# Airplane conveyor belt riddle

Discussion in 'Teacher Time Out' started by Caesar753, Jan 24, 2008.

1. ### nancy svRookie

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No... but you know what I mean... How in the heck do I explain this? The plane starts moving forward, right? which means the wheels start moving forward, right? But then the belt moves backwards, so the wheels have to roll backwards too, but the plane is moving forward because it is pushing on the air. As I read it, the belt moves in such a way as to counter the rotation of the wheels. So - for every rotation of the wheel, the belt moves the exact circumference of the wheel. If however, the wheel slides on the belt, the belt does not notice that - in my mind (which I will admit is sometimes, well.... I mean - I am taking off with my kids to ride my bike 20,000 miles after all...) the belt matches the ROTATION of the wheel, not the MOTION of the wheel!!

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Feb 1, 2008

What?

3. ### eduk8rEnthusiast

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okay, no, nobody said the plane started moving and then the conveyor belt kicks in. The plane is stationary, the wheels are touching the belt, and the conveyor belt is moving at the same speed as the engine, unless I'm reading it wrong which is a definite possibility. How can the wheels move counter to the direction of the belt, which is making the wheels spin? If the belt is moving "backward" the wheels are moving in the same direction (though not "backward"), it's not like us standing on an escalator, the wheels are spinning like when we drive on the road.

4. ### TeacherGroupieModerator

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Okay, let me try it like this...

Lay an ordinary kitchen towel on your table. That's going to be the conveyor belt. Set a cylindrical glass on its side on the towel so the open end faces toward you; hold a fork or knife by the handle in your left hand and insert it into the class so it looks like an axle. Now grasp the towel with your right hand and pull it out from under the glass, using the fork or knife to keep the glass from getting away. You should find that the towel slides out to your right (duh) - and, as seen from above, the glass spins in the opposite direction (that is, if it were rolling free, it would roll to your left).

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Feb 1, 2008

Exactly.

6. ### nancy svRookie

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Feb 1, 2008

My understanding is that the conveyor belt moves at the same speed as the WHEELS, not the engine.

7. ### DevedanderGuest

Feb 1, 2008

Thought I would chime in on this one...

I think we can all agree a plane will never take off if it cannot move forward relative to the air around it. The air moving past the wings is what creates lift.

I think we can all agree also to discount things like wind blowing over the wings due to the proper alone and vertical take off planes etc... for simplicity the plane has to move forward to take off.

This question is very interesting because it exists in several forms which differe slightly, note the original question in this post and then compare it to this question:

"A plane is standing on a runway that can move (some sort of band conveyer). 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 the opposite direction). Can the plane take off?"

Do you see the difference?

The difference is the plane I quoted above will take off, while the plane in this post will not.

Why?

We have already agreed the plane has to move forward to take off right? I hope we can all agree that the relative point we use to guage forward movement is the earth.

Well note the wording in this question which states the belt "exactly match the speed of the wheels"

Now we have to ask ourselves, when could the belt match the speed of the wheels?

Don't think about how much drag the wheels inpart and what not, just ask, when can the belt match the speed of the wheels?

Well for one when nothing is happening, the belt is at 0mph and the wheels are not rotating. Clearly in this scenario there is not going to be any takeoff... nothing is happening.

When else can it match the speed of the wheels?

Only when the plane is not moving relative to the earth.

Here is the logic behind that:

If the belt is moving backwards at 10mph, what circumstance allows the wheels to be rolling forward at exactly 10mph? The plane must be stationary.

It doesn't matter what is leading to this, how hard propellers are pushing or what ever else. If the plane was making forward movement, the wheels would be spinning 10mph + whatever forward movement the plane was making.

Think about it... If you hold a plane stationary on a belt, the wheels will rotate at the speed of the belt... if the plane is making headway against the belt, as long as the wheels are in contact the wheels MUST move faster than the belt... it's simple math...

And that's why the plane will never take off... because as long as the wheels are rotating the same speed as the belt, the plane must not be making headway. If the plane makes no headway, it will not take off.

It doesn't matter what causes the plane to move or how much friction comes from where, the proof is in the wheels.

Think of it in the car on a belt manner... yes that's differnt because the drive force comes from the wheels, but the relative wheel speed to belt speed issue remains. If the belt moves 75 mphs backwards and the wheels move 75 mphs forwards the car stays still. In order to actually make headway, the wheels must move faster than the belt. What causes this in a car is different, but the fact remains that if the wheels and belt have the same speed, the car is not moving relative to the ground (assuming the belt machanism is attached to the ground).

Now in my quoted puzzle above you will note the slight difference in that the belt matches the speed of the plane...

