Yeah, exactly, there’s no way around that. If the plane takes off then econophile’s condition 2 is obviously violated, and that’s the whole formulation of the problem. And I think that increased drag in the wheel bearings at very high speed has to be what the problem’s author was going for. That or increasing the friction of the bearings by having them fail by running them at an arbitrarily high speed, that’d do it too.
Well then, is it a physics question or some other kind of question (logic/puzzle)? It would certainly be a bad question on a physics exam - badly written. Definition of “speed of the wheels” is a big problem here and I don’t think the velocity at the hub is the most natural understanding of that. If it were, why not just say speed of the plane?
Well, hard to say what the author intended. Could have just been badly written and they meant poopy’s option 1. Could be they just meant for you to find the logical problem and say it’s an impossible situation. Getting into friction in the bearings and the fluid mechanics of the grease seems like ways to work around the problems with the question - interesting, but dunno if that’s what the author would have been thinking.
It’d be a fine physics question if the assumptions were all laid out. Don’t make it a magic treadmill, just make it a constant velocity treadmill. Stipulate which parts are indestructible and wouldn’t slip. Give a model for the friction of the wheel bearings. At what treadmill speed would the plane not take off?
Sure. I just mean it’s not well enough defined as is for a physics problem and not even really well enough for the logic problem. As I keep mentioning “speed of the wheels” is not well defined. The wheels have different speeds from the center to the outside and relative to the plane, the conveyor and an observer at the airport. Bringing up speedometers was a good idea (poopy).
The only way it’s even remotely interesting if the speed is the tangential speed as defined by econophile, right? So I assume that’s what the question means.
Still needs to be specified where the tangent is and what point the speed is relative to. Relative to an observer at the airport (this would be a natural frame of reference because that’s what you’re using for the plane and the treadmill), the bottom of the wheel is always going the same speed as the treadmill if there’s no skidding. That makes the situation trivial. Conveyor belt never moves. Plane takes off normally. As the plane speeds up the bottom of the wheel is always not moving relative to the observer and the top of the wheel is moving down the runway at twice the speed of the plane. Talking about speedometers makes it exactly clear what is meant in a very concise way.
But, yeah, tangential speed relative to the airplane (or center of the wheel) regardless of where the plane is going.
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I’m still confused. Suppose the conveyor belt goes at such a speed so that the plane’s horizontal position does not change. That means a) the plane doesn’t lift and b) it’s trivial to see that the plane doesn’t lift? So the trick to the question is to see that it (the question’s wording) doesn’t imply the plane wouldn’t move forward?
Amazing posters ruining this thread by engaging with micro, I don’t get it
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The problem is there’s very little the conveyor belt can do to stop the plane from moving forward. The jets thrust the plane forward and the wheels and conveyor should be able to spin almost all they want without stopping the plane at all. Problem is, plane moving forward would violate the condition that the belt speed has to match the wheel speed.
So, “such a speed”? What does that mean? Twenty thousand miles per hour? Unlimited?
Now can we please discuss if free will exists in a deterministic world and if 0.999… = 1. Just to get them out of the way as well.
The plane takes off using any realistic version of a threadmill no matter what speed it gets up to and a lot of people think that even that is not true. The question is ambiguous about what wheel speed the threadmill matches and any real threadmill will just reach its maximum speed and the plane takes off even if the maximum threadmill speed massively exceeds the takeoff speed. The best interpretation of the question will have the threadmill match the groundspeed of the center of the wheels which fulfills ‘matches the speed of the wheels’ and the threadmill will reach takeoff speed when the plane takes off with the wheels rotating twice as fast as the threadmill.
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Sure, but why not say “speed of the plane” if that’s what you mean?
Because that makes the question less likely to cause people to waste their time debating on an internet forum.
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Oh man, now what the hell is a threadmill?
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Everyone posting in this thread is on one.
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I just ran on a treadmill for an hour without taking off, and I’m way lighter than a plane
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Holy shit I saw this earlier start and checking in to see this is still going?
lol love this phrasing
It’s from a movie os and on the tip of my tongue
ahhh yes. “Who’s this new preacher, teacher or whatever he is?” lol " … am I not allowed to speak with Him?"
“You seemeth to be most unwelcome here.”
Please make it stop
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