Time for a sum-up

[cultureofdoubt]

So, I'm a bit surprised the plane brought out all that discussion when the freaky backwards-in-time antics of photons didn't (although that's perhaps a bit more heavy going to decipher unless you're familiar with Young's slits).

Comments

[azureskies]

Depending on the version of the question you read the conveyor belt moves back at either the speed the plane moves forwards, or such that the plane remains motionless.

I genuinely don't understand the difference here. If the conveyor belt is moving at the speed that the plane WOULD BE moving at on fixed ground, then surely the two relative speeds cancel each other out and the plane is motionless?

[cultureofdoubt]

No, in the first case the wheels can do whatever they like without affecting the motion of the plane, so the plane can go forwards while the belt goes backwards, and the wheels whizz away as necessary.

In the second case the belt moves back fast enough that whatever friction is in the wheel system gives a force to the plane to keep it in the same position.

[beingjdc]

The reason I didn't buy this concept is that for the plane to take off, the relative motion of the plane to the ground on which it stands is faster than the relative motion of the belt to the ground on which it stands, so I would argue that the plane is in fact not moving forwards at the same speed as the conveyor belt is moving backwards.

[cultureofdoubt]

With frictionless wheels the belt is free to move as it pleases though.

[beingjdc]

That it is free to move as it pleases does not detract from the fact that if the plane is moving forward, then whatever speed the belt is going at, the plane has higher speed relative to its ground than the belt does.

[cultureofdoubt]

Oh, relative to *its* ground, gotcha now. But I don't think that's what the question intends - both should be relative to the non-moving ground.

[beingjdc]

Well, if they're both moving at the same speed relative to the ground, then you've begged the question. The plane will take off if the conveyor belt is moving at the speed at which planes take off.

[cultureofdoubt]

Um, you realise the conveyor belt moves backwards?

[beingjdc]

Yes.

And the plane moves forward.

At the same speed at the conveyor belt.

Relative to the ground.

That's my point.

[cultureofdoubt]

the plane has higher speed relative to its ground than the belt does.
then
And the plane moves forward.

At the same speed at the conveyor belt.

You've lost me I'm afraid

[beingjdc]

From your original post

It moves backwards at the same speed the plane moves forwards

Now from your current post

both should be relative to the non-moving ground

So the speed of the plane and the speed of the belt, relative to the ground, are the same.

So if the belt is going backwards at the speed at which a plane takes of, the plane will necessarily take off.

The faster the belt goes to try and stop this, the faster the plane, under the terms of your thought experiment, must necessarily go itself.

[cultureofdoubt]

Ah yes, so starting from rest if the plane tried to move forward the belt would move back and the plane would stay in the same spot. And the belt would stop but then the plane would... all a bit confusing.

Think it's a slightly ill-posed problem basically.

[beingjdc]

Ah yes, so starting from rest if the plane tried to move forward the belt would move back and the plane would stay in the same spot.

No, that's your high-friction scenario. I'm not talking physics here, I'm just talking logic. If the plane is moving forwards relative to the ground at the same speed as the belt is moving backwards, then the only way the belt can stop the plane taking off is to slow down. Not because any force of nature will hold it to the ground, but because if the belt operator reduces it to a gentle walking speed, that is then as fast as the plane is allowed to move forwards, under the terms of the conundrum.

[cultureofdoubt]

What an excellent point. Although I still don't quite see how that fits with earlier comments, it has a delightfully perverse (because it is flawless, and yet still seems it shouldn't work) logic.

I think the explanation is there is no belt operator. The plane does as it pleases, but the belt is subject to the whims of the pilot.

[beingjdc]

Well yes, in that case the plane is just taking off normally. The conveyor belt is a red herring, if the plane can just speed up and slow down relative to the ground. The conveyor belt can't slow it down, or they'd be moving at different speeds again.

[cultureofdoubt]

Well quite. Although the trick would be for the belt never to let it start moving rather than to slow it down after the fact (there's a bit of slack in there for response times too).