think about this...

[Slow Play Ray]

[ QUOTE ]
[ QUOTE ]
I think (hopefully) everyone is beyond this point by now. The only question is, how retarded was the wording of the OP?

[/ QUOTE ]
- Riddle: does x + y = x?
- No.
- Yes it does! Just ignore y. Idiot.
- [img]/images/graemlins/frown.gif[/img]

[/ QUOTE ]

y = 0

duh

[CrazyEyez]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
I think (hopefully) everyone is beyond this point by now. The only question is, how retarded was the wording of the OP?

[/ QUOTE ]
- Riddle: does x + y = x?
- No.
- Yes it does! Just ignore y. Idiot.
- [img]/images/graemlins/frown.gif[/img]

[/ QUOTE ]

y = 0

duh

[/ QUOTE ]
goddamit I knew someone would say that. [img]/images/graemlins/grin.gif[/img]

[d10]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
I think (hopefully) everyone is beyond this point by now. The only question is, how retarded was the wording of the OP?

[/ QUOTE ]
- Riddle: does x + y = x?
- No.
- Yes it does! Just ignore y. Idiot.
- [img]/images/graemlins/frown.gif[/img]

[/ QUOTE ]

y = 0

duh

[/ QUOTE ]

You do realize that by admitting that 0 is the only possible value for Y in this equation, you're also saying that the only possible airspeed for a plane to be moving when it's wheels are rolling at the same speed as a conveyor its sitting on is moving in the opposite direction would be 0, right?

[jman220]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
I think (hopefully) everyone is beyond this point by now. The only question is, how retarded was the wording of the OP?

[/ QUOTE ]
- Riddle: does x + y = x?
- No.
- Yes it does! Just ignore y. Idiot.
- [img]/images/graemlins/frown.gif[/img]

[/ QUOTE ]

y = 0

duh

[/ QUOTE ]

You do realize that you just conceded to all of us that the airspeed is zero, and therefore the plane will not take off, don't you?

[fluff]

Ok, I read maybe the first 20 or so pages, then decided there is too much confusion. Here is my attempt at explaining:

1) Everyone seems to agree/understand that if there is no air movement over the wings, then no lift. This is correct. What people are confused about is whether there is actually going to be any relative movement between the airplane (wings) and the air. The answer is yes.

A simple FBD should be all that's required to establish whether the plane is moving forward or not. I'm not drawing gravity and lift since they have no effect on forward movement, and also not drawing drag, because we all agree that the thrust is going to overcome drag. Finally, and most importantly since the wheels/threadmill are frictionless they do not exert a force in anyway, so all that was a red herring.



This FBD simply establishes whether the plane moves forward or not. Clearly since there is only one force, then it has to. (Side note: What if there was friction? Well, if the thrust is going to exeed friction, it still moves forward.)

Ok, so what about the whole "wheel moving at the same speed" thing? Well this is a bit tricky. Clearly as the wheel rotates, velocity of different points on the wheel with respect to the runway is going to be different.





Suppose point A, B and C are actually all moving at the same velocity along the runway. Then the wheel is not spinning! It would instead be sliding (or slipping (!) but more on this later) along the runway.

In order for the wheel to spin, in one instant in time, point C has to move faster than point B, which has to move faster than point A! Now what are these speeds?

Point B, which is where the plane is attached to the wheel has to move at the same speed as the airplane, lets call it V1.

What about the speed at point A? This is where the "no slip condition" comes in. It simply means that the wheel is not slipping with respect to the runway. Imagine the wheel "rotating" about point A as it is moving down the runway. At that moment in time, point A has a velocity of exactly 0 with respect to the runway! (ie. it is not slipping on it) Ta da! Velocity of the wheel = velocity of runway. In fact, any point of the wheel that is in contact with the runway at any given time has velocity of zero w.r.t. the runway, regardless of how fast the rest of the wheel is moving.

Hence, plane takes off, wheels are moving at the same speed as the runway, QED. Oh and I got to show of my MS paint skillz.

Edit: However, I do suck at image hosting.

Edit 2: Aha, got it.

