A brain challenge that people get pretty passionate about

[zil]

2 minutes ago, Vort said:

You are correct.

OK, so, in this case, the conveyor belt has no effect, except to spin the plane's wheels, which, not being attached in a way so as to control the body of the plane, will just spin twice as fast (for however long they remain in contact with the conveyor), because the plane is pushing against the air (or pulling itself through the air, depending on whether it's using a prop or jets?) and thus moving relative to the ground beyond the conveyor?  The wheels have nothing to do with forward motion - they're just providing a stable support until such time as the plane's air movement is fast enough to attain lift-off?

The wheels spin at twice the speed of the plane because the plane is carrying the axles forward and the conveyor is spinning backward at the same rate, thus doubling the wheel's rotation until lift-off?

[estradling75]

17 minutes ago, zil said:

Can someone clarify something for me?  (I will then go ask my brother to explain it or confirm / correct my understanding (if I manage to think I found some) - on Saturday maybe, when I have a few hours free.)

Going back to @Vort's explanation:

We have the airplane with wheels on the conveyor belt at the start of things (#1).  Beyond the conveyor belt we have the ground, which obviously won't be moving at any time during 1 through 4.  Let us say that at #1, we have a marker of some sort on the ground, even with the wings of the aircraft.  When we reach #4, will the wings of the aircraft still be even with the marker on the ground, or will they have moved relative to the marker?

Please don't try to explain, or at least not until after you give this simple answer: "they will still be even with the marker" or "they will have moved relative to the marker".  (I'm assuming that if the wings have moved relative to the marker, they'll be east of the marker - if I'm wrong, please let me know.)   Once I know this, I can try to puzzle out for myself how that all works - which will work better for my brain than trying to understand someone else's explanation.

The plane will move relative to the marker...   The reason... (unlike a car) the wheels on an airplane are designed to grant independence of the airplane from whatever surface they are touching.  So no matter how cleverly designed the treadmill is it can not over come the wheels primary function.

[NeuroTypical]

I love the sound of engineers and pilots yelling in the morning.  It sounds like... intelligent passion.

One can keep themselves warm off the heat generated at all the brain cells crashing into each other.

4 pages into it, JohnsonJones still takes first place for his swift use of all caps.  Vort is now a close second for his use of the word "stupid".  Neither wins the bad trophy, because nobody has directed their weaponized zeal in any personal way - they're just attacking and defending principles and ideas and notions.

 

[Guest MormonGator]

15 minutes ago, NeuroTypical said:

I love the sound of engineers and pilots yelling in the morning.  It sounds like... intelligent passion.

Did you just reference Apocalypse Now? Dude, a good little LDS boy like you should not be referencing such a movie! 

[NeuroTypical]

That show was R-rated for good reason.  It has the advantage of having a parody made of it, that condenses it down to 15 minutes, has all the poignancy and brilliance, with zero violence/language/nakedidity.

[zil]

22 minutes ago, NeuroTypical said:

nakedidity

I am so not going to have fun with this word - the moderators would kick me out for sure!

[Vort]

1 hour ago, NeuroTypical said:

Vort is now a close second

Story of my life.

[Just_A_Guy]

Ok, @JohnsonJones, let’s make sure we’re on the same page here.

We envision an aircraft pointed to the left. “Forward” = to the left, from our perspective.

As the airplane moves forward on stationary ground, the freely spinning wheels rotate counterclockwise.

Start the conveyor belt so that the top surface moves backwards—whatever the rate—I say that the wheels’ counterclockwise rotation accelerates but that the plane’s forward motion continues unchecked.  If I read you right, you agree with me; because the conveyor belt is augmenting rather than counteracting the wheels’ natural spin.  

Start the conveyor belt in the other direction (top surface of belt moves forward) at a sufficient force, and by friction between tire and the belt on which it sits, you may be able to completely stop the counterclockwise spin of the wheel and basically lock the plane (horizontally) to the surface of the conveyor belt.  But for that to work, the surface of the conveyor belt has to be moving forward with at least the same speed as the wheels are naturally forced to spin by the plane’s engine-induced forward thrust.  The belt naturally brings the plane forward with it; thus airflow continues over the wings, which don't stop to ask the wheels (or any other mechanism that may be supporting the plane’s weight) for permission before they start producing lift.  So . . . What do you say I’m missing from this scenario?

