hmmm.... physics question for you guys....

[VitaminG]

Re: hmmm.... physics question for you guys....

nicely explained, Lou.

Just had to catch up on 4 pages that appeared here while I was off on lunch.

I notice that the couple of people arguing for the negative (particularly 3333 & Newc) keep insinuating that those of us arguing for the affirmative are suggesting that the plane would maintain its position (ie not moving relative to the ground) and somehow magically levitate off the conveyor. I haven't seen a single argument from the affirmative that this would be the case. The opposite, in fact. We argue that the plane would NOT maintain its position, but move forward despite the conveyor, thereby passing wind over the wings and creating lift. So no, a conveyor belt the size of the plane will not do away with runways, aircraft carriers, etc. because we argue that the belt has no bearing on whether the plane takes off or not. The plane will take off the same as ever, the only difference being that the plane's wheels will spin faster on the conveyor belt.

You can find good solid explanations of why this would be so in zeeg's, RobRR's & LouSiffer's posts above. oh, and mine too [img]/images/graemlins/grin.gif[/img]

[RobRR]

Re: hmmm.... physics question for you guys....

Thats what we have been saying the whole damn time! [img]/images/graemlins/laugh.gif[/img]

[MetalGrasshopper]

Re: hmmm.... physics question for you guys....

Yep. I feel screwed for Physics SATs this saturday. Bring on the pwnage. [img]/images/graemlins/frown.gif[/img]

[YetAnotherOne]

Re: hmmm.... physics question for you guys....

The answer depends on the conveyer. Specifically, is the conveyer: a) unpowered with a belt that turns without friction, or b) powered in such a way as it reacts to the plane?

From there, the problem is a frame-of-reference problem. Consider a bystander on the tarmac next to this mythical airplane / conveyer combination. Assume the plane is pointed west and there is no wind. In the case of a conveyer whose belt turns with no friction (but whose belt produces some friction with the plane's tires) the plane's thrust will cause the conveyer's belt to turn while the plane's wheels do not. The net result of this is that the plane will move away from our bystander and the plane/conveyer combo will accelerate until either the plane lifts off or is pitched unceremoniously off the end of the conveyer. Why? Because the conveyer's belt is frictionless the force applied to the plane / conveyer combo by the thrust from the plane's engines causes the belt to move but does not overcome the static friction between the plane's wheels and the surface of the belt, thus the belt moves and the plane along with it. As the plane moves its velocity relative to the static air eventually becomes great enough that the lift produced by the relative difference in the velocities of the plane and air becomes great enough to overcome the plane's weight and the plane becomes airborne (if the conveyer is sufficiently long). From the perspective of our static observer the plane accelerated away from his position and became airborne just as normal except it did so on a conveyer.

Now consider the other case: the conveyer is not frictionless but is powered and equipped with sensors that attempt to turn the conveyer at a speed sufficient to keep the plane in place. This time as the plane applies thrust its wheels begin to turn but the conveyer's belt simultaneously moves at an equal speed in the opposite direction. From the perspective of our static observer this time the plane will not move at all. This implies that the plane also will not move with respect to the air near the plane's wings so no lift will be produced and the plane will never become airborne.

Don't confuse the airplane scenario in which thrust is applied along a horizontal vector with the case of a rocket where the thrust is applied along a vertical vector to overcome the force applied to the rocket by the Earth's gravitational field ("weight"). Strap wheels on a rocket, lay it on the hypothetical conveyer horizontally, and fire it up & you'll get the exact same result you get with the plane in my second plane scenario. In the first plane scenario the rocket will never become airborne, it will just continue moving until it's chucked unceremoniously off the end of the conveyer because horizontal thrust won't produce any vertical force (lift if you like) to overcome gravity. Strap wheels to the rocket, point the rocket skywards, place the conveyer next to the rocket, and fire it off & the rocket will soar skyward because in this case it's producing force in a direction necessary to overcome the force of gravity.

