A plane is standing on runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in opposite direction).

The question is:

Will the plane take off or not? Will it be able to run up and take off?

The answer to this question confuses many. The reason it confuses them is because they view the plane as being propelled by a drive train through the wheels instead of viewing it as the propellers propelling the plane through the air.

Here is why the plane will take off. The propellers or jets of the plane do not push against the ground to make it move. They push against the air behind it to move. So even if the conveyor belt was moving, that would not require extra force for the plane to continue accelerating if we neglect friction. If we don't neglect friction is still would be verry possible because the friction force still isnt that great compared to the force the propelers apply on the air behind it. Whch is exactly what happens on normal takeoffs since kinetic friction does not increase with speed.

They try to trick you by making you think that planes take off by applying force though the wheels and pushing off the ground but that is very wrong. it pushes the air, which in this case is nearly stationary. So it wouldn't be much different than taking off from a normal runway. Only the ground is moving below you which makes no difference since planes dont have a drivetrain as such

Look, this is the basic rule that must be fulfilled for the plane to take off, air must flow past the wing. It is true that in this case air will flow over the wing the entire plane will accelerate relative to the air becuase the propepllers or jets provide thrust relative to the air. In other words they apply a force between the plane and the air so the plane must accelerate relative to the air. That must mean that air flows over and under the wing creating lift therefore allowing the plane to fly.

If the plane's propellers/jets push against the air then it will be propelled through that medium. The conveyor belt has nothing to do with slowing the plane down because it's not the wheels that are propelling the plane, it's the propellers (Duh!). Now the question is, is the conveyor long enough to sustain the plane for the duration of acceleration neccesary to take flight.  If the surface the plane is on is long enough (Runway length) then the plane will takeoff because it WILL accelerate regardless of what direction the ground is moving (Provided the brakes aren't on). The wheels will spin as fast as the ground speed plane speed, but (disregarding friction) the planes movement will be unaffected.

The propellers, are applying a net positive force on the plane in the direction the plane is pointed. The conveyor belt is applying a force opposite the direction of the plane that is only as large as the frictional force experienced by the plane under normal conditions.

Say we have a fan, and we turn it on to the highest setting. Why does the fan not fly away? The fan would never accelerate at all. Only objects that have a net force greater than 0 are able to accelerate. In the case of the fan the friction force is greater than the force of trust that the fan's blades provide. So the net force on the object is 0 so it never accelerates. But in the case of the plane, the friction force, compared to the force of thrust the propellers provide is so small that friction can be neglected. And the fact that both the plane and the conveyor belt accelerate does not change that because the friction force is not increased as the speed the wheels turn at is increased. The frictional force is considerably less than the force of thrust. If it wasn't then no plane would ever move.

How can a belt hold the plane in place? The plane needs to be putting forth some kind of thrust to be "Held in place" by the belt, but the belt CAN'T hold it in place because the wheels aren't driving the plane, the engines are. Engines push the plane forward. Ignore life, ignore takeoff for now. The engines with push the plane forward regardless of what surface it's on. It could be ice, sand, gravel or kryptonite, the plane will move forward because the thrust of the engines is greater than the friction from the ground. If it wasn't, no planes could take off. The plane will move forward regardless of how fast the belt is going because the wheels roll freely on an airplane, the wheels can spin as slow or as fast (Within reason) as they need to. Friction is there, yes, but it's the same friction that exists on a runway and has nothing to do with the forward motion of the airplane.

The engines push the plane forward, not the wheels. The belt could be going the max speed of the airplane and the plane would still move forward with the slightest bit of thrust because the belt is doing nothing but spinning the wheels. The problem really isn't whether or not the plane can take off, it's whether or not the belt can ACTUALLY hold the plane in place, and it can't.

The plane is accelerating relative to the air not conveyor. And about the friction, as the speed of the wheels increases the frictional force does NOT increase. The friction force is the same at 1 mph as it is at 102984792578327585437 mph ideally. So if you are thinking of a plane whose wheels have a friction force that stop it at 1 mph then it will be stopped at any other speed as well which will allow the treadmill to push the plane backwards rendering it unable to fly.

The thrust from the props will move the plane forward relative to the air around it. Now if the air were moving at the same speed the plane intends to go instead of the ground, then the plane would not fly for it would be stationary relative the medium that allows it to fly: air. But it is the ground that is moving. And it does not matter what speed the ground is going since its speed does not change how much lift can be created through the forward movement of the plane.

The engines of a plane are independent of the ground the plane is on. The plane will move forward regardless of the speed of the belt. The belt could be going faster than the forward motion of the plane and the plane would continue to move forward.

If the airspeed was zero then the plane has no chance of flying. But if the props are rotating, then airspeed will never remain at zero: allowing the plane to fly. There is airflow over the wing! The plane moves completely normally. The conveyer would still need to be the length of a normal runway because a plane needs a certain amount of space to pick up speed and lift off. The conveyer's movement has nothing to do with limiting the plane's forward motion more than if it were not on the conveyor, as it is not in the plane's medium of travel - air. If there were a car with wings in place of the airplane, then it sure as hell wouldn't move because the car's medium of travel - the ground - is moving opposite to its direction. The car NEEDS the ground in order for it to accelerate. The plane NEEDS air in order for it to accelerate. They are two different scenarios. The question is tricking you into thinking the plane works like a car.

Any plane that is capable of taking off can take of from this conveyor if it is long enough. Think of it this way. Let us look at the differences between this situation and a normal plane taking off. Both planes move forward at the same rate. The only difference is that the wheels of the plane on the conveyor turn faster. They actually turn twice as fast as the normal plane because the conveyor matches the speed of the wheels in the opposite direction. So the ratio of speed between them is 1:1 so the speed of the wheels on the plane on the conveyor is twice the speed of the normal plane. Another situation where the wheels would spin twice as fast as a normal plane would be to take the wheels off the plane and replace them with wheels that are half the radius of the normal wheels. This would cause the wheels to rotate twice as fast when this plane takes off. So everyone who argues that the plane will not take off is also arguing that reducing the radius of the wheels by half will not allow the plane to fly which is absurd. It is going to fly either way.

The friction force is constant no matter what the speed of the plane or the wheels is. one can figure the friction force by the equation: Fs= (mu)(K), where Fs is the friction force, mu is the normal force or weight of the object, and K is the coefficient of friction, kinetic in our case. Anyways, one can see from that equation that there is no factor for speed because it does not affect the frictional force. As long as the coefficient of kinetic friction and the weight of the plane stay constant, friction force stays the same. So if the plane is moving forward at 200 mph, and the belt moving backwards at 200 mph, the wheels are spinning at 400 mph, But plane is still moving forward.

The Plane Flies.