[chessforlife]

of course it can take off. obviously.

the wheels have nothing to do with anything. their spinning is irrelevant. theoretically, if there were no friction, the engines wouldnt have to be turned on at all. inertia would keep the plane still while the wheels spun.

[man]

why are the more than one posts?

if there is no wind with respect to the airplane, it will not take off. if there is no wind with respect to the runway, it will take off. lift cannot be generated without wind with respect to the plane. (wind in the negative direction of the plane's orientation.)

[fnord_too]

[ QUOTE ]
why are the more than one posts?

if there is no wind with respect to the airplane, it will not take off. if there is no wind with respect to the runway, it will take off. lift cannot be generated without wind with respect to the plane. (wind in the negative direction of the plane's orientation.)

[/ QUOTE ]

As far as I can tell, the system is impossible. The question seems to state that the plane is not moving wrt to the runnway, but this is not possible given the setup since the jets/props provide thrust and there is no way for the runway to exert an opposite force via the free rolling wheels.

[man]

[ QUOTE ]
[ QUOTE ]
why are the more than one posts?

if there is no wind with respect to the airplane, it will not take off. if there is no wind with respect to the runway, it will take off. lift cannot be generated without wind with respect to the plane. (wind in the negative direction of the plane's orientation.)

[/ QUOTE ]

As far as I can tell, the system is impossible. The question seems to state that the plane is not moving wrt to the runnway, but this is not possible given the setup since the jets/props provide thrust and there is no way for the runway to exert an opposite force via the free rolling wheels.

[/ QUOTE ]
yeah, but it's an ideal system, so plausibility isn't what we're concerned with. I think the question means to state that the plane does not move with respect to the air, though:
[ QUOTE ]
The runway moves in the opposite direction of the plane at the exact same speed as the plane's wheels. There is no wind.

[/ QUOTE ]
this of course doesn't make any sense in a strict way of speaking, because the wheels have angular velocity, not retcilinear velocity, but you get the idea. the engines of the plane have nothing to do with the system, though. they exist only as a means of propulsion so that "wind" will be generated with respect to the plane.

[fnord_too]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
why are the more than one posts?

if there is no wind with respect to the airplane, it will not take off. if there is no wind with respect to the runway, it will take off. lift cannot be generated without wind with respect to the plane. (wind in the negative direction of the plane's orientation.)

[/ QUOTE ]

As far as I can tell, the system is impossible. The question seems to state that the plane is not moving wrt to the runnway, but this is not possible given the setup since the jets/props provide thrust and there is no way for the runway to exert an opposite force via the free rolling wheels.

[/ QUOTE ]
yeah, but it's an ideal system, so plausibility isn't what we're concerned with. I think the question means to state that the plane does not move with respect to the air, though:
[ QUOTE ]
The runway moves in the opposite direction of the plane at the exact same speed as the plane's wheels. There is no wind.

[/ QUOTE ]
this of course doesn't make any sense in a strict way of speaking, because the wheels have angular velocity, not retcilinear velocity, but you get the idea. the engines of the plane have nothing to do with the system, though. they exist only as a means of propulsion so that "wind" will be generated with respect to the plane.

[/ QUOTE ]

I'm not talking about plausibility, I'm talking about possibility. If the engines are providing thrust, you cannot, as far as I can figure, have the plane not moving in relation to the conveyor belt frame (and thus the wind).

The thing about the wheels having angular velocity only is the real reason for this contradiction if I am thinking about this correctly. There is no way for the conveyor to counter the thrust of the engines so the plane will move forward. If the question said something like "the plane's wheels rest on a conveyor belt that turns with no friction" then the answer is clear, but Ray specificly says:

[ QUOTE ]
The runway moves in the opposite direction of the plane at the exact same speed as the plane's wheels

[/ QUOTE ]

I don't think there is a reasonable interpretation of that other than the wheels are not moving with respect to the conveyor frame (not considering the angular velocity) and thus the whole plan is stationary with respect to the air. I suppose the plane could be really long and the wheel axels free to move along the length of the plane, but that is quite a stretch.