Don't quit your day jobs. [img]/images/graemlins/laugh.gif[/img]

[SeventhSon]

Re: hmmm.... physics question for you guys....

Lou, you could be right, you could be wrong. If the friction in the wheels were sufficient enough such that if the conveyer supporting the plane started gradually moving backwards such that at the point the plane fired it's engines it was moving backwards at a speed equal to its take off speed, then it's not going to fly.

[SeventhSon]

Re: hmmm.... physics question for you guys....

In other words, if the the plane's take off speed is x mph. And it is experiencing a tailwind of x mph, it ain't going to fly.

Now whether the conveyer belt contraption can actually move the plane backwards such that it can experience a tailwind of x mph is a different story.

The initial set up for the question is too ambiguous as to whether the conveyor belt contraption can actually accomplish this. So that's why we have so many differing opinions.

[RobRR]

Re: hmmm.... physics question for you guys....

I just came to a realization... this is in a way, a trick question. The only way to measure the speed of a plane is its movement from one physical point to another. If the conveyor is moving 10mph backwards, then the plane HAS to be moving 10mph forward. If the conveyor is moving to match the speed of the plane, then the plane MUST be in equal opposing motion. The plane can never be stationary and the conveyor be moving, or this quesion is null and void all together.

Its been a good debate everyone, but now its over. [img]/images/graemlins/laugh.gif[/img]

[LouSiffer]

Re: hmmm.... physics question for you guys....

Again, it is hard to picture, the VERY first thing you need to get out of your head is the wheels. Minus the above mentioned friction in the bearings, they have no effect.

Our brains automatically assume the wheels are a factor. They are not by any means.

Lets try this. Lets imagine underneath this conveyer, there is a magnetice field the makes the plane hover inches above the belt. The conveyor is moving in a southward direction of 100 MPH and the plane is moving north at a velocity of 100 MPH. You would then assume that since the plane is not touching the conveyor, it will go forward. Again, this is where the tidbit about the wheels touching fools you.

Since there is friction within the bearing of said wheel, if you turned the conveyer and and let it gradually build up speed ( engines turned off on the plane ), it will push the plane backwards. Do you know what would happen if you had the conveyor at a dead stop and then pushed a button that made it go 100 MPH instantaneously? The wheels would spin at probably 90 MPH , but, the plane would then go backwards at about about 10 MPH and gradually build up speed until it hit its maximum velocity, which I can assure you would be less than 100 MPH as the plane would have some wind resistance. If you could remove the friction in the bearings 100%, the plane would just sit there while the wheels spun freely. However, removing the friction from the bearing is impossible. The wheels touching have no effect on this scenario. It is just part of an equation that doesn't need to be there. Kind of like saying " In a relay race, Joe ran the first 1000 meters in 58 seconds and Steve ran the second 1000 meters in 52 seconds. Mike threw the javeline 100 yards. Taking into consideration the length of Mike's javeline throw, what was Joe and Steve's total time?" -Lou

[SeventhSon]

Re: hmmm.... physics question for you guys....

what happens when an unstoppable force hits an immovable object?

[Newc]

Re: hmmm.... physics question for you guys....

[ QUOTE ]
what happens when an unstoppable force hits an immovable object?

[/ QUOTE ]

Nancy Grace blames the resulting cataclysm on a man [img]/images/graemlins/laugh.gif[/img]

Lou, you cannot remove the wheels from the equation. That is called "padding" your theory, and it is incorrect.

Take a stock Boeing 747 as used every day by every major airline and put it as-is on the theoretical conveyor in question, and it will not be able to take off. Period.

Regardless of bearing wear and tire friction, the belt's speed always adjusts automatically to the speed of the aircraft. This means if the bearings wear down and the friction between the tires and the belt is increased, the belt will slow down as the plane slows down. If it is decreased, and the plane speeds up, the belt speeds up.

