Plane

[RichA]

Moving backwards, I'm not sure what it counteracts. The treadmill could be programmed to go backwards at the same speed as the plane goes forwards. Plane takes off, wheels are moving double fast.

But the OP said counteracting the rotation of the wheels, so I doubt that meant speeding them up. This is the bit I initially paid no real attention to. I jumped to the conclusion the belt would be moving backwards, and regardless of its programming the plane would always take off. But, for everything in the OP to match up, the belt should move forwards with plane. Plane still takes off, but wheels don't rotate.

Assuming everything being stationary at the beginning and the belt perfectly counteracting the rotation of the wheels, I'm stuck in a loop trying to figure out whether the wheels and the belt actually move at all. Surely one has to trigger the other, but if they're perfectly matched then there can be no trigger.

 

[Deleted member 36735]

Moving backwards, I'm not sure what it counteracts. The treadmill could be programmed to go backwards at the same speed as the plane goes forwards. Plane takes off, wheels are moving double fast.

But the OP said counteracting the rotation of the wheels, so I doubt that meant speeding them up. This is the bit I initially paid no real attention to. I jumped to the conclusion the belt would be moving backwards, and regardless of its programming the plane would always take off. But, for everything to match up, the belt should move forwards with plane. Plane still takes off, but wheels don't rotate.

Nobody is actually saying there's is speeding up of the wheels by the conveyor.
Your scenario of the belt moving forward to stop the wheels rotating can be "counteracting", I agree. If the belt moves forward and continues to speed up to counteract what the speed of the wheels would be, of course the plane would reach take off speed. (Although the treadmill in the puzzle isn't big enough).

But for those of us who think the belt goes backwards, none of us are saying that the belt speeds the wheels up. What we are saying is, as the plane is thrust forward, the wheels obviously turn but the belt "counteracts" (negates/equalises) the rolling of the wheels and thus the plane doesn't move forward (like the pushbike example). We know that the engines push the plane forward, not the wheels, but if the belt is always counteracting the forward rolling, then the only way the plane can move forward is if it is skidding or not actually in contact with the belt. As it can't just levitate, we are arguing that at the starting point of being on the ground, it has to initially roll forward to gain speed, but this can't be done if the belt always matches, ie "counteracts" the speed immediately.

 

[Swango1980]

Assuming everything being stationary at the beginning and the belt perfectly counteracting the rotation of the wheels, I'm stuck in a loop trying to figure out whether the wheels and the belt actually move at all. Surely one has to trigger the other, but if they're perfectly matched then there can be no trigger.

Both being perfectly still fits, absolutely. As long as the pilot doesn't engage the engine, plane can sit there still and nothing happens. It doesn't take off.

If there is movement, the wheels have to trigger the belt. Because the programmer has designed the belt to react the wheels. So, to move the wheels the plane needs to move forward, at which point the belt can react. The only way for the belt to counteract the rotation of the wheels is to move forwards with the plane. The wheels, therefore, do not rotate.

You could try and look at any given point in time. Imagine plane was going 100mph down a runway, thus wheels where going 100mph backwards (where they contact the belt). If belt was to suddenly react at that point in time, it would need to move 100mph forwards to counteract the wheels rotation. But, given we are assuming the plane is on the belt to begin with, then the belt will simply always react to the wheels trying to move, to ensure they never rotate at all

 

[Swango1980]

Nobody is actually saying there's is speeding up of the wheels by the conveyor.
Your scenario of the belt moving forward to stop the wheels rotating can be "counteracting", I agree. If the belt moves forward and continues to speed up to counteract what the speed of the wheels would be, of course the plane would reach take off speed. (Although the treadmill in the puzzle isn't big enough).

But for those of us who think the belt goes backwards, none of us are saying that the belt speeds the wheels up. What we are saying is, as the plane is thrust forward, the wheels obviously turn but the belt "counteracts" (negates/equalises) the rolling of the wheels and thus the plane doesn't move forward (like the pushbike example). We know that the engines push the plane forward, not the wheels, but if the belt is always counteracting the forward rolling, then the only way the plane can move forward is if it is skidding or not actually in contact with the belt. As it can't just levitate, we are arguing that at the starting point of being on the ground, it has to initially roll forward to gain speed, but this can't be done if the belt always matches, ie "counteracts" the speed immediately.

This is where there is the fundamental breakdown in science, and I don't know how to provide any more clarity than has already been provided?

