Critical thinking puzzle.

[Admin]

A couple have 2 children. One of the children is known to be a boy. What is the probability of his sibling being a girl?

Note: it's not a silly trick question.

[Lord Muck oGentry]

Which one is known to be a boy when both are boys { stirs pot maliciously >:D}?

[Admin]

The only info we have is that there are 2 children, one of which is a boy.

[Aardvark]

I striggle with these but here i go for broke.

The options are boy or girl. there is a fifty fift chance of any child being a boy or girl. The fact that they already have one boy has no bearing on the chance of the second child as they are unrelated events ( other than they are all related, ba dum tish.........I thankyew)

so my answer

50% chance of being a girl

Now someone smarter than me is going to shoot down my practical logic :(

[Blue Bubble]

Off the top-of-me-head: I'd say the probability that the other is a girl is 0.5 minus the probability of the occurrence of identical twins, plus the probability of the occurrence of twins, one of which is the opposite gender.

Wasn't there a long thread about this on the JREF last year (or thereabouts) ?

[Zendal Darkman]

My money is on "blue bubbles"answer.

however.....

For every 100 baby girls, there are 106 baby boys. This is a fact.

Why more boys? Nobody knows! And it's a real puzzle because...

Other animal species have half male and half female offspring.
Men produce equal numbers of x-chromosome sperms (which make girls) and y-chromosome sperms (which make boys).
from http://www.sexratio.com/facts.htm.

I'll allow others to check the sources of this 'amazing fact' ;D

[Admin]

The answer's not 50% ???

[Aardvark]

I striggle with these but here i go for broke.

The options are boy or girl. there is a fifty fift chance of any child being a boy or girl. The fact that they already have one boy has no bearing on the chance of the second child as they are unrelated events ( other than they are all related, ba dum tish.........I thankyew)

so my answer

50% chance of being a girl

Now someone smarter than me is going to shoot down my practical logic :(



Bugger, I have had a glass or two of the fermented grape and just realised that there are mosaics to consider

Turners Syndrome and Kleinfelters Syndrome are two that spring to mind

XO
XXY
XYY

Aslo from John's reply post that the answer is not 50%. is this in fact based on the demographics posted by blue bubbles??

[vbloke]

51% boy
49% girl
?

[Lord Muck oGentry]

The only info we have is that there are 2 children, one of which is a boy.


Fair enough, John. I take that to mean: it is known of one (unspecified) child that that child is male.
If it is a Monty Hall lookalike ( or Restricted Choice problem, for bridge players), then the answer is 2/3.

[Lord Muck oGentry]

Sorry. I've just looked at the question again. On the assumptions, the answer should, of course, be 1/3, not 2/3.

[Blue Bubble]

The only info we have is that there are 2 children, one of which is a boy.


Fair enough, John. I take that to mean: it is known of one (unspecified) child that that child is male.
If it is a Monty Hall lookalike ( or Restricted Choice problem, for bridge players), then the answer is 2/3.


Ah but it's not a Monty Hall lookalike. In the Monty Hall case, you have a priori knowledge that both the car and the goat(s) exist, and can make adjustment accordingly. In John's case, we have no a priori knowledge that a girl child exists.

[vbloke]

Doing a bit more thinking about the problem...

There are a number of possible answers to this.

Consider the collection of all couples with two children. Now, consider the following two experiments:

For each couple, pick one of the two children at random. If that child is a boy, what is the probability that the other child is a boy? (Answer: the probability that both children are boys is 1 out of 2.)
Note that to perform this experiment, we need to know in advance the sex of only one child.

For each couple, if either child is a boy, what is the probability that the other child is also a boy? (Answer: the probability that both children are boys is 1 out of 3.)
Note that to perform this experiment, we must know in advance the sex of both children.

Begin with a group of 100 families, each with two children, distributed as follows:

25 families with oldest child a boy and youngest child a boy.
25 families with oldest child a boy and youngest child a girl.
25 families with oldest child a girl and youngest child a boy.
25 families with oldest child a girl and youngest child a girl.

Of this group, there are 50 families in which the oldest child is a boy. Of those 50 families, there are 25 families in which the youngest child is also a boy. In other words, out of the group of families in which the oldest child is a boy, 50% have two boys.

