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The setup and question:
An aircraft (jet or propeller) sits on a conveyor belt runway. The belt matches the speed of the wheels, but in the opposite direction to that of the attempt to take off. Can the plane take off?
QUOTE (Referenced source question translated from Russian+)
The aircraft (jet or screw) stands on the tarmac with a movable cover (type transporter). Movement of [Dvigaetsya] coating may be against the direction of take-off aircraft. It has a control system that monitors and adjusts the speed of cloth so that the wheel speed aircraft was equal to the speed blade motion. Question: Can the plane take a run on the track and take off?
If the above paraphrase is acceptable, this referenced question will henceforth be ignored entirely.
Given assumptions:
Both the wheel and belt are idealized as being indestructible, and perhaps only within the thought problem, undeformable.
If the above paraphrase is acceptable, this referenced question will henceforth be ignored entirely.
Given assumptions:
Both the wheel and belt are idealized as being indestructible, and perhaps only within the thought problem, undeformable.
Nice Setup. However, before this gets rolling, I think it needs to be acknowledged that there are two different parts of this problem. The first part is the paradox that the problem creates, and the second part is whether anything under other conditions can stop the plane.
The paradox is that the question trivializes the answer, as asked:
Your answer is correct if the airplane is defined as moving (with wheel speed being the sum of the planes ground speed and the conveyor's). In this version the wheel are described to match the belt. That is if the wheel were allowed to roll on the ground without slipping, the distance it would have covered is matched by the distance a spot on the conveyor would cover. Am I coherent enough?
The paradox is that the question trivializes the answer, as asked:
QUOTE (synthsin75+Mar 31 2011, 12:35 PM)
An aircraft (jet or propeller) sits on a conveyor belt runway. The belt matches the speed of the wheels, but in the opposite direction to that of the attempt to take off. Can the plane take off?
By the very nature of the setup, the plane is already defined to never move. This issue should be addressed in one manner or another before the second part can be addressed.
By the very nature of the setup, the plane is already defined to never move. This issue should be addressed in one manner or another before the second part can be addressed.
QUOTE (RTS-Eng+Mar 31 2011, 09:34 PM)
Nice Setup. However, before this gets rolling, I think it needs to be acknowledged that there are two different parts of this problem. The first part is the paradox that the problem creates, and the second part is whether anything under other conditions can stop the plane.
The paradox is that the question trivializes the answer, as asked:
By the very nature of the setup, the plane is already defined to never move. This issue should be addressed in one manner or another before the second part can be addressed.
Yeah, RTS-Eng is right. In any case the belt can only much the wheel in the opposite direction (of the intended movement of the plane). Truth is belt and plane's intended direction are opposite. The wheel has no direction
The paradox is that the question trivializes the answer, as asked:
By the very nature of the setup, the plane is already defined to never move. This issue should be addressed in one manner or another before the second part can be addressed.
Yeah, RTS-Eng is right. In any case the belt can only much the wheel in the opposite direction (of the intended movement of the plane). Truth is belt and plane's intended direction are opposite. The wheel has no direction
Let us say that a Thrust force F acts
on the plane in the forward
direction due to the engine.Also a
Contact force N acts on it in
opposite direction due to the
wheel.Now the same force N acts
on the wheel in the forward
direction.This force N passes
through the centre of mass of the
wheel..hence has no torque about
centre of mass.So,there must be a
friction force f acting on the wheel
in the opposite direction to rotate it.
I wont calculate the torque about
the point of contact as it is
accelerating in the ground frame
which gives rise to pseudo torques.
Let the mass of plane be M..let the
mass of tyre be m..Radius of tyre R.
And moment of inertia of tyre
about COM = I =mr^2/2. Since the
plane and the tyre have same
translational accelertion,we can
take them as one system for
writing the translational equation i.e
F - f = (M+m)a. Equation 1.
Now wrtiting the torque equation
for the wheel about COM.
fr = Iø Equation 2.where ø is the
angular acceration of wheel and is
equal to 2a/r here. Using it in
equation 2 and putting the value of
f in equation 1 we get
F = (m+M)a + (2Ia)/r^2 ..equation
3. Now I = mr^2/2.using it above
we get. a = F/(M + 2m).Now let us
analyse the result..if M = infinite, a
= 0.Also if the mass of the wheel is
infinite, a = 0. Let us now try to
calculate the friction force f..we see
f=ma or f = F/(M/m + 2)..we see
that friction force can vary from 0
to F/2.Now for any particulare
ration M/m = k , if max friction is
greater than or equal to F/(k+2),
there will be no slipping between
the tyres and the conveyor belt
and if the max friction is less the F/
k+2 ,there may be slipping ..still the
plane will move.If the plane was on
ground,we would have found that
the friction force f = F/(2M/m +3)
or F/(2k +3)..and the friction would
have varied betweew 0 and F/3..so
indeed due to this converyor
case,relatively more friction is
acting.Hence we see that in any
case of finite M and m, the plane
will move and take off.In this
solution i have ignored the friction
between tyres and plane .Brothers
if u think i am wrong please point it
out. I would love to improve my
concepts.
on the plane in the forward
direction due to the engine.Also a
Contact force N acts on it in
opposite direction due to the
wheel.Now the same force N acts
on the wheel in the forward
direction.This force N passes
through the centre of mass of the
wheel..hence has no torque about
centre of mass.So,there must be a
friction force f acting on the wheel
in the opposite direction to rotate it.
I wont calculate the torque about
the point of contact as it is
accelerating in the ground frame
which gives rise to pseudo torques.
Let the mass of plane be M..let the
mass of tyre be m..Radius of tyre R.
And moment of inertia of tyre
about COM = I =mr^2/2. Since the
plane and the tyre have same
translational accelertion,we can
take them as one system for
writing the translational equation i.e
F - f = (M+m)a. Equation 1.
Now wrtiting the torque equation
for the wheel about COM.
fr = Iø Equation 2.where ø is the
angular acceration of wheel and is
equal to 2a/r here. Using it in
equation 2 and putting the value of
f in equation 1 we get
F = (m+M)a + (2Ia)/r^2 ..equation
3. Now I = mr^2/2.using it above
we get. a = F/(M + 2m).Now let us
analyse the result..if M = infinite, a
= 0.Also if the mass of the wheel is
infinite, a = 0. Let us now try to
calculate the friction force f..we see
f=ma or f = F/(M/m + 2)..we see
that friction force can vary from 0
to F/2.Now for any particulare
ration M/m = k , if max friction is
greater than or equal to F/(k+2),
there will be no slipping between
the tyres and the conveyor belt
and if the max friction is less the F/
k+2 ,there may be slipping ..still the
plane will move.If the plane was on
ground,we would have found that
the friction force f = F/(2M/m +3)
or F/(2k +3)..and the friction would
have varied betweew 0 and F/3..so
indeed due to this converyor
case,relatively more friction is
acting.Hence we see that in any
case of finite M and m, the plane
will move and take off.In this
solution i have ignored the friction
between tyres and plane .Brothers
if u think i am wrong please point it
out. I would love to improve my
concepts.
QUOTE
Brothers
if u think i am wrong please point it
out. I would love to improve my
concepts.
if u think i am wrong please point it
out. I would love to improve my
concepts.
Your answer is correct if the airplane is defined as moving (with wheel speed being the sum of the planes ground speed and the conveyor's). In this version the wheel are described to match the belt. That is if the wheel were allowed to roll on the ground without slipping, the distance it would have covered is matched by the distance a spot on the conveyor would cover. Am I coherent enough?
I posted this too quickly. I need to re-do it. The concept was correct, but I presented it incorrectly.
QUOTE (boit+Mar 31 2011, 07:05 PM)
Your answer is correct if the airplane is defined as moving (with wheel speed being the sum of the planes ground speed and the conveyor's). In this version the wheel are described to match the belt. That is if the wheel were allowed to roll on the ground without slipping, the distance it would have covered is matched by the distance a spot on the conveyor would cover. Am I coherent enough?
yes..i have assumed that the velocity of the point of the wheel which is in contact with conveyor has the same velocity as that of conveyor..i.e no slipping...In case there was slipping, the max friction equal to k(M+m)g would have acted on the wheel..(M is mass of plane...m is mass of wheel ..k is coeff of kinetic friction).. And taking the plane plus tyre as one system, the plane would accelerate if thrust F>k(M+m)g.
yes..i have assumed that the velocity of the point of the wheel which is in contact with conveyor has the same velocity as that of conveyor..i.e no slipping...In case there was slipping, the max friction equal to k(M+m)g would have acted on the wheel..(M is mass of plane...m is mass of wheel ..k is coeff of kinetic friction).. And taking the plane plus tyre as one system, the plane would accelerate if thrust F>k(M+m)g.
Let us say that the plane is in the air and velocity of the plane is v in forward direction ...as the wheel is attached to it, the velocity of the all the points of the wheel is v in forward direction(wheel is not rotating yet) ..and thus the velocity of the lowest point of wheel is also v in forward direction ...now if we want that the velocity of the LOWEST point of the wheel be -v i.e v in bacward direction, we have to rotate the wheel in clockwise direction with angular velocity $= 2v/r..because due to this the net velocity of the lowest point of wheel wil be v - $r i.e v- 2v= -v ...this is also the velocity of conveyor belt..same holds for acceleration too..
QUOTE (Umer.banday+Mar 31 2011, 10:37 PM)
Let us say that the plane is in the air and velocity of the plane is v in forward direction ...as the wheel is attached to it, the velocity of the all the points of the wheel is v in forward direction(wheel is not rotating yet) ..and thus the velocity of the lowest point of wheel is also v in forward direction ...now if we want that the velocity of the LOWEST point of the wheel be -v i.e v in backward direction, we have to rotate the wheel in clockwise direction with angular velocity $= 2v/r..because due to this the net velocity of the lowest point of wheel will be v - $r i.e v- 2v= -v ...this is also the velocity of conveyor belt..same holds for acceleration too..
The short analytical answer to this has been: If the wheel is both translating and spinning, its angular speed is more than the belt's linear speed. Just assume a stationary belt and a rolling wheel. True, relative to the wheel COM the belt is moving backwards. but relative to the ground the angular speed of the wheel is non-zero while the belt's speed is zero. Moving the belt just goes to spin the wheel faster and always more rapidly than the belt. If plane's speed relative to the grounds equals belt's speed relative to the ground, then the angular speed of the wheel is twice. In this scenario we want the belt speed to much wheel speed. Just the way some printers spits out paper. Or a movie film reel...
The short analytical answer to this has been: If the wheel is both translating and spinning, its angular speed is more than the belt's linear speed. Just assume a stationary belt and a rolling wheel. True, relative to the wheel COM the belt is moving backwards. but relative to the ground the angular speed of the wheel is non-zero while the belt's speed is zero. Moving the belt just goes to spin the wheel faster and always more rapidly than the belt. If plane's speed relative to the grounds equals belt's speed relative to the ground, then the angular speed of the wheel is twice. In this scenario we want the belt speed to much wheel speed. Just the way some printers spits out paper. Or a movie film reel...
QUOTE (boit+Mar 31 2011, 08:01 PM)
The short analytical answer to this has been: If the wheel is both translating and spinning, its angular speed is more than the belt's linear speed. Just assume a stationary belt and a rolling wheel. True, relative to the wheel COM the belt is moving backwards. but relative to the ground the angular speed of the wheel is non-zero while the belt's speed is zero. Moving the belt just goes to spin the wheel faster and always more rapidly than the belt. If plane's speed relative to the grounds equals belt's speed relative to the ground, then the angular speed of the wheel is twice. In this scenario we want the belt speed to much wheel speed. Just the way some printers spits out paper. Or a movie film reel...
that is very good logic..but my dear brother..what exactly do u mean by the term 'wheel speed'? my tiny brain cant understand this..
that is very good logic..but my dear brother..what exactly do u mean by the term 'wheel speed'? my tiny brain cant understand this..
QUOTE (Umer.banday+Mar 31 2011, 11:17 PM)
that is very good logic..but my dear brother..what exactly do u mean by the term 'wheel speed'? my tiny brain cant understand this..
Yeah, talking of wheel speed for a wheel nailed on a wall sounds oxymoronic but for the purpose of this thought experiment, the rate of rotation multiplied by the circumference of said wheel is what is termed wheel speed. The correct way of measurement is supposed to be given in rads (I am not sure) but since we want to compare with the belt we present the angular speed as a linear speed
Unorthodox but we have to start somewhere.
Yeah, talking of wheel speed for a wheel nailed on a wall sounds oxymoronic but for the purpose of this thought experiment, the rate of rotation multiplied by the circumference of said wheel is what is termed wheel speed. The correct way of measurement is supposed to be given in rads (I am not sure) but since we want to compare with the belt we present the angular speed as a linear speed
Unorthodox but we have to start somewhere.
Sorry. I deleted my previous posting because I rushed through it too fast, and used a piece of information from a previous poster (different thread) that I assumed I could trust. However, upon reviewing my posting, I realized that I kept editing it to fix cascading problems as the result of using this previous equation. This is the same posting, but I corrected the minor errors off-line before reposting it.
QUOTE (boit+Mar 31 2011, 01:52 PM)
Yeah, RTS-Eng is right. In any case the belt can only much the wheel in the opposite direction (of the intended movement of the plane). Truth is belt and plane's intended direction are opposite. The wheel has no direction
No Boit, it is not a problem with direction. If I misunderstood you, then please tell me and we can address that misunderstanding.