A conveyor belt applies no force to a plane that can stop it moving forward relative to the air. The jet engines thrust the air around the plane, so it moves forward relative to the air. It doesn't matter what a programmer designs the conveyor belt to do. Backwards, forwards, half speed, double speed, etc. None of that can stop the plane moving forwards through air.

Put the plane in a wind tunnel, however, that would be a different story.

 

[Voyager EMH]

Nobody is actually saying there's is speeding up of the wheels by the conveyor.
Your scenario of the belt moving forward to stop the wheels rotating can be "counteracting", I agree. If the belt moves forward and continues to speed up to counteract what the speed of the wheels would be, of course the plane would reach take off speed. (Although the treadmill in the puzzle isn't big enough).

But for those of us who think the belt goes backwards, none of us are saying that the belt speeds the wheels up. What we are saying is, as the plane is thrust forward, the wheels obviously turn but the belt "counteracts" (negates/equalises) the rolling of the wheels and thus the plane doesn't move forward (like the pushbike example). We know that the engines push the plane forward, not the wheels, but if the belt is always counteracting the forward rolling, then the only way the plane can move forward is if it is skidding or not actually in contact with the belt. As it can't just levitate, we are arguing that at the starting point of being on the ground, it has to initially roll forward to gain speed, but this can't be done if the belt always matches, ie "counteracts" the speed immediately.

belt is always counteracting the forward rolling
does not equal
The conveyor belt is programmed to match the speed of plane's wheels in the opposite direction, perfectly counteracting their rotation.

There is nothing about counteracting the forward rolling. What is mentioned is rotation, not rolling.
If there is any rolling the plane will takeoff as normal.

If the conveyor belt is moving then the plane's wheels are rotating in a perfectly matched way in the opposite direction.

Counteracting their rotation
If the belt is moving left to right, then the top of the wheels are moving right to left - perfectly matched in the opposite direction. This is the only interpretation of counteracting.
Plane will takeoff.

If the wheels are not moving - then the belt is not moving - nothing to observe - nothing to discuss.

Counteracting their rotation - this wording can not be used to justify an impossibility that becomes "a thing that actually does happen". The impossibility does not happen.

 

[Deleted member 36735]

This is where there is the fundamental breakdown in science, and I don't know how to provide any more clarity than has already been provided?

A conveyor belt applies no force to a plane that can stop it moving forward relative to the air. The jet engines thrust the air around the plane, so it moves forward relative to the air. It doesn't matter what a programmer designs the conveyor belt to do. Backwards, forwards, half speed, double speed, etc. None of that can stop the plane moving forwards through air.

The extremely heavy plane starts stationary, sitting on the ground (conveyor)
How does it start to move forward before it takes off without it's wheels rolling? It can't. The belt counteracts this.

 

[Deleted member 36735]

The only way for the belt to counteract the rotation of the wheels is to move forwards with the plane. The wheels, therefore, do not rotate.

I'm sorry but on this matter of the interpretation of the meaning of the word "counteracts" you are incorrect.

As I mentioned before, because I didn't know the correct meaning of the word, I looked it up and I've posted the screenshots of the definitions and synonyms.

Yes, it can mean that the belt stops the wheels turning.

But, and this is what you are denying, it can also mean that the belt negates the effect of the wheels moving.

Stopping the wheels moving and negating the effect of the wheels moving are 2 different things, but according to the definitions, the word "counteract" can mean both.

 

[Swango1980]

The extremely heavy plane starts stationary, sitting on the ground (conveyor)
How does it start to move forward before it takes off without it's wheels rolling? It can't. The belt counteracts this.

Already been here as well.

It COULD take off without wheels. It just would be very messy.

 

[Deleted member 36735]

Already been here as well.

It COULD take off without wheels. It just would be very messy.

But all we have to go on is the wording of the puzzle.

So what's the answer, how does the plane go from zero to 10 mph initially when the only things in contact with the belt are the tyres?

 

[Swango1980]

I'm sorry but on this matter of the interpretation of the meaning of the word "counteracts" you are incorrect.

As I mentioned before, because I didn't know the correct meaning of the word, I looked it up and I've posted the screenshots of the definitions and synonyms.

Yes, it can mean that the belt stops the wheels turning.

But, and this is what you are denying, it can also mean that the belt negates the effect of the wheels moving.

Stopping the wheels moving and negating the effect of the wheels moving are 2 different things, but according to the definitions, the word "counteract" can mean both.

The wheels on a car have an effect.

The wheels on a plane have no effect (not until you apply the brakes on landing anyway)

 

[Swango1980]

But all we have to go on is the wording of the puzzle.

