#271004 - 30/11/2005 03:42
Re: Will the plane fly?
[Re: gbeer]
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pooh-bah
Registered: 20/01/2002
Posts: 2085
Loc: New Orleans, LA
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This line causes a bit of a problem for me. Quote:
The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.
This is impossible. As soon as the wheels start moving forward a little, the forward thrust has overcome inertia and friction, and the conveyor belt rolls into action. Unortunately, by moving against the plane, it has caused the wheels to turn FASTER, and as such, the belt must roll faster. Hrmmmm, if they go faster, the wheels will go FASTER. If we assume the quoted statement to be true, the belt must assume infinite speed instantly in order to match the plane's wheel's speed. Which, in "reality" could never happen since the speed of the conveyor belt would always be (speed of conveyor belt) + (speed of plane) relative to the ground.
In other words, it's akin to the paradox of having to always go half the distance to reach something, and therefore never making it. The Zeno Tort.
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#271005 - 30/11/2005 05:28
Re: Will the plane fly?
[Re: tfabris]
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carpal tunnel
Registered: 13/02/2002
Posts: 3212
Loc: Portland, OR
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Quote:
Now I wanna see them doing this one on Mythbusters. 
Say... isn't there a member of this BBS that has an RC plane? One "pca", in particular? Maybe we can convince him to build a conveyor belt... 
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#271006 - 30/11/2005 17:53
Re: Will the plane fly?
[Re: gbeer]
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pooh-bah
Registered: 15/01/2002
Posts: 1866
Loc: Austin
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Quote:
If the conveyor is moving forward, at the same speed as the wheels then, while the wheels are not turning, they are indeed moving forward, same as the aircraft.
That's the first thing that I thought. That is, that the wheels won't actually be spinning at all.
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#271007 - 30/11/2005 18:49
Re: Will the plane fly?
[Re: RobotCaleb]
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pooh-bah
Registered: 19/09/2002
Posts: 2494
Loc: East Coast, USA
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Then the conveyor belt will not be moving because the wheels are not moving.
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#271008 - 30/11/2005 18:54
Re: Will the plane fly?
[Re: FireFox31]
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carpal tunnel
Registered: 25/12/2000
Posts: 16706
Loc: Raleigh, NC US
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But if the conveyor belt doesn't move, then the wheels will start moving, at which time the conveyor belt would have to start up. I guess both the wheels and the conveyor belt would each be moving at half the speed of the plane.
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#271010 - 01/12/2005 00:26
Re: Will the plane fly?
[Re: Robotic]
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pooh-bah
Registered: 15/01/2002
Posts: 1866
Loc: Austin
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Quote:
No ... airplane motion.
Relative to the conveyor belt.
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#271011 - 01/12/2005 02:11
Re: Will the plane fly?
[Re: wfaulk]
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carpal tunnel
Registered: 17/12/2000
Posts: 2665
Loc: Manteca, California
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Quote:
But if the conveyor belt doesn't move, then the wheels will start moving, at which time the conveyor belt would have to start up. I guess both the wheels and the conveyor belt would each be moving at half the speed of the plane.
The wheels are attached to the plane they cannot move at any speed except that of the plane. Don't confuse the rpms of the wheel with it's net motion.
Edited by gbeer (01/12/2005 02:12)
_________________________
Glenn
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#271012 - 01/12/2005 03:27
Re: Will the plane fly?
[Re: ithoughti]
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carpal tunnel
Registered: 17/12/2000
Posts: 2665
Loc: Manteca, California
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Truly though the question as stated is really more in the nature of finding out something about the person(s) willing to attempt an answer.
Look back through this thread. Some of the responses show how a person tackles problems. Others posts illustrate the writers grasp of mechanics and kinematics. Some writers take a stand then endlessly validate it with practical trivia, avoiding the the fact that the provided info is ambiguous. Assumptions run rampant. Some just like a good arugment or generate one by themselves not clearly writing what they mean. (Sort of like the original question.) As an assesment tool it it can tell you a lot about people. Even if they recognize it as such, it still says something about them.
Fun abounds.
_________________________
Glenn
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#271013 - 01/12/2005 07:38
Re: Will the plane fly?
