Counter intuitive puzzle

[VirusType2]

The treadmill will not exert enough force upon the plane's wheels to counteract the acceleration caused by the plane's turbines.

In other words, wheelspin. The amount of friction of a wheel is extremely low, since the contact area is small (and in this case, the wheels freespin to a large degree) Even if the wheels can't keep up, a plane will easily overcome this small amount of friction. However, we aren't talking about frictionless wheels, we are talking about tires, which have good grip - but a treadmill isn't necessarily the ideal surface for a tire, so the plane would very easily overcome this friction.

So, if the surface of the tread-mil was equivalent to tarmac, I question whether the wheels would be positioned forward enough to where the plane wouldn't nose into the treadmill. In other words, the balance of the plane would be important, as would the amount of grip on the thread-mil.

 

[Solaris]

What, we absolutely cannot talk about the speed of the plane relative to the treadmill, given that the two things depend on each other and directly effect each others speed.

I think some of you need to take a basic physics class looking at very basic relativity.

It's far easier if we imagine it all takes place in an inertial reference frame, with an Air Traffic Control tower as the origin.

If the treadmill was going at 100mph and the plane was stationary, the planes speed would be ZERO. But if the plane has zero speed, how can the treadmill be going at 100mph? It can't as it matches the speed of the plane.

Therefore, the plane MUST be moving at a speed relative to the ATC and therefore has lift and so if it can get fast enough will take off.

 

[Higlac]

Exactly.The only way that a treadmill could keep a plane from taking off is when it is covered in telephone poles.

Er..

Yeah.

 

[xcellerate]

This is the most retarded discussion ever, as it always is.

So if we strapped some rockets onto the plane, do you think it still wouldn't take off?

 

[Escaep]

Sure wish Mythbusters would've done something like this.


Oh wait they did:

http://www.youtube.com/watch?v=0ul_5DtMLhc

http://www.youtube.com/watch?v=YORCk1BN7QY

 

[Solaris]

Here's a way to get Ennui over to our side.

Imagine the plane had lubricated ski's instead of wheels. Still think it won't take off?? What difference do wheels make then?

 

[The Monkey]

For those of you who don't think it would work in practice because of the friction, the fucking Mythbusters did it with a real plane and a huge treadmill, and guess what, it takes off.

For fuck's sake, we've had like seven threads on this subject, those who don't understand it by this point after having read all the arguments are mentally challenged.

EDIT: Ooops, didn't see the videos that were already posted.

 

[StarBob]

It wouldn't work in practice because of the friction IF the treadmill was moving at the speed at which the wheels were spinning. Their test was fairly conclusive but we had no idea how fast the plane was moving and no idea how fast the truck was moving... and even if they were moving at the same speed, it wasn't the speed at the wheel. But I guess the point everyone is tryingto make is that it's not the speed at the wheel but the relative speed that is matched.

 

[99.vikram]

Tut tut, Ennui, tut tut. There's just no goddamn way the treadmill can be forced to match the speed of the plane, unless the treadmill is powered by a motor and the plane was deliberately underpowered to only counter friction's tendency to carry it along with the treadmill's motion.

The mildest thrust would give that plane absolute forward momentum.

 

[kineaesth]

This is the most retarded discussion ever, as it always is. The whole point of the question is assuming that the treadmill matches the plane's speed exactly, which means THE PLANE IS NOT MOVING RELATIVE TO THE AIR OR GROUND OR ANYTHING BUT THE TREADMILL. Which means it cannot take off.
That's honestly why this is such a dumb question/thought experiment- nobody actually agrees on the initial conditions. If the plane moves relative to the ground, it takes off. If it doesn't move relative to the ground, it can't take off.

Consider three rewordings of the question:

1) An airplane is sitting at rest on a very powerful treadmill. You are at the controls of the treadmill, while I am at the controls of the airplane. On some signal, I begin to attempt to take flight in the plane, and you attempt to match my speed to try to keep me stationary. Will the plane take off?

2) An airplane is sitting at rest on a very powerful treadmill. You are at the controls of the treadmill, while I am at the controls of the airplane. On some signal, I throttle up the airplane and you turn on the treadmill, and we conspire by our joint effort to try to keep the plane stationary relative to the ground. Will the plane take off?

3) An airplane is sitting at rest on a very powerful treadmill. You are at the controls of the treadmill, while I am at the controls of the airplane. On some signal, I attempt to take flight in the plane, but you match my speed with the treadmill and keep me stationary relative to the ground. Will the plane take off?

Here are the absolute, 100%, bet-your-life-on-it answers to these rewordings:

Yes.
No.
Whoever asked this question is an idiot.

Answer 1 is because SCIENCE.

Answer 2 is because the pilot never increases the throttle speed above what is needed to overcome wheel friction.

Answer 3 is because it's impossible to have the plane not moving.

 

[VirusType2]

we had no idea how fast the plane was moving and no idea how fast the truck was moving..

The truck was pulling the belt at the TAKE-OFF SPEED OF THE PLANE. That's a quote.