So what's the answer, how does the plane go from zero to 10 mph initially when the only things in contact with the belt are the tyres?

The engine

 

[Deleted member 35927]

You should stop saying "been explained" because there is more than one interpretation.

It is also clear that the word "counteract" is being understood differently, not necessarily incorrectly by either side. I agree that the treadmill moving forwards "counteracts" according to synonyms, but the treadmill moving backwards most certainly also "counteracts", eg negates/equalises.

But all we have to go on is the wording of the puzzle.

So what's the answer, how does the plane go from zero to 10 mph initially when the only things in contact with the belt are the tyres?

Jet engines, 4 of them pushing through the air.
What you are trying to claim would only exist in a harry potter film

 

[Swango1980]

Jet engines, 4 of them.
What you are trying to claim would only exist in a harry potter film

I disagree. How can a broom get to take off speed with no wheels?

 

[Voyager EMH]

I disagree. How can a broom get to take off speed with no wheels?

The rules of Quidditch say it will happen so it does happen.

A conveyor belt preventing a plane from taking off is just not for muggles.
You have to use the incounteracto spell.

 

[Pin-seeker]

I know repeating things that have been posted is the trend of this FORUM but that was literally post 3

Fixed that for you.
Check out the LIV thread

 

[Golf is fun]

Having read through this, the only conclusion I can reach is that the question isn't 100% clearly written.

The most reasonable reading is that the author intended to mean that the conveyor moves at an equal speed to the wheels in the opposite direction, in which case the plane takes off because it's forward drive is not reliant on applying a force to fixed ground and getting an equal and opposite reaction, so it moves forward (although may fall off the end of the conveyor before getting airborne - but that's an extended level of pedantry).

The less reasonable response is that the conveyor stops the wheels turning, and therefore either:
a) the plane is moved forward by the conveyor and takes off (because the conveyor would have to move forward at the speed the plane would normally move forward at to keep the wheels from turning and so there is airflow over the wings),
b) you read it as the conveyor magically stops the wheels turning without moving the plane forward (RIP Physics) in which case the plane either skids along and takes off, or the level of friction between the wheels and the ground is so great that if the wheels don't turn the plane cannot move even by skidding and so doesn't take off.

We can never know the author of the questions intent, but the skidding option (successful or otherwise) is unlikely, because how can a conveyor belt make a wheel not turn without moving the object connected to the wheel forward? The only way is for the conveyor to move the object on it forwards so that the relative speed between the conveyor and the object is zero, and so if it's not this we're just throwing physics out the window and why should any other rules apply at that point, may as well make the plane time travel or something!

 

[Whereditgo]

The engines neither care nor know what the wheels are doing, they just provide thrust to move the body of the plane forwards through the surrounding air.

 

[Bobski]

I posted earlier (#529) with an attachment that annotated the issues. I think the reason the debate continues is in part due to how the problem is worded. The scenario as setup in the original post works fine if the treadmill and jet move in the same direction (as I think the phrasing suggests). So, if the plane is moving from right to left, its wheels will be rotating anticlockwise and at the point of contact with the treadmill the tyres will be moving from left to right. The conveyor belt is programmed to match the speed of the wheels in the opposite direction ie. from right to left. So, the treadmill moves right to left in the same direction as the plane, matching the accelerating speed of the jet. As the jet accelerates and takes off its wheels do not rotate. The jet lifts off pretty much as normal (in fact probably a tiny fraction earlier as there is no rolling resistance or bearing resistance from the wheels to overcome).

The problem is usually constructed differently around the inetrnet – with the treadmill travelling in the opposite direction to the plane. Here, the wording is crucial. If the treadmill is programmed to match the speed of the jet but in the opposite direction then all is well, the jet accelerates, the treadmill accelerates in the opposite direction and the plane takes off pretty much as normal. In this scenario, with jet moving right to left, the jet’s wheels will be rotating anticlockwise as usual but at twice the speed of the jet/treadmill.

