Here's the same proof I posted on the first page, because people seem to be missing it.

edit: here's also JG's post on page 3, in case people skipped that.

I just spent the last half-hour arguing with some of my friends about the plane. They steadfastly refused to believe that it could take off.

Could someone go over the plane thing again? I'm a bit confused.

It goes a little like this.

<3

Ok, HOW does it take off. I don't mean the physics or "are the wheels just there to reduce friction." No, I mean, the problem states that relative to the earth, the ground, the piece of dirt beneath your feet: the plane doesn't move. The conveyor goes backwards pulling the plane backwards. The engine thrust goes foward, pushing the plane foward. They are equal in the sense that the plane doesn't move.

Here's a diagram just to make sure I'm getting what you're saying.
Position @ 0 minutes with no thrust
plane
tower !_____*_____ conveyer

Position @ 5 minutes with thrust
plane
tower !_____*_____ conveyer

Correct? aka, relative to the earth the plane doesn't move.

So if the plane has no velocity RELATIVE to the earth, then when it takes off (and the conveyor is no longer having any effect on the plane) what's keeping it in the air? I mean, a plane can't fly without velocity... The propeller speed doesn't keep the plane up, it keeps the plane moving foward. The difference in air pressure above and below the wings provides lift (from what I remember from physics class) but if the air isn't flowing around the wings, then how does the plane get the lift needed to take off?

From what you (who are in support of the plane taking off) say, the plane would just magically hover above the conveyor? Or are you expecting it to suddenly lurch foward and fly away...

Where in the problem does it say that the plane isn't moving? I'm confused as to why people seem to think this is the case.

I thought the problem says that the conveyor belt moves at the same speed backwards as the plane moves foward, thus no movement. Or are you saying that since the wheels roll along the conveyor that the plane's thrust still moves it foward?
I'll take a few minutes to think about this, so you're saying that even though the conveyor and plane are moving at same speeds in opposite directions the fact that it has rolling wheels allows the plane to still move foward? (That's my latest guess...)
[edit] but doesn't the original problem state that the conveyor compensates for the planes speed not thrust? I'm assuming that it's compensation would ensure that the plane didn't move. So I guess then that the speed of the plane and conveyor are not the same, but that the conveyor is actually faster than the plane.

The key detail you've got wrong here is that the belt doesn't compensate for the plane's speed (or for anything else), it just matches it. Thus, the plane is moving twice as fast relative to the belt as it is in absolute terms.

Do you mean twice as fast minus the friction from the tires (unless we're also assuming that the conveyor is a frictionless surface and that the wheels are frictionless as well). Thus, relative to the gound, the plane is traveling at nearly the same speed (nearly because you have to account for the friction from the conveyor and wheels) as it would if the conveyor was not there. So the plane would take off only when enough additional thrust was provided (than if there were no conveyor) to counteract the additional friction from the conveyor. Once that additional friction were accounted for, the plane would be moving (relative to the ground) at the same speed as if the conveyor was not there.
But having the conveyor not accelerate to cancel out any movement makes the problem rather stupid in the first place: the plane CAN increase speed (relative to ground) to the normal amount needed for takeoff.

That's the key there. The conveyor isn't accelerating to cancel out movement of the plane, it's simply matching the plane's forward velocity (in reverse of course). So yes, it's silly. I think you're just overthinking the whole thing; it's quite a simple problem.

Does anyone still not get it? If I have to draw a free body diagram and calculate the forces involved, I'm not going to be happy.

Ok, so my last post was correct with what the plane's doing.
The thing I didn't get at first was that the wheels will ROLL with the conveyor, but that doesn't mean the plane will move. I immediately thought the wheels moved with the conveyor (such as if the brakes were on. and yes, now that I got that, whoever posted about the brakes earlier makes so much more sense now)
[edit] I just reread you last post Kyle and I think you slightly misread mine (maybe...) I understand now that the conveyor isn't compensating, I was saying that having it not compensate makes the problem rather stupid in the first place. [/edit] [edit2] Ok, I reread Kyle's post again, and now I'm not sure who you're addressing in if it's me, then ya I realized my mistake. If not, then maybe they need to analize the wheels a little bit more...[/edit2]

Yeah, that's true. I've just found that, in trying to explain this to several different people over the last few hours, talking about the friction (which is negligible anyway) just makes things more confusing and doesn't have much bearing on the basic concept. I treat the friction the same way I treat other things that unnecessarily irritate me: I ignore it.

ya, I understand that. (but actually, not including the friction confused me for a minute. I couldn't figure out why you were doubling the speed, then I realized you made it relative to the belt, and didn't put in friction)
Well, hopefully our little dialogue here may help everyone else understand why the plane really does take off. And why this problem is so silly.

I still don't understand this plane thing. It wouldn't take off because there is no lift.

It would take off, because there is lift, because the plane is moving forwards.

Um, no it isn't. It's not moving at all. Because it's on a conveyor belt.

The backwards motion of the conveyer belt is easy overcome by a TINY forward force from the engines due to the relatively free motion of the wheels. So if the conveyer belt is providing a backwards velocity equal to the forward velocity of the plane, the plane will still move forward at an effectively unaltered speed.

Wait, so you're saying the plane moves off of the conveyor belt and continues on the runway to take off?

BE MORE SPECIFIC.