Your analogy of planes at full throttle while on the ground during engine checks doesn’t persuade me, because the wheels for those planes are (I presume) braked and/or chocked or clamped during such tests.  We know the plane in the hypothetical has no brakes; and the belt is not described as having chocks or clamps.

Edited December 5, 2017 by Just_A_Guy

[Guest]

1 hour ago, zil said:

OK, so, in this case, the conveyor belt has no effect, except to spin the plane's wheels, which, not being attached in a way so as to control the body of the plane, will just spin twice as fast (for however long they remain in contact with the conveyor), because the plane is pushing against the air (or pulling itself through the air, depending on whether it's using a prop or jets?) and thus moving relative to the ground beyond the conveyor?  The wheels have nothing to do with forward motion - they're just providing a stable support until such time as the plane's air movement is fast enough to attain lift-off?

The wheels spin at twice the speed of the plane because the plane is carrying the axles forward and the conveyor is spinning backward at the same rate, thus doubling the wheel's rotation until lift-off?

This is exactly why a wheel's velocity is zero.

[Guest]

OK.  I just spent some time going over this thread that went three pages prior to my even reading it.  That's just not fair!  I'm the board's resident engineer and everyone already solved the problem before I got to comment.

DANG IT!!  <------- Note the ALL CAPS.

Edited December 5, 2017 by Guest

[zil]

4 minutes ago, Just_A_Guy said:

anchor the plane to the surface of the conveyor belt

Not if the wheels are free to spin however they want - they have no power to hold the plane - if the conveyor is moving forward at the same speed as the plane, the plane is moving, even if the wheels aren't spinning - in a certain sense, the conveyor in this scenario could be like those aircraft carrier catapults.  (Unless I'm confused about something - I'm operating on visuals (see below), not on understanding whatever science is governing all this.)

1 minute ago, Carborendum said:

This is exactly why a wheel's velocity is zero.

This is why I asked for the answer I asked for.  "A wheel's velocity is zero" makes no sense to me.  Dictionary definition: "the speed of something in a given direction."  The wheels are attached to the axle.  The axle (and therefore wheels) are moving forward with the body of the plane.  Therefore, the wheel appears to have a non-zero speed in a given direction.  I believe you know what you're talking about and are correct, but I don't understand it.

Your explanation is for someone who understand the use of terms I don't understand (cuz I never took those classes).  My explanation with the mark on the ground is for someone who can create a picture in their head - see the ground, see the mark, see the plane with its prop/jet operating and moving the plane, see the conveyor moving, see the wheels spinning - and thereby understand what is happening, even if they don't understand the proper terms for explaining it all.

[prisonchaplain]

I consider myself a relatively well-educated person, and like to think I can analyze with a measure of success. However, when I read the riddle, as often happens to me with such mind puzzles, I started visualizing a pink, fluffy unicorn dancing on a rainbow. Then the song kicked in, and within 30-seconds I started softly banging my head against a wall. THEN I stopped, and repeated my recovery mantra, "I will not engage in pointless mind riddles...I will not engage in pointless mind riddles ... "  Yeah...yeah...So many thanks for giving my the opportunity to practice my recovery steps. 

[Just_A_Guy]

36 minutes ago, zil said:

Not if the wheels are free to spin however they want - they have no power to hold the plane - if the conveyor is moving forward at the same speed as the plane, the plane is moving, even if the wheels aren't spinning - in a certain sense, the conveyor in this scenario could be like those aircraft carrier catapults.  (Unless I'm confused about something - I'm operating on visuals (see below), not on understanding whatever science is governing all this.)

Of course the wheels are free to spin if some other force acts on them.  But in this portion of the hypothetical, the forces trying to spin the wheels forward are perfectly balanced by the forces trying to spin them backwards.  Thus the wheels remain stationary and retain their place on the conveyor belt as they continue to support the weight of the plane.  

But, yes—as I see it, the conveyor essentially acts as a catapult; because the whole thing is moving the plane forward.  The plane is not moving relative to the forward-moving belt itself, but there is both groundspeed and (presumably) airspeed; and it’s the airspeed that generates the lift and enables takeoff.

