Actually, I just wanted to comment on this one point, because I have several people make this mistake: The thing people are missing is increasing velocity. In order for a plane to reach sufficient speed to take to the air, it must rapidly increase velocity - it is not a steady speed, but a sharply increasing one. It's not a matter of a conveyor belt simply matching an arbitrary speed (100mph one way + compensate for -100mph the other way = 200 mph). The one factor people have been forgetting is that, rather than a set steady speed, this velocity must be rapidly increased, so, therefore, by rapidly increasing the 'magic conveyor belt''s speed in the opposite direction, very quickly increasing the speed of the belt, plus the 'friction' on the plane from the belt, plus rapidly approaching the point beyond the tolerance of the wheels to maintain that rolling speed without catastrophic failure.. I don't have anything useful to add to this dead horse - just wanted to mention that one point, I meant to mention it Friday, but forgot. Carry on.
As Nero has pointed out, the solution depends on if the original question implies that the conveyor belt merely impedes or if it negates the horizontal motion of the plane. It only impedes the motion of the plane if the force of the conveyor belt pushing backwards is equal to the thrust generated by the engines since most of the force of the conveyor belt does not contribute to the backwards horizontal motion of the plane due to the wheels (yes, wheels are amazing). In this case, I agree that the plane will take off with the wheels spinning approximately twice as fast as normal. However, assuming there is some friction in the wheels, the conveyor belt just has to be generating many more times the force of the engines in order to negate the horizontal force on the plane. To borrow from the plane standing still on a treadmill example, if you have the treadmill going backwards at 10 MPH, it's not a big deal to overcome the backwards horizontal force using the engines even a tiny bit. However, imagine the treadmill going backwards at 1,000,000 MPH (if that is even possible to imagine). You could see how even the slight amount of friction in the wheels would cause a large backwards horizontal force on the plane such that regular jet engines would not be able to overcome it. So, if this theoretical treadmill is designed to take both the friction of the wheels and the thrust of the engines into account, it should be able to go fast enough to overcome the engines and keep the plane in the same spot, preventing lift off. The ice example is not the same thing as there is no backward force on the plane at all. The plane of course would fly in this example. If the plane's wheels were frictionless then the ice example would be a good analogy. If Superman were to hit the back of the plane as it was trying to accelerate but not moving due to the theoretical treadmill, the treadmill could take that into account and accelerate a great deal faster to compensate. We are talking about orders of magnitude greater but it could be done, again, in theory.
One amendment to my previous post is that the treadmill will have to accelerate to cancel out the thrust of the engines, not just go at the same speed. But the point still stands that the treadmill along with the friction in the wheels can generate enough backwards horizontal force on the plane to cancel out the engines exactly.
I don't agree with the statements which said: the wheels do not matter, the conveyor belt does not matter, they don't have anything to do with the thrust of the engine, the wheels simply turn twice as fast, frictionless wheels ... Of course they all matter. A jet engine is an engine that discharges moving jet of air to generate thrust in accordance with Newton's third law of motion. "To every action force there is an equal, but opposite, reaction force". The action force is the plane/ engine moving the air backward thru the engine, the reaction force is the air acting on the plane pushing it forward. Some of this force is required to overcome the friction between the wheels and the ground and the resistance of the air volume in front of the plane. If there is no friction and no air resistance, there would be ony a minimum force require to push the plane. i.e. motion in outer space. Next, when we introduce a moving belt, we introduce several forces for the plane's engine to overcome. We all know if the plane moves forward on the runway, air flows over and under the wings. The angle of attack of the wing with the leading edge up higher than the trailing edge causes a difference in pressure which result in the lifting of the plane. 1) Belt not moving, engine not running. No motion. No force/ work. 2) Belt moving back, engine not running The plane is moving backward on the belt as observed by a bystander. The belt is doing the work to move the plane back against the surrounding air. (If the wheels are not rolling back, there is no friction to overcome). The air is pushing on the top of the wings creating a downward force on the plane. 3) Belt moving back, engine running to match the speed. The plane is stationary to a bystander. The belt is doing the work to move the plane back. The engine is doing the work to move the plane forward. If they cancel out, no lift on the plane. 4) Belt moving back, engine running extra hard to move the plane forward. The plane is moving forward to a bystander. If the engine is strong enough to move the plane forward at the speed to create enough lift, the plane will go up. The bottom line, the plane needs more thrust to fly.
