aaaaaahhh, now I get it.
I can see this both ways.
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The problem states the treadmill keeps the plane from moving. No take off.
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No real treadmill could do that. Plane takes off anyway.
Depends on what you believe. The problem as stated, or real world physics.
No. The propeller or jet engine doesn’t power the wheels, it pulls directly on the air and sends it rearwards of the plane. This creates a forward force on the plane, thus moving it forward. Barring a ridiculous magical warp speed treadmill, any amount of spin exerted on the wheels will have no effect.
Answer me this: How is the plane on a treadmill any different than the plane sitting on the runway with engines running full speed and the brakes applied to prevent the plane from moving?
Here’s my point, according to many posts I have read on this subject, we don’t even need runways for takeoff. Just rev the engines up, keep the brakes on and you’ll take off in no time.
A planes engines don’t make it take flight. A planes engines provide forward propulsion which causes the plane to move relative to the air around it, which causes airflow over the wing which results in lift.
If there is something preventing the plane from moving relative to the air around it, it isn’t going to take off (baring a straight line 200 mph wind). So whether it is a treadmill or brakes or a chain, if the plane isn’t moving with respect to the air, it ain’t going anywhere.
And if you want to spew all the nonsense about how in the real world the tires couldn’t handle the pressure or the treadmill would eventually give out or whatever, then you obviously don’t understand the spirit of a hypothetical.
Go back. And read. Zut’s post. A gain.
There is a force preventing the plane on the runway with brakes on from moving forward; there is no such force on the plane on the treadmill with free spinning wheels.
The point is, there isn’t anything preventing the plane from moving forward in this scenario. Brakes or chain would prevent the plane from moving, the treadmill won’t.
Light bulb. I think I get it now. This is one of those problems that you can’t grasp without your own “explanation” of it. My explanation is to imagine the plane sitting on a completely frictionless surface with competely frictionless tires. When the engines are fired up, the plane will move forward, even though the tires have no friction with the surface and thus don’t rotate. Yes, I realize on a treadmill friction would be involved, but the forward movement isn’t dependent on that friction and more importantly, what the tires are doing.
Before we get enough wind over the airplane’s wings we rely on traveling on the ground. Of course if the wind speed is 200mph head on, the plane can take off, it will appear to flat, but then it looks that way to all plane passangers – they are still and the ground is moving.
The treadmill simply stops the airplane’s forward motion by countering it. The plane will never get the needed windspeed over its wings unless it actually gets to move forward, regardless of its wheels.
No, it doesn’t. All the treadmill does is spin the tires. Very little of that force is transmitted to the body of the plane.
I suggest an experiment. Get a skateboard, an excersise treadmill, and a large box fan. Secure the fan to the skateboard. Turn the fan on at high speed and see how fast the skateboard goes. Next put the skateboard on the treadmill with the fan blowing to the back. Set the treadmill at different speeds and see if the skateboard can still roll off the front.
This isn’t a perfect experiment, because the ratio of friction on the wheel bearings to the fan’s thrust is probably much higher than the same forces on an airplane. But it may shed some light on the subject.
If the plane’s wheels aren’t turning, then the treadmill won’t turn them. Point in fact, the treadmill is trying to keep the wheels braked, so the treadmill would turn to follow the plane as it moved through the air in such a way that the plane’s wheels would never turn.
This is theory #18945, based on one particular reading of the problem
Your answer is devoid of an explanation of your assumptions or “working out” and I am consequently unable to award even half marks. 0/10.
Arrggghhhh!
You have now converted the treadmill of the original question into a catapult that actively helps the plane to take off.
Go back. And read. Zut’s post. A gain.
This is an excellent summary of dozens of pages of threads. The problem states that the treadmill holds the plane stationary. The only force it has available is the moment of inertia of the wheels, and bearing friction. These are way to small to overcome the force of jet engines, but hey, that’s what the problem statement says, so maybe they’re really wimpy jet engines and really massive wheels with crappy bearings.
Oh for fuck’s sake. Why, why, why are people arguing this? The question is too vague and the answer just depends on how you interpret the question. Either define the question to take out the varibles, or let it fucking go.
Amazing how this thing is still going.
From Cecil’s column: “A plane is standing on a 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 the opposite direction). Can the plane take off?”
For this thought experiment it’s standard to assume frictionless bearings and massless wheels, because it doesn’t detract from the main point of confusion (car power vs jet power) and makes everything much simpler.
it’s trivial to show that if the treadmill is stationary (ground) and the plane takes off with v(t) linear speed and w(t) wheel angular speed, then if the treadmill is accelerating to oppose v(t) of the plane (therefore having -v(t) linear speed), the wheels will have 2w(t) angular speed.
The plane takes off anyway. There’s no ambiguity whatsoever.
This is easy to see. Under the conditions stated, have the plane sit with engines off and treadmill moving with -v_takeoff. The plane sits still. Then acelerate the plane with engine thrust to v_takeoff. Engine pushes air, air pushes engine, engine pushes plane. It takes of the treadmill but it’s wheels have to spin faster. As far as takeoff goes, this is equivalent to the scenario where the treadmill tracks the plane speed exactly. Where does this pose a problem?
Pedro, The only thing that amazes me is that people are still arguing this. Your exact argument has been stated again and again and again only to be refuted again and again and again from people who interpret the question differently.
Since no one want to actually go back and read Zut’s post, here ya go.
Ok, cool! I agree zut’s is an excellent rundown of the problem.
Imagine an unladen swallow flying above the treadmill, he will still have forward motion. Now imagine that he’s pulling a tiny wagon on a treadmill, he will still have forward motion. The contact between the wagon wheels and the treadmill have no effect on his wing’s ability to create lift.
[Obvious question/]
[Obvious answer/]
Heh. 