# Fun little physics question..

#### AcesHigh

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Something to entertain your brain a little bit.. this question has been argued and debated to death. Many of us have degrees in Physics, let's see what you think.

A plane is on a movable runway, sort of like a conveyor belt. The runway is moving the opposite way as the plane, and its speed is continuously variable with the plane (so if the plane speeds up one way the belt will correspondingly move the other).

The question here is will the plane be able to take off? Can it even move?

Keep in mind several assumptions:

1) The wheels are free rolling.
2) Plane wings need a high and low air pressure gradient to achieve lift.
3) The plane has thrusters on its wings that do not power the wheels in the way a car does.

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Yes.

#### Law2Doc

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AcesHigh said:
Something to entertain your brain a little bit.. this question has been argued and debated to death. Many of us have degrees in Physics, let's see what you think.

A plane is on a movable runway, sort of like a conveyor belt. The runway is moving the opposite way as the plane, and its speed is continuously variable with the plane (so if the plane speeds up one way the belt will correspondingly move the other).

The question here is will the plane be able to take off? Can it even move?

Keep in mind several assumptions:

1) The wheels are free rolling.
2) Plane wings need a high and low air pressure gradient to achieve lift.
3) The plane has thrusters on its wings that do not power the wheels in the way a car does.
You lost me when you used "fun" and "physics" in the same heading...

#### jebus

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No? To get the pressure difference on the wings you need forward movement... maybe?
Well, I hate you for asking this question. You just made my list - right between alex trebeck and eli whitney.

#### DrBowtie

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1) Based upon this only then no it would have no displacement.
2) Based upon this, if the wind was blowing hard enough it would lift off.
3) Based upon this it would if the thrust wasn't strictly parallel to the runway.

#### gdbaby

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Sounds like one of them there relativity questions. I am going to say no, because the plane isn't moving. This is why I got an 8 in PS, though.

A

#### angel5

The plane isn't going anywhere.

First of all, this conveyor belt is likely to be inside a building where a plane would have a difficult time taking off.

End of story.

A

#### angel5

Whoa, totally missed the conveyer belt was a runway.

Geez, couldn't even get past the question!!

#### 06applicant

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AcesHigh said:
Something to entertain your brain a little bit.. this question has been argued and debated to death. Many of us have degrees in Physics, let's see what you think.

A plane is on a movable runway, sort of like a conveyor belt. The runway is moving the opposite way as the plane, and its speed is continuously variable with the plane (so if the plane speeds up one way the belt will correspondingly move the other).

The question here is will the plane be able to take off? Can it even move?

Keep in mind several assumptions:

1) The wheels are free rolling.
2) Plane wings need a high and low air pressure gradient to achieve lift.
3) The plane has thrusters on its wings that do not power the wheels in the way a car does.
It will not take off.

I really don't think I understand your question, because it looks way too easy. As I read it, the plane is not moving relative to the surrounding air, therefore there would be no pressure gradient on the wings whatsoever.

T

#### Telemachus

You say this has been debated to death, but there would be a clear right answer if you added some missing information -- are the wheels and runway are all perfectly parallel? are the wheels/axles perfectly frictionless? Is the movement of the runway frictionless with respect to the air? Are the "thrusters" engaged, i.e. providing any force? (given the way the question was asked, let's assume yes, yes, yes, no)

If the wheels are frictionless, and perfectly parellel to the direction of conveyor belt runway movement, and the movement of the runway does not cause the overlying air to move then it does not matter what you do to the speed of the runway -- the plane's wheels spin and the rest of the plane experiences no force so it does not move relative to a stationary observer not on the runway. And since airplane wings need to move relative to air in order to generate lift, none is generated. Lastly, if the "thrusters" are doing work then of course the airplane will move relative to a stationary observer not on the runway.

#### Nikki2002

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my mind is flying away!!!!!

#### dajimmers

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Yes, it will fly. The thruster will propel the plane forward, irregardless of what's going on with the wheels. Since they are free-rolling, you can think of the plane as being on a sheet of frictionless ice. The only thing that would prevent the plane from taking off would be if the wheels did have friction, for they would be spinning faster than normal (since the runway is moving in the opposite direction as the plane. See if this helps:

I numbered the arrows so you could discuss them if you want to.

