS*f
[Edit2]
Sorry, wrong again:
OS = SuS - Y/f
Y = SuS*f
therefore: OS = Sus - Sus*f/f
therefore: OS = Sus - Sus
therefore: OS = 0
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