If the problem is worded so that the treadmill is programmed to exactly match the speed of the wheels but in the opposite direction then there are problems (for the treadmill, not the plane directly). As the plane starts to accelerate from right to left with wheels rotating anticlockwise, the treadmill is programmed to attempt to match the speed of the wheels, in this scenario moving left to right. If the treadmill was successful, the plane would not move, relative to an observer who was off the treadmill. Of course, the treadmill cannot be successful; there is virtually nothing other than a tiny amount of friction to oppose the enormous thrust from the jet’s engines so the jet must start to move. At this point the jet’s wheels must be moving faster than the treadmill (otherwise it would remain static relative to the outside observer). The problem is setup so that this cannot happen, the treadmill has to speed up to match the wheel speed. The moving treadmill futher speeds up the jet’s wheel rotation and it is clear that in this scenario the wheels are always going to be rotating faster than the treadmill is moving. The treadmill (and the wheels) will very quickly accelerate towards infinite speed, caught in this feedback loop. The physics for the plane is that if the treadmill survives long enough, the plane will take off as normal, but in reality the treadmill (and the jet’s wheels) will self-destruct extremely quickly.

The problem in this post is worded so that the treadmill and jet move in the same direction, and so it works. If we switch to considering what would happen if they moved in opposite directions the wording is critical and matching treadmill to wheel speed is not going to work. The two sides in the argument are both correct – the jet should take off regardless of what is happening at its wheels, but the treadmill (instantaneously) matching the jet’s wheelspeed is not feasible. It ‘s a good recipe for a never-ending argument.

 

[Deleted member 35927]

I posted earlier (#529) with an attachment that annotated the issues. I think the reason the debate continues is in part due to how the problem is worded. The scenario as setup in the original post works fine if the treadmill and jet move in the same direction (as I think the phrasing suggests). So, if the plane is moving from right to left, its wheels will be rotating anticlockwise and at the point of contact with the treadmill the tyres will be moving from left to right. The conveyor belt is programmed to match the speed of the wheels in the opposite direction ie. from right to left. So, the treadmill moves right to left in the same direction as the plane, matching the accelerating speed of the jet. As the jet accelerates and takes off its wheels do not rotate. The jet lifts off pretty much as normal (in fact probably a tiny fraction earlier as there is no rolling resistance or bearing resistance from the wheels to overcome).

The problem is usually constructed differently around the inetrnet – with the treadmill travelling in the opposite direction to the plane. Here, the wording is crucial. If the treadmill is programmed to match the speed of the jet but in the opposite direction then all is well, the jet accelerates, the treadmill accelerates in the opposite direction and the plane takes off pretty much as normal. In this scenario, with jet moving right to left, the jet’s wheels will be rotating anticlockwise as usual but at twice the speed of the jet/treadmill.

If the problem is worded so that the treadmill is programmed to exactly match the speed of the wheels but in the opposite direction then there are problems (for the treadmill, not the plane directly). As the plane starts to accelerate from right to left with wheels rotating anticlockwise, the treadmill is programmed to attempt to match the speed of the wheels, in this scenario moving left to right. If the treadmill was successful, the plane would not move, relative to an observer who was off the treadmill. Of course, the treadmill cannot be successful; there is virtually nothing other than a tiny amount of friction to oppose the enormous thrust from the jet’s engines so the jet must start to move. At this point the jet’s wheels must be moving faster than the treadmill (otherwise it would remain static relative to the outside observer). The problem is setup so that this cannot happen, the treadmill has to speed up to match the wheel speed. The moving treadmill futher speeds up the jet’s wheel rotation and it is clear that in this scenario the wheels are always going to be rotating faster than the treadmill is moving. The treadmill (and the wheels) will very quickly accelerate towards infinite speed, caught in this feedback loop. The physics for the plane is that if the treadmill survives long enough, the plane will take off as normal, but in reality the treadmill (and the jet’s wheels) will self-destruct extremely quickly.

The problem in this post is worded so that the treadmill and jet move in the same direction, and so it works. If we switch to considering what would happen if they moved in opposite directions the wording is critical and matching treadmill to wheel speed is not going to work. The two sides in the argument are both correct – the jet should take off regardless of what is happening at its wheels, but the treadmill (instantaneously) matching the jet’s wheelspeed is not feasible. It ‘s a good recipe for a never-ending argument.

The only ways I can think of to keep the plane grounded are if the pilot and the conveyor belt programmer are in kahoots and work together to hold it,
The other is witchcraft

 

[Voyager EMH]

In this scenario, with jet moving right to left, the jet’s wheels will be rotating anticlockwise as usual but at twice the speed of the jet/treadmill.

Great post.

I need some help with the bit above.

In my perception the circumference of the wheel will always move over the same distance of the conveyor belt and that is always equal to one circumference of the wheel.
In this respect, the speed of the conveyor and the speed of the wheels is matched. The time for one circumference length is matched and the distance is always the same as well.

I need to change my perception to accommodate the bit in bold.