The problem is that with the belt defined to match the speed of the wheel, then the wheel is therefore constrained to be immovable. If the wheel is constrained to be immovable, then the answer is trivial. Here is the proof of that assertion:
The motion of a disk is controlled by the following:
ω = v_rim/r - v_axle/r
Therefore,
v_axle = v_rim - ω * r (this is the corrected version of what a previous poster stated in another thread .)
Because the wheel rotates without slipping:
v_rim = v_conveyor
The speed of the conveyor is defined to match the angular speed of the wheel:
v_conveyor = ω * r
Substituting v_rim with v_conveyor, the previous (original/bolded) expression becomes:
v_axle = v_conveyor - ω * r
Substituting ω * r with v_conveyor, the previous expression becomes:
v_axle = v_conveyor - v_conveyor
Therefore
v_axle = 0
It makes no difference what other factors or forces play on the speed of the wheel or its axle, the problem is defined that the axle cannot move. If the axle cannot move, then the plane cannot take off. The problem in itself becomes trivial.
No Boit, it is not a problem with direction. If I misunderstood you, then please tell me and we can address that misunderstanding.
The problem is that with the belt defined to match the speed of the wheel, then the wheel is therefore constrained to be immovable. If the wheel is constrained to be immovable, then the answer is trivial. Here is the proof of that assertion:
The motion of a disk is controlled by the following:
ω = v_rim/r - v_axle/r
Therefore,
v_axle = v_rim - ω * r (this is the corrected version of what a previous poster stated in another thread .)
Because the wheel rotates without slipping:
v_rim = v_conveyor
The speed of the conveyor is defined to match the angular speed of the wheel:
v_conveyor = ω * r
Substituting v_rim with v_conveyor, the previous (original/bolded) expression becomes:
v_axle = v_conveyor - ω * r
Substituting ω * r with v_conveyor, the previous expression becomes:
v_axle = v_conveyor - v_conveyor
Therefore
v_axle = 0
It makes no difference what other factors or forces play on the speed of the wheel or its axle, the problem is defined that the axle cannot move. If the axle cannot move, then the plane cannot take off. The problem in itself becomes trivial.
QUOTE (RTS+)
Nice Setup. However, before this gets rolling, I think it needs to be acknowledged that there are two different parts of this problem. The first part is the paradox that the problem creates, and the second part is whether anything under other conditions can stop the plane.
The paradox is that the question trivializes the answer, as asked:
An aircraft (jet or propeller) sits on a conveyor belt runway. The belt matches the speed of the wheels, but in the opposite direction to that of the attempt to take off. Can the plane take off?
By the very nature of the setup, the plane is already defined to never move. This issue should be addressed in one manner or another before the second part can be addressed.
First, the question is not "what can stop the plane from taking off". It is, according to the setup, "can the plane take off".
Second, please explain the "paradox", as we are beginning a new discussion here, as per guideline 2.
I don't see how the setup bars motion as defined, please elaborate.
The paradox is that the question trivializes the answer, as asked:
QUOTE ((synthsin75 @ Mar 31 2011+ 12:35 PM))
An aircraft (jet or propeller) sits on a conveyor belt runway. The belt matches the speed of the wheels, but in the opposite direction to that of the attempt to take off. Can the plane take off?
By the very nature of the setup, the plane is already defined to never move. This issue should be addressed in one manner or another before the second part can be addressed.
First, the question is not "what can stop the plane from taking off". It is, according to the setup, "can the plane take off".
Second, please explain the "paradox", as we are beginning a new discussion here, as per guideline 2.
I don't see how the setup bars motion as defined, please elaborate.
QUOTE (boit+)
Yeah, RTS-Eng is right. In any case the belt can only much the wheel in the opposite direction (of the intended movement of the plane). Truth is belt and plane's intended direction are opposite. The wheel has no direction
I must be missing something here, as I don't see how "in the opposite direction to that of the attempt to take off" means anything else but "belt and plane's intended direction are opposite".
RTS, please define your ω term for clarity. And any reason why you chose to use the angular rather than the linear speed?
Edit: A bit of cross posting with you there. You covered the paradox already/
I must be missing something here, as I don't see how "in the opposite direction to that of the attempt to take off" means anything else but "belt and plane's intended direction are opposite".
RTS, please define your ω term for clarity. And any reason why you chose to use the angular rather than the linear speed?
Edit: A bit of cross posting with you there. You covered the paradox already/
QUOTE (synthsin75+Mar 31 2011, 04:20 PM)
Second, please explain the "paradox", as we are beginning a new discussion here, as per guideline 2.
I believe our postings crossed.
Did my posting just above yours address your concerns?
Again, I apologize for having to delete the previous version of this proof, but I found a trivial mistake (minus sign transposition) that opened it up to trivial argument. It needed to be fixed with more care.
I believe our postings crossed.
Did my posting just above yours address your concerns?
Again, I apologize for having to delete the previous version of this proof, but I found a trivial mistake (minus sign transposition) that opened it up to trivial argument. It needed to be fixed with more care.
QUOTE (RTS-Eng+Mar 31 2011, 03:30 PM)
I believe our postings crossed.
Did my posting just above yours address your concerns?
Yes.
Did my posting just above yours address your concerns?
Yes.
QUOTE (synthsin75+Mar 31 2011, 04:41 PM)
Yes.
Whew!!!
Before you edited you posting, I was really concerned I was going to have to dig too far back into my memory to explain ω. Thank goodness you didn't ask me that. 
Whew!!!
Before you edited you posting, I was really concerned I was going to have to dig too far back into my memory to explain ω. Thank goodness you didn't ask me that.
QUOTE (RTS-Eng+Mar 31 2011, 03:49 PM)
Whew!!! Before you edited you posting, I was really concerned I was going to have to dig too far back into my memory to explain ω. Thank goodness you didn't ask me that.
Found it for myself.http://hyperphysics.phy-astr.gsu.edu/hbase/rotq.html
What about the causation implied? The causation implies an initiating force of thrust upon the wheels, which the belt matches and opposes. Isn't here that the paradox is alleviated?
Before you edited you posting, I was really concerned I was going to have to dig too far back into my memory to explain ω. Thank goodness you didn't ask me that. Found it for myself.http://hyperphysics.phy-astr.gsu.edu/hbase/rotq.html
What about the causation implied? The causation implies an initiating force of thrust upon the wheels, which the belt matches and opposes. Isn't here that the paradox is alleviated?
QUOTE (synthsin75+Mar 31 2011, 05:24 PM)
What about the causation implied? The causation implies an initiating force of thrust upon the wheels, which the belt matches and opposes. Isn't here that the paradox is alleviated?
Well actually, that doesn't alleviate the original paradox I presented above. It actually creates a second paradox that I didn't want to muddy this discussion with at the moment.
The two are based on the same conditions, but are still somewhat exclusive.
The first paradox I presented prevents the axle from moving. The second paradox prevents the system from accelerating.
Because no one has yet stated that the system is accelerating, the second paradox has not yet come into play. (see rule #2).
Did I answer your question, or would you like more information on the first topic?
Well actually, that doesn't alleviate the original paradox I presented above. It actually creates a second paradox that I didn't want to muddy this discussion with at the moment.
The two are based on the same conditions, but are still somewhat exclusive.
The first paradox I presented prevents the axle from moving. The second paradox prevents the system from accelerating.
Because no one has yet stated that the system is accelerating, the second paradox has not yet come into play. (see rule #2).
Did I answer your question, or would you like more information on the first topic?
Starting from a speed of 0, what makes the wheels of the plane begin to turn?
If the question stipulates a control system that adjusts the speed of the cloth to be equal to the measured wheel speed (the wording is ambiguous, but this is, I believe, the intended meaning), then the answer is trivial - the plane cannot be allowed to generate any thrust, because it would cause the axle of the wheel to move relative to the ground, thus causing the wheel to rotate due to contact with the stationary belt, thus allowing the control system to begin to move the belt, but already violating the conditions of the question because the non-zero wheel speed does not match the zero belt speed.
However, since the question implies that the plane is required to attempt to take off, and is thus required to generate thrust, then the conditions of the question cannot be met.
Additionally, if the control system is as described, then the belt cannot accelerate as would be required to generate the thrust that would cancel the plane's thrust and prevent the plane's motion - it would be required to set the belt to a speed greater than the measured wheel speed.
If the question stipulates a control system that adjusts the speed of the cloth to be equal to the measured wheel speed (the wording is ambiguous, but this is, I believe, the intended meaning), then the answer is trivial - the plane cannot be allowed to generate any thrust, because it would cause the axle of the wheel to move relative to the ground, thus causing the wheel to rotate due to contact with the stationary belt, thus allowing the control system to begin to move the belt, but already violating the conditions of the question because the non-zero wheel speed does not match the zero belt speed.
However, since the question implies that the plane is required to attempt to take off, and is thus required to generate thrust, then the conditions of the question cannot be met.
Additionally, if the control system is as described, then the belt cannot accelerate as would be required to generate the thrust that would cancel the plane's thrust and prevent the plane's motion - it would be required to set the belt to a speed greater than the measured wheel speed.
Edit: Opps, cross posted with Argyll. He did in fact define the second paradox I mention below.
Now that we are in agreement as to what the wheels' speed constitute, lets see how we can constrain the plane to be always attempting to take off but never does. We've here
1) Unbreakable belt
2) Indestructible wheels (rim and rubber)
3) Unlimited acceleration (at least on the belt's part
4) Anticipatory mechanism
We can ignore bullet #4 if we already find the wheels turning and the belt accelerating. This may be why we speak of wheels speed (non zero value I intuitively guess) and plane's attempt to take off (as in taxing to pick up sufficient speed to create relative wind and hop int the air).
Correct me If I've moved out of the rubric of the OP dear Synth.
Ahem.
Ahem.
9) No insults or implied impugning of the skills or knowledge of another. Refuting claims, and their justification, only requires a debate of forwarded facts.
As per guideline 9 this statement is obviously meant as a very thinly veiled passive aggressive insult. Anyone can clearly see that its one and only intention is to stir up trouble. If this continues any further this thread will end exactly the same way as the other one. This has to stop here and now. If Derek cannot control himself he should not be in this thread.
Ahem.
As per guideline 9 this statement is obviously meant as a very thinly veiled passive aggressive insult. Anyone can clearly see that its one and only intention is to stir up trouble. If this continues any further this thread will end exactly the same way as the other one. This has to stop here and now. If Derek cannot control himself he should not be in this thread.
Okay, as long as you realize this is a pointless discussion. Belts break, wheels destruct, acceleration cannot be unlimited, and the only thing that can anticipated from some posters here is more idiocy.
However, that said, I will not interfere, in this "dialogue." Good luck.
I do hope this is indeed your last post here as this is even less civil than the one that proceeded it. This of course indicates you have no real intention of not violating the conditions put forward in the OP.
QUOTE (RTS-Eng+Mar 31 2011, 05:47 PM)
Because no one has yet stated that the system is accelerating, the second paradox has not yet come into play. (see rule #2).
By the way, because I already took the time to develop the principles of the first paradox, it will make it much easier to develop them for the second paradox.
I can begin doing that, but I want to make sure that (A) there are no disputes against the first paradox, and (B ) that you or anyone else wishes that I introduce the second paradox.
By the way, because I already took the time to develop the principles of the first paradox, it will make it much easier to develop them for the second paradox.
I can begin doing that, but I want to make sure that (A) there are no disputes against the first paradox, and (B ) that you or anyone else wishes that I introduce the second paradox.
QUOTE (Argyll+Mar 31 2011, 06:48 PM)
Additionally, if the control system is as described, then the belt cannot accelerate as would be required to generate the thrust that would cancel the plane's thrust and prevent the plane's motion - it would be required to set the belt to a speed greater than the measured wheel speed.
You'll soon discover Darth has no problem violating this restriction.
You'll soon discover Darth has no problem violating this restriction.
QUOTE (NoCleverName+Apr 1 2011, 12:33 AM)
You'll soon discover Darth has no problem violating this restriction.
I've crossed paths with both Darth and SZ on a different forum under a different user name, and I'm well aware of their position on this "myth".
Where they disagree with me, and apparently with many others on this forum, is in the aforementioned control system. I read the riddle as stating that the control system monitors the wheel speed and adjusts the belt speed to match that measurement. They apparently read it as a control system that dos whatever it must to ensure that those speeds always match - even though that means anticipating, or predicting, the rate of acceleration that would result in the correct amount of force to counter the thrust.
It all comes down to whether you accept a predictive control system as being in compliance with the riddle, or whether you insist on a reactive control system.
My preference, however, is for the version of the riddle that does not stipulate matching the wheel speed. In this version, if all speeds are measured relative to an external fixed observer, it is trivial to see that the plane will take off easily - but it accomplishes its goal as a riddle in requiring the reader to overcome their natural assumptions about the behavior of treadmills and their effects on wheeled vehicles.
I've crossed paths with both Darth and SZ on a different forum under a different user name, and I'm well aware of their position on this "myth".
Where they disagree with me, and apparently with many others on this forum, is in the aforementioned control system. I read the riddle as stating that the control system monitors the wheel speed and adjusts the belt speed to match that measurement. They apparently read it as a control system that dos whatever it must to ensure that those speeds always match - even though that means anticipating, or predicting, the rate of acceleration that would result in the correct amount of force to counter the thrust.
It all comes down to whether you accept a predictive control system as being in compliance with the riddle, or whether you insist on a reactive control system.
My preference, however, is for the version of the riddle that does not stipulate matching the wheel speed. In this version, if all speeds are measured relative to an external fixed observer, it is trivial to see that the plane will take off easily - but it accomplishes its goal as a riddle in requiring the reader to overcome their natural assumptions about the behavior of treadmills and their effects on wheeled vehicles.
