Yes, but if the wheel surface is frictionless, then what you’ve got is a plane on a block of wet ice. If the wheels/skids have no friction against the conveyor belt, then the belt can’t exert any force at all against the plane. No matter how you move the belt, the plane stays at rest.
We all agree that a plane with frictionless skis on a sheet of ice will be able to take off, correct?
The only way the conveyer belt can affect the plane is through the wheels. So imagine that rather than a conveyor belt moving backwards faster and faster until the wheels melt, imagine a plane where the wheels are set in blocks of concrete on said conveyor belt.
The pilot turns on the engines. The wheel struts start to creak, but the plane doesn’t move. He slowly increases the thrust. The plane starts to shake, the struts start to crack. Eventually the struts snap off and the plane shoots forward, but the speed isn’t enough and the plane crashes on it’s belly.
Now, a magic treadmill and a real-world plane is somewhat equivalent. As has been pointed out, you can transmit force from the treadmill to the plane via the wheels to counteract the force of the engines. But you can only do this so much until the wheels break off. And you’re in even worse shape, since the wheels can slip or skid on your magic treadmill, exactly as if the pilot locked the brakes on the wheels and was trying to take off from a stationary runway.
Actually scratch that, if the bearing are not frictionless I can see how the force gets transferred. However, I still stand by the case of frictionless bearings not being able to transmit any force to the axel with the exception of the normal force which counteracts gravity.
How else would automobiles move? The traction force from the pavement on the tire is transmitted to the axle through the wheel bearing. Or the other way around, if you prefer.
I’m talking about external force on the rotating body. If you’re holding the gyroscope housing, and I push on the edge of the gyroscope wheel to make it spin up, you’re going to feel that push.
Not quite; only when you are *changing *the rotational rate. Think of a flywheel spinning in the horizontal plane, hanging from a very long vertical arm. The flywheel is spinning at some high number of rpms. The flywheel is brought closer and closer to a brick wall, until it just makes contact, which slows the flywheel down - but the flywheel resists the deceleration and sort of ‘runs along’ the wall as it slows down, deflecting the long vertical axle away from plumb, even if the bearings are frictionless.
The same is true in reverse: if you hold your (nonspinning) gyroscope by the axles and bring its edge up toward a running treadmill, you will feel a force on the axle that points in the same direction as the moving surface of the treadmill until such time as the gyroscope is fully spun up. This will likely be for only a very short time; but if your treadmill was in a state of runaway acceleration itself, you would continue to feel a force on the axle. The bearings can transmit this force in the same way that they can transmit the normal force of the plane’s weight, even though they are frictionless- because the force vector is directly through the center of rotation of the wheel.
Or, on preview, what pmwgreen said. Stupid slow typing…
The OP stated that the conveyor would spin at the same speed as the wheels.
The only way for this to happen is if the plane stays on the same spot on the conveyor. I see it more as the plane keeping up with the conveyor than the other way around. The plane would only have to overcome the current rolling resistance, and not a smidge more. Grounded for life.
BUT -
If the plane started to overcome the rolling resistance, it will move down the conveyor. The conveyor would speed up, speeding up the wheels of the plane. If the plane is moving it’s a vicious cycle. The plane must be in one place for the wheels and conveyor to match RPM’s.
How about this. Lets take a plane with a slow take off speed. A Cesna 150 is what? About 75 mph?
The plane performs its take off run.
Allow the conveyor to accelerate in the opposite direction of the plane. At the same speed the plane accelerates.
The plane would have to overcome rolling resistance it would encounter at 150 mph. I think the tires and bearings could probably handle that speed. And there would be no additional wind resistance to over come. It only needs a ground speed of 75.
That’s about as close to ‘real life’ as I can think of. No frictionless bearings, or conveyors that can constantly accelerate.
I think a small plane could do it. Probably a big one too, if the tires held out.
Getting back to the OP.
As others have said, the engine, engines do not create lift by blowing air over the wing. It creates lift by pulling the plane through the air. That much, I know we can all agree on.
Well, if I’m standing holding the rope while the wheels are spinning under my feet I have zero velocity or acceleration. As soon as I pull myself towards that wall I’m accelerating towards it.
Yes you are right, Sorry. I need to think, then post… (Sketching the FBD made this obvious)
So if the acceleration of the conveyor was very large, the force on the plane could be enough to overcome the jet engines (even with frictionless bearings as long as the wheels have inertia) and the plane would not move.
The conveyor would need to accelerate continuously. A non-accelerating conveyor, even if it had a near infinite velocity, would not stop the plane moving forward. At least in the case of frictionless bearings.
I have to admit, I still don’t understand what was meant by that. It’s the action of the conveyer that makes the wheel spin in the first place, so how can it be controlled to match its own speed? The only way that sentence makes sense is if the rotational speed of the wheel is fixed, and the action of the conveyer does not affect it - which is the case with an automobile, but not with an airplane.
The plane obviously flies. The question to me is what happens to the wheels. Why are we assuming the wheels turn at all? If there are frictionless bearings in the plane’s wheels, and in the belt’s wheels, then I think the whells do not rotate and the belt movers forward with the plane. Think about it: the only friction is between the wheel and the belt. Assume that the wheels were lightly glued to the belt and the belt had no friction.
Glue isn’t an accurate description becuase something glued down is not free to rotate. The wheels in this case rotate becuase there is a force couple from friction and the force from the plane.
Yes, but they would only rotate if the belt was resisting. If the belt’s bearings have no friction then they are not applying force to the wheels. I was using the glue analogy to indicate the friction between the wheel and belt. Imagine it is an infinitely little amount of stickieness, but still enough to be more than the frictionless bearings.
The problems have been answered since posts 74 and 89.
There is a difference between ball bearing friction and the friction between the belt and the wheels. I don’t know what you mean about an infinately small amount of stickness. If that were the case there wouldn’t be enough friction to spin the wheels so the plane will slide down the conveyor belt. If the wheel is rotating there must be friction between the belt and the wheels. That friction exerts a force on the airplane that can counteract the force from the engines.
