But if it is matching the wheel speed, what does that have to do with the fuselage?
You can twist it into just about any far fetched meaning that you want to. I believe that Cecil’s answer is as reasonable as you can get.
For the fourth time: IT’S A THOUGHT EXPERIMENT.
I don’t think I’ve seen anyone in this thread actually propose building such a treadmill. In fact, I’d hazard a guess that almost everyone is completely aware that building such a treadmill is impossible. Doesn’t matter, though. It’s a thought experiment. Thought experiments are useful to explore the effects of various physical phenomena, particularly in extreme cases.
Does the question, “what would happen if the earth were to suddenly stop spinning?” bother you because it’s impossible to actually conduct the experiment? How about “what happens to a spaceship that approaches the speed of light”?
If you want to say that the belt is designed to hold the airplane still relative to the ground then all you have to say is that the belt will move backward at whatever speed is necessary to hold the airplane still relative to the ground.
That is still a practical impossibility, but the meaning is clear.
There’s no “twisting” going on. It’s a straightforward interpretation of the the question, and exactly the same interpretation that Cecil has. For reference, here’s the statement, from the last paragraph of the column:
“The speed of the wheels” could mean a lot of things; one of those thisngs is “the speed of the outside radius of the tire with respect to the inner hub.” That’s not at all unreasonable, and essentially the proginal intent of the question, I think.
If the treadmill speed with respect to the ground matches the wheel radius speed with respect to the hub, then the plane fuselage can’t be moving. If the fuselage is moving forward, then the wheel speed is greater than the treadmill speed, and the conditions of the thought experiment are broken.
I should repeat that this is exactly the same interpretation that Cecil has.
(On preview)
And that, of course, is a much better problem statement than the original. Three quarters of the argumentation in this thread and the previous one are because a) there are different versions of question, which mean different things, and b) even one particular version has multiple legitimate interpretations.
But wouldn’t the belt have to be moving in the same direction as the rotation of the wheel against the belt in order to hold the airplane still?
You can twist the meaning any way you want to try to make just about any point you want.
You have to be reasonable somewhere. I think Cecil’s explanation answers the question just fine.
Nomenclature. The tires are rotating forward and the belt is moving backward. Why, exactly, do you think that your interpretation that “the speed of the wheels” means “the speed of the wheel contact patch with respect to the ground” is more valid than my interpretation?
I repeat, one more time: This is exactly the same interpretation that Cecil has. I’m a bit at a loss to see how you can agree that his explanation answers the question, yet disagree with his interpretation of the question.
The movement of the bottom of the tire is backward in the same direction as the belt.
Just making a point that you can torture the puzzle to make just about any point that you want. Agreeing with Cecil or disagreeing with Cecil.
Talk all you want about this, but due to the ambiguity of the question, there are two answers. But Cecil is right in the end…
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If the magic conveyor belt keeps the plane stationary under engine acceleration by some unseem force (wheel friction won’t help, because if the friction is too great, the plane would move backwards and fall off of the conveyor belt), then the plane won’t fly. Since there is no unseen force mentioned in the question, then this answer is wrong.
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If the plane moves down the runway no matter how fast the belt turns, then the plane flies.
Cecil correctly states that the speed of the conveyor belt will have little effect on the engines moving the plane down the conveyor belt runway. Much like the example of standing on a treadmill with rollerblades on, and pulling on a fixed rope. you still pull yourself forward relatively easily.
Just for clarification this is exactly what Cecil said about that scenario. The part that you left off:
“This language leads to a paradox: If the plane moves forward at 5 MPH, then its wheels will do likewise, and the treadmill will go 5 MPH backward. But if the treadmill is going 5 MPH backward, then the wheels are really turning 10 MPH forward. But if the wheels are going 10 MPH forward . . . Soon the foolish have persuaded themselves that the treadmill must operate at infinite speed. Nonsense. The question thus stated asks the impossible – simply put, that A = A + 5 – and so cannot be framed in this way. Everything clear now? Maybe not. But believe this: The plane takes off.”
That does not sound to me like Cecil disagrees with me.