A stationary wheel has no direction. That's why I felt that it sounded oxymoronic to speak of a stationary wheel that is moving in the other direction. Wheel speed matches belt speed suffices. So that we don't mistake the conveyor to be doing what it usually does, that is convey goods e.g. Airplane, we say it moves in the opposite direction of plane's intended take off direction. We talk of angular speed here is it requires no direction. But here there is no displacement as the wheel is constrained never to translate. Putting the plane on tank's tracks and placing it on the belt may make a little more sense as the chain actually has an appreciable linear speed and displacement when held stationary. Not just tangential speed like the wheel.
Hope I have made it clear about the direction. Only the plane and the belt can have direction is what I meant to write at the beginning.
EDIT. (2nd editing). Seen we've crossposted. I agree with you. It is just that I can be less coherent when using my phone browser (hard to edit and the darn things hang when quickly cahnging fro upper tp lower cases or even scrolling back. I've just grabbed my laptop.
Hope I have made it clear about the direction. Only the plane and the belt can have direction is what I meant to write at the beginning.
EDIT. (2nd editing). Seen we've crossposted. I agree with you. It is just that I can be less coherent when using my phone browser (hard to edit and the darn things hang when quickly cahnging fro upper tp lower cases or even scrolling back. I've just grabbed my laptop.
QUOTE (boit+Mar 31 2011, 10:21 PM)
A stationary wheel has no direction. That's why I felt that it sounded oxymoronic to speak of a stationary wheel moving in the other direction. Wheel speed matches belt speed suffices. So that we don't mistake the conveyor to be doing what it usually does, that is convey goods e.g. Airplane, we say it moves in the opposite direction of plane's intended take off direction. Unless we talk angular speed. But here the is no displacement as the wheel is constrained never to translate. Putting the plane on tank's tracks and placing it on the belt may make a little more sense and the chain cactually has an appreciable linear speed when held stationary. Not just tangetial speed.
I can't be sure from reading what you said, but you do understand that this constraint of the wheel is the first paradox I mentioned, don't you? The wheel (axle) is already prevented from translating down the conveyor before we've even introduced any information about the plane. Technically, the problem is solved, and we can conclude the plane can't move. That's why it trivializes the problem/answer.
I can't be sure from reading what you said, but you do understand that this constraint of the wheel is the first paradox I mentioned, don't you? The wheel (axle) is already prevented from translating down the conveyor before we've even introduced any information about the plane. Technically, the problem is solved, and we can conclude the plane can't move. That's why it trivializes the problem/answer.
So I started work on the thorough explanation. I've got the table of contents and the titles of all the sections done and it's already 7 pages. This might take a little time.
QUOTE (RTS-Eng+Apr 1 2011, 06:42 AM)
I can't be sure from reading what you said, but you do understand that this constraint of the wheel is the first paradox I mentioned, don't you? The wheel (axle) is already prevented from translating down the conveyor before we've even introduced any information about the plane. Technically, the problem is solved, and we can conclude the plane can't move. That's why it trivializes the problem/answer.
I edited. Thaks for understanding what I was trying to explain (how I was in agreement). I hope the edited version is not as incoherent s the original.
I edited. Thaks for understanding what I was trying to explain (how I was in agreement). I hope the edited version is not as incoherent s the original.
QUOTE
An aircraft (jet or propeller) sits on a conveyor belt runway. The belt matches the speed of the wheels, but in the opposite direction to that of the attempt to take off. Can the plane take off?
Now that we are in agreement as to what the wheels' speed constitute, lets see how we can constrain the plane to be always attempting to take off but never does. We've here
1) Unbreakable belt
2) Indestructible wheels (rim and rubber)
3) Unlimited acceleration (at least on the belt's part
4) Anticipatory mechanism
We can ignore bullet #4 if we already find the wheels turning and the belt accelerating. This may be why we speak of wheels speed (non zero value I intuitively guess) and plane's attempt to take off (as in taxing to pick up sufficient speed to create relative wind and hop int the air).
Correct me If I've moved out of the rubric of the OP dear Synth.
QUOTE (boit+Mar 31 2011, 08:51 PM)
Yeah, talking of wheel speed for a wheel nailed on a wall sounds oxymoronic but for the purpose of this thought experiment, the rate of rotation multiplied by the circumference of said wheel is what is termed wheel speed. The correct way of measurement is supposed to be given in rads (I am not sure) but since we want to compare with the belt we present the angular speed as a linear speed Unorthodox but we have to start somewhere.
thank you brother for clearing my confusion...i mistook wheel speed as speed of COM of wheel in ground frame...but (if i understood you right) it is the speed of the circumference of the wheel in the frame of COM of wheel...did i get you right?
Unorthodox but we have to start somewhere. thank you brother for clearing my confusion...i mistook wheel speed as speed of COM of wheel in ground frame...but (if i understood you right) it is the speed of the circumference of the wheel in the frame of COM of wheel...did i get you right?
QUOTE (boit+Apr 1 2011, 04:09 AM)
1) Unbreakable belt
2) Indestructible wheels (rim and rubber)
3) Unlimited acceleration (at least on the belt's part
4) Anticipatory mechanism
You forgot one.
5) Tinkerbell and fairy dust
2) Indestructible wheels (rim and rubber)
3) Unlimited acceleration (at least on the belt's part
4) Anticipatory mechanism
You forgot one.
5) Tinkerbell and fairy dust
QUOTE (boit+Mar 31 2011, 11:09 PM)
4) Anticipatory mechanism
We can ignore bullet #4 if we already find the wheels turning and the belt accelerating.
You don't need an anticipatory mechanism. You just need to redefine how the conveyor's speed is determined. That's not a simple question to answer. Anything based on speed creates the same problem as above. Anything based on a force, also trivializes the problem.
We can ignore bullet #4 if we already find the wheels turning and the belt accelerating.
You don't need an anticipatory mechanism. You just need to redefine how the conveyor's speed is determined. That's not a simple question to answer. Anything based on speed creates the same problem as above. Anything based on a force, also trivializes the problem.
QUOTE
You forgot one.
5) Tinkerbell and fairy dust
5) Tinkerbell and fairy dust
Ahem.
QUOTE (->
| QUOTE |
| You forgot one. 5) Tinkerbell and fairy dust |
Ahem.
9) No insults or implied impugning of the skills or knowledge of another. Refuting claims, and their justification, only requires a debate of forwarded facts.
As per guideline 9 this statement is obviously meant as a very thinly veiled passive aggressive insult. Anyone can clearly see that its one and only intention is to stir up trouble. If this continues any further this thread will end exactly the same way as the other one. This has to stop here and now. If Derek cannot control himself he should not be in this thread.
QUOTE (Sithdarth+Apr 1 2011, 04:54 AM)
Ahem.
As per guideline 9 this statement is obviously meant as a very thinly veiled passive aggressive insult. Anyone can clearly see that its one and only intention is to stir up trouble. If this continues any further this thread will end exactly the same way as the other one. This has to stop here and now. If Derek cannot control himself he should not be in this thread.
Okay, as long as you realize this is a pointless discussion. Belts break, wheels destruct, acceleration cannot be unlimited, and the only thing that can anticipated from some posters here is more idiocy.
However, that said, I will not interfere, in this "dialogue." Good luck.
QUOTE
Okay, as long as you realize this is a pointless discussion. Belts break, wheels destruct, acceleration cannot be unlimited, and the only thing that can anticipated from some posters here is more idiocy.
However, that said, I will not interfere, in this "dialogue." Good luck.
However, that said, I will not interfere, in this "dialogue." Good luck.
I do hope this is indeed your last post here as this is even less civil than the one that proceeded it. This of course indicates you have no real intention of not violating the conditions put forward in the OP.
While colourful language looks pretty it gets threads closed. Newbie's aren't allowed to tell people that. Further no one has the right to decide who should/should not post on any subject other than the moderators.
Re NoCleverNames mathematical analysis in the defunct thread.
" Well, I retrieved "Darth's equation" from first principles and, in short, it's a fraud as far as holding the plane back. Or the battery.
I used the same basic strategy as should have been used had his idea been done "right". You first get a formula for the "linear mass equivalent of a rotating body". That will be:
Total K.E. = 1/2 m_e * v^2 = 1/2 I * w^2
but since v = wr
Total K.E = 1/2 m_e * v^2 = 1/2 I * (v/r)^2
m_e = I/r^2
Then, given that "mass", what is its acceleration if a certain force is applied?
F = a_b * I/r^2
a_b = F * r^2/I
... which should look familiar since it's Darth's result after incredible processing.
But what does it mean?
It means if all the force is to be used to get the object spinning in place with no linear motion than this is what the acceleration has to be.
So, Darth has his object "spinning in place". It doesn't have a linear component therefore it can't be exerting any linear force.
In other words, it has absolutely no energy to spare to hold a plane, let alone a battery in place. The theory is void.
It's over. This theory doesn't work. I got the results by just considering an object spinning in free space. We all know by Newton's laws that an object "in motion keeps that motion unless altered by an outside force". An object spinning in free space isn't going to go wandering about since it doesn't have any linear component.
But when an outside force is applied to a spinning object, say that of a plane's engines, it's going to roll right off. laugh.gif "
Not sure if your allowed to quote between threads, suppose I will find out.
Question with wheel's motion relative to the belt
KE= 1/2 MV^2
KE 1/2 I * w^2
Relative to the belt the velocity of the base of the wheel is zero whilst at the top of the wheel it it twice the axle velocity In my opinion this gives a difference between the kinetic energy of these two points. This would affect the effective mass.
Re NoCleverNames mathematical analysis in the defunct thread.
" Well, I retrieved "Darth's equation" from first principles and, in short, it's a fraud as far as holding the plane back. Or the battery.
I used the same basic strategy as should have been used had his idea been done "right". You first get a formula for the "linear mass equivalent of a rotating body". That will be:
Total K.E. = 1/2 m_e * v^2 = 1/2 I * w^2
but since v = wr
Total K.E = 1/2 m_e * v^2 = 1/2 I * (v/r)^2
m_e = I/r^2
Then, given that "mass", what is its acceleration if a certain force is applied?
F = a_b * I/r^2
a_b = F * r^2/I
... which should look familiar since it's Darth's result after incredible processing.
But what does it mean?
It means if all the force is to be used to get the object spinning in place with no linear motion than this is what the acceleration has to be.
So, Darth has his object "spinning in place". It doesn't have a linear component therefore it can't be exerting any linear force.
In other words, it has absolutely no energy to spare to hold a plane, let alone a battery in place. The theory is void.
It's over. This theory doesn't work. I got the results by just considering an object spinning in free space. We all know by Newton's laws that an object "in motion keeps that motion unless altered by an outside force". An object spinning in free space isn't going to go wandering about since it doesn't have any linear component.
But when an outside force is applied to a spinning object, say that of a plane's engines, it's going to roll right off. laugh.gif "
Not sure if your allowed to quote between threads, suppose I will find out.
Question with wheel's motion relative to the belt
KE= 1/2 MV^2
KE 1/2 I * w^2
Relative to the belt the velocity of the base of the wheel is zero whilst at the top of the wheel it it twice the axle velocity In my opinion this gives a difference between the kinetic energy of these two points. This would affect the effective mass.
This is getting a bit like "if the facts aren't on your side, argue the law". I think what is happening is we are looking for the faults in the problem setup without looking at the intent of the original problem. I believe the intent was to describe a situation that mimicked as closely as possible a car-on-a-conveyor. But then we substitute a driving force that does not depend on the conveyor for motive force.
The various problem setups we've seen all have their technical deficiencies which various posters exploit to their infuriating advantage by stretching physical reality.
Perhaps what is needed is a looser, not a stricter, setup which allows, perhaps, Darth to spin the wheels much faster than a "car-on-a-conveyor" would allow (yet keep within some semblance of physical reality).
After all, I believe that whatever is proposed as a solution, it could in principle actually be demonstrated ... perhaps at smaller scale.
The original myth said something along then lines of "monitor and adjusts" which perhaps better translated might have been "attempts to match". In any event, it certainly didn't seem to include "lock-step"-like rules ... which again are exploited for loopholes.
I wouldn't mind seeing solutions for stopping the plane that included as part of the solution the necessary conditions that have to prevail. (One silly condition might be a gravel-covered conveyor ... it would certainly likely stop the plane).
For now, the current setup is fatally flawed and we are now down to arguing about which loopholes should be allowed. That is not a good starting point.
The various problem setups we've seen all have their technical deficiencies which various posters exploit to their infuriating advantage by stretching physical reality.
Perhaps what is needed is a looser, not a stricter, setup which allows, perhaps, Darth to spin the wheels much faster than a "car-on-a-conveyor" would allow (yet keep within some semblance of physical reality).
After all, I believe that whatever is proposed as a solution, it could in principle actually be demonstrated ... perhaps at smaller scale.
The original myth said something along then lines of "monitor and adjusts" which perhaps better translated might have been "attempts to match". In any event, it certainly didn't seem to include "lock-step"-like rules ... which again are exploited for loopholes.
I wouldn't mind seeing solutions for stopping the plane that included as part of the solution the necessary conditions that have to prevail. (One silly condition might be a gravel-covered conveyor ... it would certainly likely stop the plane).
For now, the current setup is fatally flawed and we are now down to arguing about which loopholes should be allowed. That is not a good starting point.