Edited December 5, 2017 by Just_A_Guy

[mordorbund]

12 hours ago, mordorbund said:

The people advocating that the plane will fly are saying the treadmill is a red herring, so let's get rid of it just so we can consider the principles (if we get the same conclusions, then we can re-introduce the treadmill). Consider this:

Instead of a treadmill to counteract the wheels, I strip the plane of all landing gear. I then suspend the plane so that it hangs like a pendulum 100 American feet off the ground. I wait for it to get perfectly still and start the propellers or jets or whatever thrust-inducer I have.

1. Is there a force pulling the plane forward or does it remain still?

2. Is there a force pulling the plane up or does it remain still?

 

11 hours ago, JohnsonJones said:

Not positive I understand your questions...

As a NON-scientist, my thoughts would be...

Well, for the question you'd still need a force to replace the conveyor belt to provide an equal and opposite force to keep it stationary in regards to some of the considerations.  That's going to be a difficulty.  The original question was in relation to the airplane and not the wheels of the airplane having that force keep it stationary (relative to the aircraft, rather than via groundspeed, which is a pretty big difference).

without that equal force to keep it stationary, with enough thrust the plane 1. will go forward and with lift and speed it will 2. ascend.

In this example there is no treadmill. For #1, there is no force except for thrust (via the props or jets) and drag (via air resistance). You agree that planes are designed so that thrust > drag, netting a forward force. For #2, with the forward force creating airflow over the wings, we both agree that there's lift. If lift > gravity, then the plane ascends.

So now when we introduce the conveyor belt into the equation, it sounds like your saying that the conveyor belt is generating a force on the plane via the wheels to counteract the thrust from the props. So let's consider another example. Since you keep comparing it to a car, let's do that.

I have a car that's a rear-wheel drive. I drive the front two (free-spinning) wheels onto the conveyor belt and chock the other two tires just to set up the experiment. The chocked tires (the ones connected to the motor) are not on the conveyor belt. So the car is half-on half-off. I start up the conveyor belt and get it up to 60 mph. The free-spinning wheels are, well, spinning freely. I unchock the rear wheels.

1. Is there a force on the car (not the wheels) parallel to the conveyor belt (either pulling it on or pushing it off)?

2. If there is such a force, how fast does the conveyor belt need to go to "drive" the car (either pushing or pulling it)?

[zil]

7 minutes ago, Just_A_Guy said:

Thus the wheels remain stationary and retain their place on the conveyor belt as they continue to support the weight of the plane.  

That makes sense - it's them having an impact on the plane's movement which doesn't make sense to me.

7 minutes ago, Just_A_Guy said:

But, yes—as I see it, the conveyor essentially acts as a catapult; because the whole thing is moving the plane forward.  The plane is not moving relative to the forward-moving belt itself, but there is both groundspeed and (presumably) airspeed; and it’s the airspeed that generates the lift and enables takeoff.

This makes sense too.

And now I comprehend what you mean by "anchor the plane to the surface of the conveyor belt" - I was understanding that wrong, as if you were saying the wheels attached to the conveyor could stop the plane's forward motion - but that's not what you meant.

[JohnsonJones]

52 minutes ago, Just_A_Guy said:

Ok, @JohnsonJones, let’s make sure we’re on the same page here.

We envision an aircraft pointed to the left. “Forward” = to the left, from our perspective.

As the airplane moves forward on stationary ground, the freely spinning wheels rotate counterclockwise.

Start the conveyor belt so that the top surface moves backwards—whatever the rate—I say that the wheels’ counterclockwise rotation accelerates but that the plane’s forward motion continues unchecked.  If I read you right, you agree with me; because the conveyor belt is augmenting rather than counteracting the wheels’ natural spin.  

Start the conveyor belt in the other direction (top surface of belt moves forward) at a sufficient force, and by friction between tire and the belt on which it sits, you may be able to completely stop the counterclockwise spin of the wheel and basically lock the plane (horizontally) to the surface of the conveyor belt.  But for that to work, the surface of the conveyor belt has to be moving forward with at least the same speed as the wheels are naturally forced to spin by the plane’s engine-induced forward thrust.  The belt naturally brings the plane forward with it; thus airflow continues over the wings, which don't stop to ask the wheels (or any other mechanism that may be supporting the plane’s weight) for permission before they start producing lift.  So . . . What do you say I’m missing from this scenario?