I got one for you: how much dirt in grams can you get out of a hole that is 1' wide, 1' long, and 1' deep?

[hgsmith]

Re: hmmm.... physics question for you guys....

Lift equals surface area of an air foil (wing) x's velocity square x's dynamic pressure x's the coeffecient of lift (angle of attack, wing camber, center of pressure, MAC, etc.). So, all we need is relative wind. It takes relative wind and a effiecient airfoil for an aircraft to fly no matter what it is on.

I'm going to play my guitar now [img]/images/graemlins/headbang.gif[/img]

[zeegler]

Re: hmmm.... physics question for you guys....

Good explanation Lou. The thing that these guys still don't understand, is that they think the purpose of the conveyor is to allow the plane to take off in a short distance. It is not. It merely serves to pose a problem, that we must solve. Unless an aircraft is VTOL, it needs momentum to take off. The argument here, is whether the plane could accelerate against the backwards force of a moving conveyor. The answer is a simple yes, because the backwards moving belt does not exert any (significant) force on the plane. If you were to tow the plane with a truck, the truck would only have to overcome the rolling resistance of the tires, and (assuming a flat surface) the initial weight of the aircraft. This of course does not equate to the ability to lift the plain, merely to roll it along the ground. I'm not sure exactly what this figure is, but it's a lot less than the weight of the airplane. It makes sense that a truck would be able to tow an airplane regardless of whether there was a conveyor or not. Now just replace the truck, with a jet engine. Would a jet engine have enough thrust to roll itself along a flat runway? We all know that of course it would, otherwise it would never take off. So would it have the iota of extra thrust needed to compensate for the insignificant rolling resistance of the tires being rolled in the opposite direction? Of course it would. That is the only thing resisting the plane's forward motion.

[YetAnotherOne]

Re: hmmm.... physics question for you guys....

Not such a good explanation Zeeg.

Momentum is mass * velocity, what a plane requires before it can take off due to the lift produced by its wings is a sufficient velocity relative to the air through which it is moving. A plane attempting to move forward at a velocity of X on a conveyer moving backwards at a velocity of -X has a velocity of zero relative to the air through which it is attempting to move (note that zero velocity in this frame of reference also implies a zero momentum). No velocity, no takeoff.

The conveyer *does* exert significant force on the plane. If it's moving in at a mirror image velocity to the plane the force the conveyer exerts on the plane is equal to the force the plane exerts on the conveyer. If the problem presents a conveyer that "matches the speed" of the plane then BY DEFINITION these forces will always be equal. When you begin by defining the velocities you've also defined the forces as being exactly equal. When you later assert that the plane will "overcome" the force exerted by the conveyer you've stepped outside the boundary you initially set for the problem. Apples & oranges as it were.

In towing the plane, the truck would have to initially overcome the (greater) static frictional forces between the non-moving plane and the runway then, once the plane is moving, it must overcome the (lesser) rolling friction between the plane and the tarmac, the force air exerts on the now-moving plane, frictinoal forces in bearings in the wheels, the truck, etc. You don't overcome the plane's "weight", weight is a measure of the gravitational attraction between the plane's mass and that of the Earth (and other objects).

But the central problem in your thesis is that you've set a condition and then ignored it. If the conveyer matches the speed of the plane, the plane cannot other than remain static (unmoving) relative to a stationary observer (the air) near the plane / conveyer system. No motion relative to the air = no lift = no takeoff.

[Deneb]

Re: hmmm.... physics question for you guys....



I wish I had an explanation.

[RobRR]

Re: hmmm.... physics question for you guys....

The plane moves in the air, not the ground. What you somehow seem to be missing is that if the plane is not physically moving, neither is the conveyor. This isnt like a car were talking about, in order for the conveyor to move opposite to match the plane, the plane first has to have forward motion. How can you honestly think free rolling wheels can hold an airplane in place at full thrust?