WILL IT FLY?

It will take off right after the wheels start sliding/explode from the treadmill rolling too fast

If it could dont you think it would be incorporated onto aircraft carriers? Instead of a ramp
>planes can take off while stationary
Ya ok

>>planes can take off while stationary
except its not stationary

the plane will move forward until it reaches its take off speed for which it will just take off

the plane either rolls off the conveyor belt or takes off, depending on how large the belt is

the wheels have nothing to do with anything, they're red herrings

No shite but they need the wheels to get moving or else they would scrape their undercarriage

the wheels do not "get them moving" they're there ONLY to roll on, they're frictionless

No the belt will match the speed of the wheels. Have you ever ran on a treadmill? You dont go anywhere

>No the belt will match the speed of the wheels. Have you ever ran on a treadmill? You dont go anywhere
The wheels do not provide thrust for the plane

what force counter acts the force of the turbines?

It doesnt matter what provides thrust, if you get rollarblades and attach a rocket to your back and stand on a treadmill you will not move forward.

Yes it does

Theres only one source of thrust in this equation, the wheels provide no resistance, nothing

No it doesnt, the plane could drag the wheel forward

>stand on a treadmill you will not move forward.
yes you will, assuming the rollerblades are frictionless you certainly would

>747
> is NOT powered by the Wheels! !!!!
Jet Engines push / pull AIR

>It doesnt matter what provides thrust
The morons have arrived.

So if a hamster runs on a wheel fast enough it will move forward?

You all are retarded. The wheels are a red herring. It's the air moving over the wings that matter. Either the wings can move through the air and create lift like an airplane taking off. Or the air can pass over the wings like a in wind turbine.
Like a

No because unlike a jet, a hamster doesn't move the air with a fucking turbine engine

Then why do planes have to move to take off?

So air can run over their wings.

Unlike you or a hamster that relies on your legs for propulsion. A jet's method of propulsion does not rely in gripping the ground to shoot itself forward. It uses a turbine to push itself forward. The wheels do NOTHING, they could be sleds or skates, unless some equal and opposite force goes against the turbines the plane WILL move forward

They are right though, retard. Most of people in this thread is missing the point of the question, the conveyor belt thing is in the question to let us assume that the plane WILL NOT MOVE. If the plane doesn't move forward it can't fly. This board is full of autistic retards that can't even comprehend the nature of a simple question like this.

OP HERE, WHY ARE WE ASSUMIG THE WHEELS ARE FRICTIONLESS?!?!? THIS IS SUPPOSED TO BE A REAL SITUATION

kek'd

>Most of people in this thread is missing the point of the question, the conveyor belt thing is in the question to let us assume that the plane WILL NOT MOVE.
>This board is full of autistic retards that can't even comprehend the nature of a simple question like this.
If you actually read any of the posts in this thread, or any of its predecessors, you would understand people's objection to that part of the question.
Yes, the question assumes the plane won't be able to move forwards. However, the justification given for that assumption is nonsense - spinning the wheels won't keep the plane from accelerating, and therefore the claim "the conveyor belt is designed to exactly match the speed of the wheels" is unreconcilable.

>WHY ARE WE ASSUMIG THE WHEELS ARE FRICTIONLESS
Because if we start including factors like friction, the question simply becomes "what breaks first", and that's not terribly interesting.

Wheels aren't frictionless.

Exactly, meaning that the turbines depend on the wheels in order to translate the thrust into forward motion. But this forward motion would be counteracted by the conveyor belt which would prevent any lift from being generated

Wheel bearings will be turning at twice the design speed, that is the only difference.

they're virtually frictionless

a 747 puts out 50k pounds of thrust PER engine

the wheels might generate a few hundred pounds of friction resistance.

>the turbines depend on the wheels
NO THE WHEELS APPLY NO POWER

REPLACE THE WHEELS WITH SKATES OR SLEDS you stupid shit

the turbines apply a force

what force goes against the plane to stop it from accelerating?

the treadmill applies zero force to the plane because the wheels are (virtually) frictionless

>the wheels provide thrust
mo they don't the wheels don't do anything they're free spinning

SUCK OFF, THE THRUST MOVES THE PLANE WHICH MOVES THE WHEELS AND THE WHEELS ROLL THE PLANE ALONG ITS PATH BUT IF THE WHEELS ARE BEING ROLLED BACK BY THE BELT HEN IT CANT MOVE FORWARD

Yes I get that, but the rolling friction is what allows the plane to progress forward but the treadmill keeps it back

THE WHEELS ARE FREELY MOVING AS LONG AS THE BRAKES AREN'T BEING APPLIED YOU FAGGOT

FAGBAG MILLIONAIRE! THE PLANE NEED THE ROLLING FRICTION TO ROLL FORWARD WHICH GETS COUNTERACTED BY THE BELT

The treadmill applies no force on the plane

Velocity is scalar force is a vector

>velocity is scalar
Are you retarded?

