A harmless little riddle

OH YEAH wrote:

I agree that there are two possible interpretations of the riddle. That does not mean that the two interpretations hold equal value. If a reference frame is not stated in a physics problem, usually it is assumed that the reference frame is the earth. Because of this, I think that "the plane will take off" is the more correct answer.

I agree with you, and I also made this admission a while back. In fact, for a long time, I was of the opinion that the "doesn't take off" group was just plain wrong. But after re-reading the riddle, I did discover it is open to interpretation.

I still agree that the "more correct" answer is that it will take off with the wheels going approximately twice the speed of both the airplane (airspeed) and the treadmill belt.

Though, I'm not sure there is a "more correct" answer to a riddle. Perhaps if it were posed on a physics test. But even on a physics exam, if a student put down his interpretation, I'd give full credit.

Jesus. Explain to me how, with the jet engines on, the plane is NOT going to push itself through the air and eventually take off? It HAS TO. There's no other way.

Speed isn't 'wheel speed relative to the treadmill belt'

The riddle says that the treadmill matches the plane's speed. There's no way that the plane can be held back under ANY scenario: ergo, the plane gains ground and airspeed, the treadmill speeds up in the opposite direction, and it takes off!

Explain to me how the plane won't push itself through the air. You can't, and you're just avoiding it.

I can't believe this post is still alive.

According to the ORIGINAL question, THE PLANE TAKES OFF.

The treadmill would have to move several times faster then the speed the plane is moving foward to prevent the plane from taking off.

The treadmill applies a small amount of torque to the plane. The engines produce a lot of thrust, much more then the amount of torque the treamill applies to the plane.

If the treadmill only moves the exact opposite of the speed of the plane moving foward, the plane will take off because the thrust of the jet engines is more powerfull then the torque of the treadmill if the treadmill is moving the same speed as the plane in the opposite direction.

Can the treamill counteract the thrust of the plane? yes. But then we would have to change the original question, can the treamill counteract the force of a plane at takeoff? yes. But the treadmill would have to spin in the opposite direction of the plane at speeds many times faster then the planes foward speed. That is, if you could figure out how to make such a treadmill. If the treadmill had some kind of really powerfull nuclear reactor or some kind of other really powerfull type of generator, this generator could possibly produce enough power to keep the plane stationary. To counteract the force of the jet engines sucking in air which they push out the back, the treadmill would have to spin many, many times faster then the relative speed of the plane moving foward. But whatever is powering the treadmill would have to be, very, very powerfull and capable of very, very high rpm's. At some point the tires would melt off (this would probably happen before the wheel bearings fail).

wail wrote:

Explain to me how the plane won't push itself through the air. You can't, and you're just avoiding it.

You just don't get it because you refuse to look at the problem differently. We're not saying that the plane won't take off IF you interpret "speed the plane is moving" to be relative to the ground.

However, IF the plane IS moving, relative to the ground, THEN the speed of the wheels IS GREATER than the speed of the treadmill, right? It has to be or else the plane would remain stationary. Now, I'm not saying this scenerio is impossible, in fact, it's entirely possible and of course, the plane would take off.

HOWEVER - And this is what you're missing, IF you interpret "speed the plane is moving" to mean "speed the plane is moving relative to the ground," then this scenerio VIOLATES the conditions of the original riddle. Essentially, under this interpretation, you're saying "if a plane remains stationary relative to the ground on a moving treadmill, will the plane take off?" The obvious answer is NO.

Now, stop instantly trying to refute what KnowItAll and I are saying, and really thing about it. There is most definately an interpretation of the riddle in which the plane will not take off, BUT NOT BECAUSE THE TREADMILL PROVIDES MORE FORCE TO THE PLANE THAN THE ENGINES DO, ONLY BECAUSE UNDER THIS INTERPRETATION, THE PLANE VIOLATES THE CONDITIONS OF THE RIDDLE IF THE PLANE BEGINS FORWARD MOTION RELATIVE TO THE GROUND!!

That should read...

HOWEVER - And this is what you're missing, IF you interpret "speed the plane is moving" to mean "speed the plane is moving relative to the TREADMILL," then this scenerio VIOLATES the conditions of the original riddle. Essentially, under this interpretation, you're saying "if a plane remains stationary relative to the ground on a moving treadmill, will the plane take off?" The obvious answer is NO.

OK, I did know what tangential velocity means, for the record, but somehow was too dumb make the groundspeed connection i guess. Anyway, yessiree and KnowItAll do have a legitimate interpetation under the assumption of the infinitely powerful treadmill. I can't believe I didn't get that before. So I've switched to the 2 equally-viable interpretations camp, for what that's worth. My apologies for all the hateful things I said.

