Will the Airplane Fly??????????

[Alpha_One]

Yes. Hindi naman yung gulong ang nagpapaandar dun sa eroplano eh, yung thrust nung engine(s). Bibilis lang ikot ng gulong nung eroplano.

[mbeige]

Again, the conveyor is supposed to only match the plane's speed, and it only acts on the plane's wheels. Thus, the wheels are moving twice as fast, but the plane is still moving at the same speed.

Duh, my mistake, the answer should be NO... because by the time the plane has reached its 150 mph take-off speed, the wheels are going 300 mph, and they'll overheat, blow-out, and the wheel hubs will catch in the conveyor belt, causing it to seize, and tons of metal airplane and steel-plated conveyor belt strips will be flying through the air at speeds of over 100 mph...

I can just imagine it now...

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Again, trick question... because the conveyor moves with speed, and speed does not equal force. That's why a water skier can be doing 40 mph over the water while only holding on to a line with arms that can't even push him at 10 mph... because he's exerting more force on the line with his arms than the water is exerting on his feet.

But the keyword here is lift. There is no lift because the plane is stationary, and there is no mention of any wind so we will assume there isn't any. Hence, no wind, no Bernoulli effect, no lift, regardless of the condition of the wheels of the plane.

And one important thing the question asked was would there be lift with the conveyor belt being driven opposite the plane's direction, meaning if the plane faces to the left, the conveyor belt turns clockwise. If the conveyor belt pushed the plane forward, meaning if the directions were not opposite each other, then yes, there would be lift if the velocity was high enough to produce a lower pressure above the wings and a higher pressure below the wings, to create lift.

Mathematically speaking, if the velocity of the plane were V, and the velocity in respect to the conveyor belt was -V (opposite in direction but having the same magnitude), then they will cancel each other out, so the plane will be stationary. The only way there will be lift is if there is wind going across the wings, and the only 2 ways to achieve it are by moving the plane forward (which does not happen) or by having a huge fan blow the air towards the plane to simulate its actual speed. Of course, the latter will not take off too, because it will just hover for a few seconds and eventually fall back to the ground (no momentum).

[Alpha_One]

But the keyword here is lift. There is no lift because the plane is stationary, and there is no mention of any wind so we will assume there isn't any. Hence, no wind, no Bernoulli effect, no lift, regardless of the condition of the wheels of the plane.

And one important thing the question asked was would there be lift with the conveyor belt being driven opposite the plane's direction, meaning if the plane faces to the left, the conveyor belt turns clockwise. If the conveyor belt pushed the plane forward, meaning if the directions were not opposite each other, then yes, there would be lift if the velocity was high enough to produce a lower pressure above the wings and a higher pressure below the wings, to create lift.

Why would the plane be stationary? Engine thrust would still be pushing the plane forward, the conveyor belt wouldn't do a damn because the wheels are just there to keep the plane from scraping the runway.

[mbeige]

Why would the plane be stationary? Engine thrust would still be pushing the plane forward, the conveyor belt wouldn't do a damn because the wheels are just there to keep the plane from scraping the runway.

Assuming the wheel bearings of the plane have negligible friction, and considering that the original question stated that:

This conveyor has a control system that tracks the plane's
speed and tunes the speed of the conveyor to be exactly the same (but
in the opposite direction) instantly.

Then the moment the plane moves forward 1mph, the conveyor belt brings it backwards -1mph. The important word here is "instantly". The wheels in this situation essentially function to provide negligible friction between the conveyor belt and the plane's engine (force). It's like walking on ice barefoot, it's very slippery and any attempt to push back with your foot will result in a slide, that gets you nowhere. Or even if it did get you somewhere, it won't be far. And if you bring this analogy back to the plane, it won't have enough speed to generate lift.

[nerbyoso]

exactly alpha one!

given enough thrust i dont think a plane/missile/projectile will even need a runway.

[mbeige]

exactly alpha one!

given enough thrust i dont think a plane/missile/projectile will even need runway.

It's an airplane, not a rocket. Even if it had thrust, it needs lift to take off! Thrust will only push it forward, but what happens here? Negligible yung friction and the conveyor belt instantly brings the velocity to zero dahil yun ang nakalagay sa condition ng tanong.