#### Zoom-Zoom

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This is a vector problem...

It wont take off. Think of it this way....If the runway was moving the plane forward it might take off at a certain speed without even moving its wheels because there would be enough air flowing under the wings to create lift. Now, if the plane is turned around you will need enough forward velocity from the wheels to counteract the backwards wind velovity. Thus, the plane needs to be moving forward faster than the backwards runway is moving to take off...approx how fast is determined by the speed it would take the airplane to create lift normaly + the speed it takes to overcome the backwards movement + friction loss and all that jazz

#### Zoom-Zoom

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dajimmers said:
Yes, it will fly. The thruster will propel the plane forward, irregardless of what's going on with the wheels. Since they are free-rolling, you can think of the plane as being on a sheet of frictionless ice. The only thing that would prevent the plane from taking off would be if the wheels did have friction, for they would be spinning faster than normal (since the runway is moving in the opposite direction as the plane. See if this helps:

I numbered the arrows so you could discuss them if you want to.
Not necessarily. The wheels (and plane) will move forward in relation to the runway but not in relation to the surrounding air. Of course, this assumes the plane is real... has friction

#### robh

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dajimmers said:
Yes, it will fly. The thruster will propel the plane forward, irregardless of what's going on with the wheels. Since they are free-rolling, you can think of the plane as being on a sheet of frictionless ice. The only thing that would prevent the plane from taking off would be if the wheels did have friction, for they would be spinning faster than normal (since the runway is moving in the opposite direction as the plane. See if this helps:

I numbered the arrows so you could discuss them if you want to.
Correct. The plane will move forward and lift off. If I apply a force to the plane, assuming that force is not countered by an equal force in the opposite direction, the airplane will accellerate. F=ma.

#### Zoom-Zoom

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Hmmm...I forgot that airplane wheels are free-rolling. Hmm, I guess it would take off..but It would have to be completely frictionless to do so if the airplane speed eqactly matches the runway speed.

#### dajimmers

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Zoom-Zoom said:
Not necessarily. The wheels (and plane) will move forward in relation to the runway but not in relation to the surrounding air. Of course, this assumes the plane is real... has friction
OK, here's an example of what I'm saying, and it's nearly the same thing:

Imagine you are trying to run up an icy slope. You are running as fast as you can. However, the slope and friction of the ice is just right, so that you go no where. If you stop running, you slide down the slope. But if you keep running at full speed, you stay stationary, relative to an observer off the slope (and the air around you).

This is just like the plane's wheels and conveyer/runway.

Now, imagine a rocket is strapped to your back. You will most definitely be able to ascend the slope under the rocket's power.

Only if the frictional force generated by the maddening spinning of the wheels was as great as that generated by the thruster would the plane not move. Now, it would probably need a longer runway to take off, but it will still move.

#### DrFeelgoodMD

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i agree with dajimmers

#### OwnageMobile

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So if we assume that the wheels are frictionless, you basically can ignore what they rest on; furthermore that what they rest on is moving. So without a doubt, the plane can move, and hence take off, with frictionless wheels.

Now if "free rolling" doesn't imply frictionless, and the conveyor belt can exert a force on the plane, then the plane won't take off, since it cannot move.

Quite a simple question. I too question if some special fact which happened to make the question worth our time, was left out.

#### dajimmers

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To make this pre-allo worthy:

If, when going on your next interview, your runway turns into a giant conveyer belt when the pilot is about to hit the thrusters, run up to the cabin and tell him/her to floor it, and you'll still take off.

You can never be too careful about these things.

#### medicalbound

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Yes, the plane will fly. The plane's relationship to the runway or the ground does not matter; it is the relationship to the air that provides the lift required for flight. The thrust is applied to the air, and not the ground. The airplane would therefore accelerate relative to the air...lift...flight.

#### OwnageMobile

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You have to state whether the wheels are frictionless or not. Two different answers.

#### DrBowtie

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The thing is that as the thrust causes the plane to accelerate, the belt accelerates in the opposite direction at equal rates.