>says the retard who thinks he can counter act a force with a velocity

The planes thrust is in the engines the wheels have nothing to do with it.

The treadmill has no way to apply an opposing force on the engines

The thrust causes a force which causes a velocity but this velocity is counteracted by the belt.
Me - 1
Dumb cunt user - 0

You can't counter act a "velocoty" the wheels can spin as fast as they can and nothing is opposing the thrust of the engines

Friction like brakes on the wheels causes a force that would slow down the plane the wheels are free spinning and virtually frictionless

The Velocity of the plane isn't even measured by the wheel speed

The plane is completely separate from the treadmill

The treadmill going in reverse wouldn't accelerate the plane any faster

Thank you OP. This thread is wonderful.

>causes a Velocity

Shit I didn't know force = mass * velocity

Me - 0
Smart cunt user - all of em

I got it like 5 posts ago I'm just being a diva roach.

Thanks anons, turns out I was wrong but I'll take my loss in return for newly gained basic physics knowledge.

if only the wheels could affect the thrust of a plane how would even it move after leaving the ground

Bu...bu...but
Muh friction

This is a very small problem
Nested in a big problem with lots of messy things to get you mixed up and confused. Essentially the only thing that matters is the forces acting on the wheel. As the turbines produce forward thrust the axel moves foreward applying a leftward force to the wheel. The wheel experiences this force and wants to move leftward but as it is in contact with the surface it also experiences a force of static friction at the point in which the wheel contacts the treadmill. Due to the low coefficient of friction between the axel and the wheel and the high coefficient of friction between the wheel and the surface instead of sliding on the surface the wheel rotates around the axel. As it rotates it experiences some amount of static
Friction, but this quickly becomes kinetic friction. As the wheel rotates the surface moves in congress with it changing its relative state of motion. Since the plane is only moving forward relative to the treadmill and not the air around it the plane experiences essentially no air resistance (and thus no lift). As thrust increases the treadmill increases its speed such that it matches the rotation of the wheel. At that point we're fine, but the turbines are shooting matter out the back increasing its velocity relative to the atmosphere. This will continue up until the point at which the forward thrust produced by the turbines overcomes the maximum static friction in the wheels. At which point it does not matter how quickly you spin the treadmill. The plane will move forward.

Imagine applying the brakes to the wheels as the thrust increases. What happens? Well the turbines continue to increase forward thrust and the treadmill keeps spinning faster all the same, but once that maximim force of friction acting on the wheels is overcome the plane will move forward dragging the wheels against the treadmill. This will happen whether the wheels are spinning or not.

yes, the wheels are not connected to the driveshaft. It will roll along the treadmill, because the velocity relative to a point on the treadmill is not what matters. It's the velocity relative to the air. Relative to a point on the treadmill (at least while that point is moving to the right), it will take of at 2*takeoff speed.

As written the plane cannot take off.
Why? Chose your answer:
1) In order to meet the restrictions of the scenario the plane cannot move using its engines, period. Any movement produced by its engines would violate the setup.
2) If by some miracle the plane has a non-zero wheel speed, by the setup the conveyor belt exactly matches but in the opposite direction and thus there cannot be any non-zero airspeed.

Not following the setup as presented is not acceptable in any meaningful discussion.

The real answer is that the question was either made by an inbred mongoloid who doesn't know how a planes work, or by a troll, and in either case shouldn't be discussed at all

Changing the definition of a plane just to stoop down to the retardation of the question is foolish and pointless

...

At last I see the light.

This, since no air is providing the necessary lift the plane will never take off.

I sincerely enjoy that someone took the time to make this. Thanks for sharing bud.

Yes OP, it will fly.

Think about it in the following way:

When an airplane moves on a runway, it's essentially following a one dimensional coordinate system. A number line, if you will. As x increases, the plane gets closer to take off.

In this scenario, the same thing holds, except that the coordinate system is the treadmill, and it loops around. That doesn't matter though, because the plane is still progressing longitudinally, and its wheels are rolling, so it will take off, guaranteed.

You have fallen victim to a masterful ruse

the fun begins when the first tire bursts

This is the only correct answer in this thread, I can't believe sci is this retarded

>However, the justification given for that assumption is nonsense - spinning the wheels won't keep the plane from accelerating

Dude, the conveyor belt is there to set the constraint [math]r \dot{\theta}=v[/math] where [math]\dot{\theta}[/math] is the planes wheels angular velocity and v the speed of the conveyor belt. Once this constraint is set true, it doesn't matter where the thrust comes from, it doesn't matter how fast the wheels spin, the plane will not move forward, hence it will not take off.

no because the wings will not gain any lift. when you run on a tread mill there isn't any wind resistance to push you back, this is the same reason why it will not take off.