From the same group, there are 75 families in which at least one child is a boy. Of those 75 families, there are 25 families in which the other child is also a boy. In other words, out of the group of families in which at least one child is a boy, only 33% have two boys.

This is a bugger of a problem as the wording is ambiguous and it can have several answers.

Someone check my reasoning, please!

[Admin]

They're great these puzzles aren't they? ;D

They key to solving it is recognising that we don't know whether the boy was born first or second; we simply know that out of the 2 children one of them is a boy.

There are 4 ways of having 2 children:

Boy - Boy
Boy - Girl
Girl - Boy
Girl - Girl

As one is a boy, the girl-girl option is ruled out which leaves:

Boy - Boy
Boy - Girl
Girl - Boy

So if one is a boy there's a 67% chance that the other sibling is a girl.

NOTE: If we know whether the boy was born first or second the chances are 50% as expected.

It's a good little puzzle as it shows how easy it is for intuition to be wrong.

[Lord Muck oGentry]

A lot depends on how we come to know that one child is a boy. Assuming we have asked to see a child at random, I counted the prior possibilities ( seen child first) :

1. B1 B2
2. B2 B1
3. B G
4. G B
5. G1 G2
6. G2 G1

The last three possibilities are ruled out when we see a boy. Of the remainder, twice as many give a boy pair as a mixed pair.

I have checked my answer with Lady Muck, and she is of the firm opinion that I can't count for toffee. And shouldn't be let out on my own... :) She makes it even money.

JJ's answer ( and vbloke's, if I'm following it correctly) is that the question is, in effect: what is the ratio of mixed pairs to boy pairs in the real world? ( 2:1)

So I have come to the conclusion that I don't understand the question :)

[Admin]

These type of questions tend to take on a complexity of their own. ???

It's also important to only deal with the information at hand.

It's interesting though, as if you're posing as a psychic and you know a person has 2 children, one of which is a boy, then stating that the other one is a girl will be correct 2 times out of three.

I wonder how many knowingly fraudulent psychics use such statistical tricks to tip the scales in their favour? :ponder:

[median]

Interesting stuff, John.
This does give an insight into how easy it is for people to arrive at the 'wrong' conclusion.
During the train of dialogue, the Monty Hall problem was mentioned.
This solution had all manner of academics and mathematics PhD's arguing against the correct answer.
A sobering thought then that even learned men need not have an intuitive grasp of such things. (Am I being skeptical enough?)
Practical example; Dr Roy Meadows and the cot death incidents.
His (mis) calculations were based upon calculating porobabilities for independent events!!

[Admin]

The thing I like about puzzles like this is that they show that intuition and common sense can actually be quite wrong.

Yes, Sir Roy Meadows made a major blunder in calculating the odds of multiple cot deaths in a family. He took the figure of 1 in 8500 as the odds of one cot death and then multiplied it by itself to work out the odds of two cot deaths in the same family - which he said were ~1 in 73,000,000.

His mistake was to ignore the fact that other factors could make it more likely to occur in the same family (genetics, housing conditions, etc.)

He treated each cot death as an independent event and that's why he came up with the wrong figure.

[fontwell]

Although you later clarified the question, I'd just like to say this. You originally said,

"A couple have 2 children. One of the children is known to be a boy. What is the probability of his sibling being a girl?"

Now the thing is that "One of the children is..." is ambiguous in everyday English and could be intended to mean "A particular child is..." or "A total of one child is ". These two meanings have different implications for the the total number of boys.

Now, when you follow that by saying "...the probability of his sibling..." you really are talking about particular child (i.e. 'him') and you are are asking the about the probability of that one child's sibling being a girl. When this sentence follows the ambiguous first sentence it implies that "One of the children" is in fact a particular one, because we subsequently talk about 'him'.

Therefore after extracting the everyday English language meaning from the original question, it is not really actually asking the question you intended.

I dare say a lawyer would try to have it that the question could mean what you wanted it to but one could equally well ague the other case, so at the very least it is unclear.