-The thrust easily overcomes the friction of the wheel. The friction of a wheel is extremely small, else wheels wouldn't roll!

-The wheels are free-spinning, so this reduces any tire-grip friction to an extreme amount.

-A conveyor belt doesn't have the grip of tarmac, so friction is extremely small here too.

 

[Stigmata]

Just think about it mechanically. The wheels are free-moving. They offer insignificant friction, and provide no thrust. The velocity of the air moving over the wings is what's going to determine whether the plane takes off, because the amount of lift is dependent on how fast the air moves over the wings.

 

[YROC]

If you attach a piece of toast with peanut butter spread on one side to the back of a cat, which side will hit the floor?

 

[Ennui]

Tut tut, Ennui, tut tut. There's just no goddamn way the treadmill can be forced to match the speed of the plane, unless the treadmill is powered by a motor and the plane was deliberately underpowered to only counter friction's tendency to carry it along with the treadmill's motion.

The mildest thrust would give that plane absolute forward momentum.

Derp derp, I addressed that, which is why I said magic treadmill I understand that in any real-world situation the plane would take off due to friction and the impossibility of the treadmill to exactly match its reverse speed. I'm just banging on about how its stupid because the answer depends on how the question is worded (see the thing KA quoted in his post).

 

[The Monkey]

Even if the speeds of the treadmill and the plane were exactly matched, the plane would still move and take of almost entirely unhindered by the treadmill.

 

[Ennui]

Magic treadmill accounts for friction. How many times to I need to repeat that I understand that the answer should generally be YES. I just think this is a silly discussion because 95% of the argument is about the initial conditions of the thought experiment.

 

[The Monkey]

The problem is, though, that in each of the three scenarios you listed before, the plane would take off.

 

[PvtRyan]

 

[15357]

Err, what is that?

 

[VirusType2]

It's a turn table! (a record player)

 

[The Monkey]

I didn't know an iPod looked like that on the inside! How does it even fit?

 

[kineaesth]

Magic treadmill accounts for friction. How many times to I need to repeat that I understand that the answer should generally be YES. I just think this is a silly discussion because 95% of the argument is about the initial conditions of the thought experiment.

Most of the "NO" camp people like to think that the question says "SOMETHING SOMETHING PLANE ON A TREADMILL but the treadmill keeps the plane stationary relative to the ground"

In this (impossible) situation, clearly the plane would not move. But this situation cannot occur.

 

[Vegeta897]

Ennui, why is it impossible for the treadmill to match the plane's speed? The plane's speed is relative to the stationary objects, ie. a person watching or more importantly the air moving around the plane's wings. So we have that speed, say 100mph, then the treadmill surface would be moving 100mph in the opposite direction, again the speed is relative to stationary objects. This means the wheels have a speed of 200mph.

What is impossible or magic about this?

 

[15357]

Damn it will you guys stop messing with my head? In the real world with my model glider experiment the wheels will always move faster than the treadmill, but if the wheels generate more-than-negligible friction and the speed of said treadmill mathches the speed of the wheels and friction accounted the plane will not gather airspeed

think of an glider on ice with two strings attached the front will pull and generate thrust but the latter will match the force ensuring that the glider does not move in which the friction of the wheels and the treadmill is supposed to do

 

[Tacoeaterguy]

ITT: Science lesson on motion.

But getting back to the original motive of the thread, if possible, I remember my dad telling me about the Monty Hall 3 door puzzle thing. I was only about 10 years old, and I didn't really understand how it wasn't a 50 % chance of getting the prize, but I think I get it now.

I just searched for some counter intuitive puzzles google, and I found this one, but it's really quite stupid.

"If you were to fully develop the entire tree for all possible chess moves in a single chess game, the total number of board positions far exceeds the number of atoms in the universe."

I don't see how this one would make you think at all. There's no way this could exceed the number of atoms in the universe. Unless I'm missing something. I can't really find anymore decent ones, but they sure are interesting and certainly make you think.

Edit: Oh.

 

[Solaris]

I don't see how this one would make you think at all. There's no way this could exceed the number of atoms in the universe. Unless I'm missing something. I can't really find anymore decent ones, but they sure are interesting and certainly make you think.

Given the rules of chess, you could play a game that would last forever. So clearly, it's true.

 

[Tacoeaterguy]

Given the rules of chess, you could play a game that would last forever. So clearly, it's true.

Oh I get it now. Didn't really think about that. I must suck at these.

 

[Krynn72]

Found Vegeta's flash video. Made me laugh because I just now, almost four years later, realized you were chewing gum while recording.

http://img450.imageshack.us/img450/3793/airplane22dg.swf

I just ordered the book that the guy quoted from in my OP (called The Power of Logical Thinking), and he seemed to suggest that there were several puzzle-type things like this in it. So if there are, I'll post them as I come across them.

 

[Krynn72]

Just got it today, and there are a ton of these in it. Heres a couple of the good ones I came across so far.


A pretty easy one:

The city of Elizabeth was ordered by the Superior Court to conduct a lottery for the award of taxicab medallions. There are twenty medallions to be won, and each contestant can only win once. Thirty-two drivers participated, with a thirty-third driver disallowed.

