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Seager 2006-10-27 02:26 AM

brain teaser (plane on a conveyor belt)
 
This has been all over the internet and a college msg board I frequent. Several engineers have gotten this wrong it it bothers me. I want to see if the unicyclist community eats this alive as I hope they do.

Yes, I do have the correct answer.

A plane is standing on runway that can move (some sort of conveyor belt.) The plane moves in one direction, while the conveyor moves in the opposite direction. This conveyor has a control system that instantly tracks the plane speed and tunes the speed of the conveyor to be exactly the same (but in opposite direction).

The question is:

Will the plane take off or not? ?

Dave Coleman 2006-10-27 03:06 AM

Ooh, i just read up on this and, my bad - yes the plane can take off. Apparently its all about the air moved by the jet engines, not the movement of the wheels on the conveyor belt.

http://www.kottke.org/06/02/plane-conveyor-belt

Goats_On_Unicycles 2006-10-27 03:14 AM

I thought about this for a while. My thinking is that the plane can take off.

sugarloafur 2006-10-27 03:15 AM

Quote:

Originally Posted by Dave Coleman
Ooh, i just read up on this and, my bad - yes the plane can take off. Apparently its all about the air moved by the jet engines, not the movement of the wheels on the conveyor belt.

http://www.kottke.org/06/02/plane-conveyor-belt

Jet engines don't make air move over the wing, they simply move air to move the plane. If the plane isn't moving (relative to non-conveyor belt), then neither is the air, thus no lift.

There are many ways of thinking about this problem, including frictionless wheels, and in terms of Force and in terms of Velocity.

If you really want to get confused... read this. Anyway, I've concluded that since there are different ways of thinking about this problem, there are different solutions.

Dave Coleman 2006-10-27 03:16 AM

My first speculation was that if the plane isnt moving forward, how can it use the energy from the air to actually lift off the ground?? But i guess the real answer makes sense...

squirrel 2006-10-27 03:21 AM

pretty simple problem since the wheels on a plane merely hold it up....

Now, if you put a huge fan behind the plane, and had it blow air forward as fast as the plane was moving, then it could probably not take off (although doing this in real life would be difficult)

john_childs 2006-10-27 03:28 AM

They should use this magical conveyor belt to land the plane. Have the conveyor moving backwards at the same speed as the plane is moving forwards. You'd be able to land on the spot with a very short runway.

Brilliant!

Oh, wait? That wouldn't actually work now would it. ;)

UniBrier 2006-10-27 03:28 AM

I think the wheels will be spinning twice as fast as normal at the point of take off.

sugarloafur 2006-10-27 03:38 AM

It will liftoff, all depending on how you think about the problem.

My sequence of thoughts:
-Tires on plane are meant to be as low of friction as possible
-If plane was held in place and belt moved beneath it, tires would spin
-If plane was no longer held in place and belt moved, tires would spin (plan might go backwards a little too ~ friction)
-Now, stop the belt, and add thrust.
-From above, plane isn't affected by belt speed (ideally)
-Add thrust to engines, plane beings to move forward faster and faster until enough lift is created for liftoff...

That's my most recent thought process... there are flaws, such as the concept of frictionless tires.

monkeyman 2006-10-27 03:45 AM

Hasn't this thread already been done? Or am I deja vu-ing?

darchibald 2006-10-27 03:53 AM

You aren't deja-vuing it has been done, and it was a long one. The plane won't take off. The only reason a plane takes off is air moves over its wings fast enough to lift it. If the plane is not moving - in comparison to the ground - no air is moving over the wings so it doesn't lift. It does't matter how fast the wheels/treadmill go.

Now what would happen if you got a giant fan and put it in front of the plane and blew wind at it?

David

john_childs 2006-10-27 03:56 AM

Quote:

Originally Posted by darchibald
You aren't deja-vuing it has been done, and it was a long one. The plane won't take off. The only reason a plane takes off is air moves over its wings fast enough to lift it. If the plane is not moving - in comparison to the ground - no air is moving over the wings so it doesn't lift. It does't matter how fast the wheels/treadmill go.

Now what would happen if you got a giant fan and put it in front of the plane and blew wind at it?

David

Where does it say the plane is not moving in comparison to the ground?

sugarloafur 2006-10-27 03:57 AM

Quote:

Originally Posted by darchibald
You aren't deja-vuing it has been done, and it was a long one. The plane won't take off. The only reason a plane takes off is air moves over its wings fast enough to lift it. If the plane is not moving - in comparison to the ground - no air is moving over the wings so it doesn't lift. It does't matter how fast the wheels/treadmill go.

Now what would happen if you got a giant fan and put it in front of the plane and blew wind at it?

David

....
Quote:

Originally Posted by john_childs
They should use this magical conveyor belt to land the plane. Have the conveyor moving backwards at the same speed as the plane is moving forwards. You'd be able to land on the spot with a very short runway.

Brilliant!

Oh, wait? That wouldn't actually work now would it.

I'm not going to post in this thread again.

harper 2006-10-27 04:11 AM

Quote:

Originally Posted by Seager
Yes, I do have the correct answer.

How do we know that you have the correct answer?

Speed with respect to what?

Seager 2006-10-27 05:00 AM

Quote:

Originally Posted by harper
How do we know that you have the correct answer?

If you google this there are exhaustive proofs as to what the correct answer is.

To clarify, the question is CAN the plane take off. This assumes a long enough conveyor belt/runway. This also assumes they have full use of their engines.


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