Interestingly, the difficulty people have with answering this sort of question in general is that they tend to re interpret questions to be the very one you have asked, so it behoves you to ask the question in an un ambiguous form such as

"A couple have 2 children. At least one of them is known to be a boy. A particular child is found to be a boy, what is the probability that he has a sister."

and give the punters a fighting chance, because its still easy to get it wrong.

[Admin]

Well it's always difficult to word questions properly as people do indeed interpret them rather than take in exactly what they say.

I think the key to this question is that the birth order is not revealed. If we know that the boy was first (or second) born then the chances of his sibling being a girl are 50% as expected by chance.

[doubting thomas]

I hate these sort of puzzles for two reasons,

1. i'm crap at solving them
2. its completely irrelevant to anything whatsoever, a bit like sudoku

[Admin]

Oh, I think these type of connundrums can be very educational. Once you get the answer (and understand it) it can show you a new way of grasping how things really work compared to how we think they do.

Shall we do the "all ravens are black" one? :D

:eek:

[vbloke]

Mary's father has five daughters Nana, Nene, Nini, Nono. What is the name of the fifth daughter?

[seren]

Mary :D

[seren]

Have you looked at that one about the plane? Not sure if it's critical thinking so much as knowledge of physics, but it was all over the net last year.


A plane is standing on runway that can move like a conveyer belt. 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).


Can the plane take off?

[vbloke]

Yes, because the wheels of the plane are not powered, it's the engines doing the work, so the plane isn't 'stationary' but moving, relative to the ground and the air, so the required amount of lift would still be generated and the plane could take off.

[Mongrel]

I'd say no, for a jet anyway, fairly sure the same would cover prop planes as well.
'All' the engines do is push the plane foward
From an observers point of view the plane is stationary
Without foward motion there's no air being pushed over\under the wings (besides ambient)
Without air motion over the wing surfaces there is no lift
No lift = plane not taking off

EDIT - And looks like you may have opened a can of worms Seren, the PhysOrg forum has 338 pages (http://forum.physorg.com/index.php?showtopic=2417&st=0) devoted to the arguments discussion

[Mojo]

Mary's father has five daughters Nana, Nene, Nini, Nono. What is the name of the fifth daughter?


Is Mary male or female?

[vbloke]

I like the cut of your jib, young fellow-me-lad.

For the purposes of this question, Mary is female.

[Admin]

Have you looked at that one about the plane? Not sure if it's critical thinking so much as knowledge of physics, but it was all over the net last year.


A plane is standing on runway that can move like a conveyer belt. 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).


Can the plane take off?


I would say yes it could. It's down to the method of propulsion. A plane does not rely on its wheels for drive or thrust so the engines would still propell it forward. The plane takes off relative to air speed.

If a plane had a take-off speed of 100MPH and there was a 100MPH wind behind it, then it couldn't take off.

That's my quick answer. I reserve the right to change my mind. ;D

[Hazen]

Without foward motion there's no air being pushed over\under the wings (besides ambient)
Without air motion over the wing surfaces there is no lift
No lift = plane not taking off

Agree with this: airflow over the wings generates lift, hence the reason aircraft take off into wind, to maximise the effect for forward ground speed. Same goes for prop powered

[Admin]

I think the trick in the question is that it leads us to assume that because the belt is running backwards that it prevents the plane from moving forwards. In reality it will only make the plane's wheels spin twice as fast.

If we had Chitty Chitty Bang Bang trying to take off under those conditions it would never move forward as its propulsion is via its wheels. I think that's the picture that we get with this puzzle - the belt preventing forward motion.

A plane, however, does not use its wheels for propulsion. It uses a jet or propellers to force air backwards (and itself forwards) and that force is not cancelled out by the conveyor belt.

An analogy is to have a rocket at one side of the runway which is fired forward. The belt will have no impact on the rocket as it's thrusting through the air above it.

Now, put the rocket on wheels (an ACME rocket :D) and fire it. It will thrust forward in exactly the same way as before and the only effect on the wheels is that they will spin faster than they would have done if the belt weren't moving.

I don't know if that helps visualise it better, but the plane will take off as it thrusts forward in the same way as a rocket, not a car. Trust me, I'm a smart arse. ;D

[Hazen]

Good point. Engines push against air not ground.
Conceded.

