<p>someone was wrong when they wrote this riddle was harmless. =P</p>
<p>It is harmless. Currently, RiverPhoenix is continuing to argue in PMs that under his interpretation - that the treadmill matches the speed of the plane relative to the treadmill - the circular definition means the treadmill goes infinitely fast, and hence the plane can’t take off.</p>
<p>No, it means that the treadmill goes at the very large, Finite speed, that is neccessary for the speed of the plane to be zero. Please get your facts straight before ■■■■■■■■.</p>
<p>If the treadmill matches the plane’s speed relative to the treadmill itself, we essentially have |V<em>t| = |V</em>p| + |V<em>t|. It looks like there is an infinity that’s going to come into play, but the (apparent) iteration converges: I now see your issue, you are falling into Zeno’s paradox. For any |V</em>p| (this is the speed of the plane relative to the ground), there is some finite |V_t| that will stop the plane all together (relative to the ground). When the treadmill reaches this speed, the equation holds.</p>
<p>River,</p>
<p>I have tried as long as I could to stay out of the last batch of arguments… but I couldn’t hold it in any longer… you should stick to your philosophy and stay away from the math and physics… because you have not said a single insightful or even valid mathematical or physics statement. </p>
<p>Everything you have posted in this thread is completely absurd.</p>
<p>…erm, have you considered that you might not be right? It’s absurd in the sense that I am deliberately misreading the problem, and that I am letting the treadmill’s speed be insanely large… but what I said isn’t wrong, and I just meant to demonstrate that the problem might be viewed as ambiguous. And I have completed my course 18 degree, so it might be too late to get out of math</p>
<p>If you were really so sure of yourself you wouldn’t need to overhype your claims to my ignorance</p>
<p>Just so everybody understands, here’s a little of the physics of what would actually happen with this (assuming the tires/wheels don’t fly apart), if we also let the thrust of the plane go to infinity.
In the ideal case, we just say that frictional force is mu*N, N the normal force. If that’s the case, then the velocity of the treadmill wouldn’t be able to stop the thrust, since mu cannot be higher than 1. In this case, what I said would still hold because of the inertia in the wheels due to the ridiculous acceleration of the treadmill. But note this (Source: <a href=“Force”>Force)</p>
<p>Part of the standard model of surface friction is the assumption that the frictional resistance force between two surfaces is independent of the velocity of relative movement. While this is approximately true for a wide range of low speeds, as the speed increases and air friction is encountered, it is found that the friction not only depends on the speed, but upon the square and sometimes higher powers of the speed. If there are fluid lubricants involved, then viscous resistance is encountered, and it is speed dependent.</p>
<p>Frictional force just models interatomic forces, so it’s understandably a bit odd.</p>
<p>Very quickly the converor belt will be moving at impossible speeds, but this is a hypothetical question, and it is indeed able to stop the plane while moving at a finite speed as long as the plane’s speed is finite.</p>
<p>Now, if we don’t assume a perfect world, then there’s another interesting thing that might happen (aside from tires blowing out).
Very quickly after the aircraft attempts to move forward, the conveyor belt is spinning under the aircraft at thousands of feet per second. Friction between the air at the surface of the converor belt and the belt will cause the air to move with respect to the ground next to the belt. At some point the magic belt will be moving fast enough to generate enough airflow over the wings that the aircraft will lift off the belt, again assuming the belt and wheels/tires are magic and do not fly apart. So, yes the aircraft will lift off the belt. What happens next is the subject of another debate.</p>
<p>In fact, I am finding this version of the problem rather more interesting.</p>
<p>River,</p>
<p>You are digging yourself much deeper in this whole, and have done nothing to prove yourself capable of doing any analysis of engineering physics. </p>
<p>I’m not going to waste my time arguing all of your absurd and WRONG statements, but I will make a few painfully obvious statements that will show that you don’t even have a grasp of the basics… </p>
<p>“since mu cannot be higher than 1.”</p>
<p>What?! There is no physical or mathematical limit on mu, the coefficient of friction. There are many material on material combinations that have coefficients well above 1. </p>
<p>“as the speed increases and air friction is encountered, it is found that the friction not only depends on the speed, but upon the square and sometimes higher powers of the speed.”</p>
<p>This assumption is based on taking into account wind resistance (drag on the airframe) and has nothing to do with internal friction forces of the wheels or the bearings. The friction of the treadmill on the wheels and the wheel bearings on the aircraft will still remain relatively constant. </p>
<p>“we just say that frictional force is mu*N”</p>
<p>That is the frictional force acting as the force on the tire (between the tire and treadmill), and not the force acting on the airframe and opposing the forward motion of the airplane. </p>