QUOTE (NoCleverName+Apr 1 2011, 11:07 AM)
This is getting a bit like "if the facts aren't on your side, argue the law". I think what is happening is we are looking for the faults in the problem setup without looking at the intent of the original problem. I believe the intent was to describe a situation that mimicked as closely as possible a car-on-a-conveyor. But then we substitute a driving force that does not depend on the conveyor for motive force.
The various problem setups we've seen all have their technical deficiencies which various posters exploit to their infuriating advantage by stretching physical reality.
Perhaps what is needed is a looser, not a stricter, setup which allows, perhaps, Darth to spin the wheels much faster than a "car-on-a-conveyor" would allow (yet keep within some semblance of physical reality).
After all, I believe that whatever is proposed as a solution, it could in principle actually be demonstrated ... perhaps at smaller scale.
The original myth said something along then lines of "monitor and adjusts" which perhaps better translated might have been "attempts to match". In any event, it certainly didn't seem to include "lock-step"-like rules ... which again are exploited for loopholes.
I wouldn't mind seeing solutions for stopping the plane that included as part of the solution the necessary conditions that have to prevail. (One silly condition might be a gravel-covered conveyor ... it would certainly likely stop the plane).
For now, the current setup is fatally flawed and we are now down to arguing about which loopholes should be allowed. That is not a good starting point.
If this post is directed at my question which was not intended to be a point of law you are under no obligation to answer it.
The various problem setups we've seen all have their technical deficiencies which various posters exploit to their infuriating advantage by stretching physical reality.
Perhaps what is needed is a looser, not a stricter, setup which allows, perhaps, Darth to spin the wheels much faster than a "car-on-a-conveyor" would allow (yet keep within some semblance of physical reality).
After all, I believe that whatever is proposed as a solution, it could in principle actually be demonstrated ... perhaps at smaller scale.
The original myth said something along then lines of "monitor and adjusts" which perhaps better translated might have been "attempts to match". In any event, it certainly didn't seem to include "lock-step"-like rules ... which again are exploited for loopholes.
I wouldn't mind seeing solutions for stopping the plane that included as part of the solution the necessary conditions that have to prevail. (One silly condition might be a gravel-covered conveyor ... it would certainly likely stop the plane).
For now, the current setup is fatally flawed and we are now down to arguing about which loopholes should be allowed. That is not a good starting point.
If this post is directed at my question which was not intended to be a point of law you are under no obligation to answer it.
QUOTE (privatepaddy+Apr 1 2011, 07:35 AM)
If this post is directed at my question which was not intended to be a point of law you are under no obligation to answer it.
No, this is a general oservation about the futility of the current discussion.
No, this is a general oservation about the futility of the current discussion.
QUOTE (NoCleverName+Apr 1 2011, 12:03 PM)
No, this is a general oservation about the futility of the current discussion.
The present discussion will return to the Russian version of the myth because it is the "Original" As I previously stated no one has ever answered my question regarding the regenerative or positive feedback nature of the control system which acts more like a switch relay and motor contactors coupled to a mega watt power supply.
The maths has never really been challenged until your effort in the now defunct thread. What I expected was a basic but complete mathematical description of the problem it should not just work for just the one condition Like sithdarths
What we want is A_p to be zero in case 3 I imagined the same formula would predict each case.
The need for the high acceleration in the direction opposite to the planes direction sets in place angular momentum/torque which the plane thrust must over come since this thrust is via the axles where torque is minimum. I am not saying anything about the correctness of any of this but if a thread is not there to educate or entertain what is it for?
The present discussion will return to the Russian version of the myth because it is the "Original" As I previously stated no one has ever answered my question regarding the regenerative or positive feedback nature of the control system which acts more like a switch relay and motor contactors coupled to a mega watt power supply.
The maths has never really been challenged until your effort in the now defunct thread. What I expected was a basic but complete mathematical description of the problem it should not just work for just the one condition Like sithdarths
What we want is A_p to be zero in case 3 I imagined the same formula would predict each case.
The need for the high acceleration in the direction opposite to the planes direction sets in place angular momentum/torque which the plane thrust must over come since this thrust is via the axles where torque is minimum. I am not saying anything about the correctness of any of this but if a thread is not there to educate or entertain what is it for?
You brought up a few points there, PP. First, the "regenerative" or "feedback loop" characteristics of the control system has been recognize by more than one poster. (Darth denies that this happens ... but he must invoke very special circumstances for this to be true. Those circumstances are generally not agreed to by most posters).
As to the input and outputs to the wheel, you are correct in your observation that a torque is applied to the wheel giving it angular momentum. That being the case, only a torque can remove angular momentum (converting it to linear momentum). No one has identified the torque that accomplishes that requirement.
As to the input and outputs to the wheel, you are correct in your observation that a torque is applied to the wheel giving it angular momentum. That being the case, only a torque can remove angular momentum (converting it to linear momentum). No one has identified the torque that accomplishes that requirement.
QUOTE (NoCleverName+Mar 31 2011, 06:33 PM)
You'll soon discover Darth has no problem violating this restriction.
Violation of guideline #2. This is a "reference to previous discussions in other threads".
Violation of guideline #2. This is a "reference to previous discussions in other threads".
QUOTE (Argyll+)
I've crossed paths with both Darth and SZ on a different forum under a different user name, and I'm well aware of their position on this "myth".
Violation of guideline #2. This is a "reference to previous discussions in other threads, on other topics, or about other versions of this question".
Violation of guideline #2. This is a "reference to previous discussions in other threads, on other topics, or about other versions of this question".
QUOTE (Derek1148+)
You forgot one.
5) Tinkerbell and fairy dust
Violation of rules 5 and 9. 5-not a counter claim, and possibly 9-not a debate of facts, which may be misconstrued as implying insult.
5) Tinkerbell and fairy dust
Violation of rules 5 and 9. 5-not a counter claim, and possibly 9-not a debate of facts, which may be misconstrued as implying insult.
QUOTE (Sithdarth+)
As per guideline 9 this statement is obviously meant as a very thinly veiled passive aggressive insult. Anyone can clearly see that its one and only intention is to stir up trouble. If this continues any further this thread will end exactly the same way as the other one. This has to stop here and now. If Derek cannot control himself he should not be in this thread.
Very good use of the guidelines, as they were meant to work. If any poster continues in a manor that violates these guidelines, all posters following them are advised to, as per 10, ignore them as invalid. The claimed use of "fairy dust" constitutes an unfounded accusation.
Very good use of the guidelines, as they were meant to work. If any poster continues in a manor that violates these guidelines, all posters following them are advised to, as per 10, ignore them as invalid. The claimed use of "fairy dust" constitutes an unfounded accusation.
QUOTE (Derek1148+)
Okay, as long as you realize this is a pointless discussion. Belts break, wheels destruct, acceleration cannot be unlimited, and the only thing that can anticipated from some posters here is more idiocy.
Already addressed in the "given assumptions" of the first post, and another definite violation of #9. Contributors are advised to not engage this poster any further.
Already addressed in the "given assumptions" of the first post, and another definite violation of #9. Contributors are advised to not engage this poster any further.
QUOTE (privatepaddy+)
Re NoCleverNames mathematical analysis in the defunct thread.
Violation of #2, "reference to previous discussions in other threads". All claims must be forwarded anew.
Violation of #2, as above.
Those who ignore history are doomed to repeat it.
If there are two people who second (agree to) this change, the following will become our new "OP question".
An aircraft (jet or propeller) sits on a conveyor belt runway. The belt monitors and adjusts its speed to that of the wheels, but in the opposite direction to that of the attempt to take off. Can the plane take off?
I disagree with this new wording. It does not alleviate the first paradox, it just makes it more confusing. The wording is self-defeating and the problem remains pre-determined to the plane not moving by the definition of the problem.
I cannot think of a similar wording to the original version that doesn't also fall into the same paradox. I would like to find one, but the only thing I can thing of is simply, "how can the plane be stopped".
Violation of #2, "reference to previous discussions in other threads". All claims must be forwarded anew.
QUOTE (NoCleverName+)
(Darth denies that this happens ... but he must invoke very special circumstances for this to be true. Those circumstances are generally not agreed to by most posters).
Violation of #2, as above.
That's the only corrections I have for now, hopefully they become self-correcting as we progress, otherwise I won't be able to keep up and this thread will end poorly. EDIT: My corrections are only here to provide some proof of compliance.
I'll post my actually replies in next post.
Violation of #2, as above.
That's the only corrections I have for now, hopefully they become self-correcting as we progress, otherwise I won't be able to keep up and this thread will end poorly. EDIT: My corrections are only here to provide some proof of compliance.
I'll post my actually replies in next post.
QUOTE (synthsin75+Apr 1 2011, 11:31 AM)
Violation of #2, as above.
Those who ignore history are doomed to repeat it.
QUOTE (NoCleverName+Apr 1 2011, 05:07 AM)
The original myth said something along then lines of "monitor and adjusts" which perhaps better translated might have been "attempts to match". In any event, it certainly didn't seem to include "lock-step"-like rules ... which again are exploited for loopholes.
Good idea.
Proposed change to setup.
Since "monitor and adjusts" is a more concise definition of "matches", and perhaps would allow the discussion to move forward more productively, I propose we agree to a new question, as per:
"7) The form of the question will be agreed upon and henceforth in this thread be referred to as the "OP question". No other versions or alterations will be allowed. "
If there are two people who second (agree to) this change, the following will become our new "OP question".
An aircraft (jet or propeller) sits on a conveyor belt runway. The belt monitors and adjusts its speed to that of the wheels, but in the opposite direction to that of the attempt to take off. Can the plane take off?
Given assumptions added with this change:
The axle is allowed to translate, allowing the wheel to advance on the belt, but the belt can then accelerate sufficiently to bring that translation to either a stop or return it to its original position.
Whether the belt is allowed to merely stop or also reverse any gained translation is up for debate.
Good idea.
Proposed change to setup.
Since "monitor and adjusts" is a more concise definition of "matches", and perhaps would allow the discussion to move forward more productively, I propose we agree to a new question, as per:
"7) The form of the question will be agreed upon and henceforth in this thread be referred to as the "OP question". No other versions or alterations will be allowed. "
If there are two people who second (agree to) this change, the following will become our new "OP question".
An aircraft (jet or propeller) sits on a conveyor belt runway. The belt monitors and adjusts its speed to that of the wheels, but in the opposite direction to that of the attempt to take off. Can the plane take off?
Given assumptions added with this change:
The axle is allowed to translate, allowing the wheel to advance on the belt, but the belt can then accelerate sufficiently to bring that translation to either a stop or return it to its original position.
Whether the belt is allowed to merely stop or also reverse any gained translation is up for debate.
It seems that NCN does not think that the acceleration of the wheel can impose a force that is effective on the center of the wheel. If I am wrong please correct me. But if this was the case then a wheel rolling down a ramp would go just as fast, or actually faster than an object, wheel or not, skidding down the ramp. But even with the negative acceleration from kinetic friction a sliding object will beat a rolling object down the ramp. And to help back this up you might want to watch this video:Physics of Rolling. NCN might even recognize the school it was videoed at 
QUOTE (Subduction Zone+Apr 1 2011, 09:45 AM)
It seems that NCN does not think that the acceleration of the wheel can impose a force that is effective on the center of the wheel. If I am wrong please correct me. ... NCN might even recognize the school it was videoed at
Could be misconstrued as impugning the skills or knowledge of a poster as per:
"9) No insults or implied impugning of the skills or knowledge of another. Refuting claims, and their justification, only requires a debate of forwarded facts. "
The acceleration had not been properly forwarded yet.
The rest of your post challenges the facts, and is well within the guidelines. Especially the reference.
Could be misconstrued as impugning the skills or knowledge of a poster as per:
"9) No insults or implied impugning of the skills or knowledge of another. Refuting claims, and their justification, only requires a debate of forwarded facts. "
The acceleration had not been properly forwarded yet.
The rest of your post challenges the facts, and is well within the guidelines. Especially the reference.
Don't worry synth ... SD, I'm just guessing that rolling is slower than sliding (all things being equal) because of the energy required to perform both rotation and linear versus just linear alone. But good guess, right? But all things REALLY have to be equal, because sufficient static friction will stop sliding but has absolutely no effect on rolling. But what I mean by equal escapes me at the moment ... we're building a moving wall right now.
QUOTE (synthsin75+Apr 1 2011, 10:44 AM)
If there are two people who second (agree to) this change, the following will become our new "OP question".
An aircraft (jet or propeller) sits on a conveyor belt runway. The belt monitors and adjusts its speed to that of the wheels, but in the opposite direction to that of the attempt to take off. Can the plane take off?
I disagree with this new wording. It does not alleviate the first paradox, it just makes it more confusing. The wording is self-defeating and the problem remains pre-determined to the plane not moving by the definition of the problem.
I cannot think of a similar wording to the original version that doesn't also fall into the same paradox. I would like to find one, but the only thing I can thing of is simply, "how can the plane be stopped".
QUOTE (RTS-Eng+Apr 1 2011, 07:50 PM)
QUOTE (synthsin75+)
If there are two people who second (agree to) this change, the following will become our new "OP question".
An aircraft (jet or propeller) sits on a conveyor belt runway. The belt monitors and adjusts its speed to that of the wheels, but in the opposite direction to that of the attempt to take off. Can the plane take off?
An aircraft (jet or propeller) sits on a conveyor belt runway. The belt monitors and adjusts its speed to that of the wheels, but in the opposite direction to that of the attempt to take off. Can the plane take off?
I disagree with this new wording. It does not alleviate the first paradox, it just makes it more confusing. The wording is self-defeating and the problem remains pre-determined to the plane not moving by the definition of the problem.