Edit: btw, if so, that is outside the bounds of the problem as far as I'm concerned. In my version of the problem, the conveyor belt is placed in front of the lake to stop cheaters. So no, the plane doesn't take off.

YEAHAGH IT ISN'T THAT BLOODY HARD! THESE TWO "RIDDLES" AREN'T!!!! WHY IS THERE FOUR PAGES! IT PAINS ME TO READ THIS AND CAUSES ME TO TYPE IN ALL CAPS? IS THAT WHAT YOU WANTED? FOR ME TO SOUND LIKE AN IDIOT! THANKS, NOW I'M STUCK IN CAPS LOCK MODE, GOD DANG IT!

For the .999=1: Look at Pommy's equation! THAT's IT! DONE!

As far as the plane: The plane's engines MOVE AIR. THE WHEELS DO NOTHING! THEY DO NOT MATTER! As was said, the engines move wind. The wheels have nothing to do with the engines. WHY WON'T THE WIND BE MOVING? WHAT IS STOPPING THE WIND? NOTHING!

A fan moves wind. It doesn't have wheels. Yet it can move wind. How is it different?

Huh? Maybe if the wind is blowing in exactly the right direction at 100mph, otherwise, not. btw: the engines don't blow air over the wings. That's what creates lift.

You can assume the runway is infinitely long if you want, the plane will still take off.

No, my assumption is that the plane remains on the conveyor belt until airborne and that the conveyor belt is about as long as the plane.

I'm trying to see it the way you are, but I can't. The wheels don't really exert any apprecaible force on the plane. The movement of the air, caused by the engine, is what moves the plane forward. The wheels will just be spinning faster. Why do you think the wheels would stop the plane? The power does not come from the wheels.

Freelancer: Draw a free body diagram.

My assumption is that the plane stays in one spot. If the plane is actually moving 70mph in relation to the ground at some point, then of course it can go airborne. If it actually is moving FORWARD, then that should have been made clear in the problem.

Your assumption that the plane stays in one spot is where you're going wrong.

It's utterly irrelevant how long the conveyer belt is, it can be 10cm or a million miles. The plane will either move forward on the conveyer belt and onto solid ground and take off, or just move forward on the conveyer belt and still take off.

The plane moves forward relative to the overall conveyer belt.

No, you see, in my version of the problem, the conveyor belt is only as long as the plane, and completely surrounded by explosive mines. If the plane doesn't take off while on the conveyor belt, it gets blown up. Not taking off in place is cheating, because the original problem statement led me to believe a plane could take off without any forward movement.

Wheels and friction and all that **** is irrelevant. Either the plane is moving forward, or it's not. If it is moving forward, OF COURSE IT CAN TAKE OFF!!!! If it's not, OF COURSE IT CAN'T. The problem is that the problem statement didn't make it clear that the plane is moving forward.

Well then, I hope I'm not on that plane, because I'll get blown up.

Also, what would be stopping it from moving forward? It'd be a flawed question otherwise.

.

Flawed question then.

Actually, that's what I first thought too, that it would lift off stationary if the answer was "yes". It wasn't asked well. But it just doesn't make sense then.

It's not a flawed question. It's a god damned riddle. You just feel like making excuses for the fact that you were wrong. Look earlier in this thread. I said it wouldn't take off, and then I thought about it, and I realized it would take off... and then I said I was wrong. It's simple. The riddle fooled you; deal with it.

i was wrong.

Bill tortured me in #massassi until I admitted it.

pwned.

A false explanation for lift has been put forward in mainstream books, and even in scientific exhibitions. Known as the "equal transit-time" explanation, it states that the parcels of air which are divided by an airfoil must rejoin again; because of the greater curvature (and hence longer path) of the upper surface of an aerofoil, the air going over the top must go faster in order to "catch up" with the air flowing around the bottom. Therefore, because of its higher speed the pressure of the air above the airfoil must be lower. Despite the fact that this "explanation" is probably the most common of all, it is false. It has recently been dubbed the "Equal transit-time fallacy." There is no requirement that divided parcels of air rejoin again, and in fact they do not do so. Such an explanation would predict that an aircraft could not fly inverted, which is demonstrably not the case. The explanation also fails to account for aerofoils which are fully symmetrical yet still develop significant lift. Any textbook claiming to be a serious work on the topic will never promote the Equal Transit-time fallacy.

holy plagiarism batman

The conveyor belt matches the SPEED of the plane. If the plane ended up stationary, then the speed of the plane would be ZERO, wouldn't it? That must make all you people insisting the plane wouldn't move stop and think for a second mustn't it?

The plane does not push against the ground beneath it. The plane pushes against the air.

What the ground beneath the plane does only affects the negligable amount of friction at the tyre axles. The overall thrust on the plane relative to the air stays roughly the same whatever's going on with the ground.

Therefore the planes rolls forward and reaches take-off speed at roughly the normal distance from its start point relative to the Earth.

As Freelancer framed it ("The plane does not move") it would be flawed.

SNAKES ON A PLANE [/COLOR]

Yeah, that's also why the speed is always shown relative to the air and not relative to the ground (yes, some planes also show their groundspeed with the help of GPS). If a plane get's into a wild storm, where the air is as fast as the plane and the plane flies in the opposite direction, then the plane stands still, relative to the ground.
That would be an analogue to the car on the conveyor belt.