Physics Question for you.....

[Russianwolf]

Like Mike said, you're rationalizing. Once again, here's a direct quote from his initial post. Read it carefully:

"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 opposite direction)."

actually he has a point in that, although I don't know if he intended it.

If the conveyor matches the speed of the body of the plane then the wheels in our problem will have to spin at a speed of twice that. And the plane would take off.

BUT,

If it were a car on the conveyor what would happen? The car would start moving but the conveyor would hold it stationary, resulting in no speed and the conveyor would stop, allowing the car to move again...........

I've got a headache. The conveyor is linked to the speed gauge in the vehicle (plane or car).

[scorrpio]

Like Mike said, you're rationalizing. Once again, here's a direct quote from his initial post. Read it carefully:

"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 opposite direction)."

Hmm, I see. Too bad the original description lacks the reference point. If the system tracks the object speed relative to a fixed external point , then you are correct. If system tracks object speed relative to conveyor itself, then my scenario takes place.

[scorrpio]

now you are rationalizing. what if I stated:
a. conveyor has no speed limitation
b. wheels are indestructible
c. bearings are indestructible and frictionless
d. tires have 100%traction at all times (until/if they leave contact with the conveyor in takeoff)

Ooooh, you don't want to go there. As conveyor - and thus tangent wheel rim speeds - approach the speed of light, their mass, two scenarios become possible:
1. As passage of time slows for the conveyor and the wheels, they end up in the past relative to the plane, which, having lost its wheels and having not yet built up sufficient lift-off speed, crashes to the ground.
2. Conveyor and wheel masses approach infinity, causing a gravitational collapse.

[LarryG]

And exactly what does 'matching' mean?

Like Mike said, you're rationalizing. Once again, here's a direct quote from his initial post. Read it carefully:

"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 opposite direction)."

[LarryG]

10 pages.

The number of pages is a function ... well, of something, but I don't know what. Maybe a profile setting? OMB, there are only three pages.

[scorrpio]

BTW Scorpio your scenario doesn't apply because the OP stipulates that the conveyor only matches the plane's speed, not exceeds it.

And exactly what does 'matching' mean? Let's say, it's not an airplane, but a car. The wheels of a car are spinning at a rate that would move the car at 100mph on a normal road. However, in its effort to MATCH that speed, the belt has to move at 100mph in the opposite direction. The result is that the car is standing still, moving a 0mph. So, the car itself is moving at 0mph. The conveyor, matching that, moves at 100mph. How is it done? Apparently, the conveyor increases speed until the object stops moving. If the object does not stop, the conveyor speed will increase indefinitely until something reaches a limit.

[Russianwolf]

Knowing that we have several engineers on the board, I thought it would be interesting to see how far this discussion went and if any of the engineers initially had it wrong.

10 pages.

[Russianwolf]

It's not much of a trick, IMO. Your question was "Will the plane take off or not?"

No, it will not take off unless it fires up the engines!

Humbug!

JR

actually my initial response upon seeing this question the first time was "that's two different questions. 1) will it take off and 2) is it able to take off."

The answer to the second is "yes", but the answer to the first is "only if it attempts to take off". Or at least those were my responses.

[LCHIEN]

I pointed out somewhere that the conveyor speed is totally a red herring, it really matters not a whit whether it matches, positive OR negative and what the actual speed is.

[Tom Miller]

Where I got stuck, at first, was when I assumed the conveyor's job was to spin at such a speed as to cancel out the plane's forward motion.

But when I looked at it in terms of force balance, I realized that even with some amount of friction involved, there's no way to know how fast the conveyor has to move to counter the thrust of the engine. It certainly has nothing to do with the speed of the plane.

Gravitational force doesn't really enter into it. If the plane can reach a sufficient speed relative to the ground (tower, etc.), and thus the air, then it will have the lift required to overcome gravity. (If friction is non-zero, then the friction force, which is counter to the thrust, is proportional to the plane's weight, as usual.)

Regards,
Tom

[Russianwolf]

See my above post. In its effort to match the speed of plane, the conveyor will accelerate to the limit - weather it's the limit of:
a. conveyor speed.
b. wheel strength.
c. bearing capacity.
d. tire traction.

My vote goes to blown tires and a nasty accident.

now you are rationalizing. what if I stated:
a. conveyor has no speed limitation
b. wheels are indestructible
c. bearings are indestructible and frictionless
d. tires have 100%traction at all times (until/if they leave contact with the conveyor in takeoff)

[LarryG]

the conveyor will accelerate to the limit

As I say in my Okay-Now-I-Get-It post above, the limit is imposed in the OP: Mike clearly stated that the conveyor matches the plane's speed, not exceeds it. So "the limit" is exactly the same speed at which the plane is moving:

"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 opposite direction)."

[scorrpio]

But as the wheel are free spinning and not needed for propulsion, the plane can take off almost as normal (wheels will spin at twice rpm as normal but not impede the takeoff).

See my above post. In its effort to match the speed of plane, the conveyor will accelerate to the limit - weather it's the limit of:
a. conveyor speed.
b. wheel strength.
c. bearing capacity.
d. tire traction.

My vote goes to blown tires and a nasty accident.

[LarryG]

The tires only bear the weight of the plane and have no relation to any of the planes movements.

Aw, geez. Why didn't you say that seventy-odd responses ago?!?

Seriously, it's amazing how a simple statement -- providing it's presented the right way -- can provide so much more clarity than can pages and pages of highly-detailed explanations.

Also, prior to seeing your latest reply, I had a troubling thought (troubling WRT my argument, I mean) that helped open my mental blinders. The thought, which should have occurred to me sooner, was what happens when a vehicle on glare ice loses traction and begins to slide. It's exactly as you said: the wheels are merely supporting the vehicle's weight and have no relation to any of the vehicle's movements. Okay, in this scenario, the ice under the wheels is not moving. What I suddenly realized was that it could be moving and it wouldn't matter at all.

I'm still going to maintain, however, that this hypothetical airplane would not experience an entirely normal take-off roll, but one that was longer than normal. The plane would still have to overcome the conveyor's tendency to try to carry it along with it. Exactly how long this would take would be a function of how abruptly the plane accelerates and how abruptly the conveyor starts running.

BTW Scorpio your scenario doesn't apply because the OP stipulates that the conveyor only matches the plane's speed, not exceeds it.

[JR]

She will fly.

It's a "trick" question in that the "trick" is the junction between the conveyor and the plane.

It's not much of a trick, IMO. Your question was "Will the plane take off or not?"

No, it will not take off unless it fires up the engines!

Humbug!

JR