Since this question says "the conveyor has a system that tracks the speed of the plane and matches it exactly in the opposite direction", the plane will NOT take off. The plane's engine keeps working harder and harder, so does the belt. No forward motion, no lift.
The wheels aren't propelling the plane. Did you not even read the thread? This argument was explained long ago, and there is no need to rehash it.
Fatty, I read many posts in this thread, many of them are very smart, except for yours. You did not understand the problem and still don't.
This means if the plane is going 10 mph, the conveyor belt is moving at a speed of 10 mph. Which means the plane's wheels will be moving at 20 mph, but the plane is still moving at 10 mph. The plane in this situation will still reach the speed necessary to lift off, but it will require a very small amount of additional thrust to overcome the resistance caused by the conveyor belt. If the speed necessary for lift off is 150 mph, then the plane's wheels will be spinning at 300 mph just before it lifts off.
Its pretty simple. The plane moves forward due to the force of the propeller. The plane moves up due to the lift created by the flow of air under the wings. While the plane is on the conveyor belt, there will not be enough air flow under the wings to give it lift. Eventually, if the engine is strong enough, the plane will overcome the friction of the conveyor belt and move forwards no mater how fast the belt moves in the opposite direction. This is forward propulsion - not flight! Once its off the conveyor belt it can generate enough air speed to lift up and fly. It will not fly on the conveyor belt, but the conveyor belt can not prevent the plane from moving forwards. Everyone gets half credit.
You will have to prove to me why the wheels would magically move as twice the speed without the engine doing the extra work? If the wheel moves at speed S1, there is a friction F1 proportional to S1 that the engine has to overcome. If the wheel moves at speed S2, there is a friction F2 proportional to S2 that the engine has to overcome. If the post had not said the conveyor speed "matches" the speed of the plane, I would agree you only need a small amount of extra work from the engine to take off but you still require extra work. If the belt keeps increasing its speed to match and the plane stays stationary to an outside observer, there will be no lift.
A thought experiment commonly cited in discussions of this question is to imagine you're standing on a health-club treadmill in rollerblades while holding a rope attached to the wall in front of you. The treadmill starts; simultaneously you begin to haul in the rope. Although you'll have to overcome some initial friction tugging you backward, in short order you'll be able to pull yourself forward easily. ______ How can you read this analogy from page two and not understand what will happen to the plane?
You and your tricky tricks! There is no rope on the plane !11!! Do you think the rope and treadmill experiment is safe for BBSers to try at home? You are trying to hurt your opposition now!
Because it is a bad analogy that assumes that the treadmill will maintain a constant speed once the rollerblader establishes forward progress. In fact, based on the riddle, the treadmill will speed up and once the rollerblader establishes forward progress.
There are all kinds of frictions, static friction, kinetic friction, rolling friction. It's hard to move a stationary object but once you get it moving, it's easier. It it's rolling, it's easier still. But you still have to overcome the friction.
I can't tell you how I hate to post a non-joke in this thread, but here goes. According to 747 stats, a jet weighs about 100,000 lbs. So that's basically the max possible force available to any type of friction you'd worry about (via the normal force). So, with decent wheels, only a tiny fraction of that would actually end up arising as friction of the wheels against axle. But take a ridiculous case, wheels of licorice on an axle made of a roll of sandpaper. Make it the most friction-logged axle since the invention of the wheel. Even then, the thrust of two jet engines, roughly 120,000 lbs, would overcome a frictional force equivalent to the entire weight of the jet! And for those who say you need a quick increase in speed to take off -- don't think so. You can accelerate slowly (and some planes do), if you have a very long runway.
Actually, it's a great analogy -- because it allows you to picture exactly what the plane will do when it engages its engine(s).