[Alpha_One]

Mathematically speaking, if the velocity of the plane were V, and the velocity in respect to the conveyor belt was -V (opposite in direction but having the same magnitude), then they will cancel each other out, so the plane will be stationary. The only way there will be lift is if there is wind going across the wings, and the only 2 ways to achieve it are by moving the plane forward (which does not happen) or by having a huge fan blow the air towards the plane to simulate its actual speed. Of course, the latter will not take off too, because it will just hover for a few seconds and eventually fall back to the ground (no momentum).

The velocity of the plane and the runway can't cancel each other out. Velocity is change in position, and the plane's position is independent of that of the treadmill este runway. Kung two equal but opposite "velocities" acting on the plane, saka sila magka-cancel out.

Now, if the question was that the runway will exert a force opposite that and acting on the airplane, then the plane will not move.

Pero kung speed lang nung runway ang pinaguusapan, lilipad yung eroplano.

At the moment of takeoff: Relative to the wind, airplane will be running at takeoff speed, the runway will be running at takeoff speed towards the other direction. Relative to each other, the plane and the runway will be passing each other at TWICE the take of speed.

[Alpha_One]

Assuming the wheel bearings of the plane have negligible friction, and considering that the original question stated that:

Then the moment the plane moves forward 1mph, the conveyor belt brings it backwards -1mph. The important word here is "instantly". The wheels in this situation essentially function to provide negligible friction between the conveyor belt and the plane's engine (force). It's like walking on ice barefoot, it's very slippery and any attempt to push back with your foot will result in a slide, that gets you nowhere. Or even if it did get you somewhere, it won't be far. And if you bring this analogy back to the plane, it won't have enough speed to generate lift.

Here's where the trick comes in. Sabi sa tanong yung speed ang matched hindi yung force. Kung umaandar yung eroplano 1MPH, yung runway umaandar ng 1MPH pabalik. Relative to each other, they're running at 2MPH.

It's an airplane, not a rocket. Even if it had thrust, it needs lift to take off! Thrust will only push it forward, but what happens here? Negligible yung friction and the conveyor belt instantly brings the velocity to zero dahil yun ang nakalagay sa condition ng tanong.

Nowhere in the question did it say that the wind moves in the opposite direction. Assuming "no wind" (wind ang '0mph' reference) plane moves at 1MPH against the wind, runway moves at 1MPH against the wind in the opposite direction, plane and runway moves against each other at 2MPH.

[mbeige]

The velocity of the plane and the runway can't cancel each other out. Velocity is change in position, and the plane's position is independent of that of the treadmill este runway. Kung two equal but opposite "velocities" acting on the plane, saka sila magka-cancel out.

The plane's position, relative to the conveyor belt, remains the same because the force that the plane exerts on the conveyor belt is cancelled by the conveyor belt applying the same force but opposite in direction to the plane via the wheels. Therefore, the wheels rotate and act as a bearing, allowing the plane to remain on top of the conveyor belt. Like it is stated on the question, once the plane gains a certain speed, it is instantly brought to zero by the conveyor belt because it is already stated that the belt will instantly provide the same speed but opposite in direction. Hence, the plane's speed relative to the conveyor belt is zero.

Now, if the question was that the runway will exert a force opposite that and acting on the airplane, then the plane will not move.

The runway can only exert the force to the wheels, not to the plane itself, because the wheels will be freewheeling.

Pero kung speed lang nung runway ang pinaguusapan, lilipad yung eroplano.

What do you mean?

At the moment of takeoff: Relative to the wind, airplane will be running at takeoff speed, the runway will be running at takeoff speed towards the other direction. Relative to each other, the plane and the runway will be passing each other at TWICE the take of speed.

It cannot take off because it is stationary! Relative to the wind, the plane is stationary. Buti sana kung totoong runway yon, then yes. That's because the runway in this situation is moving on the opposite direction.

[niky]

Exactly. The conveyor matches the airplane's speed. Thus, the airplane moves forward at 30 mph. Instantly, the runway moves backwards at 30 mph. The wheels of the plane are now moving at 60 mph.

We have to consider this as a frictionless exercise, as by having the conveyor move at exactly the same time as the plane, you're creating a fictional universe in which there is no lightspeed delay anyway... :hysterical:

In the absence of friction in the wheels or the conveyor bearings, all that happens is the wheels move twice as fast, the belt moves one way, the plane moves another, and it'll take off... with exactly the same amount of thrust it would have needed to take off from a stationary runway.