This will allow the plane to take off because right in the problem it says "tracks the planes speed". If the plane has speed, that is the only thing there needs to be sufficient amounts of to take off.

Let's say the plane must go 100mph to take off... well if the plane is going 100mph it will take off. It doesn't matter how fast the belt is going under it.

But wait you say, if the belt goes 100mph backwards it will slow the plane down right?

Ah but no... read the problem... the belt matches the planes speed... so by definition even if the belt puts massive drag on the plane, the wording dictates the plane still is going at the same speed.

So in effect you could remove the wheels entirely from the plane and run the belt at 100mph... you know what? Despite sparks and tearing of metal, the problem dictates the plane is moving forward at a matching speed of 100mph. Since that's what it takes to lift off, the plane will lift off.

So you see, these problems are either incredibly tricky, or just have a huge loophole... the issue is that the wording of the problem creates a system that in and of itself decides what the plane does and does not do...

If the belt speed matches the wheel speed, the object cannot be moving... that's just math.

If I say the belt is moving backwards at x mph and the plane is moving forwards at x mph there is no question in what is happening... you can leave the belt out entirely because it says right there "the plane is moving forward at x mph" who cares what the belt is doing or what effect it has... the plane is moving at x mph and if that's fast enough to take off, that's all that counts.

People think that you must factor the drag of the belt into the speed of the plane, you don't... the plane is traveling forward at the same speed the belt is travelling backwards... who cares what it takes to achieve this, the problem says it happens and that's all that counts.

8. ### TeacherGroupieModerator

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nancy sv, do I get a sticker, huh, huh??

9. ### eduk8rEnthusiast

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Feb 1, 2008

Thank you, Deveander, now that makes sense.

TG, sorry, but that analogy just doesn't work for me. First of all, your spoke or axle isn't attached to your wheel in that example, it has no impact on anything. Second, the glass rolls off because it's pushed off in the opposite direction by the motion of the towel. And third, what about the table cloth trick where you pull the tablecloth off the table but everything stays in it's place on the table because it was done so there was no friction. Anyway, have fun arguing, I've got to go.

10. ### TeacherGroupieModerator

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'k8r, it doesn't matter whether there are spokes or not - in fact, an earlier version of my post directed you to use a rolling pin (of the ball-bearing variety) rather than the glass, but it doesn't make a difference.

Try it this way: lay the glass on the towel and give the right-hand edge of the towel a tug. The glass will roll toward the left.

11. ### AmersCohort

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Feb 1, 2008

Wow. I had never heard of this myth until I saw it on Mythbusters the other day. I had no idea people were debating it here too! I thought it was confusing then, and I think it's confusing now! Everytime I think I understand it, it gets explained a different way, and I get confused all over again!! Physics is just not my thing. Plus, I don't know very much about how airplanes work in the first place.

12. ### DaveFCompanion

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As someone who has owned an aviation business and an airplane owner for many years, I know about these things. Forget about airspeed, ground speed and all of that stuff. When dealing with anything that flies, there is a simple formula that must be understood:
LIFT=\$\$\$\$\$

Airplanes don't fly without money! No money= Drag

Too much drag, no fly! :lol:

13. ### eduk8rEnthusiast

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What you're saying works only if you take the plane away from the wheels. The glass moves because it isn't attached to anything, much less something big and heavy and there's nothing to keep it from rolling. With a plane sitting on the wheels, the thing isn't going to move forward it will stay in the same place. And since Irish Dave and Deveander can actually explain this question in a matter that makes sense using physics and mathematics, that tells me they know what they are talking about. I'll take their version.

14. ### eduk8rEnthusiast

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Very funny! :lol::lol:

15. ### nancy svRookie

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Yes darling - you can even have three stickers!!

16. ### smalltowngalMultitudinous

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Feb 1, 2008

Dave, I think that is the best explanation I've heard so far! :lol:

17. ### IrishdaveEnthusiast

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Feb 2, 2008

Good points
The Plane's lack of motion is in relationship to the earth
But the plane is moving in relationship to the belt.
That is what is causing the confusion.

I believe if I could remember my "Vector" Math I could show you the equation for it.

18. ### IrishdaveEnthusiast

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Feb 2, 2008

"Physics is just not my thing." is why people are scratching their heads
:lol::lol:

19. ### DevedanderGuest

Feb 2, 2008

Sure it is... but the belt is not moving in relation to the belt...

The problem is that you can lable whatever you want as the reference point for what you consider movement relative to, but you can't change reference points midway, so it's either the earth or the belt, but not both or one at a time.

So either the plane is not moving in relationship to the earth and the belt is, or the plane is moving in relationship to the belt, but the belt is not...