6

#### 67192

F(net) = mass*acceleration. Only net force acting on plane = thrusters. Forward motion generates pressure difference above/below wings, so plane takes off.

Although, I think dajimmers picture diagram explains it best! Daj- where were you when I took physics?!

#### medicalbound

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BrettBatchelor said:
The thing is that as the thrust causes the plane to accelerate, the belt accelerates in the opposite direction at equal rates.
The belt accelerates what though? It will only accelerate the wheels which have nothing to do with the forward thrust of the plane. Yes, the wheels will spin faster in the opposite direction, but this does not negate the acceleration of the plane due to the opposite and equal force applied on the air by the thrusters.

#### kam9933

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The plane will neither move, nor take-off. The thrusters accelerate the plane according to F=ma. Since the wheels are free-rolling and have friction, the forward acceleration is negated by the conveyor belt. The conveyor belt serves as friction in the opposite direction. Therefore, no matter how much the plane accelertes it will not attain a velocity. Since no velocity is attained the plane will have zero displacement and will not create any pressure gradient with the air.

In regards to dajimmers standing on ice with a rocket strapped to the back example, what you forget is that, the ice in that example is stationary, whereas the conveyor is not.

#### DrBowtie

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medicalbound said:
The belt accelerates what though? It will only accelerate the wheels which have nothing to do with the forward thrust of the plane. Yes, the wheels will spin faster in the opposite direction, but this does not negate the acceleration of the plane due to the opposite and equal force applied on the air by the thrusters.
True. I guess I assumed the movement of the wheels weren't independent of the plane. Tricky problem. I'd have to look at it on paper more closely

#### OwnageMobile

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(Has it been long enough for those posters?)

You have to state whether the wheels are frictionless or not. Two different answers.

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The lift due to air is solely responsible for whether the plane will take off or not.

Air lift is proportional to the plane's velocity relative to the air.

If I understand how the problem is put, there IS friction in the wheels. The plane is set such that it's velocity relative to the belt surface is perfectly counteracted by the velocity of the surface. Thus, the plane is stationary with respect to the air.

As it is stationary, it has no velocity relative to the air, and will not take off.

If the wheels are frictionless ( ), the belt cannot do work on the plane (so it's totally irrelevant), and if the plane has enough velocity, it will have the lift required to take off.

#### DrBowtie

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The lift due to air is solely responsible for whether the plane will take off or not.

Air lift is proportional to the plane's velocity relative to the air.

If I understand how the problem is put, there IS friction in the wheels. The plane is set such that it's velocity relative to the belt surface is perfectly counteracted by the velocity of the surface. Thus, the plane is stationary with respect to the air.

As it is stationary, it has no velocity relative to the air, and will not take off.

If the wheels are frictionless ( ), the belt cannot do work on the plane (so it's totally irrelevant), and if the plane has enough velocity, it will have the lift required to take off.
Well if the plane is stationary what if a gust of air blows over the wing?

#### OwnageMobile

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Yup

Damn these speedy replies; that was "yup" to merc's articulation.

#### medicalbound

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OwnageMobile said:
(Has it been long enough for those posters?)

You have to state whether the wheels are frictionless or not. Two different answers.
It makes no difference. Ground speed is not a factor for flight.

#### OwnageMobile

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I'm just gonna let you think about that one. ^

#### cfdavid

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I say no. The plane will not take off.

Another way to look at it is simply to imagine a car on some rollers. the car can be doing 70mph according to the speedometer, but ofcourse it's just "spinning its wheels". So, if you put your hand out the window, you wouldn't feel any "wind". That's because there's no relative motion.

Think of a treadmill. If you could run super fast, your hair would still not look like it would if you were actually moving that fast.

So, with no relative motion to the air, there could be no lift due to the lack of pressure differential, since the air on the top AND bottom of the wings would not be moving at all relative to the plane etc.

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BrettBatchelor said:
Well if the plane is stationary what if a gust of air blows over the wing?
Well, if the wind was well sustained and organized, I don't see why it wouldn't take off. Only it wouldn't go forward. It would go backward, since it doesn't have that extra thrust to go forward.

