Plane on a treadmill...

[Funkstar]

But you also have the additional speed added to the wheels by the plane moving forward, so the treadmil matches that, which the wheels match with the addition of the plans speed... which the treadmil matches and so on and so on.


should we maybe close this thread now, because it is just going to get silly isn't it?

[Howard]

One of the key things in this riddle, why many get it wrong, is the line "The conveyer belt is designed to exactly match the speed of the wheels, moving in the opposite direction."

Which of course is very misleading, because it's actually the wheels that match the speed of the treadmill, not the other way around.

Yeah it's all misleading 'cos the treadmill doesn't mean squat



I haven't even read the damn thread yet



Edit: I swear "autopilot" used to be someone else....

[Funkstar]

Dangerous_Dom

[bsodmike]

The fun aspect of this thread is that, evne though the correct answer has been posted (many times) until it sits right in your head, you are never gonna be satistfied..hence a very very active thread

Maybe we should have a few more brainteasers about

[Durzel]

Just to complicate things, it wouldn't matter if the wheels weren't frictionless really - all it would mean is that it would be very slightly harder for the plane to take off, but it would be so negligible as to be irrelevant (i.e. massive lb/ft of thrust vs small rubber wheels).

I think people who are getting this wrong are assuming that the wheels are driven, as in the plane rotates the wheels to gather speed (like a car).

Just to throw another science oddity into the mix - if there was a car on the treadmill in this same scenario neither the car nor the treadmill would move. Assuming the "reaction" of the treadmill was instantaneous, any force that the car would impart on the treadmill when moving forwards would be instantly counterbalanced - therefore the car would not move, the cars wheels would not rotate and the treadmill would not move either.

[IBM]

But what about the force generated by the engine on the wheels? Does it just disapate, like my faith in the rules of physics?

[JPreston]

Just to complicate things, it wouldn't matter if the wheels weren't frictionless really - all it would mean is that it would be very slightly harder for the plane to take off, but it would be so negligible as to be irrelevant (i.e. massive lb/ft of thrust vs small rubber wheels).

That's right, but you assume the wheels are frictionless before mechanical engineers start calculating alloy strenghs and so on. Purely to make things simpler.

I think people who are getting this wrong are assuming that the wheels are driven, as in the plane rotates the wheels to gather speed (like a car).

I know, how can they be this stupid...

....if there was a car on the treadmill in this same scenario neither the car nor the treadmill would move. Assuming the "reaction" of the treadmill was instantaneous, any force that the car would impart on the treadmill when moving forwards would be instantly counterbalanced - therefore the car would not move, the cars wheels would not rotate and the treadmill would not move either.

Eh? At first the car, treadmill and wheels would be stationary but there is a driver trying his best to move down the treadmill (which does indeed react instantly). The car stays stationary no matter what, the wheels can be turned but the treadmill negates the rotation. Say the car tops out at 150mph, then when the driver floors it the wheels are spinning at 150mph and the treadmill moves 150mph in the opposing direction. But the car doesn't move of course.

[Durzel]

Actually I misread (I think?) what was said elsewhere about it...

As you point out, one problem here is the wording of the question. Your version straightforwardly states that the conveyor moves backward at the same rate that the plane moves forward. If the plane's forward speed is 100 miles per hour, the conveyor rolls 100 MPH backward, and the wheels rotate at 200 MPH. Assuming you've got Indy-car-quality tires and wheel bearings, no problem. However, some versions put matters this way: "The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation." This language leads to a paradox: If the plane moves forward at 5 MPH, then its wheels will do likewise, and the treadmill will go 5 MPH backward. But if the treadmill is going 5 MPH backward, then the wheels are really turning 10 MPH forward. But if the wheels are going 10 MPH forward . . . Soon the foolish have persuaded themselves that the treadmill must operate at infinite speed. Nonsense. The question thus stated asks the impossible -- simply put, that A = A + 5 -- and so cannot be framed in this way.

[MadduckUK]

the planes tires would be travelling at twice the rated speed. possibly causing them to explode, making the plane crash, and of course it crashes onto the belt going the other way. BOOM

answer: plane DOESNT take off, but instead is destroyed in fireball

[Funkstar]

please tell me you are trying to be funny Madduck

[MadduckUK]

what makes you think that?

[Funkstar]

well, virtually all your posts are non-serious... and that answer is just plain wrong.

[MadduckUK]

well a lot of tyres that michelin make for aircraft are rated at 160Mph. while the takeoff speed for a 737 for example is 150mph. could the tire withstand speeds going up to 300mph?

[bsodmike]

Haha, in his 'not so serious attitude' he does make a relevant point, i.e. 300mph = over heated tires which will melt/explode.

Since the tires are going to be rotating at twice the ideal take-off speed, it's safe to say it'll 'never' take off - but if the tires would accommodate twice the 'rated' velocity, there shouldn't be a problem.

Assuming the "reaction" of the treadmill was instantaneous, any force that the car would impart on the treadmill when moving forwards would be instantly counterbalanced - therefore the car would not move, the cars wheels would not rotate and the treadmill would not move either.

I do not agree with you here - either the motor driving the treadmill will explode and/or the car's would, not to mention the insane stress on the belt surface and tire contact area...

In reality I'd expect the tires to be spinning in one direction at (for example) 100mph, while the belt will be travelling in the opposite direction at the same speed - but the car (body) would remain stationary.

[JPreston]

About 200 hundred posts ago I posted that we can all assume the tyres are rated for infinite speeds.

Otherwise we need to ask all kinds of stupid questions like what is the air temperature, what is the octane rating of the fuel, what alloy are the bearings made of. It's a treadmill the size of a runway FFS. Obviously it's not a real-world question.

[badass]

Haha, in his 'not so serious attitude' he does make a relevant point, i.e. 300mph = over heated tires which will melt/explode.

Since the tires are going to be rotating at twice the ideal take-off speed, it's safe to say it'll 'never' take off - but if the tires would accommodate twice the 'rated' velocity, there shouldn't be a problem.



I do not agree with you here - either the motor driving the treadmill will explode and/or the car's would, not to mention the insane stress on the belt surface and tire contact area...

In reality I'd expect the tires to be spinning in one direction at (for example) 100mph, while the belt will be travelling in the opposite direction at the same speed - but the car (body) would remain stationary.

The car would be doing half the speed it was doing on the conveyor - simple really

Car does 10 MPH on the conveyor- conveyor will be doing 5 MPH backwards, car will be moving 5 MPH forwards.

This is the ONLY way the question could work, as if the conveyor in the palne example does the wheel speed backwards, it will result in a positive feedback loop because as soon as the plane gains any speed, the conveyor would have to accelerate at infinate acceleration in order to match the wheel speed.

Bet thes goes on forever now