As I remember the problem, the plane’s wheels are supposed to be frictionless so that their rotation is uncoupled from the rest of the plane’s motion. Hence the speed of the conveyor belt is irrelevant and the plane always takes off. Now, if you had a helicopter on a turntable...
What I mean is, on hearing that I thought of a conveyor belt whose top surface was moving at a speed -x with respect to the air, and a plane on top of it moving at a speed x with respect to the top of the conveyor belt, i.e. the plane was stationary with respect to the air. But on reading the Snopes link what was actually meant was that the conveyor belt was moving at speed -x and the plane’s engines were working as hard as needed to move at speed x on stationary ground with no wind.
While at the same time the rolling speed of the plane, which is the sum of it’s forward movement and the speed of the treadmill, is supposed to be equal to the speed of the treadmill. Which is impossible if the plane moves forward.
I’m not sure what you mean by “rolling speed of the plane”, “it’s forward movement”, and “speed of the treadmill”. The phrase “rolling speed” sounds like it refers to the component of the plane’s forward motion due to the turning of its wheels, but that’s not a coherent thing to talk about if one accepts my assumption that the wheels are uncoupled from the plane.
Rolling speed = how fast the wheels turn, described in terms of forward speed. So it’s the circumference of the wheels multiplied by their angular speed. And the wheels are not uncoupled from the plane they are driven by the plane. It was only assumed that the friction in the wheel bearings is irrelevant.
Forward movement of the plane = speed of the plane relative to something not on the treadmill. I guess I should have called it airspeed, which it would be if there is no wind.
Speed of the treadmill = how fast the surface of the treadmill moves.
And that is more time than I wanted to spend rehashing this old nonsense. The grandparent was only meant to explain why the great grandparent would not have settled the issue, not to settle it on its own. The only further comment I have is the whole thing is based on an unrealistic setup, which becomes incoherent if you assume that it is about real planes and real treadmills.
And that is more time than I wanted to spend rehashing this old nonsense.
Fair enough. I have to chip in with one last comment, but you’ll be happy to hear it’s a self-correction! My comments don’t account for potential translational motion of the wheels, and they should’ve done. (The translational motion could matter if one assumes the wheels experience friction with the belt, even if there’s no internal wheel bearing friction.)
As I remember the problem, the plane’s wheels are supposed to be frictionless so that their rotation is uncoupled from the rest of the plane’s motion. Hence the speed of the conveyor belt is irrelevant and the plane always takes off. Now, if you had a helicopter on a turntable...
What I mean is, on hearing that I thought of a conveyor belt whose top surface was moving at a speed -x with respect to the air, and a plane on top of it moving at a speed x with respect to the top of the conveyor belt, i.e. the plane was stationary with respect to the air. But on reading the Snopes link what was actually meant was that the conveyor belt was moving at speed -x and the plane’s engines were working as hard as needed to move at speed x on stationary ground with no wind.
While at the same time the rolling speed of the plane, which is the sum of it’s forward movement and the speed of the treadmill, is supposed to be equal to the speed of the treadmill. Which is impossible if the plane moves forward.
I’m not sure what you mean by “rolling speed of the plane”, “it’s forward movement”, and “speed of the treadmill”. The phrase “rolling speed” sounds like it refers to the component of the plane’s forward motion due to the turning of its wheels, but that’s not a coherent thing to talk about if one accepts my assumption that the wheels are uncoupled from the plane.
Rolling speed = how fast the wheels turn, described in terms of forward speed. So it’s the circumference of the wheels multiplied by their angular speed. And the wheels are not uncoupled from the plane they are driven by the plane. It was only assumed that the friction in the wheel bearings is irrelevant.
Forward movement of the plane = speed of the plane relative to something not on the treadmill. I guess I should have called it airspeed, which it would be if there is no wind.
Speed of the treadmill = how fast the surface of the treadmill moves.
And that is more time than I wanted to spend rehashing this old nonsense. The grandparent was only meant to explain why the great grandparent would not have settled the issue, not to settle it on its own. The only further comment I have is the whole thing is based on an unrealistic setup, which becomes incoherent if you assume that it is about real planes and real treadmills.
Fair enough. I have to chip in with one last comment, but you’ll be happy to hear it’s a self-correction! My comments don’t account for potential translational motion of the wheels, and they should’ve done. (The translational motion could matter if one assumes the wheels experience friction with the belt, even if there’s no internal wheel bearing friction.)