Trust me, I've a smart arse.
And a very clever backside it is too.

[Mongrel]

OK - my answer (not that I'm hedging ::)) was based on the following assumptions;

The original question is aimed at laymen, thus imprecise language therefore I read it as "as the plane applies more power the conveyer belt moves faster to give a net ground speed of 0". From a standing start the pull\push from the motor still has to use the wheels and their friction Vs. the ground to achieve foward movement > increased air flow > lift. All the while the lift is less than the weight of the plane it's not going anywhere.*

I think of it as a a glider strapped to a big truck. Get the truck up to 80MPH (not real number) and the glider will have enough lift to take off. Put the same glider and truck combo on the conveyer and accelerate the truck to 80 and the glider pilot is in for a long afternoon...

*And yes, helicopters, harriers, Osprey tilt rotors and the few other VTOL craft are disallowed in this experiment*

[Admin]

It's just a game and I haven't done it yet but I thought I'd post it before I forget: http://www.theconspiracygame.co.uk/conspiracy/

'Tis a conspiracy!!! :o

[seren]

There are various different wordings of that plane puzzle and people do seem to agonise over the language.

I think the consensus is that it would take off (for the reasons John has mentioned), and in fact some small scale experiments have taken place to prove it. But there are some who won't be swayed and say it isn't possible.

Someone must have enough money to build a giant conveyer belt and finally put this one to bed! :)

[Admin]

I think that it's necessary for the wording in these puzzles to be less than perfect otherwise spelling everything out would give it all away.

I'll do this experiment when I take delivery of my first Lear Jet. 8)

[Skepticus Rex]

if the conveyor belt adjusts it's speed to be the same as the plane (not sure how that would work, but for the purposes of the problem lets assume it can do that), then it doesn't matter how the plane is moving, it's speed will be adjusted to.

now, the plane is sitting on the conveyor belt on it's wheels, so as the conveyor moves, the wheels (and therefore plane) are pulled backwards. the engines pushing against the air are pushing forward against this motion, so it stands still.
remember,
"Without foward motion there's no air being pushed over\under the wings (besides ambient)
Without air motion over the wing surfaces there is no lift
No lift = plane not taking off"

so the plane will not take off.


it makes sense if you don't think of the plane as being held stationary, think of it as being pulled backwards and pushed forwards at the same time. this is exactly the same as being held stationary, but you remember why it's held stationary, and so don't get distracted by how the plane moves, which it doesn't matter.

[Admin]

A conveyor belt spinning at, say, 150MPH will not push the plane back at 150MPH it will simply spin its wheels at 150MPH.

The belt will offer no resistance (to all intents and purposes) to the forward motion of the plane so as soon as thrust is applied it will move forward as normal.

The plane will take off as normal but its wheels will be spinning at twice the speed that they would have done had the belt not been turning.

[Skepticus Rex]

but the plane is actually resting on the conveyor belt. the axle can't be frictionless, so the conveyor belt wouldn't spin the wheels backwards, it would move the plane backwards, at the speed it moves.
the plane engine will cause the wheels to roll forward, at whatever speed it can push them (which is the speed the conveyor belt matches), and that will move the plane forward over the belt.
however, the belt is moving backwards, so the two motions cancel out.

[Mongrel]

The way I got my head around it eventually is to think of the fuselage as having a long threaded bar through the middle, due to the way it's fixed at the ends the bar rotates and the plane travels along it's length. This represents the Jet\propellor pulling the craft foward.

Now stick this contraption above a conveyor belt - no matter how fast that conveyor is going the body will still move along the threaded bar.

[Ginger Rogers]

Actually I thought it was going to be more likely to be another boy.

As I recall from genetics at school (oooh that was a while ago now) Boys are Y chromosomes and girls are X. Men have only Y chromos, women have X's and Y's therefore the odds are already higher of a child being a boy.

You see more families with several boys than girls don't you?

some people keep having kids cos they want a girl but keep getting boys. Like my aunt who had 3 boys and victoria beckham.

Please correct me if i'm talking cobblers!

[Admin]

but the plane is actually resting on the conveyor belt. the axle can't be frictionless


Yes there will be a small amount of friction caused by the spinning of the wheels' axles; but this is the only force the forward thrust has to counter.

