[QUOTE=mantion1@yahoo.com]
…150"*3.1415926535897932384626433 (from memory) = 471 inches (about)/ 12 = 39 ft diameter..
…
I was just bored and wanted to waste your time and show off that I know pie to the 26th place. Of course I could of looked it up, but sadly I didn’t.
[/QUOTE]
I could have been more impressed.
But if the plane had crashed with a 60s war protester on board, then that person’s father would Mississippi.
gah, I’m no good at these. Y’alls are lucky I didn’t go with my first instinct on this pun.
[QUOTE=mantion1@yahoo.com]
…The RPMs really don’t matter, I was just bored and wanted to waste your time and show off that I know pie to the 26th place. Of course I could of looked it up, but sadly I didn’t…
[/QUOTE]
When come back bring pi.
[QUOTE=Elendil’s Heir]
When come back bring pi.
[/QUOTE]
:smack:
I’m cross. Why’d Missouri like this be brought up again.
[QUOTE=don’t ask]
I’m cross. Why’d Missouri like this be brought up again.
[/QUOTE]
I knew it was a Mystic when I brought it up.
I’d say it’s Olentangy enough by now.
Yukon all stop it now.
I think it’s kind of Volga to tell us all what we should do.
thanks to zut for already paving the way, but i’d just like to copy what i pasted on the off-topic boards to here so that maybe cecil would considering revising his answer.
this question is being debated because people can’t just read and realize the problem is the poorly defined (scratch that, i’ve changed my mind to expertly worded) question itself!!!
let’s analyze “the original question” (the wording is crucial) as posted various places:
“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 opposite direction).”
now. let’s make one thing very clear here. where does the question define “plane speed” ? remember, speed is a measurement of rate of movement, and ALL MOVEMENT MUST BE DEFINED by both the “thing moving” and “the thing observing the moving object” or “the thing the moving object is being measured against”. it doesn’t suffice to say “well, obviously the question implies it’s moving with respect to x” because the question is actually designed to make that x as ambiguous as possible.
also, to address some more criticism against my argument that the question is ambiguous, consider where it defines the movement mentioned in the red highlights. again, If we remember that all movement is relative, we’re reminded that you need to define what things are moving in relationship TO. The questions also purposefully omits these key reference points.
the way I see it, “plane speed” can be defined in several ways, but they all fall into one of two camps:
camp 1: plane relative to observer on normal ground
camp 2: plane relative to treadmill
camp 1 includes all these interpretations:
plane relative to air (assuming no wind) – this is the best definition of “plane speed” because plane speed is almost always defined by air speed
plane relative to (non-moving) earth
plane relative to treadmill when treadmill is not moving.
camp 2 includes all these interpretations:
plane relative to treadmill at all times
plane’s “wheel speed”
plane’s speedometer
look, if you’re in camp 1, it takes off every time and the wheelspeed is 2x the treadmill or air speed. this is easy to understand. as for the red highlights, the plane could be moving “east” while the conveyor belt’s top surface travels “west”. this assume the original motions are being defined by their relationship to the ground.
if you’re in camp 2, the plane never moves at all in relationship to the air or ground because this interpretation forbids it. it doesn’t even matter if you want to get into the whole arguments of friction or not, i repeat, the question specifically forbids the plane from ever getting any airspeed at all if you interpret it this way. it also doesn’t matter that this is scientifically impossible considering how low the wheel friction is and how great the thrust is… it’s a riddle… not a science question, and yes, magical treadmill means indestructible wheels and bearings and the ability to reach “greater than c” speeds. as for the red highlights, the plane’s direction of motion is opposite to that of the treadmill, and their speeds match. BOTH of their “movements” are defined by each other it is perfectly valid to talk about the “plane moving” in this manner, because all motion is relative. this is why many educated people are originally interpreting the question this way, and they’re perfectly “correct” in doing so.
why are so many people having such a problem realizing this question was intentionally crafted to be ambiguous? before I ever heard this riddle, I had never once heard the term “plane speed”. actually, considering this and how hotly debated this question is… i’ve come to the conclusion that serious credit is due to the question’s writer. whoever originally wrote it in this form is quite brilliant, as it includes just enough to:
1: get really dim-witted people to think the plane won’t move 'cause they don’t realize planes aren’t driven by the wheels
2: get quite a few average-minded people to think it will move (camp 1).
3: get well-educated, scientific-minded people who analyze questions in detail to seriously think camp 2 is supposed to be 'the correct answer" since such specific details are missing and the conveyor belt is hinted at being super-powerful.
