Anyone who doesn't see this needs to be mercilessly beat about the thing that's supposed to be a head on their shoulders... <img src="/forums/images/graemlins/lol.gif" alt="" />

If they don't understand, it's probably already happened <img src="/forums/images/graemlins/lol.gif" alt="" />

Well ain't that somethin <img src="/forums/images/graemlins/ignore.gif" alt="" />

If you were traveling at the speed of light would your headlights still work? How about your wipers?

Kevin <img src="/forums/images/graemlins/wink.gif" alt="" />

Define still work. Yes they would still operate but would they illuminate your path in front of you? And your wipers would freakin fly off the car along with the paint...lol

Get serious - it would depend if you were going the speed of light on a treadmill! Then, your headlights would work fine.

The way I see it, the problem can be broken into three parts, none of which are equationally connected to each other. That of the plane's fuselage and it's relationship to the air, that of the wheels and their relationship to the conveyor and that of the fuselage and its relationship to the wheels. To simplify the problem, lets consider the wheel bearings to be frictionless (no heat/can't lock up/cannot induce movement on their own accord).

Part I: The wheels/fuselage relationship.
The wheels sit under the plane and provide a "frictionless" support between the fuselage and the ground. Since the ground is "stationary" and the plane must move to attain lift, the wheels break all physical connection between the fuselage and the ground while it is overcome by gravity (lift comes later).

Part II: Wheels/Conveyor relationship
Consider that the wheels have perfect physical connection to the conveyor through friction (no slip). According to Newton an object at rest remains at rest unless acted upon by an outside force. So, when the conveyor moves, the wheels turn, but, because of the fricionless bearings, have no effect on the fuselage. This induces relative motion between the conveyor and fuselage, but no true motion (speed over geographical ground) or relative motion through the air (still no lift).

Part III: Fuselage/Air relationship
The fuselage is connected to the engine. The engine has an output shaft that is connected to a propeller. The shaft is coupled to the engine by another frictionless thrust bearing. This means there is a physical connection between the propeller and the fuselage. When the propeller turns, it cuts the air causing a low pressure area to form on the front of the propeller and a high pressure area on the rear. Because of this pressure differential, the propeller pulls forward taking the fuselage with it.

The outcome:
Because the propeller is now pulling the previously stationary object forward, it is achieving relative motion with the motionless air (no wind) and static geography. As the plane moves forward and relative motion between the fuselage (with wings) and air increases speed, vertical lift occurs and takeoff is achieved. The key is that the wheels do nothing in this case except keep the fuselage from making physical contact with the conveyor while lift has not overcome gravity.

I hope I made my thoughts clear as mud...

Oh, looky there. As I was exposing my mental retardation by typing that long explanation, the conversation took another turn. I'm a total De-De-Deee... <img src="/forums/images/graemlins/notooth.gif" alt="" />

Happens to the best of us...

Come on over...



<img src="/forums/images/graemlins/smile.gif" alt="" />

I believe this may be the problem of some to comprehend the terms of the original word problem. My answer still stands with the understanding that

A) The experiment begins with zero work (aircraft engines off, conveyor belt off)
B) No wind
C) Zero friction in the wheels
D) Ground speed is understood as relative to a point on the ground - not on the conveyor
E) Infinite technology to commence the experiment I.E. (and by far the most important) the conveyor belt moves exactly to the induced speed of the plane at precisely the same time.

Gravity holds the plane to ground. The free spinning wheels are a conveyor in themselves - allowing the plane to create forward motion without (in our case) any friction.

In our windless scenario the thrust has to propel this object forward to take off speed - which is also ground speed.

Now remember the original post? The conveyor matches the speed of the plane. All you Yes-It-Willers are assuming that at some point the planes thrust overpowers the the speed of the belt. It doesn't. It aint going anywhere. And in fact the conveyor will hardly move.

Again I defer to my R/C airplane experiment -

1) Hold it above your head at full throttle and let it go - that thing on your head will be mercilessly beat <img src="/forums/images/graemlins/butwiggle.gif" alt="" />.

2)Now step on a 500ft treadmill, power it up and start running matching speeds so you remain stationary relative to a linear space (on the ground NOT the treadmill), hold the plane above your head and gently let go - again you will feel pain.

3)Now get on it again. Put the treadmill on slow and start running. Eventually if you are fast enough you will gain enough speed over the treadmill to provide enough airflow over the wings to produce lift - the ground speed (speed relative to the ground NOT the treadmill) is equal to the TakeOff speed. If you let go the plane will fly away.

BUT #3 IS NOT THE SITUATION POSTED IN THE PROBLEM

This riddle is #2.

If I still haven't converted you there is no hope.

There is nothing new under the sun

Can we beat 400 pages? <img src="/forums/images/graemlins/pfft.gif" alt="" />