The key to this puzzle is in understanding that the plane's propulsion is independent of the conveyor belt (i.e. it's not pushed forward by its wheels).

[Skepticus Rex]

The key to this puzzle is in understanding that the plane's propulsion is independent of the conveyor belt (i.e. it's not pushed forward by its wheels).


when a plane is sitting on the ground, it's weight is on the wheels, yes?
when a plane taxis along the ground, it's weight is still on the wheels, but it is pushed forwards by the engine, so it moves along, but at a steady height, so the weight is still the same on the wheels (lift will negate some of the weight, but only at higher speeds).

the conveyor belt moves backwards, and anything on it will move bodily backwards, if no other force is on it. so a plane sitting on it will move entirely backwards (as long as the conveyor belt has enough power to move that much weight), the wheels will not turn.

when the engine is pushing forward that will push on the wheels, making them roll forward. but the surface that the wheels are resting on is moving backwards at the rate that the engine is pushing them forwards (that is the only way of thinking of the conveyor belt matching the speed of the plane, because if the plane was not moving, it would have no speed, and so the conveyor belt would stop).
therefore, the two movements will balance out, i can't find the words to explain exactly what happens to the wheels. i might make a flash animation later to demonstrate.
this means that the body of the plane will remain completely stationary, even with engine on full tilt. just the wheels will rotate on the axle.
and because the plane isn't moving, there won't be any extra air passing under the wings, so there won't be any lift.

[vbloke]

Yes, the plane can take off. The key is that the plane's wheels *freewheel*, they are not driven. the conveyor belt therefore provides NO force to the plane (OK, there's a little friction in the bearings which could provide a couple of pounds force to a normal aeroplane, but that's insignificant compared to the thrust. For a RC plane, the situation should be similar). The prop pushes the plane through the air until it reaches takeoff AIRspeed, which is the same no matter how fast the wheels are going. So if you were inside watching the instruments, you would observe that the wheels are spinning at a GROUNDspeed different than the indicated AIRspeed, but that does not matter, since it is AIRspeed you need in order to take off. (Caps added for emphasis).

[Skepticus Rex]

ok, if you have anything in your house like a trolley of some sort, or even a toy car. anything with wheels that are *freewheel*. put it on a rug (or a piece of paper for the toy car, but you'd need to weigh it down if it's really light). then, pull at the rug, horizontally. i think you will find that rather then the trolley staying still with it's wheels rotating, the whole thing will be pulled in the direction you're pulling.
that is what happens to the plane on the conveyor when it's engines arn't running.
in order for the plane to do what you are claiming it does (the plane staying still, with rotating wheels) there would have to be a negligable amount of friction between the plane's axle(s) and the wheels, and a lot of friction between the wheels and the belt.
you seem to be claiming that there is hardly any friction between the plane and it's wheels. do you know how much a plane weighs? if you know that a plane weighes tonnes, yet still insist on minimum friction, then either you don't understand how friction works, or there has been a breakthrough in making frictionless technology for wheels that i havn't heard of.
since you're on the computer, you're probably at a desk. slide your hand along the top of the desk, it should move pretty easily. now, press your hand down on the desk, put the weight of your torso on it, then try and slide it along the desk, while still pressing down. it's very hard, in fact, if you're pressing as hard as i meant, then you probably can't shift it at all.
the increase in the force down on the table has increased the friction between your hand and the table, meaning you need a lot more sidewards force to move it along.

now, a plane weighs tonnes, and it's entire weight is resting on the wheels. the less surface area you're pressed against, the more friction there is, since the forces are concentrated. yet you seem to think you can neglect friction out of your equations as negligable.

vbloke, you're talking about airspeed while the plane is still on the ground. when something is still on the ground, it's airspeed is the same as it's groundspeed. ie. there is no difference between the speed of the wheels and the speed of the tip of the tail.
when a plane is moving on the ground, it behaves (mechanically) like any ground vehicle, no matter the propulsion. do you think there are great differences between how horsedrawn carts and cars overcome gravity and friction to move? yet one is powered by moving the wheels directly, and the other is pulled along.
a wheelbarrow is pushed along in exactly the same way as a jetplane is while it's on the ground, how do you think that would behave on a conveyor belt?