<p>“Friction between the air at the surface of the converor belt and the belt will cause the air to move with respect to the ground next to the belt. At some point the magic belt will be moving fast enough to generate enough airflow over the wings that the aircraft will lift off the belt”</p>
<p>Why don’t you do a bit of research on boundary layer theory and realize how wrong and absurd your statement is. </p>
<p>That’s all I have time and motivation to address right now, but your statement of relative motion to the treadmill is still wrong and absolutely nonsense. You have no one here who supports your argument, even as simply an academic exercise (which it obviously is not because it’s so clearly wrong). </p>
<p>I’m happy that you are so entertained and amused at absurd and wrong situations that have no basis in math or physics, real or even imagined.</p>
<p>in cases where you want to say mu is greater than one, that is usually better described as adhesion; at any rate you cannot make mu as high as you want.</p>
<p>the frictional force acting on the airframe is proportional (with a small constant) to the frictional force on the wheel because the bolts and axels, all the way up to the airframe, cannot be absolutely perfect.</p>
<p>Sorry mate, you aren’t going to win this one. I understand that you object to the whimsy of what I’m saying, that’s why I prefaced it many times… Why can’t you just accept that you are talking about the problem from a practical perspective, and I am talking about it from an innate perspective, related to the actual complexity of the problem.</p>
<p>I’ll make this quick… but you are wrong on both points… </p>
<p>My argument has nothing to do with fixing the coefficient of friction. My point was to show your lack of understanding of basic physics.</p>
<p>Adhesion is in no way defined by coefficients of friction. You might have passed your math classes… but you certainly haven’t done the same in physics. </p>
<p>I’m not saying there is no friction acting on the airframe… I am saying it is not mu*N. All of my analysis that I did in explaining this riddle was done assuming normal and reasonable frictions. </p>
<p>I am not objecting to your point of view, but objecting to the WRONG statements you are claiming as truth. You are not claiming this as a philosophical argument, but a physical and mathematical one. Your arguments do not pass any mathematical, physical, or even logical tests.
But I’ve had enough of your nonsense… I’m done with you … you have not shown a single shred of intelligence and insight in this thread that makes you worth my time to debate this with you any longer.</p>
<p>From Dr. Math, about the question can mu be greater than 1 (you normally learn that it’s not, but sometimes it actually can be).
(Source: <a href=“Classroom Resources - National Council of Teachers of Mathematics”>Classroom Resources - National Council of Teachers of Mathematics)</p>
<p>Aluminum on Aluminum 1.3
Copper on Copper 1.3
Iron on Iron 1.0
Rubber on Steel 1.6</p>
<p>The first three can perhaps be explained in terms of something other
than “friction” (e.g., “galling,” which is the phenomenon that
requires the frame and slide of a pistol to be made from different
materials), but that’s not the case for the fourth.</p>
<p>However 1.6 has been found to be approximately a natural limit on the coefficient of friction.</p>
<p>Also, I said that the friction on the wheel was mu*N, not the airframe; I took a proportionality there as given (I ignored these things that don’t matter, as n->infinity and consider only the complexity).</p>
<p>“All of my analysis that I did in explaining this riddle was done assuming normal and reasonable frictions.”
Right. I think you understand my point of view now. Before I thought you were saying that even in the infinitely powerful treadmill case, it wouldn’t work. In my opinion, the purpose of riddles can often be to consider absurd situations. In some sense, the gedanken experiments are in this category.</p>
<p>But I’ve had enough of your nonsense… I’m done with you … you have not shown a single shred of intelligence and insight in this thread that makes you worth my time to debate this with you any longer.
I do think that you show intelligence, and I’ll even give you the benefit of the doubt that if I met you in real life you would be more classy.</p>
<p>
</p>
<p>Sky has been classy throughout this entire discussion. Sky didn’t say you didn’t display any intelligence - Sky said you didn’t display enough to make the debate worthwhile.</p>
<p>Can you please address the points being made?</p>
<p>i did… this is getting ridiculous, all the more so because the bifecta of slorg and sky are saying the things that I should be saying
Even were my math somehow wrong (sky doesn’t really claim that himself at this point), it’s pretty much been established that you’re a ■■■■■ (or you just can’t read)… can’t we lock threads like these?</p>
<p>sky – I’m disappointed. Your discussion with me was very civil on your side, and you didn’t lose your patience. Don’t insult your opponent. It makes you look bad, though you are quite right on the substantive issue.</p>
<p>I second the motion for the thread to be locked.</p>
<p>Where did sky ever insult anyone? Please point it out.</p>
<p>Last sentence in post #130 perhaps? Mass, mass where is the mass.</p>
<p>Sky wasn’t accusing Phoenix of being stupid. Sky was merely defining his limits of debate. Obviously, Phoonix isn’t very stupid; rather, Sky only wants to debate with geniuses.</p>
<p>Also, Sky was being purely factual when discussing Pheonix’s nonsense. Much of Pheonix’s arguments IS nonsense.</p>
<p>So can you please point out a single instance where Sky insulted anyone? Please do.</p>