Asshole.

yessiree wrote:

HOWEVER - And this is what you're missing, IF you interpret "speed the plane is moving" to mean "speed the plane is moving relative to the ground," then this scenerio VIOLATES the conditions of the original riddle.

Are you this stupid? No it doesn't! What YOU'RE missing is that under any physically possible scenario, the plane must push itself through the air. This is a given: any other interpretation must ignore the basic laws of physics.

The orginal wording:

"An airplane is sitting on an enormous treadmill. As the plane starts its engines, the treadmill runs in the opposite direction at the same speed the plane is moving. Can the plane take off?"

Given that the plane MUST move forward relative to the ground and the air, the treadmill's only course of action is to move backwards relative to the ground. What other movement could possibly happen? The treadmill's movement is airplane dependent, and in this case the treadmill matching the plane's speed could be either airspeed or ground speed. It doesn't matter how fast the treadmill is moving, or in what direction. The plane still takes off.

I guess if you want to consider physical impossibilities, then a whole host of wacked out sh*t could potentially happen.

admire the persistance anyway wrote:

OK, I did know what tangential velocity means, for the record, but somehow was too dumb make the groundspeed connection i guess. Anyway, yessiree and KnowItAll do have a legitimate interpetation under the assumption of the infinitely powerful treadmill. I can't believe I didn't get that before. So I've switched to the 2 equally-viable interpretations camp, for what that's worth. My apologies for all the hateful things I said.

Asshole.

Holy Shit. I think that's the first time in letsrun history anyone's 1) admitted someone else may be right about something they disagree about and 2) apologized for the hateful things they said.

Now I feel bad about posting under different names calling all the "no fly" people f***ing idiots before I understood the the alternate interpretation.

My apologies, *admire the persistance anyway*, you are a gentleman and a scholar.

you don't even want to know how many other names I've had on this thread.

[quote]wail wrote:

The orginal wording:

"An airplane is sitting on an enormous treadmill. As the plane starts its engines, the treadmill runs in the opposite direction at the same speed the plane is moving. Can the plane take off?"

Given that the plane MUST move forward relative to the ground and the air... [\quote]

And that "given" statement is exactly why it won't fly!

IF it MUST move forward relative to the air, then the plane violates the condition of the riddle IF you interpret "speed the plane is moving" to mean "speed the plane is moving relative to the treadmill."

You are interpreting "speed the plane is moving" to mean "speed the plane is moving relative to the ground/air" and you refuse to acknowledge that "speed the plane is moving relative to the treadmill" is just as valid of an interpretation.

yessiree wrote:IF it MUST move forward relative to the air, then the plane violates the condition of the riddle IF you interpret "speed the plane is moving" to mean "speed the plane is moving relative to the treadmill."

You are interpreting "speed the plane is moving" to mean "speed the plane is moving relative to the ground/air" and you refuse to acknowledge that "speed the plane is moving relative to the treadmill" is just as valid of an interpretation.

You're talking yourself in circles - if you interpret the riddle to mean 'the speed relative to the treadmill' then you have to accept that the plane doesn't thrust itself through the air, which is impossible, so you must REJECT this alternative interpretation.

admire the persistance anyway wrote:

you don't even want to know how many other names I've had on this thread.

HA! You know, wejo's probably laughing his ass off seeing the same 4 IP addresses constantly switching sides and psuedonyms arguing over this shit for 40 pages.

wail wrote:

You're talking yourself in circles - if you interpret the riddle to mean 'the speed relative to the treadmill' then you have to accept that the plane doesn't thrust itself through the air, which is impossible, so you must REJECT this alternative interpretation.

I believe you are the one talking yourself in circles.

What you've basically just said is that you have to reject this interpretation because under this interpretation the plane doesn't fly.

I'll leave it up to the other posters to judge the validity of your statement...

yessiree wrote:

I believe you are the one talking yourself in circles.

What you've basically just said is that you have to reject this interpretation because under this interpretation the plane doesn't fly.

I'll leave it up to the other posters to judge the validity of your statement...

Uh...what I basically just said is that, under the alternative interpretation the plane doesn't push itself through the air. This is wrong. Reject interpretation.

I guess what I'm saying is: my interpretation could happen in the reall world. Yours couldn't. I win.

There's no way I'm about to read 800+ posts, but here's one random one that I'll reply to ...

wail wrote:

How does an airplane fly? It flies because the engines are pushing air like crazy to generate thrust to make it lift off.