I cannot think of a similar wording to the original version that doesn't also fall into the same paradox. I would like to find one, but the only thing I can thing of is simply, "how can the plane be stopped".
I second synthsin75 but also find it hard to disagree with RTS-Eng. Contracted into six word both the new and the older (first) version just asks, "How can the plane be stopped?"
I cannot think of a similar wording to the original version that doesn't also fall into the same paradox. I would like to find one, but the only thing I can thing of is simply, "how can the plane be stopped".
I second synthsin75 but also find it hard to disagree with RTS-Eng. Contracted into six word both the new and the older (first) version just asks, "How can the plane be stopped?"
I was not trying to impugn NCN's knowledge. I was trying to nail down his beliefs.
Okay, NCN and others I do hope you realize for analysis purposes it is perfectly okay to rotate a frame of reference. You just have to be careful to rotate the forces appropriately when you do this. We can rotate the ramp as seen in the video. Lets set the angle of the ramp arbitrarily at 10 degrees. The forces on the wheel are mgsin(10) parallel to the ramp and mgcos(10) normal to the ramp. So lets mentally rotate the ramp 10 degrees and see what happens. If it is a solid cylinder or wheel it will accelerate at (2/3)gsin(10) down the ramp. Now, if there was no force it would accelerate at gsin(10) that indicates that the rotating wheel generates a counter force to that lowers the acceleration. The only thing that could cause that counter force is the acceleration of the wheel. That shows that an accelerating wheel will generate a lateral force.
Okay, NCN and others I do hope you realize for analysis purposes it is perfectly okay to rotate a frame of reference. You just have to be careful to rotate the forces appropriately when you do this. We can rotate the ramp as seen in the video. Lets set the angle of the ramp arbitrarily at 10 degrees. The forces on the wheel are mgsin(10) parallel to the ramp and mgcos(10) normal to the ramp. So lets mentally rotate the ramp 10 degrees and see what happens. If it is a solid cylinder or wheel it will accelerate at (2/3)gsin(10) down the ramp. Now, if there was no force it would accelerate at gsin(10) that indicates that the rotating wheel generates a counter force to that lowers the acceleration. The only thing that could cause that counter force is the acceleration of the wheel. That shows that an accelerating wheel will generate a lateral force.
QUOTE (boit+Apr 1 2011, 07:09 AM)
Now that we are in agreement as to what the wheels' speed constitute, lets see how we can constrain the plane to be always attempting to take off but never does. We've here
1) Unbreakable belt
2) Indestructible wheels (rim and rubber)
3) Unlimited acceleration (at least on the belt's part
4) Anticipatory mechanism
We can ignore bullet #4 if we already find the wheels turning and the belt accelerating. This may be why we speak of wheels speed (non zero value I intuitively guess) and plane's attempt to take off (as in taxing to pick up sufficient speed to create relative wind and hop int the air).
Correct me If I've moved out of the rubric of the OP dear Synth.
The key statement here is Now that we are in agreement as to what the wheels' speed constitute, lets see how we can constrain the plane to be always attempting to take off but never does.. In essence it is asking if the plane can be stopped using these tools set up in that manner. Wheres the answer is trivial to some, it is mind boggling to most. Yours truly had to be convinced in a series of steps and demonstrations.
1) Unbreakable belt
2) Indestructible wheels (rim and rubber)
3) Unlimited acceleration (at least on the belt's part
4) Anticipatory mechanism
We can ignore bullet #4 if we already find the wheels turning and the belt accelerating. This may be why we speak of wheels speed (non zero value I intuitively guess) and plane's attempt to take off (as in taxing to pick up sufficient speed to create relative wind and hop int the air).
Correct me If I've moved out of the rubric of the OP dear Synth.
The key statement here is Now that we are in agreement as to what the wheels' speed constitute, lets see how we can constrain the plane to be always attempting to take off but never does.. In essence it is asking if the plane can be stopped using these tools set up in that manner. Wheres the answer is trivial to some, it is mind boggling to most. Yours truly had to be convinced in a series of steps and demonstrations.
We have not resolved any changes to the wording of the question, so any further discussion of its meaning or physics involved is moot until we do so. .
My only problem with changing the question to "how can the plane be stopped" is that we'd be essentially dealing with a landing rather than take off. IOW, this question would become "can you completely stop the forward motion of a landing plane at the instant it makes contact with a moving runway".
That seems very fare from any possible interpretation of our OP question. Thoughts?
What we've already shown it that the original question has to be greatly altered to even attempt to apply physics to it as anything other than a riddle.
My only problem with changing the question to "how can the plane be stopped" is that we'd be essentially dealing with a landing rather than take off. IOW, this question would become "can you completely stop the forward motion of a landing plane at the instant it makes contact with a moving runway".
That seems very fare from any possible interpretation of our OP question. Thoughts?
What we've already shown it that the original question has to be greatly altered to even attempt to apply physics to it as anything other than a riddle.
I disagree about the need to alter the original question to deal with it physically. All you have to deal with is analyzing the consequences of the question as it was asked. Different people have different points where they disagree with our contention that the belt can hold the plane in place. For example NCN seemed to disagree that the belt could impart any force at all on the plane. I would hope that the MIT link I gave let him see that that was wrong. It will take a bit more analysis to show that the belt can or can't react instantaneously to the wheels. That seems to be RTS' main contention, though he seemed to be agreeing with NCN about the belt not giving the wheels a lateral force.
I am trying to go through this a point at a time. There is no point in going on to RTS' claim until we get the force on the wheels situation cleared up.
I am trying to go through this a point at a time. There is no point in going on to RTS' claim until we get the force on the wheels situation cleared up.
QUOTE (Subduction Zone+Apr 1 2011, 01:36 PM)
I disagree about the need to alter the original question to deal with it physically.
The reason why the original wording needs to be changed has been stated with a proof to accompany it. Proof of Paradox 1 To date, it has not been disputed. If you wish to dispute it, then you must adhere to rule #5 of the OP rules.
The reason why the original wording needs to be changed has been stated with a proof to accompany it. Proof of Paradox 1 To date, it has not been disputed. If you wish to dispute it, then you must adhere to rule #5 of the OP rules.
QUOTE (Subduction Zone+Apr 1 2011, 01:36 PM)
It will take a bit more analysis to show that the belt can or can't react instantaneously to the wheels. That seems to be RTS' main contention, though he seemed to be agreeing with NCN about the belt not giving the wheels a lateral force.
I have made no such assertion at this time, nor at any time in the past. There isn't really a rule for "putting words in my mouth", but the closest rule would be #2, where this discussion starts anew. (ETA: In hindsight, this also falls under Rule #5, in that you have asserted I made a statement or claim, but have not substantiated the existence of that statement or claim.)
I have made no such assertion at this time, nor at any time in the past. There isn't really a rule for "putting words in my mouth", but the closest rule would be #2, where this discussion starts anew. (ETA: In hindsight, this also falls under Rule #5, in that you have asserted I made a statement or claim, but have not substantiated the existence of that statement or claim.)
RTS, I did not "put words" into your mouth. If you reread my post I clearly wrote "it seems" that means you came off that way to me, it invites clarification.
And your "Proof of Paradox" is no more than a statement of the tautological defense of the problem. That is not satisfactory since it does not say why the wheel would stay in place. That is why the first thing, in my mind, that needs to be done is an analysis of the forces on the wheel.
And your "Proof of Paradox" is no more than a statement of the tautological defense of the problem. That is not satisfactory since it does not say why the wheel would stay in place. That is why the first thing, in my mind, that needs to be done is an analysis of the forces on the wheel.
SD ... I have not had time to consider your argument in detail but I can say that as far as pure rolling is concerned you need a torque to change the angular momentum. Gravity or the normal force will NOT induce or retard rolling because these forces vector right thru the COM. On the other hand, the frictional force at the point of contact IS a torque and CAN induce or retard rolling.
Strictly speaking a force thru the center will induce or retard LINEAR progress down the ramp. To the extent that rolling is COMBINED with that linear motion is up to how much friction is playing a role simultaneously creating torque.
Of course, once rolling is taking place then SOME of the available energy mgh MUST be devoted to rotation ... what's left will go to linear momentum. How that divides up probably depends on the mass (linear) and moment of inertia (angular) of the object.
Strictly speaking a force thru the center will induce or retard LINEAR progress down the ramp. To the extent that rolling is COMBINED with that linear motion is up to how much friction is playing a role simultaneously creating torque.
Of course, once rolling is taking place then SOME of the available energy mgh MUST be devoted to rotation ... what's left will go to linear momentum. How that divides up probably depends on the mass (linear) and moment of inertia (angular) of the object.
QUOTE (Subduction Zone+Apr 1 2011, 02:27 PM)
And your "Proof of Paradox" is no more than a statement of the tautological defense of the problem. That is not satisfactory since it does not say why the wheel would stay in place. That is why the first thing, in my mind, that needs to be done is an analysis of the forces on the wheel.
Either adhere to Rule #5 or withdraw your objection. I welcome the debate, but not when the only argument amounts to you saying, "that's wrong". You are more than welcome to say it is wrong, and I will not object, but you need to substantiate your dispute under the rules of this thread.
Either adhere to Rule #5 or withdraw your objection. I welcome the debate, but not when the only argument amounts to you saying, "that's wrong". You are more than welcome to say it is wrong, and I will not object, but you need to substantiate your dispute under the rules of this thread.
QUOTE (NoCleverName+)
On the other hand, the frictional force at the point of contact IS a torque and CAN induce or retard rolling.
I am in total agreement with you here, unless something else is implied.
I am in total agreement with you here, unless something else is implied.
QUOTE (boit+Apr 1 2011, 03:44 PM)
I am in total agreement with you here, unless something else is implied.
If there's a really good joke in there I'm missing it ... a bit tired right now.
If there's a really good joke in there I'm missing it ... a bit tired right now.
QUOTE (RTS-Eng+Apr 1 2011, 07:34 PM)
Either adhere to Rule #5 or withdraw your objection. I welcome the debate, but not when the only argument amounts to you saying, "that's wrong". You are more than welcome to say it is wrong, and I will not object, but you need to substantiate your dispute under the rules of this thread.
I agreed with your analysis, but pointed out that it was not a true "paradox" since you were only saying that the plane does not move by analysis of the initial conditions. Yes, you could leave it at the trivial solution that you found but that is not satisfactory to a physicist. The question is not "does the plane stay in place?", since as you pointed out that is the trivial solution. It should be more on the order of "Why does the plane sit in place?". You were calling something a "paradox" when it wasn't a paradox at all?
I suppose by invoking rule number 3 I could claim that you proved a point, that the plane does not move, but that you did not have enough support to call that consequence of the way that the question was asked a "paradox".
I agreed with your analysis, but pointed out that it was not a true "paradox" since you were only saying that the plane does not move by analysis of the initial conditions. Yes, you could leave it at the trivial solution that you found but that is not satisfactory to a physicist. The question is not "does the plane stay in place?", since as you pointed out that is the trivial solution. It should be more on the order of "Why does the plane sit in place?". You were calling something a "paradox" when it wasn't a paradox at all?
I suppose by invoking rule number 3 I could claim that you proved a point, that the plane does not move, but that you did not have enough support to call that consequence of the way that the question was asked a "paradox".
QUOTE (Subduction Zone+Apr 1 2011, 02:07 PM)
I agreed with your analysis, but pointed out that it was not a true "paradox" since you were only saying that the plane does not move by analysis of the initial conditions. Yes, you could leave it at the trivial solution that you found but that is not satisfactory to a physicist. The question is not "does the plane stay in place?", since as you pointed out that is the trivial solution. It should be more on the order of "Why does the plane sit in place?". You were calling something a "paradox" when it wasn't a paradox at all?
I suppose by invoking rule number 3 I could claim that you proved a point, that the plane does not move, but that you did not have enough support to call that consequence of the way that the question was asked a "paradox".
You can't change the question willy-nilly. Any change to the question must be presented, discussed, and agreed upon before you can present arguments pertaining to that altered question. According to #7.
And according to #5, you must counter the claim, that being that he question define the wheel as unable to rotate. Please show mathematically how this is possible, or discuss interpretations or alternate wording for the question.
"It seems" statements will be taken as a rebuttal to a perceived claim, and will require rebuttal of the facts presented to be valid.
I suppose by invoking rule number 3 I could claim that you proved a point, that the plane does not move, but that you did not have enough support to call that consequence of the way that the question was asked a "paradox".
You can't change the question willy-nilly. Any change to the question must be presented, discussed, and agreed upon before you can present arguments pertaining to that altered question. According to #7.
And according to #5, you must counter the claim, that being that he question define the wheel as unable to rotate. Please show mathematically how this is possible, or discuss interpretations or alternate wording for the question.
"It seems" statements will be taken as a rebuttal to a perceived claim, and will require rebuttal of the facts presented to be valid.
QUOTE (synthsin75+Apr 1 2011, 03:31 PM)
Violation of guideline #2. This is a "reference to previous discussions in other threads, on other topics, or about other versions of this question".
So it is. My apologies.
It seems to me that every attempt to paraphrase or reword the question only complicates the issue further.
It seems to me that the answer hinges upon two key variables: the frame of reference from which the speed of the plane is measured, and the nature of the control system (reactive or predictive).
Any attempt to reword the question should focus on eliminating these variables from interpretation.
So it is. My apologies.
It seems to me that every attempt to paraphrase or reword the question only complicates the issue further.