4: get the best critical thinkers out there to recognize a well-crafted question when they see it. i should note that zut’s posts are almost exactly in line with what i’m trying to say here. he goes on to provide many, many more interpretations and assumptions that could still change the problem further, while I’ve chosen to reduce it to the two mainly-debated points as ‘camps of thought’.
bravo, question maker. does anyone know where this original wording of the question came from? the author should get some much-deserved credit.
I don’t get what the problem with the original question
It’s obvious that since the treadmill is touching part of the airplane and pushing against it, it is applying force to it.
If that force happens to match that of the engines thrust, the plane won’t move.
[QUOTE=____]
It’s obvious that since the treadmill is touching part of the airplane and pushing against it, it is applying force to it.
[/QUOTE]
Wrong.
[QUOTE=Fear Itself]
Wrong.
[/QUOTE]
IF the wheels were not connected to the plane they could spin without affecting it, but since they’re connected, if you push them back you’re pushing the plane itself back, thus applying a force to it. or are you saying that’s wrong?
[QUOTE=____]
IF the wheels were not connected to the plane they could spin without affecting it, but since they’re connected, if you push them back you’re pushing the plane itself back, thus applying a force to it. or are you saying that’s wrong?
[/QUOTE]
That’s wrong. The wheels are on bearings, they just spin, transmitting no significant energy to the plane.
[QUOTE=Fear Itself]
That’s wrong. The wheels are on bearings, they just spin, transmitting no significant energy to the plane.
[/QUOTE]
The wheels are being moved backwards by the treadmill, if the plane wasn’t moving foward, the whole plane would move backwards along with them(no spinning would be involved, you’re moving the ground-treadmill underneath the plane along with it.), that’s a fact.
The foward movement of the plane causes the wheels to spin, if the treadmill moves faster than the wheels are made to spin by the engines’ thrust, it will push the whole plane backwards.
[QUOTE=____]
…if the treadmill moves faster than the wheels are made to spin by the engines’ thrust, it will push the whole plane backwards.
[/QUOTE]
No, it won’t. With the engines providing thrust, the only thing the treadmill can do is make the wheels spin faster. Yes, there are frictional losses in the wheel bearings, so that some rearwards force is transmitted to the plane by the treadmill, but this is such a small amount compared to the engine thrust. It would require an impractically powerful treadmill to even significantly reduce the plane’s forward speed. I suspect that in the real world, the wheel bearings would fail from the high-velocity rotation before you could even prevent a plane from taking off in this manner.
[QUOTE=____]
The wheels are being moved backwards by the treadmill, if the plane wasn’t moving foward, the whole plane would move backwards along with them(no spinning would be involved, you’re moving the ground-treadmill underneath the plane along with it.), that’s a fact.
The foward movement of the plane causes the wheels to spin, if the treadmill moves faster than the wheels are made to spin by the engines’ thrust, it will push the whole plane backwards.
[/QUOTE]
This is true at very low accelerations and no output from the planes engines. In the real world, the friction of the bearings is so small compared to the thrust of the engines and the inertia of the plane that the when the conveyor moves backward the wheels do essentially free wheel and have no significant effect on the planes movement relative to the ground.
Of course that assumes one way of interpreting the problem, there are many others.
Everyone be Ferry. Don’t be Cross. Have Mersey.
I hate that I’m even posting here. That fact of the matter is that there is friction in the bearings. If a plane were standing still with the engines off and the treadmill started moving backwards, the plane would also start moving backwards. That proves (along with common sense) that there is friction.
I don’t recall reading where the plane in question was defined. No one said that it had jet engines. No one specified the power/weight ratio of the plane.
What if the plane were extremely underpowered? What if the plane needed a 10 mile long runway to get up enough speed to take off? What if the plane were setup that it would fly - but just barely? If it had even a fraction of a HP less and it wouldn’t be able to get off the ground.
Then, the “insignificant” amount of friction would indeed become significant. The plane would not be able to take off.
I know we can block users on this board. Anyway we can block stupid ass, poorly worded questions as well?
[QUOTE=brewha]
I hate that I’m even posting here. That fact of the matter is that there is friction in the bearings. If a plane were standing still with the engines off and the treadmill started moving backwards, the plane would also start moving backwards.
[/QUOTE]
Actually, that is not necessarily true; if the acceleration is enough to defeat the friction, the wheels will start to rotate, and then continue to rotate, under the “stick/slip” principle that is a consequence of the fact that, under virtually all conditions, the static friction between two surfaces is something like an order of magnitude more than the dynamic friction.