[Re: RobotCaleb]
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pooh-bah
Registered: 06/04/2005
Posts: 2026
Loc: Seattle transplant
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Quote:
Quote:
No ... airplane motion.
Relative to the conveyor belt.
To clarify:
No wheel motion.
Belt motion.
Airplane motion (relative to the air/airport/rest of world).
The 'No' referred only to the first item. The second and third items were simple results of what logically would follow.
Ok- seriously, this thread and me are done.
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#271014 - 01/12/2005 07:48
Re: Will the plane fly?
[Re: lectric]
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Anonymous
Unregistered
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lectric and JBorgen are right. Itīs impossible to build such a coveyor belt.
Conveyor belt speed must equal the wheel speed, according to this problem.
Those two speeds can only be equal when the air speed of the plane is 0.
Once the engines start up, the air speed will be greater than 0, which means the wheels must turn faster than the conveyor belt.
So the only way the conveyor belt can match the speed of the wheels is when everything is stationary (belt speed, wheel speed, and air speed all must equal 0). The plane will fly, but itīs impossible for the belt to match the wheel speed.
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#271015 - 01/12/2005 14:25
Re: Will the plane fly?
[Re: gbeer]
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carpal tunnel
Registered: 25/12/2000
Posts: 16706
Loc: Raleigh, NC US
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Quote:
The wheels are attached to the plane they cannot move at any speed except that of the plane. Don't confuse the rpms of the wheel with it's net motion.
True. Maybe.
It says that conveyor belt moves opposite the direction of rotation at the speed of the wheels. If what you're saying is right, then it moves at the speed of the wheels (that is, the same speed as the plane), but that means that the wheels wouldn't be rotating, so I think your way of reading it isn't internally consistent. Of course, the real answer may be that no real-world situation actually matches the criteria of the question.
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#271016 - 01/12/2005 16:18
Re: Will the plane fly?
[Re: Robotic]
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pooh-bah
Registered: 13/09/1999
Posts: 2401
Loc: Croatia
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Ah, then I missread the problem. In this case, of course, those who said that the plane would take off a bit earlier (because the engine does not have to oversome the wheel rotational friction) are right.
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#271017 - 01/12/2005 20:49
Re: Will the plane fly?
[Re: bonzi]
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carpal tunnel
Registered: 20/12/1999
Posts: 31594
Loc: Seattle, WA
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No, the problem was just poorly worded. I've now seen variants on the puzzle that word it more clearly. The idea is that the conveyor belt is supposed to try to stop the plane from taking off, not help it to do so. The idea of the problem is to make you (briefly) think that the plane won't move, until you realize that planes don't use their wheels for power.
The problem is really a lot simpler than what we've made it out to be in this thread. Its only goal was to make you go "Oh, duh, right, the propeller thrusts against the air, not the ground."
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#271018 - 01/12/2005 20:59
Re: Will the plane fly?
[Re: tfabris]
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carpal tunnel
Registered: 13/07/2000
Posts: 4180
Loc: Cambridge, England
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Quote:
The problem is really a lot simpler than what we've made it out to be in this thread. Its only goal was to make you go "Oh, duh, right, the propeller thrusts against the air, not the ground."
It's a bit more subtle than that; it's also asking "Does the force due to friction increase with speed?". If yes, then there's a belt speed at which the thrust is balanced-out, and the plane doesn't take off. If no, the plane takes off.
And in fact the answer is that friction doesn't increase with speed, but that's a slightly surprising fact, and plenty of people's "folk" understanding of physics won't encompass it.
Peter
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#271019 - 01/12/2005 21:01
Re: Will the plane fly?
[Re: peter]
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carpal tunnel
Registered: 25/12/2000
Posts: 16706
Loc: Raleigh, NC US
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Well, that's not entirely true, as it's very possible for the axle components to be made of materials that expand when heated, and it would be possible for it to freeze as the heat due to friction increases.
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Bitt Faulk
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#271020 - 01/12/2005 21:55
Re: Will the plane fly?
[Re: tfabris]
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Anonymous
Unregistered
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Quote:
The problem is really a lot simpler than what we've made it out to be in this thread. Its only goal was to make you go "Oh, duh, right, the propeller thrusts against the air, not the ground."