Besides, kites are stationary with respect to the ground, yet they can fly precisely because the air is moving rapidly past them.

#### DrBowtie

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Well, if the wind was well sustained and organized, I don't see why it wouldn't take off. Only it wouldn't go forward. It would go backward, since it doesn't have that extra thrust to go forward.

Besides, kites are stationary with respect to the ground, yet they can fly precisely because the air is moving rapidly past them.
So basically it all comes down to the wind speed?

#### Chris127

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lol, I think the best aspect of this thread is the way different people respond. Some of you whip out the physics formulas and attempt to find the answer within the calculator, some simply make practical analogies to other situations, and yet others get into discussing specific components and capabilities of the plane itself. Its interesting

#### medicalbound

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OwnageMobile said:
I'm just gonna let you think about that one. ^
I've been a pilot since 1998, it is airspeed that is the deciding factor for flight not groundspeed. Here is an example: the rollout speed for a Cessna is about 65 knots (airspeed). If you theoretically have a 60 knot direct headwind, you would have to be going only 5 knots relative to the ground to start flying. That is also why a plane can fly 200 knots (ground speed) with only enough thrust to fly at 100 knots in the air (100 knot tailwind).

The outcome of the problem would be different if the power were applied to the wheels, but it is not.

#### OwnageMobile

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medicalbound said:
I've been a pilot since 1998, it is airspeed that is the deciding factor for flight not groundspeed. Here is an example: the rollout speed for a Cessna is about 65 knots (airspeed). If you theoretically have a 60 knot direct headwind, you would have to be going only 5 knots relative to the ground to start flying. That is also why a plane can fly 200 knots (ground speed) with only enough thrust to fly at 100 knots in the air (100 knot tailwind).

The outcome of the problem would be different if the power were applied to the wheels, but it is not.

I'm refering to the fact that the problem pivots on whether the wheels are frictionless or not.

I'm not questioning that airspeed is how planes create lift (see what brett said about a gust of wind)

#### medicalbound

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OwnageMobile said:
I'm refering to the fact that the problem pivots on whether the wheels are frictionless or not.

I'm not questioning that airspeed is how planes create lift (see what brett said about a gust of wind)
Okay, let's change the approach. The wheels have to have static friction or else they wouldn't be affected at all by the runway. They are free rolling. What is counteracting the force of the thrusters to keep the plane stationary?

#### cfdavid

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medicalbound said:
I've been a pilot since 1998, it is airspeed that is the deciding factor for flight not groundspeed. Here is an example: the rollout speed for a Cessna is about 65 knots (airspeed). If you theoretically have a 60 knot direct headwind, you would have to be going only 5 knots relative to the ground to start flying. That is also why a plane can fly 200 knots (ground speed) with only enough thrust to fly at 100 knots in the air (100 knot tailwind).

The outcome of the problem would be different if the power were applied to the wheels, but it is not.
yeah, but aren't jet engines located UNDER the wing. so, if the jet sucks air out from in front of the wing, and then spits it out through the back of the wing, there would actually seem to be a LOWER pressure UNDER the wing, thereby causing a downward force. This would make flight even less likely.

am i missing something?

#### rockitman

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Yes, It would take off, and the question about whether or not the planes wheels are frictionsless does not matter.

Think of it like this:
Replace the jet engines with cables and winches producing the same amount of forward impulse. Start pulling the plane forward with the winches and at the same time start pulling the runway/treadmill/conveyor backward. Is it going to stop the plane from moving forward across the earth's surface?

Of course not. The wheels are just going to spin at higher RPM.

Jet engines or cables being pulled by winches will both move the airplane forward and the wheels have nothing to do with it.

#### OwnageMobile

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medicalbound said:
The wheels have to have static friction or else they wouldn't be affected at all by the runway. They are free rolling.
Yeah, this is what I too am saying (kinda, but your statement seems a bit contradictory/ambiguous when you use static friction and free rolling together)

What I am saying:

Case #1: Wheels are frictionless Answer = yes, the plane can take off.
Case #2: Wheels are not frictionless Answer = no, the plane doesn't move.