[Mongrel]

Get the same toy car, the rug, a bit of string and an assisstant.


Control - pull the car at a measured rate across the rug using the bit of string. If there's a way to automate this all the better (Drill bad, old 33RPM record player good ;))

Test - Pull the car at the same rate across the rug, while you're doing this get an assistant to pull the rug in the opposite direction in a controlled fashion.

Does the car still move foward at the same pace?

[Skepticus Rex]

before going onto the full experiment that mongrel suggests, has any of the people who were proposing minimal friction tried what i suggested with the hand on the desk?

[vbloke]

before going onto the full experiment that mongrel suggests, has any of the people who were proposing minimal friction tried what i suggested with the hand on the desk?

Your hand isn't designed to roll, so it's a worthless analogy. Try doing the same thing with a wheeled toy car or similar, I'll bet you it moves fairly easily.

Also, the plane is under power, so the conveyor moving backwards is tracking the forward momentum of the plane. Your previous example of a toy car on a rug is again a worthless analogy because the car is unpowered.

There is always going to be drag because of friction on the wheels, but the whole point is that the plane would be *moving* if there was no conveyor belt underneath it. It doesn't matter that there is drag on the wheels as the conveyor tracks the speed of the plane - when it starts up, it would be moving slowly, overcoming inertia and gradually accelerating.

The fact that a plane weighs tonnes is also irrelevant, as by that logic, planes shouldn't be able to fly anyway as they're too heavy.

The best 9and perhaps only) way to settle this would be to get a treadmill and a RC plane and try it out.

[Skepticus Rex]

the example of the hand on the desk was to demonstrate the principles of friction that seem to be lacking in your understanding of the world.
the example of the trolley/truck on the rug was to show that the conveyor belt moving the plane (when the engines arn't running) wouldn't spin the wheels, it would move the entire plane backwards.

since it would be very unpractical to perform an experiment to test the entire situation, with mongrels idea it would be very hard to match the speeds (the the matching speeds is the crux of the whole thing). performing the simple tests i have suggested would show who is right on the principles of friction and the bearing of weight on that.

the plane weighing tonnes does matter when there is no lift. ie. from when the plane first starts up to when it gets enough speed to generate lift. and since the plane is presumably started up while on the conveyor, and the conveyor is started at the same time, then the weight and the friction of that weight being pressed against the ground is very important to the issue of whether the plane will move or not.

edit: i do hope everyone remembers that speed is relative. when you are talking about speed generating lift, it is the speed relative to the air. if the plane is held pretty much still on the conveyor belt, then there is no speed relative to the air (except the wind).

[vbloke]

I understand friction very well, thank you.

Your tests erst on the assumption that friction has a part to play in the movement of the plane and whilst I agree that it does, the whole scenario replicates exactly what happens thousands of times a day at airports all over the world, in that an aeroplane starts it's engines and moves down a runway under it's own power.

Replacing the runway with a conveyor belt is merely a device for the puzzle - it will behave in the exact same way as a runway, except that an observer who is stood by the side of the conveyor will see the plane remain stationary.

Since the relative idea of watching the plane versus actually being the plane would play out here, then being the plane, under power, engines at full blast, means that relative to the stationary air, you are moving at top speed and therefore lift will be generated and you can take off.

In much the same way, a sufficiently powerful wind striking a stationary plane would cause it to take off.

[Skepticus Rex]

the conveyor belt is not like a runway, in the fact that it is powered in the opposite direction of the planes movement. it isn't forced backwards by the planes movement like a loose belt, it is actually powered backwards. how is that like a runway?

my friction argument isn't against planes moving in general, the force of the engines is more than enough to overcome the friction. i was using that to counter the idea that the conveyor belt would do nothing more than spin the planes wheels backwards, leaving the plane stationary.

[Mongrel]

edit: i do hope everyone remembers that speed is relative. when you are talking about speed generating lift, it is the speed relative to the air. if the plane is held pretty much still on the conveyor belt, then there is no speed relative to the air (except the wind).