Reference planes (lol pun!)

If it was a car that had thrust through its wheels connected to the conveyor belt - no it wouldn't move, just like a runner on a treadmill.

But the thrust is delivered to the air from the planes engines - so no connection to the belt, the plane will move.

No, because the plane will remain stationary relative to the air around it, and thus will achieve no lift.

It's not a car, the forward thrust is not provided by a drive-train connected to the wheels.

In this situation, the rolling friction of the planes wheels is different than the static friction (assuming no slip) of the driven wheels ona drive-train.

With the plane's engines thrusting it forward and the conveyor belt moving at the same speed in an opposite direction, the wheels will have an angular velocity/acceleration that is double that of a plane taking off on a runway.

The real catch here is whether or not the bearings in the plane's wheels can handle the heat/deformation of double the expected rotational force.

This. The acceleration of the belt (and corresponding angular acceleration of the wheels) would have to be ABSOLUTELY INSANE to produce enough friction to counteract thrust and fulfill the described criterium, but as long as that criterium is fulfilled the plane cannot move.
>The wheels are frictionless
Not in reality. I'm not talking the minuscule rolling friction either - spinning the wheels up in RPM requires friction from the belt (or some other input). In theory, with enough power and strong enough equipment, the belt could hold the plane in place against it's own thrust at least for a brief moment, before accelerating beyond the speed rating of the tires and blowing everything up.

The other possibility is that the plane spools up the engines, and the treadmill TRIES to hold it in place but still FAILS to do what it's "designed to" do. In this case, the plane would then be able to move (despite the treadmill's best efforts) and take off.

But that's wrong, faggot, and if you knew how to do a free body diagram you would know why.

All that happens with your magi-fucking-conveyor belt is that the wheels spin like mother fuckers.

What happens if you drop the plane from a great height, and turn on the engines at the same time? Assume the plane falls evenly reminaing on its belly, and neglect air-resistance from the downward motion.

You motherfuckers are retarded talkin bout fuckin wheel friction n shit. The plane will not take off BECAUSE of the treadmill. It keeps the plane stationery, so the aerodynamically structured vehicle cannot use the AIR to achieve liftoff. The plane must achieve a minimum speed through an atmosphere to get off the fucking ground, otherwise you are blowing up a treadmill trying to hold back 4 jet engines playing a winning battle of tug-o-war

what if you put some kind of controller that damped the response of the treadmill to the plane's wheels?

Airplane on a treadmill is an extremely old engineering troll. I've even heard that it's been posted on Fidonet, so there's a chance that this image is older than the average Veeky Forums poster.

You are retarded to think a Velocity is on par with a force

What force counter acts the thrust of the engines?

Its a bullshit problem that implies overwhelmingly unrealistic friction will counter the forward thrust of the plane. If there is no risk of tire failure, then heat and friction will hold it in place and the plane never moves. You motherfuckers are a meme

Its is stated the treadmill keeps the plane in place (((somehow))) so it doesn't matter if it would actually work, thats irrelevant. Cheat physics man

If the air hostess serves coffee fast enough to counter the planes forward motion, will it still be able to take off?

The question is nonsense.

No, the bearings in the wheel would explode under normal loading and double velocity.

Wow faggot, you're so fucking right. I'm a dumb piece of shit, sorry. I thought if the treadmill speeds matched with the planes wheels it wouldn't be able to move. Is there still hope for me in physics? This is now an academic failure thread.

So, why are you here discussing it?

The definition of a plane has not been changed.

You must be a real boring person in person.

The real answer is yes

The actual answer, ie, the one that the one who asked the question is looking for, depends
Usually you can find out what they want you to "realize" in a simple dialogue

>Will it take off
>Yes
>But it's stationary
>Oh, you're right, No
It's just an appeal to their intelligence

747 is not a rocket, and must have air moving across its wings in order to fly. At first, the belt would prevent this from happening, so lift would not occur.

Even if the wheels were frictionless, flight is achieved through airpressure which is not being generated by a non moving wing. The best you could argue with frictionless wheels is that the lack of friction implies the plane's already flying.

How fast would a treadmill need to be spinning backwards in order to hold the plane in position through the minor friction inherent in the planes wheels?