Your analogy of planes at full throttle while on the ground during engine checks doesn’t persuade me, because the wheels for those planes are (I presume) braked and/or chocked or clamped during such tests.  We know the plane in the hypothetical has no brakes; and the belt is not described as having chocks or clamps.

You are right, but actually, and if you put a chain or something else on the tires, it actually is pretty relevant, hence the engine checks. 

This is depending on if one reads the riddle as a PILOT and about an AIRPLANE...or whether they read it as a non-pilot and as a CAR.  The riddle specifies that the aircraft is stationary.  Almost every analysis done by someone who thinks the plane can take off throws this idea out, or that the conveyor keeps the plane stationary...they have to because the riddle itself is nonsense and an impossibility.

Those reading it as a car imagine an engine which is directly connected to the wheels.  Hence, at least one set of wheels are not free spinning.  They are controlled.  The only wheels in that scenario that are free spinning is if you have a front or rear wheel drive.  In many instances they recognize that there is a difference between airspeed and groundspeed.  We'll make it simple...In this scenario they see it then that the engine is producing a thrust vector of (we'll make up a number) 10.  The wheels only get a thrust vector of 5.  Much of this is due to friction and is different than that of the plane.  Hence, the thrust vector of the resistance is also 5.  it is obvious that the thrust is greater than the friction, and hence as the thrust moves the plane forward it moves with more power as the thrust itself is not accounted for (aka...the plane is NOT stationary, and the conveyor can somehow magically do this, both of which many toss out because it is an impossibility, but it is STILL part of the consideration...hence by tossing it out, they change the question).  The plane thus has that extra thrust.

In addition, with a plane there is the added number that says, a plane needs to have 5 Thrust accelerating I order to take off.  Well, if the thrust going in the opposite direction is only 5, it is obvious it can still take off, as the total thrust vector is unaccounted for.

This is a VERY simple way of viewing it, but it is this idea that people address, rather than the full question.

However, many pilots are going to view it very differently, because we can see situations where a similar thing would occur, AND, as some are very literal people, if it was as simple as the above statement seems to make it...then WHY isn't it being done on a regular basis?  Where is the actual physical evidence?  If an aeronautical engineer truly agreed with that...why isn't it done?  The lack of physical evidence is far more telling than anything else.  In all science, you can come up with an idea or hypothesis, but until you actually have something to back it up, it's not really anything provable.  They mythbusters went with the idea of the above scenario (and rather badly I might add with some of the choices they made, but it's all we have in that regard) where it is obvious that the pilot's groundspeed becomes faster than what they are going (his wheels turn at the predicted rate and than faster than that rate, as his groundspeed actually becomes FASTER as his wheels are NOT countered by the speed they are going on their momentum, in addition, with his thrust, he can take off at a certain point with very little forward thrust or movement...which he eventually does...lucky he was in a plane which he could do such a thing in).  It basically discounts the two points above...and applies it to groundspeed and only groundspeed.

We still haven't actually gotten to the riddle yet though, we are still tossing things out...so what does the opposite side say about the above modified riddle.

But the question isn't ABOUT groundspeed, it's about keeping the actual airplane stationary...and doing this by a conveyor belt.  In this fantasy world then, we have to conclude that somehow the conveyor belt has a perfect friction and that this ability lets the conveyor belt completely negate the Aircrafts thrust vector.  Aka...you have the Aircraft thrust vector moving forward...but the reverse is a vector that matches it instantly (no delay, which is another item many who utilize the idea above) and makes it stationary. 

In theory, if a conveyor belt matched the thrust vector, and you saw this, despite the friction of the wheels, you'd say...the total vector is greater than that of the forward vector on the wheels, hence this means that the aircraft MUST be moving backwards.  Right?  However, we ALSO know that the plane has to be stationary, which means the plane must be in a constant acceleration.  Of course if that is true, than the vectors of both must be increasing equally at the same time, hence creating an infinite loop where the aircraft will never take off.  In addition, it will NEVER get enough thrust vector to actually generate the thrust to take off.  In this one, the plane has a vector of 10 acceleration, but instead of a vector of 5 in the opposite direction for the wheels, it is a direct vector against the aircraft itself, since it is the aircraft specified.