I think itīs a little more complicated then that, because the problem states an impossible premise - that the conveyor belt can match the speed of the wheels.
In order for the belt speed to match the wheel speed, the plane must remain stationary (Imagine running on a tread mill). But the thrust is applied to the air and so the plane moves forward, forcing the wheels to turn faster than the conveyor belt.
So the conveyor belt will never even move. The only possible speeds it can match the wheel speed at are 0 and infinity.
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#271021 - 01/12/2005 22:03
Re: Will the plane fly?
[Re: peter]
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Anonymous
Unregistered
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Quote:
"Does the force due to friction increase with speed?". If yes, then there's a belt speed at which the thrust is balanced-out, and the plane doesn't take off. If no, the plane takes off.
I donīt think thatīs true. Once the engines apply thrust to the air, the plane will move forward. And once the plane has moved forward at all, the belt has been defeated as the wheels haved turned faster.
That is unless the belt can go from a standstill to infinity miles per hour instantaneously.
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#271022 - 02/12/2005 02:06
Re: Will the plane fly?
[Re: ithoughti]
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carpal tunnel
Registered: 17/12/2000
Posts: 2665
Loc: Manteca, California
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Quote:
The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.
This part of it is entirely self consistant, though it seems otherwise. Neither half of the statment says anything to counter the other, as long as it is accepted that the first half of the statment is talking about net speed (linear) while the second half is talking about rotational speed. Two compleatly different things.
The belt can move to do both, match the speed of the wheel (linear), and move to oppose the rotation of the wheel at the same time. It's the same motion for the belt. The net effect is that the wheel is never allowed to spin.
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#271023 - 02/12/2005 02:54
Re: Will the plane fly?
[Re: ]
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carpal tunnel
Registered: 14/01/2002
Posts: 2858
Loc: Atlanta, GA
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Quote:
But the thrust is applied to the air and so the plane moves forward, forcing the wheels to turn faster than the conveyor belt.
Not true, I think. Just because the plane is moving foward doesn't necessarily mean the wheels are turning faster. I've skidded out on ice in my car enough to know that the wheels don't have to turn to get foward motion. Once the plane has overcome the friction (not hard), the conveyor belt will no longer have to speed up because the wheels won't turn any faster.
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Rome did not create a great empire by having meetings; they did it by killing all those who opposed them.
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#271024 - 02/12/2005 05:10
Re: Will the plane fly?
[Re: JeffS]
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Anonymous
Unregistered
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You are talking about the belt moving in the opposite direction of the plane, right?
Think of a car on an oversized treadmill. If you set the treadmill to 25 mph, and set the cruise control on your car to 25 mph, then youīre not going to move anywhere (air speed will equal 0 with no wind). If you hit the gas and drive 30 mph then youīll move forward and your air speed will be 5 mph, and the wheels will be turning 5 mph faster than the belt.
So the only time that the wheel speed and belt speed are equal is when the air speed is zero. When the thrust of the car is applied to the wheels the belt can always keep up and the airspeed will remain at zero. But when you switch on the JATO rocket attached to the back bumper of your car, then the thrust is applied to the air which of course makes the airspeed (and earth-ground-speed) increase, forcing the wheels to turn faster than the belt. If the belt tries to keep up by spinning faster, then itīll only further increase the speed of the free-rolling wheels.
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#271025 - 02/12/2005 11:15
Re: Will the plane fly?
[Re: ]
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carpal tunnel
Registered: 19/01/2002
Posts: 3584
Loc: Columbus, OH
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Correct...untill the wheels reach their limit, at which point the plane will begin to drag its wheels accross the runway if the engine is strong enough.
Think of the wheels being locked in place so they don't spin. That's all this problem does. It removes the turning of the wheels from the equation completely. If a plane can take off with its wheels locked in place, then it can take off on a conveyor belt runway.
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#271026 - 02/12/2005 14:02
Re: Will the plane fly?
[Re: JBjorgen]
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pooh-bah
Registered: 09/08/2000
Posts: 2091
Loc: Edinburgh, Scotland
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not exactly - some aircraft may have trouble taking off if they had locked axles which prevent the wheels turning...due to friction. All aircraft with wheels should suffer no ill effects taking off from a conveyor belt (excluding possible axle or wheel failure at high rotation speeds)
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#271027 - 02/12/2005 14:48
Re: Will the plane fly?