This is what got me hung up for a while as well. What you have to remember is that a planes wheels are unpowered, whilst there is pressure down on them they don't propel the plane foward, they're dragged along with from the body.


since it would be very unpractical to perform an experiment to test the entire situation, with mongrels idea it would be very hard to match the speeds (the the matching speeds is the crux of the whole thing). performing the simple tests i have suggested would show who is right on the principles of friction and the bearing of weight on that.

I don't disagree that it would be hard to match the speeds, it's a very crude experiment but it's easy to extropolate up from it. If what you're saying is true then pulling slowly on the string while pulling quickly on the rug will cause the car to go backward....

If you have a suitably high thrust engine on the plane it wouldn't matter if you replaced the wheels with skids - friction can be overcome with lots of power (although it'd still make a edawful racket)

[vbloke]

the conveyor belt is not like a runway, in the fact that it is powered in the opposite direction of the planes movement. it isn't forced backwards by the planes movement like a loose belt, it is actually powered backwards. how is that like a runway?
Perhaps you misunderstood - a conveyor acts exactly like a runway - a piece of flat ground that the plane runs along whilst it's under power. The fact that it's moving is irrelevant. If the conveyor was not moving, the plane would move forward.


my friction argument isn't against planes moving in general, the force of the engines is more than enough to overcome the friction. i was using that to counter the idea that the conveyor belt would do nothing more than spin the planes wheels backwards, leaving the plane stationary.

Then why bring it up? It's not relevant.

[Skepticus Rex]

they don't propel the plane foward, they're dragged along with from the body.

i know they don't propel the plane forward. however they arn't dragged behind the plane, they are pushed by the plane, which makes a big difference.


If what you're saying is true then pulling slowly on the string while pulling quickly on the rug will cause the car to go backward....
no, because the car is actually attached to the string. if the car was powered forward by a motor, but the conveyor was faster, then it would move backward relative to the surrounds, yes.


- friction can be overcome with lots of power


not if there is equal power in the other direction.

and again, the friction argument was just used to apply to what would happen with the engine turned off. i agree that the engines power can overcome the friction on the wheels. what i was saying is that the conveyor wouldn't be able to overcome the friction between the wheels and the plane enough to move them independantly of the plane body.

edit, vbloke posted while i typed:
"The fact that it's moving is irrelevant. If the conveyor was not moving, the plane would move forward."
that doesn't make much sense. if the conveyor wasn't moving, then the plane would move, i agree with that. but that has nothing to do with the fact that its moving, which it is, as part of the scenario.

i brought up the thing about the friction on the wheels because people were suggesting that if the conveyor was moving while the engine of the plane was off, the plane would stay still.

[Mongrel]

no, because the car is actually attached to the string. if the car was powered forward by a motor, but the conveyor was faster, then it would move backward relative to the surrounds, yes.


Well the screw thread experiment (http://www.ukskeptics.com/forum/index.php/topic,165.msg5491.html#msg5491)was a better analogy than the string, but the string is easier to replicate but still a valid. For it to be a valid analogy you need the wheels to be disassociated from the propulsion.

Here is a very nice picture of a very nice plane, the Lockheed F-104 Starfighter;http://i16.photobucket.com/albums/b24/Mongrel01/F-104_2-714465.jpg
Notice the thrust, is applied along the long axis of the plane. In the simplified experiment you could replace the string and pulling with a rod and pushing, the effect will be the same

[Skepticus Rex]

the string wouldn't be able to accurately show whether the car/whatever would move backwards, because it is literally attached, thereby preventing the car from moving backwards, unless the thing on the other end of the string moves.

[Admin]

Or imagine one of those missiles being fired horizontally over the conveyor belt - it would fly straight over it no matter what the belt was doing.

Now think of the missile in the same set up only it had wheels that were touching the belt. It would fly straight over the belt in exactly the same manner and the only effect the belt would have is to spin the wheels faster than if it wasn't moving.

Planes' propulsion is like that of a missile. The thrust of the jet will propel the plane forward with respect to the air and the belt will have a negligible effect on its progress forwards. All the conveyor belt will do is make the wheels spin twice as fast as they otherwise would have done.