In this you get an loop that will result in the plane never taking off.  Many say that in addition, if it were possible, the wheels or belt would be destroyed (tires can only turn so fast), but this, is obviously NOT allowed by the original question in THIS tread.

So, in this scenario, why did the Mythbusters idea work?  Because they only addressed the vectors that dealt directly with the wheels (that vector of 5 for simplicities sake) rather than that of the aircraft, hence they ignored the idea that the aircraft (not the wheels) is supposed to stay stationary.  This means, if you look closely at their final, you can see the aircraft slowly moving forward.  In addition, once it gets airborne, it obviously moves forward.  The magic conveyor does not keep it stationary.

So, here we have both sides of what is seen commonly, but why don't we see this more often then if those who are thinking it will take off are correct?  The ones who say it is not possible, obviously currently have the evidence on their side (as in physical evidence and the rules of flying as we understand it), while those who say it is have almost no evidence on theirs (physical evidence that shows it actually is done...their only piece is normally that one mythbuster's episode which as I said, is seen as highly flawed).

So what is my thinking on this this then and how did I come up with the idea I did (beyond the fact that the actual question is heavily flawed in it's premise and is an impossibility in and of itself...as no conveyor belt has the perfect ability to negate an aircraft's forward movement, hence cannot be applied in any fashion and is...in fact nonsense?).

since this is already long explaining the two different takes which disagree most of the time in these threads...I'll give the other below in a secondary post...if you don't mind

[JohnsonJones]

The thing that I was thinking about in relation to the question, is if we take the question seriously with the magic conveyor belt.  IF, it is actually doable, why don't we see it more often. 

Vort pointed it out, though I recognized it already (as I had stated, groundspeed is not airspeed, however, it is necessary for the aircraft to show forward movement in order to generate airspeed and airflow over the wings).  Basic physics state that if you have no airflow, you cannot fly...period.  It is the principle of the air flowing over and under the wings that cause lift, and without that, you will have NO lift.  This is a basic principle to all flying.  In addition, an object that is not moving generates no airflow.

It is correct, that a plane does not fly in relation to how it moves on the ground, that is inconsequential, what matters is it's movement in relation to the air around it.  The question specifies however, that the plane is STATIONARY.  If we do not toss this out as nonsense, then we have to say that the plane IS STATIONARY...which means all it's forward movement of the aircraft itself (not the movement of the wheels) is stationary.  A stationary aircraft cannot fly. 

So then I started to think of examples of this in reality, rather than fantasy land.  You have river takeoffs.  Contrary to what some think, there are some aircraft that will have a very hard time, or not even able, to be able to take off going upstream against a strong river current.  The plane instead will never generate the airspeed in improper conditions.  This is somewhat similar to the question, the thing is, why is this so if the people who state a plane will be able to take off are correct?  (and I haven't figured that out completely yet).  At the same time, that same plane may have difficulties with a downstream takeoff with some bad conditions also...so there's also that to consider.  You also have planes that do take off upstream as their engines more then compensate for any obstacle, the same with downstream...but each has different variables to consider.  I used the river, because it is an actual moving runway...and perhaps the closest we may actually get to a conveyor belt in real life that moves at a constant rate.  Normally, that movement  is something that you need to counter in your own movement (aka...if talking vectors, our positive vector must exceed the river's negative friction vector, along with any wind vectors and air friction vectors).

So, how does this apply to the wheels.  Once again, we view the wheels and airflow as separate, but this time rather than seeing it as a car, we'll view it as an aircraft.  In this case, then, what role does a wheel actually play?  If it's not part of the thrust of the aircraft, what is it?

A free spinning wheel is a REFLECTION of what the aircraft is doing.  It is rolling because the aircraft's own movement is forcing it to move I a certain direction.  Thus, in theory, what should a conveyor belt do in regards to a wheel?  It should cause a counter reflection of the wheel.   Hence, the forces that cause the wheel to turn one way in the first place, should be shown to be exactly opposite in regards to the wheel if we are using a vector of opposing force.

How would this be done?

Well, first, once again, this is impossible.

However, we'll imagine we have a world of perfect friction, where the plane and the belt will only turn the wheel relative because they have 100% friction between them and can reflect these forces via the wheel.

This means, that the airplanes forward movement is negated, and the airplane itself is actually stationary.  If this is reflected upon the wheel, this should mean the wheel itself is also stationary.

