so then, this conveyer belt will keep the plane from going forward?
The plane will take off! The wheels and conveyer belt are irrelevant to the question.
Lets assume that the wheels on a plane spin freely, that there is no friction. That means there is nothing to hold the plane back as the conveyer belt moves, the wheels just spin more quickly.
Unlike a car, a plane doesn't use its wheels for propulsion. If you put a car on such a conveyer belt, or a rotating drum like they use to dyno or smog check a car, the car doesn't move because the ground is providing no resistance to the wheels of the car. This only matters because the wheels are the means of purpultion. If you put a propeller on the car while it was on the rotating drums it would start to move forward.
Another way to picture this is with a person balancing on a log in a river. Now, they can run forward and backwards to keep their balance, but if somebody pushes them they will likely move forward (fall down). The only reason they don't fall in the first place is that their legs provide the rest of their body resistance to push against. If that resistance wasn't there, as if they had rollerskates on, they would fall right away.
So the plane would take off because the means of propulsion are not the wheels, but the engine. So all of your aerodynamic theory, while correct, is irrelevant because the plane does move forward and therefore lifts.
Or here is another way to think about it. Go to the super-market with a Hotwheels. When you are at the checkout counter, push the Hotwheels the opposite direction of the conveyor belt. As long as you continue pushing the Hotwheel, the car will move forward despite the conveyor belt moving 'backward'. If you left go of the car it will stop and move with the conveyor belt. But as long as the amount of force forward you put on that car through your hand is greater than the friction between the wheels and the rest of the car, the car will move forward. This is the same thing as the plane. As long as the force of the engines is greater than the friction of the wheels, the plane will move forward.
Oh, well if you assume that the plane can't move, then of course I agree that the place can't take off (unless it's in a huricane or something, and the wind speed is great enough to cause the plane to lift.)
This sounds like a job for.... mythbusters!
So I emailed them :)
The issue at hand is not if the plane will take off. The issue is whether or not a jet engine can move a wheeled object on a conveyer belt. Use a rocket car instead of an airplane. Would the car move? I think it would. The force of the rocket must be balanced somehow, and it won't be balanced by having the wheels spin. The equal and opposite force would be the car moving forward relative to an outside observer.
By extension, a plane would move forward, generate lift, and would take off.
No no no, the bear is white because it's a polar bear.
I ran into Mr. Cruft's office completely flustered, having not fully read his update. We're on the same page.
It's hilarious to me that this problem has caused such a ruckus in the blogosphere. This is a case of a truly simple physics problem being overthought in all the wrong ways.
The whole problem comes down to this: THE PLANE WILL NOT TAKE OFF UNLESS IT ACHIEVES SUFFICIENT AIRSPEED.
Assuming there is not a sufficiently strong headwind, the problem can then be reduced to a simple force-balance problem. The conveyer belt will exert a force on the plane which exactly balances the thrust of the engine, so the plane doesn't gain any airspeed by running its engine.
Some of the stupid mistakes I've been seeing:
1)Contrary to what many have proposed, the conveyor belt exerts a force on the plane EVEN THOUGH THERE ARE WHEELS BETWEEN THE PLANE AND THE BELT: If you put a rolling suitcase on a moving sidewalk it doesn't roll in place, the belt drags it forward.
2)Planes generate lift by accelerating their wings through the air, not vice versa. The suggestion that planes fly by blowing air over their wings is analagous to suggesting that a sailboat could be propelled by mounting a ducted fan onboard which blows air into the sail.
3)The problem does not change depending on the form of thrust: A rocket plane, jet plane, prop plane, and jeep with wings will all behave identically according to the original wording of the problem.
it seems to me that this is more a problem of two vectors.
you've got a line of movement (airplane) A, and a line of movement (conveyor belt) B. The two vectors are moving opposite one another.
IF A = B, the plane does not move, and because it is stationary, EVEN if the engine is blasting, it's not going to take off because of said laws of thermodynamics. EVEN IF A > B, the plane will not necessarily take off. obviously, if B > A, the plane is going to slip off the conveyor. at this point the entire question becomes moot because too many forces and vectors get involved. I think that if the back end of the plane slipped off the conveyor and fired the engine upwards, it would do a bit of a hop, then crash and burn.
this is, of course, because it hasn't generated enough speed to generate any lift with its wings.
as to the "no friction, wheels spinning freely comment," again, another vector. this one would be the downward force the airplane is applying to the ground via gravity. that force is transmitted to the ground through the wheels- if you can make some wheels that don't suffer some sort of friction under that mass, I'd be impressed.
not that it matters. if friction is zero, the plane is going to be sliding all over the place as it is.
and finally, while on the ground, the airplane absolutely IS using its wheels for "propulsion." the engine rumbles, vector forward, wheels turn, the plane is moving. if you strapped the plane to some cinder blocks it wouldn't be moving forward, even WITH the forward vector of force (and if it does, I don't want to be anywhere near it). I understand that the wheels in a car are imperative to the movement (because of the transfers from engine to wheels), but the airplane has to use its wheels to gain enough speed on the ground TO take off.
and finally, I meant "said laws of aerodynamics" in my above comment, not "thermodynamics."
also, you change the problem entirely when you add the rope (to the skateboard). the problem is force of the plane--> vs
put mike on a skateboard on a 1,000 ft. long treadmill without the rope, assume he can't get off the treadmill's sides, set it to move against him as fast as he can use his legs to move forward, and you'd have almost the same picture.
except that the original question wasn't "can the plane get off the conveyor?" it was more or less "without moving, can the plane take off?"
The problem with this question is in the wording. The conveyor belt's speed matches some MEASUREMENT of the airplane's speed, and compensates to go in the reverse direction. Now most people automatically think "well the plane won't move in space, and so it won't take off."
The problem is aircraft mainly use airspeed indicators (think of a glorified pressure gauge) to determine proper takeoff speed, not auto speedometers (which calculate using wheel revolutions and circumfrences). If the conveyor was attatched to that, it will easily take off. Also, if it is attatched to a radar gun at a stationary position outside the plane/belt system, it will take off. The only way it WOULDN'T take off is if the measurement that the conveyor belt recieves from the airplane is the a calculation of the wheel speed. In THAT case it would be a really stupid question (it would be like 2 gears moving at the same speed in opposite directions).
So the problem says: "This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction)."
Assuming a sufficiently long conveyor belt, the only difference between a plane in this condition and a plane taking off from a stationary runway is that it's wheels will spin twice as fast.
I suppose it is possible that the dynamic friction due to the wheels spinning faster may be too much for the planes forward thrust to overcome to reach take-off velocity, but that seems an underconstrained complication of the problem. Besides, a plane sees much more dynamic friction from aerodynamic forces above a certain speed.
The problem does not state that there is a mechanism to hold the plane in place.
I think a much more interesting question is: "Given an aeroplane set on a sufficiently long conveyor belt that accelerates the plane to take-off velocity, will the plane take off?"
put more physics stuff about how airplanes lift off of the ground. thank you :p