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OwnageMobile said:
Yeah, this is what I too am saying (kinda, but your statement seems a bit contradictory/ambiguous when you use static friction and free rolling together)

What I am saying:

Case #1: Wheels are frictionless Answer = yes, the plane can take off.
Case #2: Wheels are not frictionless Answer = no, the plane doesn't move.
Of course, that is the correct answer.

#### OwnageMobile

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je1985 said:
Yes, It would take off, and the question about whether or not the planes wheels are frictionsless does not matter.

Think of it like this:
Replace the jet engines with cables and winches producing the same amount of forward impulse. Start pulling the plane forward with the winches and at the same time start pulling the runway/treadmill/conveyor backward. Is it going to stop the plane from moving forward across the earth's surface?

Of course not. The wheels are just going to spin at higher RPM.

Jet engines or cables being pulled by winches will both move the airplane forward and the wheels have nothing to do with it.
No. You aren't taking into consideration that the conveyor in the problem exerts a force on the wheels that matches the force from the jets. So your winch cable would snap (possibly making the plane fly backwards?)

#### cfdavid

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je1985 said:
Yes, It would take off, and the question about whether or not the planes wheels are frictionsless does not matter.

Think of it like this:
Replace the jet engines with cables and winches producing the same amount of forward impulse. Start pulling the plane forward with the winches and at the same time start pulling the runway/treadmill/conveyor backward. Is it going to stop the plane from moving forward across the earth's surface?

Of course not. The wheels are just going to spin at higher RPM.

Jet engines or cables being pulled by winches will both move the airplane forward and the wheels have nothing to do with it.
forward relative to what? the bottom line is that there would be no air movement relative to the wings. i agree that friction or no friction on the wheels is not a factor in this problem.

but, it's the movement of the air that matters, thereby creating a pressure differential over/under the wings that creates the buoyancy.

#### rockitman

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No. You aren't taking into consideration that the conveyor in the problem exerts a force on the wheels that matches the force from the jets. So your winch cable would snap (possibly making the plane fly backwards?)

No, incorrect. The conveyor in the problem does not exert a force that matches the jets. The conveyor only matches the speed of the wheels. However, the speed of the wheels does not have anything to do with the speed of the plane. The plane would slowly move forward along the convyeor. It would be able to take off, however, the belt would have to be much longer than an average runway.

#### TheMightyAngus

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cfdavid said:
forward relative to what? the bottom line is that there would be no air movement relative to the wings. i agree that friction or no friction on the wheels is not a factor in this problem.

but, it's the movement of the air that matters, thereby creating a pressure differential over/under the wings that creates the buoyancy.
So if the plane is stationary relative to the conveyor belt, it is stationary relative to the air. No "wind", no take-off.

#### dajimmers

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Someone send this to MythBusters, I want to see them make a plane explode or something!

Whether or not there is friction isn't the only factor. If there is friction, you must create enough frictional force to counteract the force of the thrusters. The only way to create frictional force is to spin the wheels ever faster. All of the friction will be generated by the ball bearings of the wheels (think of Rollerblade wheels, and their ABEC 3 vs. ABEC 5 ratings, basically friction ratings). I don't know the friction constants or whatever of the wheels, but I'm sure the treadmill and wheels would have to be moving insanely fast to create this much frictional force. And, I doubt any real-world wheels could handle that much heat. Therefore I suggest the answer is:

1. IF ball bearings are frictionless, plane will accelerate and fly normally
2. IF ball bearings have some friction, plane will still move forward, but at a slower acceleration
3. IF ball bearings have "normal" friction, wheels will explode, plane will hit very fast moving treadmill, chaos will ensue.

#### Dakota

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TheMightyAngus said:
So if the plane is stationary relative to the conveyor belt, it is stationary relative to the air. No "wind", no take-off.
And as many others have said, if the wheel-plane connection is frictionless (the wheel-ground can have all the frictionyou want) then the plane will be able to move forward relative to the conveyor belt (and thus you can fly).

And to again make the pre-allo connection, you will still be on time to your interview if you are on this aircraft.