It seems to me that the answer hinges upon two key variables: the frame of reference from which the speed of the plane is measured, and the nature of the control system (reactive or predictive).
Any attempt to reword the question should focus on eliminating these variables from interpretation.
QUOTE (synthsin75+Apr 1 2011, 03:19 PM)
... define the wheel as unable to rotate.
I suspect we might end up with a cross-posting if you edit yours, but I did not assert the wheel can't rotate. I said it can't advance. The speed/velocity of the axle is fixed, but the wheel is free to rotate.
Sorry, just clarifying.
I suspect we might end up with a cross-posting if you edit yours, but I did not assert the wheel can't rotate. I said it can't advance. The speed/velocity of the axle is fixed, but the wheel is free to rotate.
Sorry, just clarifying.
QUOTE (Argyll+Apr 1 2011, 03:24 PM)
It seems to me that every attempt to paraphrase or reword the question only complicates the issue further.
It seems to me that the answer hinges upon two key variables: the frame of reference from which the speed of the plane is measured, and the nature of the control system (reactive or predictive).
Any attempt to reword the question should focus on eliminating these variables from interpretation.
I fully agree, and this is what I also stated in my first posting on this topic. We first need to understand (and/or correct) the wording of the problem before we can pursue a solution that meets the problem. This is not a trivial task.
It seems to me that the answer hinges upon two key variables: the frame of reference from which the speed of the plane is measured, and the nature of the control system (reactive or predictive).
Any attempt to reword the question should focus on eliminating these variables from interpretation.
I fully agree, and this is what I also stated in my first posting on this topic. We first need to understand (and/or correct) the wording of the problem before we can pursue a solution that meets the problem. This is not a trivial task.
QUOTE (RTS-Eng+Apr 1 2011, 02:25 PM)
I suspect we might end up with a cross-posting if you edit yours, but I did not assert the wheel can't rotate. I said it can't advance. The speed/velocity of the axle is fixed, but the wheel is free to rotate.
Sorry, just clarifying.
Sorry, you're right of course.
Also, please refrain from making claims in response to unfounded claims, stick to facts. As per #10: "Any accusations forwarded, whether of these guidelines or not, without evidence will be considered unjustified and invalid." So any such should be ignored entirely, rather than engaged upon. Thanks.
Also, please refrain from making claims in response to unfounded claims, stick to facts. As per #10: "Any accusations forwarded, whether of these guidelines or not, without evidence will be considered unjustified and invalid." So any such should be ignored entirely, rather than engaged upon. Thanks.
I fully agree, and this is what I also stated in my first posting on this topic. We first need to understand (and/or correct) the wording of the problem before we can pursue a solution that meets the problem. This is not a trivial task.
Do you have a proposed wording?
Sorry, just clarifying.
Sorry, you're right of course.
QUOTE
There isn't really a rule for "putting words in my mouth"
Also, please refrain from making claims in response to unfounded claims, stick to facts. As per #10: "Any accusations forwarded, whether of these guidelines or not, without evidence will be considered unjustified and invalid." So any such should be ignored entirely, rather than engaged upon. Thanks.
QUOTE (->
| QUOTE |
| There isn't really a rule for "putting words in my mouth" |
Also, please refrain from making claims in response to unfounded claims, stick to facts. As per #10: "Any accusations forwarded, whether of these guidelines or not, without evidence will be considered unjustified and invalid." So any such should be ignored entirely, rather than engaged upon. Thanks.
I fully agree, and this is what I also stated in my first posting on this topic. We first need to understand (and/or correct) the wording of the problem before we can pursue a solution that meets the problem. This is not a trivial task.
Do you have a proposed wording?
QUOTE (RTS-Eng+Apr 1 2011, 08:32 PM)
I fully agree, and this is what I also stated in my first posting on this topic. We first need to understand (and/or correct) the wording of the problem before we can pursue a solution that meets the problem. This is not a trivial task.
It seems to me that if the frame of reference is a fixed external observer, then the answer is trivial: the plane WILL take off.
Using the wheel speed (or belt frame of reference, i.e. the plane's speed relative to a fixed point on the infinite plane established by the horizontal surface of the belt on which the plane rests and with which the plane's wheels are in contact) obviously makes the question non-trivial, and makes the second variable relevant.
I think we can all agree that a predictive control system would, in a thought experiment scenario as described in the OP of this thread where materials are indestructible and available power is infinite, be able to prevent the plane from moving. If this is true, then this answer is likewise trivial: the plane WILL NOT take off.
The interesting - non-trivial - case, then, is when the wheel speed is used and a reactive control system is required.
It seems to me that if the frame of reference is a fixed external observer, then the answer is trivial: the plane WILL take off.
Using the wheel speed (or belt frame of reference, i.e. the plane's speed relative to a fixed point on the infinite plane established by the horizontal surface of the belt on which the plane rests and with which the plane's wheels are in contact) obviously makes the question non-trivial, and makes the second variable relevant.
I think we can all agree that a predictive control system would, in a thought experiment scenario as described in the OP of this thread where materials are indestructible and available power is infinite, be able to prevent the plane from moving. If this is true, then this answer is likewise trivial: the plane WILL NOT take off.
The interesting - non-trivial - case, then, is when the wheel speed is used and a reactive control system is required.
Factors we wish our question to address:
1) A conveyor belt countering the thrust of a plane
2) A means for that conveyor belt to do so, in some relation to the speed of the wheels (angular velocity)
3) Allow for an honest attempt to take off
4) Not be a self-defeating question
Anyone wish to prioritize, or add to/subtract from, these?
1) A conveyor belt countering the thrust of a plane
2) A means for that conveyor belt to do so, in some relation to the speed of the wheels (angular velocity)
3) Allow for an honest attempt to take off
4) Not be a self-defeating question
Anyone wish to prioritize, or add to/subtract from, these?
QUOTE (Argyll+)
The interesting - non-trivial - case, then, is when the wheel speed is used and a reactive control system is required.
Very much agreed. Although I know the first objection to that will be allowing for an arbitrary delay, once again making it a trivial question.
Very much agreed. Although I know the first objection to that will be allowing for an arbitrary delay, once again making it a trivial question.
QUOTE (NoCleverName+Apr 1 2011, 10:50 PM)
If there's a really good joke in there I'm missing it ... a bit tired right now.
The words that intrigued me were friction (i guess static friction) at the point of contact is a torque and can induce or RETARD rolling. This simply means the belt can retard wheels' forward motion if there were any. If the belt was acting on the top of part of the wheel i.e. Contact point at ninety degrees, it will induce the wheel to roll.
The words that intrigued me were friction (i guess static friction) at the point of contact is a torque and can induce or RETARD rolling. This simply means the belt can retard wheels' forward motion if there were any. If the belt was acting on the top of part of the wheel i.e. Contact point at ninety degrees, it will induce the wheel to roll.
Since any delay in reaction to wheel speed would be cumulative, making the question trivial, do we need to define the control system as a hybrid reactive/predictive? IOW the belt could react to the wheel speed (angular velocity) with some finite delay (at least governed by the speed of light to maintain a positive causation) but also add speed based on a prediction of the axle's translational speed.
Would that be possible even as an engineering problem? The longer the wheel rolls the more accurate the control system's prediction of the plane's speed?
Would someone please analyze that, and tell me if it would produce a trivial result?
Would that be possible even as an engineering problem? The longer the wheel rolls the more accurate the control system's prediction of the plane's speed?
Would someone please analyze that, and tell me if it would produce a trivial result?
QUOTE (synthsin75+Apr 1 2011, 03:32 PM)
Also, please refrain from making claims in response to unfounded claims, stick to facts. As per #10: "Any accusations forwarded, whether of these guidelines or not, without evidence will be considered unjustified and invalid." So any such should be ignored entirely, rather than engaged upon. Thanks.
My apologies for not making greater note of #10. However, shouldn't this be a topic covered somewhere? It is an issue that does have historical precedent, so I would like to know the proper manner in which to address such information.
I thought that my later edit to call this out under a failing of #5 was appropriate, as it was a claim to something I stated, but there was no substantiation that I have ever stated it.
I defer to you. Without a proper ruling, members would be free to restate wording or meaning of others without the ability to call this practice into question under the rules. Ignoring the practice is not a solution, as that is the equivalent of trying to un-ring a bell.
The practice of calling it out works when the misinterpretation is incidental, such as your own re-statement of a statement I made. However, when the misinterpretation is not incidental or accidental, then calling it out is not effective without a specific rule to substantiate it.
Do you have a rebuttal to RTS' mathematical assertion that this wording defines the plane as unable to translate? If not, there is no discussion of this wording, as the answer is trivial.
Please show how the current wording can be interpreted (leading to a possibly less ambiguous wording) that allows anything but a trivial answer. I have already forwarded such:
"We have a hydraulic cylinder with wheels on one end attached to a solid support on the other. The wheels rest on a conveyor belt. Given a specified force by the hydraulic cylinder, what would the belt have to do to counter it? What would be the relation between the force and wheel's angular velocity/acceleration?"
Would this be equivalent to your interpretation of the spirit of the question, at least physics-wise? If so, would you agree that it is less ambiguous?
My apologies for not making greater note of #10. However, shouldn't this be a topic covered somewhere? It is an issue that does have historical precedent, so I would like to know the proper manner in which to address such information.
I thought that my later edit to call this out under a failing of #5 was appropriate, as it was a claim to something I stated, but there was no substantiation that I have ever stated it.
I defer to you. Without a proper ruling, members would be free to restate wording or meaning of others without the ability to call this practice into question under the rules. Ignoring the practice is not a solution, as that is the equivalent of trying to un-ring a bell.
The practice of calling it out works when the misinterpretation is incidental, such as your own re-statement of a statement I made. However, when the misinterpretation is not incidental or accidental, then calling it out is not effective without a specific rule to substantiate it.
QUOTE (synthsin75+Apr 1 2011, 03:32 PM)
Do you have a proposed wording?
No, I do not have a proposed wording, aside from the one that I mentioned, but I believe we agree that this changes the problem too drastically from the original meaning.
No, I do not have a proposed wording, aside from the one that I mentioned, but I believe we agree that this changes the problem too drastically from the original meaning.
In my opinion, a delay in the control system would be inappropriate, in that it would mandate a forward movement of the axle. Similarly, a reactive control system that compensates is no different that the ideal control system, and the plane is still bound to never move.
What is needed to be changed is what the control system responds to. However, as I briefly alluded to earlier, reacting to a "Force" or "Thrust" also trivializes the problem.
As much as I dislike this answer (because it changes the whole meaning of the original wording), is to change the problem to be "what can be done to stop the plane". This is a question that can be answered (whether yes or no) without being pre-defined by the question.
What is needed to be changed is what the control system responds to. However, as I briefly alluded to earlier, reacting to a "Force" or "Thrust" also trivializes the problem.
As much as I dislike this answer (because it changes the whole meaning of the original wording), is to change the problem to be "what can be done to stop the plane". This is a question that can be answered (whether yes or no) without being pre-defined by the question.
I could reformulate the question to make wheel speed (angular) match both the belt and the plane speed measured by an observer and yet the wheel neverslips. Here plane mimicks the belt exactly. Guess how? 
QUOTE (RTS-Eng+Apr 1 2011, 03:12 PM)
My apologies for not making greater note of #10. However, shouldn't this be a topic covered somewhere? It is an issue that does have historical precedent, so I would like to know the proper manner in which to address such information.
I thought that my later edit to call this out under a failing of #5 was appropriate, as it was a claim to something I stated, but there was no substantiation that I have ever stated it.
I defer to you. Without a proper ruling, members would be free to restate wording or meaning of others without the ability to call this practice into question under the rules. Ignoring the practice is not a solution, as that is the equivalent of trying to un-ring a bell.
The practice of calling it out works when the misinterpretation is incidental, such as your own re-statement of a statement I made. However, when the misinterpretation is not incidental or accidental, then calling it out is not effective without a specific rule to substantiate it.
Sorry, I should have clarified that better. You're reference to the guidelines was correct, and you weren't necessarily in violation. But according to #10, such unfounded claims are "considered unjustified and invalid", so refuting them is unnecessary. Better to say "that's not what I said/meant" rather than the accusatory "putting words in my mouth". If someone misrepresents you, just ask for a quote to back it up, and if not given, ignore it as invalid. Or like you did, point out the violation.
I thought that my later edit to call this out under a failing of #5 was appropriate, as it was a claim to something I stated, but there was no substantiation that I have ever stated it.
I defer to you. Without a proper ruling, members would be free to restate wording or meaning of others without the ability to call this practice into question under the rules. Ignoring the practice is not a solution, as that is the equivalent of trying to un-ring a bell.
The practice of calling it out works when the misinterpretation is incidental, such as your own re-statement of a statement I made. However, when the misinterpretation is not incidental or accidental, then calling it out is not effective without a specific rule to substantiate it.
Sorry, I should have clarified that better. You're reference to the guidelines was correct, and you weren't necessarily in violation. But according to #10, such unfounded claims are "considered unjustified and invalid", so refuting them is unnecessary. Better to say "that's not what I said/meant" rather than the accusatory "putting words in my mouth". If someone misrepresents you, just ask for a quote to back it up, and if not given, ignore it as invalid. Or like you did, point out the violation.
QUOTE (boit+Apr 1 2011, 05:59 PM)
I could reformulate the question to make wheel speed (angular) match both the belt and the plane speed measured by an observer and yet the wheel neverslips. Here plane mimicks the belt exactly. Guess how?
Not a claim, rebuttal, or proposal for new wording of the question. Playing guessing games are not productive in any way. If you have an idea, state it.