I like this idea though in regards to the conveyor belt as it answers another question. 

The treadmill type question we adapted it to above actually does not provide a reflection vector for the wheels.  If we view wheel movement as a reflection of the force upon them, then it is their spinning that is the actual movement/vector that they have.  When a plane is moving, the wheel vector of 5 is a separate vector then the plane's own forward vector of 10.  However, when we do the treadmill idea which I showed in my post above(the post prior to this one), the actual WHEEL movement is doubled.  Instead of showing a counter to the airplane, or even the wheels, it actually just doubles the wheel's vector. They now have an independently moving vector of 10.

However wheels are reflecting the forces upon them.  Thus, for the plane to remain stationary, the wheels also should reflect this.  This could require MORE energy to do than the opposite.  To stop the wheel vector with an opposing force, could require more energy, and thus this would also explain WHY one would not actually perform this experiment...it is NOT cost effective.  In presenting an opposite force to the plane of a vector of 10 (numbers are arbitrary, just to give something one can see as a representative number), requires two times the energy of something that is only opposing a force of 5.  The wheels however, are merely a reflection of that force and the forces acting upon them.

As you I mentioned, and you aptly pointed out...we see this all the time when the plane is actually stationary. 

On the ground the chalks are a safety feature, but they are not necessarily the thing that keeps the plane from moving...as all things on aircraft with backups, they are a back up feature (and most aircraft have one or two backups in case of a primary system failure...airplanes are actually safer than cars).  Since the wheels are unnecessary to the equation, and are only a reflection of the forces acting upon it, you are absolutely correct.  All we need is someway to keep the aircraft completely stationary (as per the question).  It assumes a conveyor belt in the "riddle" which is impossible, but in real life, there ARE things that are possible to do this.

You can have a plane with full engines going, but it is still stationary.  As we say the wheels are merely a reflection of the forces upon them, they don't actually matter in regards to whether the conveyor belt is keeping the plane stationary or not.  The direct force keeps the plane stationary, the wheels are just a reflection of what the forces are doing.

In that matter, as you say...you could have the wheels chalked, you could have the entire wheel assembly chained to the ground, the difference as I see it negligible. 

However, we then have real world examples of this, and thus the question then comes up...in these examples...does the airplane fly.  The answer is, I haven't seen it yet.  The reason most would say it does not, there is not enough airflow across the wings to result in flight.  Even if the engines are at full thrust, if the brakes are acting in the opposite vector to resist this and thus keeping the plane stationary, the plane does not take flight.

Why do I use these examples, because I prefer REAL world and REAL life examples if we are tackling this to things that people may think, but have never been demonstrated.

That does NOT mean this is the correct answer (afterall, many thought the world was flat and we know now it is round, many thought we could never escape the atmosphere, and yet now we've been to the moon), just that as I think of what is REAL and what occurs in the REAL world...the most relevant would be this result.

Edited December 5, 2017 by JohnsonJones

[Rob Osborn]

I cant believe were still debating this issue. There is a part of my brain that is fried from being part of this silly thread. I am completely mind blown over this. This reminds me of the popular monty hall door problem and how it confuses so many people. It goes like this- There are three doors of the which one of them is a brand new car and the other two are duds, one is a goat and the other a fake christmas tree.  You first pick one door but cant look at it. The host then looks behind the other two doors and always picks a dud. He then asks if you would like to keep your original door or trade it for the last unpicked door. Is it better to always keep your original unseen door or trade it for the other door? 

[SilentOne]

26 minutes ago, Rob Osborn said:

The host then looks behind the other two doors and always picks a dud.

If that were the case, of course you would want to stay with your original door. However, he doesn't always pick a dud because the door with the prize must always be one of the options. So if you had originally picked the door with the prize, he would have to pick a dud. If you originally picked a dud, he would have to pick the door with the prize.

[zil]

1 minute ago, SilentOne said:

If that were the case, of course you would want to stay with your original door. However, he doesn't always pick a dud because the door with the prize must always be one of the options. So if you had originally picked the door with the prize, he would have to pick a dud. If you originally picked a dud, he would have to pick the door with the prize.

If you picked a dud, he would pick the remaining dud.  There are two duds, one prize.