If you want to use the earth, my argument holds, if you use the belt as the reference point, then the belt will never be moving (in realation to itself) and so it can never satisfy the argument that it is moving at the same speed as the plane.

That is one place where people seem to get confused... you can't say one is moving in relation to one thing, and the other is moving in relation to something else in the same argument.

20. ### DevedanderGuest

Feb 2, 2008

Thanks!!

I have been through this plane and conveyor belt problem litterally dozens of times in different places... just tonight it hit me that this line of logic settles all the arguments!

21. ### BrentGuest

Feb 10, 2008

The plane doesn't actually have a relationship with the conveyor belt, since the belt exerts no force on the plane. If there's no force being exerted on the plane, then it won't make any difference whether the conveyor belt is stationary, or matching the plane's speed, or matching the wheel's speed, or going 200mph - it won't put any pressure on the plane.

Actually, take force two off. Not necessary.

Now, think about it again. If the belt is matching the wheel's speed, how much force is the belt putting on the plane to keep it from moving? Or even better, if the belt is not moving, how much force are the wheels putting on the belt to make it move?

hxxp:\/img168.imageshack.us/img168/1838/screenshotmy9.png
(forgive the drawing, was using an online editor)
1) is the action (force) exerted by the plane on the air
2) is the equal and opposite reaction (force) exerted by the plane on the air

As you can see, acceleration is not provided by the ground or wheels, but by the engine's action on the air. If acceleration was actually provided by the ground, then planes would be automobiles.

Since the engine is doing all the work, what purpose do the wheels have? Why, to help the plane move freely across the ground of course. And which works better for helping the plane move: wheels that turn very easily, or wheels that are very hard to turn? Obviously, easy to turn wheels are desirable for helping the plane move freely across the ground.

So if the wheels turn very easily, what effect would turning the wheels have on the plane's speed?

Here's another angle: The belt is, in effect, doubling the speed of the wheels (the plane has to move to give the wheels speed; the wheels will go at the same speed as the plane; the belt will go the same speed as the wheel - the wheel is now going twice as fast). Given this logic, will replacing the wheels on a plane with ones half the size (which would rotate twice as fast) cause a plane not to take off?

To put it simply, unless the plane is stationary, there is no way for the belt to match the speed of the wheels. If the plane is stationary, then the belt has no need to turn. If the plane moves forward at 5mph, then the wheels are rotating at 5mph. If the belt tries to move the same speed, then the wheel will go 10mph - since the plane is already moving, the speed of the belt is added to the speed of the wheel/plane. Moving the belt rotates the wheels in the direction they are already moving, which makes them rotate faster.

22. ### DevedanderGuest

Feb 11, 2008

Brent,

If you look at

hxxp://forums.atozteacherstuff.com/showpost.php?p=556721&postcount=87

(I have too few posts to post a link so just replace the hxxp with http or look at post 87 in this tread)

I think you will see I arrived at much the same conclusion. Many people get caught up in whether a belt could effect the wheels and how and where drag comes from and how much there is...

But quite simply the problem states that the belt MUST match the wheel speed and there is no way for it to do so if the plane is making any forward headway. The physics can be left entirely out of it.

This could either be unintentional by whoever made up the problem (thinking the same way many others do and not considering that the plane cannot be moving forward while the wheels and belt speed match) or it could be the clever hidden answer that's right under your nose type question.

Either way it's nice to see someone else arriving at the same answer I did!

23. ### IrishdaveEnthusiast

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Feb 11, 2008

Devedander & Brent

Does the plane take off?

24. ### GyurioGuest

Sep 27, 2008

one riddle two riddles

--------------------------------------------------------------------------------
Right now teachers at my school are talking about the famous airplane on the conveyor belt riddle:

"Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway. The conveyer belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?"
(*** THIS is the first riddle)

I think that there's no way the plane will take off. Planes take off due to lift, which is created by air moving over the wings. If the plane is stationary on the conveyor belt, there's no air moving over the wings and no lift.
(**** THIS is the second riddle)

What do you guys think?

------------------------------------------------------------------

Well in my oppinion the answers are
1 YES and with ease - the added wheels-rolling-on-the-ground-resistance, at double speed then normal, is neglectable
2 It depends on the PROPPELLER(s) to blow enough air under the wings for liftoff - thus of their number and position
Of course we suppose enough power is supplied by the engine(s)
That is more probable with a small scale model - their power/weight ratio is huge
Atest could be something like this:
1 Attach the model by its tail to an articulated light beam fixed to the ground. It will prevent it to advance.
2 Put some scales uner the model
3 Turn its engine at full power.
4 See what the scales readding are

In fact I would have done it myself if I had the plane model, maybe someone can help ?

PS I Hope my english didn't prevent me to present my point of view