Not a claim, rebuttal, or proposal for new wording of the question. Playing guessing games are not productive in any way. If you have an idea, state it.
QUOTE (synthsin75+Apr 2 2011, 12:35 AM)
Not a claim, rebuttal, or proposal for new wording of the question. Playing guessing games are not productive in any way. If you have an idea, state it.
I have and I did, but I think I'll wait until you all get the rules and regs sorted so I can precede to break a few
I have and I did, but I think I'll wait until you all get the rules and regs sorted so I can precede to break a few
QUOTE (privatepaddy+Apr 1 2011, 06:43 PM)
I have and I did, but I think I'll wait until you all get the rules and regs sorted so I can precede to break a few
These are sorted. What is not sorted is the wording for a question that does not have a trivial answer.
These are sorted. What is not sorted is the wording for a question that does not have a trivial answer.
QUOTE (Umer.banday+Mar 31 2011, 06:55 PM)
Let us say that a Thrust force F acts
on the plane in the forward
direction due to the engine.Also a
Contact force N acts on it in
opposite direction due to the
wheel.Now the same force N acts
on the wheel in the forward
direction.This force N passes
through the centre of mass of the
wheel..hence has no torque about
centre of mass.So,there must be a
friction force f acting on the wheel
in the opposite direction to rotate it.
I wont calculate the torque about
the point of contact as it is
accelerating in the ground frame
which gives rise to pseudo torques.
Let the mass of plane be M..let the
mass of tyre be m..Radius of tyre R.
And moment of inertia of tyre
about COM = I =mr^2/2. Since the
plane and the tyre have same
translational accelertion,we can
take them as one system for
writing the translational equation i.e
F - f = (M+m)a. Equation 1.
Now wrtiting the torque equation
for the wheel about COM.
fr = Iø Equation 2.where ø is the
angular acceration of wheel and is
equal to 2a/r here. Using it in
equation 2 and putting the value of
f in equation 1 we get
F = (m+M)a + (2Ia)/r^2 ..equation
3. Now I = mr^2/2.using it above
we get. a = F/(M + 2m).Now let us
analyse the result..if M = infinite, a
= 0.Also if the mass of the wheel is
infinite, a = 0. Let us now try to
calculate the friction force f..we see
f=ma or f = F/(M/m + 2)..we see
that friction force can vary from 0
to F/2.Now for any particulare
ration M/m = k , if max friction is
greater than or equal to F/(k+2),
there will be no slipping between
the tyres and the conveyor belt
and if the max friction is less the F/
k+2 ,there may be slipping ..still the
plane will move.If the plane was on
ground,we would have found that
the friction force f = F/(2M/m +3)
or F/(2k +3)..and the friction would
have varied betweew 0 and F/3..so
indeed due to this converyor
case,relatively more friction is
acting.Hence we see that in any
case of finite M and m, the plane
will move and take off.In this
solution i have ignored the friction
between tyres and plane .Brothers
if u think i am wrong please point it
out. I would love to improve my
concepts.
A small suggestion the format of your post makes it hard to follow so I took the step of copying it to notepad and reformatting it. I am not a highly educated person like these other gentleman so I am still making my way through it. My suggestion is if it is possible could you format any replies so they become easier to follow. Thanks
on the plane in the forward
direction due to the engine.Also a
Contact force N acts on it in
opposite direction due to the
wheel.Now the same force N acts
on the wheel in the forward
direction.This force N passes
through the centre of mass of the
wheel..hence has no torque about
centre of mass.So,there must be a
friction force f acting on the wheel
in the opposite direction to rotate it.
I wont calculate the torque about
the point of contact as it is
accelerating in the ground frame
which gives rise to pseudo torques.
Let the mass of plane be M..let the
mass of tyre be m..Radius of tyre R.
And moment of inertia of tyre
about COM = I =mr^2/2. Since the
plane and the tyre have same
translational accelertion,we can
take them as one system for
writing the translational equation i.e
F - f = (M+m)a. Equation 1.
Now wrtiting the torque equation
for the wheel about COM.
fr = Iø Equation 2.where ø is the
angular acceration of wheel and is
equal to 2a/r here. Using it in
equation 2 and putting the value of
f in equation 1 we get
F = (m+M)a + (2Ia)/r^2 ..equation
3. Now I = mr^2/2.using it above
we get. a = F/(M + 2m).Now let us
analyse the result..if M = infinite, a
= 0.Also if the mass of the wheel is
infinite, a = 0. Let us now try to
calculate the friction force f..we see
f=ma or f = F/(M/m + 2)..we see
that friction force can vary from 0
to F/2.Now for any particulare
ration M/m = k , if max friction is
greater than or equal to F/(k+2),
there will be no slipping between
the tyres and the conveyor belt
and if the max friction is less the F/
k+2 ,there may be slipping ..still the
plane will move.If the plane was on
ground,we would have found that
the friction force f = F/(2M/m +3)
or F/(2k +3)..and the friction would
have varied betweew 0 and F/3..so
indeed due to this converyor
case,relatively more friction is
acting.Hence we see that in any
case of finite M and m, the plane
will move and take off.In this
solution i have ignored the friction
between tyres and plane .Brothers
if u think i am wrong please point it
out. I would love to improve my
concepts.
A small suggestion the format of your post makes it hard to follow so I took the step of copying it to notepad and reformatting it. I am not a highly educated person like these other gentleman so I am still making my way through it. My suggestion is if it is possible could you format any replies so they become easier to follow. Thanks
QUOTE (synthsin75+Apr 2 2011, 12:47 AM)
These are sorted. What is not sorted is the wording for a question that does not have a trivial answer.
Ok you have a real aeroplane on a fantasy conveyor belt the belt is capable extraordinary feats controlled by a control system that has two settings stop and flat chat due its regenerative effect. This is in turn caused by the wording wheel speed matching belt speed one in meters per time period and the other in radians per time period, mixed units.
Modern control systems require a form of calibration and anticipation eg a conveyor belt system feeding gravel and sand into a concrete mixing plant. the feed rates onto the belt or the belt speed its self must be adjusted depending on the location in the process.
To define a control system as described in the "Russian" version is nonsensical.
So In my opinion unless there is some form of limitation on the control system and wheel speed V belt speed it will end in the same old run around. If this limitation is put in place those that support it will cry foul.
edit
What is really needed is a sin bin so that offenders can be ignored for x number of posts of x time
Ok you have a real aeroplane on a fantasy conveyor belt the belt is capable extraordinary feats controlled by a control system that has two settings stop and flat chat due its regenerative effect. This is in turn caused by the wording wheel speed matching belt speed one in meters per time period and the other in radians per time period, mixed units.
Modern control systems require a form of calibration and anticipation eg a conveyor belt system feeding gravel and sand into a concrete mixing plant. the feed rates onto the belt or the belt speed its self must be adjusted depending on the location in the process.
To define a control system as described in the "Russian" version is nonsensical.
So In my opinion unless there is some form of limitation on the control system and wheel speed V belt speed it will end in the same old run around. If this limitation is put in place those that support it will cry foul.
edit
What is really needed is a sin bin so that offenders can be ignored for x number of posts of x time
Okay, if we want the question to be "what can be done to stop the plane", we might as well simplify it much further. IOW, it's no longer about a plane at all. An equivalent, simplified setup in the spirit of "what can be done to stop the plane" would be something like this:
We have a hydraulic cylinder with wheels on one end attached to a solid support on the other. The wheels rest on a conveyor belt. Given a specified force by the hydraulic cylinder, what would the belt have to do to counter it? What would be the relation between the force and wheel's angular velocity/acceleration?
Absolutely no need for any control system. Obviously this could only be done by accelerating the belt. Just keep accelerating until the cylinder is stopped.
How's that for a bastardization?
We have a hydraulic cylinder with wheels on one end attached to a solid support on the other. The wheels rest on a conveyor belt. Given a specified force by the hydraulic cylinder, what would the belt have to do to counter it? What would be the relation between the force and wheel's angular velocity/acceleration?
Absolutely no need for any control system. Obviously this could only be done by accelerating the belt. Just keep accelerating until the cylinder is stopped.
How's that for a bastardization?
QUOTE (synthsin75+Apr 2 2011, 05:44 AM)
Okay, if we want the question to be "what can be done to stop the plane", we might as well simplify it much further. IOW, it's no longer about a plane at all. An equivalent, simplified setup in the spirit of "what can be done to stop the plane" would be something like this:
We have a hydraulic cylinder with wheels on one end attached to a solid support on the other. The wheels rest on a conveyor belt. Given a specified force by the hydraulic cylinder, what would the belt have to do to counter it? What would be the relation between the force and wheel's angular velocity/acceleration?
Absolutely no need for any control system. Obviously this could only be done by accelerating the belt. Just keep accelerating until the cylinder is stopped.
How's that for a bastardization?
This is entirely up to you, you have far longer experience in debating such matters. I am here to learn
We have a hydraulic cylinder with wheels on one end attached to a solid support on the other. The wheels rest on a conveyor belt. Given a specified force by the hydraulic cylinder, what would the belt have to do to counter it? What would be the relation between the force and wheel's angular velocity/acceleration?
Absolutely no need for any control system. Obviously this could only be done by accelerating the belt. Just keep accelerating until the cylinder is stopped.
How's that for a bastardization?
This is entirely up to you, you have far longer experience in debating such matters. I am here to learn
SD: I looked again at your comment about rotating the frame of reference in the 26-100 video and for the life of me I can't make any sense out of what you are trying to say. I am familiar with that lecture and the fact is it pretty much discredits the whole "lateral acceleration" theory. I'm sure Prof Levin would have drawn the "mystery force" on the blackboard free body diagram if it was there. He didn't. That because a professor of physics at MIT knows there is no such thing.
This is one area where things are pretty clear: angular momentum is changed only by a torque. Yes, a countering force passing through the center WOULD cause a torque at the contact point. However, this is problematical because THAT torque counters the torque generated by friction resulting in a much smaller total torque. Unfortunately, a "much smaller total torque" means less torque to produce angular momentum, That is, LESS rotation. In the case of "rolling without slipping" that would mean not only would the object seem to lose lateral speed it would also lose rotational speed. If the "theory" held water, then we should see the object more or less roll to a stop while trying to advance down hill.
This is one area where things are pretty clear: angular momentum is changed only by a torque. Yes, a countering force passing through the center WOULD cause a torque at the contact point. However, this is problematical because THAT torque counters the torque generated by friction resulting in a much smaller total torque. Unfortunately, a "much smaller total torque" means less torque to produce angular momentum, That is, LESS rotation. In the case of "rolling without slipping" that would mean not only would the object seem to lose lateral speed it would also lose rotational speed. If the "theory" held water, then we should see the object more or less roll to a stop while trying to advance down hill.
QUOTE (privatepaddy+Apr 2 2011, 12:52 AM)
A small suggestion the format of your post makes it hard to follow so I took the step of copying it to notepad and reformatting it. I am not a highly educated person like these other gentleman so I am still making my way through it. My suggestion is if it is possible could you format any replies so they become easier to follow. Thanks
i am sorry my dear brother..but i dont have a computer..i posted this from my mobile opera .jar browser..still..i will try to improve my posts from future..i apologize once again..
i am sorry my dear brother..but i dont have a computer..i posted this from my mobile opera .jar browser..still..i will try to improve my posts from future..i apologize once again..
QUOTE (Umer.banday+Apr 2 2011, 01:38 PM)
i am sorry my dear brother..but i dont have a computer..i posted this from my mobile opera .jar browser..still..i will try to improve my posts from future..i apologize once again..
Not a problem no need to apologise just post the way you can.
Not a problem no need to apologise just post the way you can.
NCN, a frame of reference is merely the "window" that you are observing an object from. Usually in physics an inertial frame of reference is used to ease calculations. A ramp may be changed into a horizontal surface by rotating the frame of reference that you use. An object on it will have a force of gravity down of mg*cos(theta) and a horizontal force on it of mg*sin(theta) where theta is the angle that the ramp was rotated to make it horizontal, it is also the slope of the ramp. In other words if you rotate a 20 degree ramp 20 degrees mentally it is now horizontal. The same forces are on it, we have only redefined up and down.
By rotating it we can see that the object accelerates at a rate of (2/3)g*sin(theta) assuming that it is a solid cylinder or wheel. Newton says that it accelerates by a = F_net/m, where F_net are the net forces. Since we know that one of the forces is mg*sin(theta) we know there is a back force of (1/3)mg*sin(theta). The rolling ramp test shows that there is a back force due to rolling. If the object was sliding on a frictional surface there would be no back force and it would accelerate at g*sin(theta).
By rotating it we can see that the object accelerates at a rate of (2/3)g*sin(theta) assuming that it is a solid cylinder or wheel. Newton says that it accelerates by a = F_net/m, where F_net are the net forces. Since we know that one of the forces is mg*sin(theta) we know there is a back force of (1/3)mg*sin(theta). The rolling ramp test shows that there is a back force due to rolling. If the object was sliding on a frictional surface there would be no back force and it would accelerate at g*sin(theta).
QUOTE (Subduction Zone+Apr 2 2011, 02:51 PM)
NCN, a frame of reference is merely the "window" that you are observing an object from. Usually in physics an inertial frame of reference is used to ease calculations. A ramp may be changed into a horizontal surface by rotating the frame of reference that you use. An object on it will have a force of gravity down of mg*cos(theta) and a horizontal force on it of mg*sin(theta) where theta is the angle that the ramp was rotated to make it horizontal, it is also the slope of the ramp. In other words if you rotate a 20 degree ramp 20 degrees mentally it is now horizontal. The same forces are on it, we have only redefined up and down.