[SilentOne]

@zil I misread @Rob Osborn's post. I thought he was saying that if you pick Door A and he picks Door B, you would have to choose between A and B. Rereading, I see that Door B would be thrown out and you'd pick between A and C.

[Rob Osborn]

The host in this game always looks at the two doors which werent picked and opens one of them containing a dud and then asks if you want to keep your original door or trade it for the last door. Do you keep your door or trade?

[JohnsonJones]

1 hour ago, Rob Osborn said:

I cant believe were still debating this issue. There is a part of my brain that is fried from being part of this silly thread. I am completely mind blown over this. This reminds me of the popular monty hall door problem and how it confuses so many people. It goes like this- There are three doors of the which one of them is a brand new car and the other two are duds, one is a goat and the other a fake christmas tree.  You first pick one door but cant look at it. The host then looks behind the other two doors and always picks a dud. He then asks if you would like to keep your original door or trade it for the last unpicked door. Is it better to always keep your original unseen door or trade it for the other door? 

This is also sort of counter intuitive.  When you originally can choose a door, you have a 1/3 chance of being correct.  When he then reveals what is behind one of the doors you did NOT choose, that leaves two doors.  If you choose the other door, you have a 50/50 chance of being correct, which is greater than your chances previously (50% is greater than 33.333...%).  The reason is he has revealed one answer that is absolutely not correct, where as before, you had a 2 in 3 chance of choosing an incorrect one.  Furthermore, he is going to reveal one that is NOT correct, rather than one that IS correct. (which affects it as Zil already notated).  It is because of this action of his (if it were equal chances of him revealing the right door rather than what was a wrong door...it could change this...but the game is he reveals a WRONG door) that makes the best choice (but not always the right choice...if that makes sense) to always do the trade.

It can have a little bit more complex explanation than that, but I've been longwinded enough for this thread already...

Edited December 5, 2017 by JohnsonJones

[Guest]

3 hours ago, zil said:

This is why I asked for the answer I asked for.  "A wheel's velocity is zero" makes no sense to me.  Dictionary definition: "the speed of something in a given direction."  The wheels are attached to the axle.  The axle (and therefore wheels) are moving forward with the body of the plane.  Therefore, the wheel appears to have a non-zero speed in a given direction.  I believe you know what you're talking about and are correct, but I don't understand it.

I should have said NET velocity.  At any given point, the top of the wheel will have a velocity equal and opposite to the bottom of the wheel.  Thus the net velocity is zero.

This scenario says no motor or brakes, etc.  meaning the plane and wheels are not rotationally connected.  Without being rotationally connected, the wheel can never have an effect on the airplane's velocity.  All it does is cause the wheels to spin.  But the airplane can have an effect on the wheel.  Here's why.

The airplane creates a force against the axle.  The axle then causes motion of the center of the wheel as a whole.  Here is the great paradox.  How can the wheel have a net zero velocity, yet still move overall?  ANSWER: Point of reference.  The net zero velocity of the wheel is in reference to the axle.  The net velocity of the wheel in reference to the ground is whatever the engines can produce.  If the engines are not running, the net velocity of the airplane is zero. The Conveyor belt NEVER changes the wheel's net velocity because it can never cause the wheel to have an effect on the axle.

[zil]

5 minutes ago, Carborendum said:

I should have said NET velocity.  At any given point, the top of the wheel will have a velocity equal and opposite to the bottom of the wheel.  Thus the net velocity is zero.

This scenario says no motor or brakes, etc.  meaning the plane and wheels are not rotationally connected.  Without being rotationally connected, the wheel can never have an effect on the airplane's velocity.  All it does is cause the wheels to spin.  But the airplane can have an effect on the wheel.  Here's why.

The airplane creates a force against the axle.  The axle then causes motion of the center of the wheel as a whole.  Here is the great paradox.  How can the wheel have a net zero velocity, yet still move overall?  ANSWER: Point of reference.  The net zero velocity of the wheel is in reference to the axle.  The net velocity of the wheel in reference to the ground is whatever the engines can produce.  If the engines are not running, the net velocity of the airplane is zero. The Conveyor belt NEVER changes the wheel's net velocity because it can never cause the wheel to have an effect on the axle.

Uh huh.  I'm gonna go pick up my new fountain pen and ink at the post office now.