[Skepticus Rex]

it would only be the same if the missile was fired while its wheels were touching the conveyor belt, and if the speed of the belt could still be matched with the missile. also, the missile would have to be self-propelled, and launched by it's own power.

i'm going to review the scenario of the puzzle now, because we keep getting sidetracked (mainly my fault i'm afraid).

a plane, self-propelled, sitting on wheels is placed on a conveyor belt.
this belt has the ability to move in the opposite direction the plane moves, matching the force exactly (apart from the direction, obviously).
they are both started at the exact same time, so the planes engine pushes it forwards on it's wheels (since it hasn't left the ground yet), while the conveyor belt moves the wheels backwards.

that is the actual situation, what actually happens at the start.
if anyone disagrees with that then we're working on difference scenarios, and thats why we can't agree.

i'm going to make an animation to show what i think happens, since i can't explain it very well in words. it will take a while, so i shall put up a link later.

[Admin]

I know what you mean skepticus as I went though the same reasoning myself. It's only when you realise that the plane is self-propelled and it applies no force through the conveyor belt (it's thrusting via the exhaust from its jet) that you work out that the belt would not prevent the plane moving forward.

It was the missile analogy that did it for me. Fire it horizontally across the belt and the belt has no effect (obviously) but then think of the same missile tied to a tea trolley and fired. It would still shoot forward as its propulsion is via the exhaust gasses behind it.

[Skepticus Rex]

ah! i've suddenly realised what i was doing wrong.

the way i went through what was happening was this:
1st premise: when the plane is not powered, the conveyor will move the whole thing backward (i still think that's true, although some people seemed to disagree).
2nd premise: when the engine is on, it will push the wheels forwards over the belt.

both of these are true - on their own.
my mistake was to put the two together (hence the cancelling out of forces). i thought of the plane moving backward as a given, which it isn't unless the belt is exerting an attractive force on the wheels.
when the plane isn't moving, gravity on the plane has the same affect as a force attracting the wheels (well, the entire plane) to the belt. that is why it will move backward with the belt, but when the force of the engine has overcome the friction with the belt, then the plane, and therefore the force attracting the wheels to the belt, is moved forwards.
i was thinking of the wheels being attracted to the belt all the time, as something seperate from the gravity. if there was such a force, then the plane would stay still. but there isn't...

i apologise profusely for dragging this thing out, i got really mixed up there.
yes, the plane would be able to take off, because it will move against the belt just like a runway (although the force of the belts movement will not have no affect, it would increase the friction between the wheels and the belt when the plane was trying to move, so more energy would be needed to overcome it.), which is exactly what you were trying to tell me vbloke, i'm sorry.

[median]

Now if you had a plane with a massive frictional adhesion to the conveyor (huge wheels) and a conveyor belt with a high gearing then this might be a different matter ???

But let's not go there eh O0

[wollery]

1st premise: when the plane is not powered, the conveyor will move the whole thing backward (i still think that's true, although some people seemed to disagree).Not wishing to be overly pedantic (yeah right, ed.), but since the wheels are free spinning the plane might not move backwards at the same speed as the conveyer belt, unless the belt was accelerated quite slowly.

Inertia's a bitch! ;)

[Skepticus Rex]

Not wishing to be overly pedantic (yeah right, ed.), but since the wheels are free spinning the plane might not move backwards at the same speed as the conveyer belt, unless the belt was accelerated quite slowly.

Inertia's a bitch! ;)


the wheels arn't free spinning when the planes engine isn't running, because the entire weight of the plane is resting on them (unless it's a plane where the tail touches the ground when it's stationary, in which case the conveyor belt would move it whether the wheels are free spinning or not).

[wollery]

the wheels arn't free spinning when the planes engine isn't running, because the entire weight of the plane is resting on them (unless it's a plane where the tail touches the ground when it's stationary, in which case the conveyor belt would move it whether the wheels are free spinning or not).
If the wheels aren't free spinning then the plane would have real difficulty taking off!

But to answer your point properly, I did say that the plane would move backwards at the same speed as the conveyor if it was accelerated slowly!

[vbloke]

Mythbusters had a go at the plane on a conveyor belt problem.

http://mythbustersresults.com/episode97