Later however, a second lottery was held in order to allow that thirty-third person an equal chance to win a medallion after all. In this second lottery, thirteen contestants participated, including the twelve unsuccessful contestants from the first lottery. There is only one medallion to be won in this lottery.

Is this arrangement fair? [explain why]

There are three prisoners on death row. They are told that one of them has been chosen at random to be executed the next day, and that the other two will be freed. One of the prisoners privately begs the warden to tell him the name of at least one of the people who will be freed. The warden says "Susie will be freed."

What is the chance that that the prisoner who asked the question will be the one executed?

There is a single path up a mountain. A climber begins his ascent at 6:00am and reaches the top at 6:00pm. The next morning he begins his descent at 6:00am and reaches the bottom at 6:00pm. Each day of climbing he travels at different speeds during the climb, resting in different areas, stopping for lunch, etcetera. What are the chances that there is a spot that he passes at the exact same time both days?

A shopkeeper has two new baby beagles thats she is trying to give away, but she doesnt know the genders of either one. You tell her you only want a male, and she phones the person who is bathing them and asks "Is at least one a male?" to which he responds "yes."

What is the probability that the other one is male?

And one last one.

There is a racetrack that is one mile around. If you drive around the track once at 30mph, how fast will you need to drive the second lap in order to average 60mph for both laps?

 

[Vegeta897]

1. No it's not fair, first lottery had 5/8 chance of winning, second lottery had 1/13 chance.

2. 66.6% I'm guessing, because this sounds like that one problem

3. Stumped me

4. 50%?

5. Impossible to achieve 60mph average after doing the first lap at 30. To achieve 60mph average for a distance of two miles he'd need to finish in 2 minutes. But driving 1 mile at 30mph would take 2 minutes, so he used up all his time.

 

[Krynn72]

Damn, I was hoping I could ninja edit another one in there without anyone missing it. Check my post again for the one with the two dogs (second to last puzzle).

I'll wait for more replies to post the answers.

 

[Stigmata]

1. No; the cab drivers in the first contest and second contest have different probabilities of winning a medallion (12/32 and 1/13).

2. 50%

3. 100%; he passes the first molecule of his upwards journey at exactly 6:00am both days, and reaches the top at 6:00pm both days.

4. 50%

5. This question isn't worded properly. The correct answer for this question is 90mph. The correct answer for the correct question is the speed of light, or c (well, technically 0.999*c).

Sadly, the only one I'm absolutely sure of is number 5.

 

[Vegeta897]

Stig, you read 3 wrong. The first day he went up the mountain, the second day he went down it.

And how is 5 worded wrong? 90mph wouldn't be a valid answer no matter what, that makes no sense.

Also for question 1 you mean 20/32 (or 5/8) not 12/32.

 

[Krynn72]

5 is worded right. I made sure of it.

 

[Stigmata]

Yes, I definitely read #3 wrong.

#5 is definitely worded incorrectly though. "Average 60mph for both laps" implies that the laps are being added together as discrete speeds, and not as divisions of one contiguous movement. 30mph + 90mph / 2 = 60mph. "Average 60mph for the duration" is when you get the crazy answer.

 

[99.vikram]

Yes, I definitely read #3 wrong.

#5 is definitely worded incorrectly though. "Average 60mph for both laps" implies that the laps are being added together as discrete speeds, and not as divisions of one contiguous movement. 30mph + 90mph / 2 = 60mph. "Average 60mph for the duration" is when you get the crazy answer.

Good point, but you applied a little too much intelligence in your 'correct' answer. c is a finite speed, and gives a define average != 60mph. Nothing less than infinity will give 60mph average, so the answer is that it is impossible to get 60mph.

 

[Stigmata]

If you consider general relativity, c is "infinity" as far as the system containing physical interactions is concerned. Does that solve the problem, or would we need to reconsider the accuracy of the "30mph" measurement as well?

 

[Vegeta897]

Stig, you're wrong. Just because light may be the fastest thing in the universe that doesn't make its speed infinite. Light travels at a finite speed. If that weren't true, light years would not be a definable distance. So the answer remains 'it's impossible'.

 

[Stigmata]

It's not infinite to you and me, but it's the highest speed that has any meaning or relevance in physics, i.e. the universe. The idea of moving faster than that is the closest you can get to empirical nonsense.

In that context (or if you prefer; From the perspective of matter and energy), the speed of light is effectively infinity. It's the highest possible speed of anything, ever. And because time and velocity are inversely and logarithmically proportional, objects technically "infinitely approach" the speed of light and do not actually attain it. So again, taken from the perspective of matter, light speed is infinity; a bound that can never be reached.

[edit] If someone here knows I'm wrong, speak up. I'd hate to educate this forum with pseudoscience and accidental lies.

 

[Vegeta897]

But again, that doesn't mean it's instantaneous. It still takes time for it to travel a distance.

The fact that nothing can go faster than the speed of light is the exact reason why the answer is 'impossible'.