Plane on conveyer belt question (with video)

[f '(x)]

My initial thought was that the plane wouldn't be able to take off. If the conveyor is moving in the opposite direction as the plane, at the same speed, then the plane wouldn't move relative to the ground (as if you're running on a treadmill, you're not actually changing position relative to the room you're in) and therefore there would not be any more air flow over the wings than if it was sitting still, parked in one spot. (again, if you're running on a treadmill, you won't feel the breeze in your face that would be felt if you were actually running on the ground) I am also assuming you know the physics behind a plane taking off.
However people in the comments section of the video said it was a stupid myth because the plane will "obviously" take off no matter how fast the conveyor is moving due to the plane being propelled by the propeller rather than the wheels.
Can anyone explain how this works? My feeling is that it was tested incorrectly.

 

[94JZA80]

well think about it...the engine provides power to the prop, not the wheels. its the prop in conjunction with the air that propels the plane forward via Newton's 3rd law, not the wheels in conjunction with the ground. so why would we have any reason to believe that the plane would not move forward when its motion is dependent only on the speed of the surrounding air, and not at all on the speed of the ground underneath it? actually, in reality there will be some friction/rolling resistance/whatever that will factor into the equation as a minimal amount of drag so long as the wheels rotate freely, but it'll never be substantial enough to keep a plane from taking off from a conveyor belt.

 

[CWatters]

My initial thought was that the plane wouldn't be able to take off. If the conveyor is moving in the opposite direction as the plane, at the same speed, then the plane wouldn't move relative to the ground (as if you're running on a treadmill, you're not actually changing position relative to the room you're in) and therefore there would not be any more air flow over the wings than if it was sitting still, parked in one spot. (again, if you're running on a treadmill, you won't feel the breeze in your face that would be felt if you were actually running on the ground) I am also assuming you know the physics behind a plane taking off.
However people in the comments section of the video said it was a stupid myth because the plane will "obviously" take off no matter how fast the conveyor is moving due to the plane being propelled by the propeller rather than the wheels.
Can anyone explain how this works? My feeling is that it was tested incorrectly.

Consider what would happen if you took a long pole with you on the running machine. While running reach behind yourself with the pole and use it to push yourself away from the nearest wall. You will move relative to the room right?

The plane is doing the same only instead of using a pole it's using a "jet of air" produced by the engine.

 

[A.T.]

If the conveyor is moving in the opposite direction as the plane, at the same speed,

Same speed relative to what?

If the the plane is moving relative to the belt at the same speed (but opposite direction) as the belt relative to the air, then the plane is at rest relative to the air and cannot take off. But how do you enforce such a constraint, if the wheels are free to spin and the propeller pushes off the air?

If the the plane is moving relative to the air at the same speed (but opposite direction) as the belt relative to the air, then the plane moves relative to the air and can take off. The wheels just spin faster than in a normal take off.

My feeling is that it was tested incorrectly.

The problem is ambiguously stated and in some interpretations not testable practically. They used an interpretation which is testable, and got the correct result for that.

 

[Lsos]

Same speed relative to what?

There are two variables in this problem: the belt speed and the plane speed. It doesn't make sense to measure their speeds relative to each other or relative to themselves. In that regard, I'd say the problem is NOT ambiguous and open to interpretation.

Usually the ground is the best reference point in these types of problems.

What usually ends up being problematic is that people instinctively feel that wheel speed (or speed indicated on a speedometer) = object's speed. This is obviously wrong, but since people are so often exposed to it it's hard to think around it. They set this as a fixed assumption, and then attempt to mold everything else around it.

 

[A.T.]

What usually ends up being problematic is that people instinctively feel that wheel speed (or speed indicated on a speedometer) = object's speed.

If you don't explicitly specify what the reference for the speed is, then you cannot blame the people for assuming whatever reference they want.

 

[rcgldr]

Usually the ground is the best reference point in these types of problems.

The air would be a better reference, since there could be a tail wind or a head wind.

For the treadmill analogy, imagine that the person is wearing skates, and as suggested by CWatters, is using a long pole to push away from a wall that faces the back end of the treadmill. The treadmill speed would only affect rolling resistance of the skate wheels (angular inertia of the skate wheels would be an issue during accelerations), which hopefully is small compared to the force the person can generate by pushing the pole against that wall.

 

[Lsos]

If you don't explicitly specify what the reference for the speed is, then you cannot blame the people for assuming whatever reference they want.

Wheel speed is only indicative of an object's speed only in a specific and narrow set of circumstances. While I cannot blame the reader for assuming that it applies in this case, I nor the creator of the riddle cannot take responsibility for this. The reader is wrong, and it is their problem.