[Re: ithoughti]
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new poster
Registered: 21/11/2001
Posts: 40
Loc: Maine, USA
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Quote:
The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.
My interpretation of this is that the linear belt speed must match the linear speed (forward motion) of the wheels (the planes ground speed) but in the opposite direction of rotation.
It does NOT mean that the conveyor must match the ROTATIONAL speed of the wheels, as the resulting linear belt speed would be dependant on the ratio of the diameters of the planes wheels and the belts wheels.
So, we know that the conveyor belt is attached to the ground, and the plane is on the belt.
Assume the plane accelerates to some ground speed x, before the belt turns on.
The planes wheel is moving forward with the plane at the same speed x.
The planes wheel is rotating in a clock-wise (CW) direction.
The planes wheel is also moving at some rotational velocity proportional to its diameter (both of which are irrelevant).
With the plane moving at speed x, the belt turns on (see attached diagram).
The conveyor belt wheels are rotating counter clock-wise (CCW) opposite to the rotation of the planes wheels. The linear speed of the belt is the same as the planes ground speed x.
In conclusion:
The only difference between this takeoff, and takeoff from a normal runway, is that the planes wheels will be rotating twice as fast as normal. Yes, the plane will take off.
-Jeff
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#271028 - 04/12/2005 01:16
Re: Will the plane fly?
[Re: insightful]
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Anonymous
Unregistered
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The only possible speeds that the belt can match the wheels are zero and infinity. Thereīs no inbetween, so itīs pointless to talk about friction.
The belt would have to accelerate from 0 mph to infinity instantaneously. Once the engines start, then the plane will move forward. If the plane is moving forward then the wheels are moving faster than the belt.
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#271029 - 04/12/2005 02:18
Re: Will the plane fly?
[Re: ]
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carpal tunnel
Registered: 19/01/2002
Posts: 3584
Loc: Columbus, OH
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Quote:
The only possible speeds that the belt can match the wheels are zero and infinity. Thereīs no inbetween, so itīs pointless to talk about friction.
Wrong. I know I was saying the same thing earlier in the thread, but it's not true. The belt always matches the wheels. The wheels have a mechanical limit to how fast they will spin due to friction, etc... The two speeds are 0 and the limit of the wheels.
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#271030 - 04/12/2005 04:09
Re: Will the plane fly?
[Re: ]
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old hand
Registered: 15/02/2002
Posts: 1049
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I don't think this is true. As the plane accellerates (relative to the ground or stationary air), the conveyor-belt runway will accellerate in the same direction as the plane, causing the wheels to remain motionless (relative to the plane and conveyor-belt). The whole conveyor-airplane "assembly" will accellerate; the plane due to thrust, and the conveyor because its controller is programmed to negate wheel motion.
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#271031 - 04/12/2005 18:58
Re: Will the plane fly?
[Re: TigerJimmy]
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addict
Registered: 25/06/2002
Posts: 456
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Quote:
the conveyor-belt runway will accellerate in the same direction as the plane, causing the wheels to remain motionless (relative to the plane and conveyor-belt).
This is the confusion due to the extremely poorly-worded question.
- One group of people think the question means the conveyer belt moves with the plane, keeping the wheels stationary (or rather, non-rotating).
- The other group thinks the question means the belt moves against the plane, in an attempt to keep the center of mass of the plane stationary.
Your analysis falls into the first group.
Almost everyone else on this thread has been analyzing this from the second perspective.
I think it is pretty obvious for "Group A" people that the plane takes off and the wheels don't spin.
It is for all the people who interpreted this question in the "Group B" style that this discussion is mostly about.
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#271032 - 04/12/2005 20:51
Re: Will the plane fly?
[Re: tfabris]
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addict
Registered: 24/07/2002
Posts: 618
Loc: South London
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Quote:
The problem is really a lot simpler than what we've made it out to be in this thread. Its only goal was to make you go "Oh, duh, right, the propeller thrusts against the air, not the ground."
Well I'll agree with you Tony if nobody else will, I think people here are reading far too much into this "problem"! 
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