Will a plane take off on a conveyor belt?

even at 120 mph the plane will be airborn.

 

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this implies the plane wheels will also rotate at infinite RPMs.
the plane will be airborn before that happens.

 

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Aha, BUT! the real question with the observers is:
Who gets to say how fast the belt is moving? (that is: relative to who is the speed of the belt taken?) Since it's the belt's speed that has to match the wheel's perihperal speed (which is the velocity the axis moves at realtive to the object the wheel is resting on.)

This if our observer who decides how fast to run the belt is the plane (or on it), He pushes the throttle in, and looks at his speedomter attached to one of his wheels and says "Well im going 20mph now, better see if I need to change the belt speed" He looks out the window and sees: that the belt is already moving backwards at 20mph relative to him, thus he does not increase the belts speed, and takes off. It should also be noted that he sees the ground also going backwars at 20mph and thus can rest asured that he has airspeed.

While a person on the ground would see the belt resting stationary, the plane going forward at 20mph, and the plane taking off.
The two observers dissagree as to weather the belt was moving at the correct speed, however since the OP didnt specify who the observer was or should I say: relative to what/who the velocities had to be measured, the plane can take off.

And remember the question was weather it could take off; not if it could take off in all scenarios, but just if there was the possibilty in a scenario. And obviously there is. This tally's 3 or 4: a 'perfect scenario', an observer being the plane scenario, a 'realistic' scenario with the wheels sliding, and from Janus' post: a realistic scenario with the belt giving out before the plane did.

Everyone else has assumed the belt has to move backwards relative to the ground, but the ground is no more a fixed observer than the plane.

Furthurmore, 2Inquisitive, you do not deduct the speed the belt is moving from the plane's speed. Only a fraction of its backwards speed would carry the plane back, the rest would torque the wheel, uselessly. try this:
Grab a lego car or something with wheels that can roll somehwat realisticly and a peice of paper. Find a level surface and place the paper on it with the car on the paper. Now move the paper away (as levely as possible, liek a conveyer.) Do this at several different speeds.
You will find that at fairly slow speed the wheel's Rolling Resistance is not overcome by the paper and it moves back at the same speed, wheras at higher speeds when the wheels do roll, it doesnt move back at the same speed.
The easiest way to see if its moving at the same speed is to mark is starting position on the paper and see if it is still there afterwards.

-Andrew

PS: Janus great post.
EDIT:

Right, this actualy supports my above argument:
The ground connot be the observer for the belt's speed in any situation, otherwise this loop would happen and our belt would destroy itself the instant the plane made its wheels move.
So yes Leo, the wheels would spin with an infinit velocity, except in a realistic scenario in which the belt and the belt's motor would find itself out of commision...

 

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andbna,

Aha what?? The observer doing the measuring, obviously. Speed is a relative measurement, motion relative to the one doing the measuring. An observer on the plane does not measure the speed of the belt passing underneath the plane as the same speed as that of an observer on the ground measures it in his frame of reference.

Utter bullshit. The example was of a speedometer connected to the plane's wheel, which was measuring the speed of the belt passing under the wheels as 240 mph. You must deduct the speed of the belt relative to the ground to arrive at the speed of the plane relative to the ground. The difference determines whether the plane can lift off or not.

 

That is my point, with the added conclusion that if we say the observer who measures the belt speed is on the plane. Then while the belt is stationary relativ to the ground: the belt will always appear (to the observer on the plane) to move with the same speed of the wheels peripheral speed (in opposite direction). And thus the problem is solved and is no different than a nomral take-off.

I think we are in agreeance; if you mean "deduct the speed of the belt, relative to the ground, from the wheel's peripheral speed" then we are.

What I thought you meant was deduct the belt's speed relative to the ground from the plane's speed and therfore the plane would not be moving relative to the ground...
anyway that aside...

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So it seems we are on the same side of the points we are arguing.. dont you just love the problems with langauge? >.>
-Andrew

 

Ok. There is a cylindrical rocket inside a cylindrical launcher.
The rocket is resting on ground and pointing skywards and
fixed on the walls of the rocket are some roller wheels.
The launcher is a vertical tube with conveyer belt at its walls.
Now the speed of the conveyer belt can be adjusted to try to match the speed of the wheels.

3.2.1.. the rocket fires. Can the conveyer belt and roller wheels hold the rocket still?

 

I thought this question was essentially answered with: It's basically a trick question.

The conveyor belt "matching the speed of the wheels" seems to mean that the velocity of the conveyor belt (at the point where it touches the wheels) matches and opposes the tangential speed of wheels at the spot they touch the belt.

First, there is a trivial solution where the speed of the wheels and the conveyor belt are both zero.

If the wheels are spinning at all and the belt is exactly, instantaneously, matching that speed (but in the opposite direction), then the wheels as a whole would seem to have zero forward velocity. The spinning of the wheel and the spinning of the belt allow for no forward velocity.

If the plane itself *had* any forward velocity, then the "speed" of the wheel at the point of contact with the conveyor belt would have to be greater than the opposing "speed" of the belt./*

With the engines of the jet providing thrust, there is no reason to imagine such a conveyor belt *could* exist...the plane or the engines would have to be physically limited/restrained to prevent the jet engines from overwhelming the conveyor belt and causing the wheels to move faster than the belt. (That speed differential would result in the wheels rolling "forward" relative to their starting position on the belt, hence the plane moves forward. In the absence of such a differential, the wheels—and plane—would be stationary relative to the belt.) That said, the unlikely conveyor belt setup is an assumption of the problem, rather than something to be disregarded.

In order to make the problem work, as written, something has to be restraining the engines' ability to move the plane. That's not specified in the problem, but not expressly forbidden either. The alternative is to ignore the constraint "The conveyor belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction" and decide that that conveyor belt simply always fails to work as advertised.

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/* I suppose I am imagining free spinning wheels, firmly on the ground. There are two other related possibilities that occur to me:

(i) the wheels could be "skidding" along the belt, rather than rolling freely. Then (rough on the tires though that may be), the speed of the wheels and of the belt could be identical despite the forward velocity of the plane itself (I have a sneaking suspicion the friction would cause many planes to bang their noses into the conveyor belt—ending the flight—but I suppose it depends on the design of the plane, the amount of friction and the torque that creates on the plane); or

(ii) the plane could be "skipping" along the belt. This is basically a variant of the "skidding" theory, but with less friction (as there would only be friction in the moments the plane's wheels touched the belt, rather than continuously). The plane would have to built up enough velocity to start skipping along, of course, the wheels would have to skid during the part where they got up to that speed.

 

the conveyor belt has no effect on the forward motion of the axle, save for friction losses.

in my opinion the only way the plane will not take off is if it rests directly on the belt. (no wheels at all)

 

Every airplane is totally independent of wheel traction for acceleration.

The only important factor is airspeed of the wing versus the air.

Airplane acceleration is performed by the action of thrust having no necessary relation to groundspeed.

Bottom line: yes, an airplane can take off. Fifty years ago an F-100 with RATO could take off with no concern about groundspeed. In the present day a Harrier would have no trouble either. Both can chronically take off with zero groundspeed.

 

Thanks One Raven. Simply put.
Therei s no difference between a plane on a conveyor belt and a plane lifted in a harness with someone with very quick hands spinning the wheels manually. Another question. If the wheels spun fast enough and someone gave the plane a prod, could it take off as a gyroscope? It could have big wheels if you like.