The folks that entertain the notion that the plane will not take off are promulgating this problem as a “thought” experiment, much in the same way that thinking about a spacecraft achieving C is a “thought” experiment. In a “thought” experiment, anything is possible, including a device ( such as a treadmill ) that will exert enough force on the aircraft to prevent forward movement and thus liftoff. A treamill does exert some force on the aircraft, and given enough acceleration ( think in terms of C), that force could prevent forward movement of the aircraft. Of course, in this case, instead of a treadmill, a good length of chain would suffice.
Yesh, you guys must have been a blast for your Physics teacher:
Teacher: Ok we have massless…
WHAT! Every physical thing has mass.
Teacher: I know, just assume for this problem…
No, I won’t take part in fantasy world
How about relativity?
Teacher: Alright class, we have a rocket travelling at .9C
WHAT! That is impossible with our technology.
Teacher: I know but its just for a thought experiment…
Thought experiment? Bah, you mean fantasy land. I will have no part in this.
Teacher: Ok class, we have a rocket travelling at .9C and two barn doors close around it
WHAT! Its impossible for a door to open and close around a rocket travelling at .9C.
Teacher: Enough! :grabs gun and starts shooting:
The treadmill cannot stop the plane from taking off just by moving. If just moving the treadmill would be enough to stop the plane, then you have a plane that couldn’t take off on a runway, either. The treadmill also cannot prevent the plane from taking off by accelerating: Although an insanely accelerating treadmill could prevent the plane from moving relative to the ground, that insane treadmill would also generate a very strong wind over the wings. So if you’re going to say that the treadmill stops the plane, you’re going to have to also say how it does it. And if you start out by saying “The treadmill, by some unspecified method, prevents the plane from taking off”, then not only are you doing no better than by saying “the Rubic’s cube by some unspecified method stops the plane from taking off”, but you’re also answering the question a priori. If you start with the premise that the plane is somehow prevented from taking off, what’s the question?
If there is any friction in the wheel bearings, then there then magical treadmill can accelerate fast enough so that the force from that friction equals the thrust from the engines.
Exactly
The question is either “Will a plane take off from a treadmill moving in the opposite direction that matches the forward speed of the center of mass?” or “Will a plane take off from a treadmill that moves with the speed of the edge of the plane’s tire?” The only premise that I start with is the description of the problem. It is true that in the second case the description makes it impossible for the plane to take off but that is no different from the description in the first case making it possible for the plane to fly.
But this thought experiment contradicts itself, in a way. The notion of a plane on
a treadmill assumes the tires are spinning freely and fully functional. In that case,
the plane takes off. If the tires are not freely spinning, and friction is a factor, then just take the wheels off and lay the plan fuselage on the treadmill. Then the question becomes, can the plane overcome the friction without being destroyed. That seems to be a separate question and not part of the thought experiment at all.
Which is easy for the treadmill to measure. The treadmill doesn’t need to monitor the wheels at all, all it needs to do is monitor the position of the aircraft and accelerate as required to keep it in its original position. In doing that it will, by default, be matching the speed of the wheels.
What if we covered the treadmill and left just enough of it exposed to allow it to contact the aircraft’s wheels? What if, instead of a treadmill, we had threads sets of undercarriage identical to the aircraft’s but upside down. The aircraft sits on them and they accelerate at what ever speed is necessary to keep the aircraft from moving forwards.
I agree with everything else you say (and I thought your people whistling analogy was hilariously accurate.)
Should be “…three sets of undercarriage…” not “threads”.
So, do you agree with Cecil’s interpretation of the question? I should point out that Cecil interprets the question as: “If the plane moves forward at 5 MPH, [and] if the treadmill is going 5 MPH backward, then the wheels are really turning 10 MPH forward.” An interpretation that you’ve previously described as “twisting the meaning around.”
First, post #106.
Second, the question is: Is there a mechanism by which force can be transferred from a treadmill to a plane and counteract the thrust of the engine? (Rotational wheel inertia being an answer, by the way.) If that’s the question, I don’t see why it’s so unreasonable to not specify how the treadmill stops the plane, since that’s the point of the question. (Or, at least, the question that I find interesting. I really don’t want to get into an argument about whether this question is really the question.)
Not necessarily–it depends on your assumptions. (And with the right assumptions, you’re completely correct.) I refer again to post #106.
No, Cecil said this about stating the question that way, “The question thus stated asks the impossible – simply put, that A = A + 5 – and so cannot be framed in this way.”
I agree with Cecil.