The answer to the question is NO.
The plane cannot attempt a takeoff as the belt cannot prevent it from taking off if it attempts to take off.
If the plane attempts to take off one of the conditions cannot be met: the conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction.

baka, of course the plane can take off.
if the plane has a take of velocity of x m/s
the wheels will feel and apparent 2x m/s
however the conveyor belt cannot stop the aircraft from producing trust and therefore lift.
the conveyor only interacts with the wheels, which aren't powered in anyway.
Think about this, can a plane fly over a moving conveyor belt when its wheels aren't touching it, of course it can. The same applies for taking off on a conveyor as well.

the problem is you can't prevent the plane from moving. the wheels really don't matter. especially if the wheels were frictionless, the plane's just going to move forward unhindered, and then take off

this was literally on mythbusters faggots

It takes off.
youtube.com/watch?v=YORCk1BN7QY
youtube.com/watch?v=4owlyCOzDiE

Energy analysis using classical mechanics. The thrust energy of the plane's turbine is the input, the forward motion of the plane is the output.

[math]u(t)=\frac{1}{2}m\dot{x}^2+\frac{1}{2}J\dot{\theta}^2[/math]

, where m is the mass of the plane, x is the position of the plane, theta is the relative angular position of the plane's wheel, and J is the moment of inertia of the plane's wheel. Assume the wheel does not slip on the contact between the wheel and the runway. Taking the runway's speed to be equal to the wheel speed,

[math]\dot{x_2}=r\dot{\theta}[/math]

, where x2 is the relative x-position of a fixed point on the runway and r is the radius of the wheel. However, the rotation is also related to the velocity x of the airplane in relation to the velocity of x2. That is, when the plane moves forward, the wheel's actual rotation speed depends on the difference in speed between the plane and the runway.

[math]r\dot\theta=\dot{x}-\dot{x_2}[/math]

Setting both x and x2 as positive toward the right and theta as positive toward the counterclockwise direction, it can be seen by intuition that when velocity x is greater than velocity x2, theta has a negative velocity, negating the above equation to this one:

[math]r\dot\theta=\dot{x_2}-\dot{x}[/math]

In conjunction with the first theta-x2 relation, this necessitates that the x-velocity is equal to zero. Therefore:

[math]u(t)=\frac{1}{2}J\dot{\frac{x_2}{r}}^2[/math]

That is to say that in a classical force analysis, all the energy goes into the rotation of the wheel. When the plane tries to move forward, the wheel will rotate to accommodate not just its new speed, but also its new kinetic energy, which necessarily negates the plane's forward thrust entirely. Gyroscopic action screws this one in a classical analysis.

The speed of the wheels here was obviously not the same as the speed of the conveyor. The wheel's speed was the speed of the conveyor PLUS the speed of the airplane.

Energy analysis using classical mechanics. The thrust energy of the plane's turbine is the input, the forward motion of the plane is the output.

[math]u(t)=\frac{1}{2}m\dot{x}^2+\frac{1}{2}J\dot{\theta}^2[/math]

, where m is the mass of the plane, x is the position of the plane, theta is the relative angular position of the plane's wheel, and J is the moment of inertia of the plane's wheel. Assume the wheel does not slip on the contact between the wheel and the runway. Taking the runway's speed to be equal to the wheel speed,

[math]\dot{x_2}=r\dot{\theta}[/math]

, where x2 is the relative x-position of a fixed point on the runway and r is the radius of the wheel. However, the rotation is also related to the velocity x of the air plane in relation to the velocity of x2. That is, when the plane moves forward, the wheel′s actual rotation speed depends on the difference in speed between the plane and the runway.

[math]r\dot{\theta}=\dot{x}-\dot{x_2}[/math]

Setting both x and x2 as positive toward the right and theta as positive toward the counterclockwise direction, it can be seen by intuition that when velocity x is greater than velocity x2, theta has a negative velocity, negating the above equation to this one:

[math]r\dot{\theta}=\dot{x_2}-\dot{x}[/math]

In conjunction with the first theta-x2 relation, this necessitates that the x-velocity is equal to zero. Therefore:

[math]\frac{1}{2}J\dot{\frac{x_2}{r}}^2[/math]

That is to say that in a classical force analysis, all the energy goes into the rotation of the wheel. When the plane tries to move forward, the wheel will rotate to accommodate not just its new speed, but also its new kinetic energy, which necessarily negates the plane's forward thrust entirely. Gyroscopic action screws this one in a classical analysis.

The speed of the wheels here was obviously not the same as the speed of the conveyor. The wheel's speed was the speed of the conveyor PLUS the speed of the airplane. Hail memescience.

Guess it just doesn't want to take that closing math tag. Enjoy your wider browser ¯\_(ツ)_/¯

Well done sir.

>This thread is still alive

These alleged simulations visibly fail to match the problem description.

Of course they do. As everyone else in this thread has pointed out, the problems description is incoherent.

The plane won't take off.

It uses engines to move and the wheels are his legs.

Therefore even at maximum thrust, his wheels will be locked in place? Therefore the plane won't gain momentum.

my fooking sides

It takes off with the wheels rotating at twice the speed of a normal take-off.

t. engineering professor

You fail to adhere to the given instructions, go hang yourself.