You left out a HUGE section of physics/logic. Yes, the engines are pushing against the air like crazy. Yes they generate thrust, but this thrust is NOT what makes the plane take off. That thrust is used to push the wings thru the air surrounding them. As the entire wing sections MOVE thru the surrounding air, this air flows over and under the entire wing section. The wing is curved on top, so the air up there moves faster than the air on the bottom of the wing (since it "travels" further, ie, from the leading edge of the wing to the trailing edge). This difference in air speeds creates the lift needed to make the wing rise, taking the rest of the plane with it. If the wing section doesn't move thru the air, the lift isn't created, and the plane doesn't leave the ground.

wail wrote:

yessiree wrote:

I believe you are the one talking yourself in circles.

What you've basically just said is that you have to reject this interpretation because under this interpretation the plane doesn't fly.

I'll leave it up to the other posters to judge the validity of your statement...

Uh...what I basically just said is that, under the alternative interpretation the plane doesn't push itself through the air. This is wrong. Reject interpretation.

I guess what I'm saying is: my interpretation could happen in the reall world. Yours couldn't. I win.

Like I said, I'll leave it up to the other posters to judge the validity of your statement.

Meanwhile, I'm going to hop a plane and take off from a mile long treadmill, you know, since mile long treadmills that can support airplanes exist in the real world.

It's amazing how obvious it is that some of you have never taken a basic physics course.

Ok, so how does a plane with its engines on not accelerate forward on a treadmill?

There are two things that can restrict it, one is dumping energy into the wheels of the plane, the other is dumping energy through internal friction of the wheels on the plane.

I'll give simple examples to explain both, and then you can just extrapolate them out to the plane and treadmill. But before I do that, I will say that in this scenario, it is a requirement that this treadmill is capable of insane accelerations, because when you work through the physics and calculate the accelerations needed to stop a plane with jet engines, the accelerations are very high. So, on to my examples:

Dumping energy into the wheels of the plane:

If you are standing on rollerblades on a treadmill and the treadmill starts, you initially have to hold onto the rails as the treadmill accelerates and your wheels accelerate to match the treadmill's speed. Why? Because your rollerblade wheels want to stay at rest, and you have to transfer energy into them to get them to spin. So you holding onto the rails as they accelerate is exactly equivalent to a force of a engine pushing your forward (holding you in place). Now the faster your treadmill accelerates, the more force you're going to have to apply to those rails to keep yourself from going off the back. So you can see that as acceleration rises, so does the force necessary to keep you on the treadmill. So, given that, and assuming a treadmill with very high acceleration capabilities, it could counteract the force of the jets trying to push the plane forward. But there's more...

Dumping energy into internal resistance of the wheels:

Now you are rolling on the treadmill, let's say at 10MPH on your rollerblades. If you let go of the treadmill, there is internal friction in your wheels, and they will begin to slow, and you will slide off the back of the treadmill. So there is a force required to keep you in place on the treadmill. This is an additional force, that in the problem, would be provided by the force of the airplane engines.

So the force of the engines can be counteracted by an acceleration of the plane's wheels, and through internal friction in the plane's wheels.

It is possible, assuming a treadmill capable of extremely high levels of acceleration.

And some of you are getting mixed up with crazy stuff. For example saying the treadmill matches the force of the engines, not the speed and such. If the plane is stable on the treadmill (not moving relative to the ground), then of course the treadmill is matching the force of the engines AND the speed of the wheels. If the forces are equal, there will be no linear acceleration down the treadmill, so the speed of the treadmill belt will exactly match the speed of the plane's wheels.

Digest that and let me know if you have any questions. I fully understand this, so saying "No! You dumbass!" will get you nowhere.

And I can make an equally compelling argument using physics for why the plane WILL take off, if we assume that "speed" means air speed.

Ok?

I've never tried this, but if all the high school physics I've taken means anything, then you will in fact require no more force to hold yourself on a treadmill going 100mph versus a treadmill going 10mph. Again, that's just what the force diagrams from AP physics say.

Again, in my understanding frictional force is a constant function of normal force and a frictional constant. The speed of the treadmill does NOT enter into the equation anywhere that I can see. All you have proven with this example is that the force of friction can overcome a zero force from the engines.

The main force to overcome here is not the horizontal force from the rolling resistance but rather the vertical, gravitational forces acting on the plane. These forces are overcome by the plane generating airspeed over the wings by thrusting itself through the air. This is why it doesn't really matter if the treadmill is moving or not.

You're right, the treadmill only acts on the wheels. If we can assume that the plane has the ability to take off on a static runway, it need only overcome that small additional amount of resistance provided by the wheels.