Physics Question for you.....

[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

[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.

[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.

[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.

[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.

[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.

[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)."

[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.

[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.

[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).

[LarryG]

If it were a car on the conveyor what would happen?.

But has been pointed out many times, it's not a car. It's an airplane. And as everyone has now agreed, the conveyor will not stop the plane from moving. So no one who is thinking objectively would argue that "plane speed" can possibly mean anything but its speed relative to some fixed point on the ground. The conveyor speed is dependent on the speed of the airplane, not the other way around.

This will be my last post to this thread, since all this recent discussion amounts only to an attempt to alter the original problem as it was stated.

[Russianwolf]

I was just thinking about it. The original question doesn't say HOW the conveyor "senses" the speed. So lets say for a moment that there is a radar gun tracking the plane and that tells the conveyor how fast to go (so we are reading the speed of the body of the plane in relation to the radar station).

Even if the plane were powered by it's wheels it would eventually lift off (assuming it could go any speed).

Reason: Lets say you needed 100MPH of ground/air speed to acheive lift and flight. Plane starts at 100MPH radar reads and conveyor goes 100MPH. Conveyor would slow down as the body speed of the plane slowed until they both reached 50MPH (plane is trying to go 100MPH forward but 50 MPH backward yeilding a body movement of 50 MPH forward). If the plane increased speed to 200MPH the conveyor would counteract half of this and yeild 100MPH which is needed for lift and flight.

how many times can we beat a dead horse?

[scorrpio]

I will reiterate - in reference to what is speed being tracked?
1. In reference to a fixed point outside of the conveyor:
As object moves over the conveyor, the system tracks its absolute position, and adjusts conveyor speed till it matches speed of the object. If this was a car showing 100mph on its speedometer, the system would take the conveyor to 50mph. Relative to the fixed reference point, car is moving at 50 mph, and so does the conveyor.
In case of a plane, whetever speed plane's engines give it, is matched by the conveyor, causing the wheels to spin twice faster than they would on a stationary runway, but not affecting the overall plane's ability to take off.

2. If the system tracks speed at which object moves relative to the conveyor itself, however, the picture changes drastically. In case of a car, no matter how fast the car goes, conveyor matches the speed at which the car passes over its surface, keeping the car motionless for an outside observer.
In case of a plane, the system becomes recursive. No matter how fast the conveyor goes, the tracking system perceives plane body moving at a greater speed, and continues to accelerate the belt in its effort to match.

[TheRic]

.....how many times can we beat a dead horse?

Taking into account the planes air speed, and the speed of the conveyor belt, we know the wheels will be humming along. So this should give us plenty of time to beat it for awhile. Now if the conveyor belt is limited in length, then we would have finite time (and numbers) to beat the horse.

I'm going to go with the conveyor belt is one large loop, since most are, therefore we would have infinite amount of time and numbers to beat the horse. As the speed of the beatings approach the speed of light, and taking the mass of an average sized horse, we can...........

I think the real question is what is the maximum page length allowed?!

[Russianwolf]

Taking into account the planes air speed, and the speed of the conveyor belt, we know the wheels will be humming along. So this should give us plenty of time to beat it for awhile. Now if the conveyor belt is limited in length, then we would have finite time (and numbers) to beat the horse.

I'm going to go with the conveyor belt is one large loop, since most are, therefore we would have infinite amount of time and numbers to beat the horse. As the speed of the beatings approach the speed of light, and taking the mass of an average sized horse, we can...........

I think the real question is what is the maximum page length allowed?!

and if we dropped a bullet on the conveyor, what impact would it have? and how fast would it be traveling afterwards?