By rotating it we can see that the object accelerates at a rate of (2/3)g*sin(theta) assuming that it is a solid cylinder or wheel. Newton says that it accelerates by a = F_net/m, where F_net are the net forces. Since we know that one of the forces is mg*sin(theta) we know there is a back force of (1/3)mg*sin(theta). The rolling ramp test shows that there is a back force due to rolling. If the object was sliding on a frictional surface there would be no back force and it would accelerate at g*sin(theta).
when the body slides on the frictional surface, a back force KN acts..where N is normal rxn and k is friction coeff...isnt it?
By rotating it we can see that the object accelerates at a rate of (2/3)g*sin(theta) assuming that it is a solid cylinder or wheel. Newton says that it accelerates by a = F_net/m, where F_net are the net forces. Since we know that one of the forces is mg*sin(theta) we know there is a back force of (1/3)mg*sin(theta). The rolling ramp test shows that there is a back force due to rolling. If the object was sliding on a frictional surface there would be no back force and it would accelerate at g*sin(theta).
when the body slides on the frictional surface, a back force KN acts..where N is normal rxn and k is friction coeff...isnt it?
I am still suprised when someone argues that the belt is helping the wheel roll faster in the opposite direction when it is pulled under. That will only happen after you've stopped pulling the belt. The angular momentum that wheel had picked up is what makes it roll forward, translating. How far and how fast the wheel will roll depends on the final speed the belt had picked before stopping. It doesn't matter if it had maintained that speed for one minute or one year. With a constant acceleration, the wheel will surely be pulled back on the direction of the belt. My phone is low on battery so can't write more. Solar charger joint two miles away. Thanks heavens it cost thirteen cents, american currency:)
QUOTE (boit+Apr 2 2011, 03:27 PM)
I am still suprised when someone argues that the belt is helping the wheel roll faster in the opposite direction when it is pulled under. That will only happen after you've stopped pulling the belt. The angular momentum that wheel had picked up is what makes it roll forward, translating. How far and how fast the wheel will roll depends on the final speed the belt had picked before stopping. It doesn't matter if it had maintained that speed for one minute or one year. With a constant acceleration, the wheel will surely be pulled back on the direction of the belt. My phone is low on battery so can't write more. Solar charger joint two miles away. Thanks heavens it cost thirteen cents, american currency:)
Well some of us are less educated than others, we plod along trying to make sense of the world and some posts, do they actually add or detract from the human condition or the understanding of the universe, perhaps you should partake of more libation? then again not
Well some of us are less educated than others, we plod along trying to make sense of the world and some posts, do they actually add or detract from the human condition or the understanding of the universe, perhaps you should partake of more libation? then again not
QUOTE (Umer.banday+Apr 2 2011, 03:16 PM)
when the body slides on the frictional surface, a back force KN acts..where N is normal rxn and k is friction coeff...isnt it?
Yes, there is a back force on a sliding body. But there is also a back force on a body that has a rotational acceleration. If there wasn't the rolling object would accelerate just as quickly as an object sliding without friction.
Yes, there is a back force on a sliding body. But there is also a back force on a body that has a rotational acceleration. If there wasn't the rolling object would accelerate just as quickly as an object sliding without friction.
QUOTE (Subduction Zone+Apr 2 2011, 03:44 PM)
Yes, there is a back force on a sliding body. But there is also a back force on a body that has a rotational acceleration. If there wasn't the rolling object would accelerate just as quickly as an object sliding without friction.
I am confused..but its my fault...i think i dont have full details of the case you are discussing..
Here is what i know..
1) A solid cylinder of mass M and radius R is released from the top of a ramp.
2) The ramp has an angle ø
Here is what i dont know..
1) Is there friction between the cylinder and ramp?
So brother..Please give me the details.
I am confused..but its my fault...i think i dont have full details of the case you are discussing..
Here is what i know..
1) A solid cylinder of mass M and radius R is released from the top of a ramp.
2) The ramp has an angle ø
Here is what i dont know..
1) Is there friction between the cylinder and ramp?
So brother..Please give me the details.
You pretty much have it. The cylinder undergoes "pure rolling". That is rolling without any sliding. So the friction results in rolling only, no sliding. So it is static friction, or the force of traction. It has been claimed by some that a torque on the radius of a rotating object will not give any linear force on the center of an object. The ramp experiment shows that not to be the case. There is no kinetic or sliding friction.
I hope that clarifies things a bit.
I hope that clarifies things a bit.
QUOTE (Umer.banday+Apr 2 2011, 12:21 PM)
I am confused..but its my fault...i think i dont have full details of the case you are discussing..
Do not be confused. SD and Darth are peddling a bizarre theory that when a rolling object is accelerated there is a countering force through the center of mass than can be harnessed to stop linear motion yet allow rolling. Nobody but them are under the delusion such a force exists and they consistently misinterpret what is actually going on in order to bolster their theory.
They like to point to a cylinder rolling down a ramp. They claim that if you get the ramp itself in motion uphill (sort of like a conveyor-on-a-ramp) that the resulting halting of the object's progress down the ramp is due to this reverse force.
They do not understand that what is really going on is that the object is being lifted up by the ramp's backward motion as fast as it is rolling downhill. Sort of like being in orbit.
Do not be confused. SD and Darth are peddling a bizarre theory that when a rolling object is accelerated there is a countering force through the center of mass than can be harnessed to stop linear motion yet allow rolling. Nobody but them are under the delusion such a force exists and they consistently misinterpret what is actually going on in order to bolster their theory.
They like to point to a cylinder rolling down a ramp. They claim that if you get the ramp itself in motion uphill (sort of like a conveyor-on-a-ramp) that the resulting halting of the object's progress down the ramp is due to this reverse force.
They do not understand that what is really going on is that the object is being lifted up by the ramp's backward motion as fast as it is rolling downhill. Sort of like being in orbit.
QUOTE (NoCleverName+Apr 2 2011, 05:22 PM)
Do not be confused. SD and Darth are peddling a bizarre theory that when a rolling object is accelerated there is a countering force through the center of mass than can be harnessed to stop linear motion yet allow rolling. Nobody but them are under the delusion such a force exists and they consistently misinterpret what is actually going on in order to bolster their theory.
They like to point to a cylinder rolling down a ramp. They claim that if you get the ramp itself in motion uphill (sort of like a conveyor-on-a-ramp) that the resulting halting of the object's progress down the ramp is due to this reverse force.
They do not understand that what is really going on is that the object is being lifted up by the ramp's backward motion as fast as it is rolling downhill. Sort of like being in orbit.
I believe you are breaking several of the rules of this thread here NCN. Our theory is not bizarre, and is supported by the various links we have supplied. Did you not understand my point about rotating the frame of reference when observing the ramp? That is as much accepted science as Newtonian physics. In fact it predates it since they are very often called Galilean Transformations.
They like to point to a cylinder rolling down a ramp. They claim that if you get the ramp itself in motion uphill (sort of like a conveyor-on-a-ramp) that the resulting halting of the object's progress down the ramp is due to this reverse force.
They do not understand that what is really going on is that the object is being lifted up by the ramp's backward motion as fast as it is rolling downhill. Sort of like being in orbit.
I believe you are breaking several of the rules of this thread here NCN. Our theory is not bizarre, and is supported by the various links we have supplied. Did you not understand my point about rotating the frame of reference when observing the ramp? That is as much accepted science as Newtonian physics. In fact it predates it since they are very often called Galilean Transformations.
QUOTE (Subduction Zone+Apr 2 2011, 12:37 PM)
I believe you are breaking several of the rules of this thread here NCN. Our theory is not bizarre, and is supported by the various links we have supplied.
Actually you are both breaking several rules, but the significant two are rules #2 & #5. You are arguing information that has not yet been presented and are not supporting claims that are being made.
Darth hasn't presented the information you two are arguing, and also SZ is making assertions about this information without providing the supporting information because Darth hasn't submitted it.
NCN, I have a request for you. Would you mind cleaning up your original assertion and presenting it formally in this thread for discussion? State what you are attempting to show, List the Known's and Assumption's (if any), explain the justifications for each step in the equation process, and define the variables used (some of your variables were kind of cryptic).
Actually you are both breaking several rules, but the significant two are rules #2 & #5. You are arguing information that has not yet been presented and are not supporting claims that are being made.
Darth hasn't presented the information you two are arguing, and also SZ is making assertions about this information without providing the supporting information because Darth hasn't submitted it.
NCN, I have a request for you. Would you mind cleaning up your original assertion and presenting it formally in this thread for discussion? State what you are attempting to show, List the Known's and Assumption's (if any), explain the justifications for each step in the equation process, and define the variables used (some of your variables were kind of cryptic).
What is wrong with the material I have presented? I had links and math that I derived from my links. No one has formally answered those posts. All I have seen are NCN's negations.
QUOTE (RTS-Eng+Apr 2 2011, 02:02 PM)
NCN, I have a request for you. Would you mind cleaning up your original assertion and presenting it formally in this thread for discussion? State what you are attempting to show, List the Known's and Assumption's (if any), explain the justifications for each step in the equation process, and define the variables used (some of your variables were kind of cryptic).
I don't understand what you mean by "original assertion". ... unless you mean where I got Darth's magic equation without having to resort to a plane-on-a-conveyor.
As to rules 2, 3 or whatever...if someone represents their "junk science" to some unsuspecting poster as fact, I won't hesitate to strike back fast.
SD: Rotate the friggin' frame all you like ... it changes NOTHING because the normal force and the gravitational force both go thru the COM of the object. Torque could care less about rotation of the frame because, well, it's already rotating, isn't it?
I don't understand what you mean by "original assertion". ... unless you mean where I got Darth's magic equation without having to resort to a plane-on-a-conveyor.
As to rules 2, 3 or whatever...if someone represents their "junk science" to some unsuspecting poster as fact, I won't hesitate to strike back fast.
SD: Rotate the friggin' frame all you like ... it changes NOTHING because the normal force and the gravitational force both go thru the COM of the object. Torque could care less about rotation of the frame because, well, it's already rotating, isn't it?
QUOTE (NoCleverName+Apr 2 2011, 11:22 AM)
Do not be confused. SD and Darth are peddling a bizarre theory that when a rolling object is accelerated there is a countering force through the center of mass than can be harnessed to stop linear motion yet allow rolling. Nobody but them are under the delusion such a force exists and they consistently misinterpret what is actually going on in order to bolster their theory.
"9) No insults or implied impugning of the skills or knowledge of another. Refuting claims, and their justification, only requires a debate of forwarded facts. "
"Bizarre" and "delusion" are needlessly inflammatory and can be misconstrued as conflicting with the above guideline. Please stick to refuting the facts, as you have otherwise done, without the personal characterizations. Thank you.
"9) No insults or implied impugning of the skills or knowledge of another. Refuting claims, and their justification, only requires a debate of forwarded facts. "
"Bizarre" and "delusion" are needlessly inflammatory and can be misconstrued as conflicting with the above guideline. Please stick to refuting the facts, as you have otherwise done, without the personal characterizations. Thank you.
Many people here are still talking right past the actual question. Unless I get some positive feedback on any proposed change to the "OP question", all assertions referring to another interpretation or wording is irrelevant and a violation of the guidelines.
NO one has seconded (agreed to) ANY change of the OP question. So, having determined the OP question to be trivial, all subsequent discussions are OFF-TOPIC.
NO one has seconded (agreed to) ANY change of the OP question. So, having determined the OP question to be trivial, all subsequent discussions are OFF-TOPIC.
QUOTE (NoCleverName+Apr 2 2011, 09:45 PM)
I don't understand what you mean by "original assertion". ... unless you mean where I got Darth's magic equation without having to resort to a plane-on-a-conveyor.
As to rules 2, 3 or whatever...if someone represents their "junk science" to some unsuspecting poster as fact, I won't hesitate to strike back fast.
SD: Rotate the friggin' frame all you like ... it changes NOTHING because the normal force and the gravitational force both go thru the COM of the object. Torque could care less about rotation of the frame because, well, it's already rotating, isn't it?
NCN, no the frame is not rotating, it was rotated. And you should use consistent logic in your arguments, when you say the object "could care less" about the rotation you are actually saying that it matters.
You should try to debunk my claims with actual science. I have posted a link to a lecturer from MIT who explains why an object rolls slower down a ramp than it would if it slid frictionlessly. Rotating the frame of reference is designed to help you to understand that there is a back force. If the back force is not from our claim what is your explanation?
As to rules 2, 3 or whatever...if someone represents their "junk science" to some unsuspecting poster as fact, I won't hesitate to strike back fast.
SD: Rotate the friggin' frame all you like ... it changes NOTHING because the normal force and the gravitational force both go thru the COM of the object. Torque could care less about rotation of the frame because, well, it's already rotating, isn't it?
NCN, no the frame is not rotating, it was rotated. And you should use consistent logic in your arguments, when you say the object "could care less" about the rotation you are actually saying that it matters.
You should try to debunk my claims with actual science. I have posted a link to a lecturer from MIT who explains why an object rolls slower down a ramp than it would if it slid frictionlessly. Rotating the frame of reference is designed to help you to understand that there is a back force. If the back force is not from our claim what is your explanation?
QUOTE (synthsin75+Apr 2 2011, 11:55 PM)
Many people here are still talking right past the actual question. Unless I get some positive feedback on any proposed change to the "OP question", all assertions referring to another interpretation or wording is irrelevant and a violation of the guidelines.
NO one has seconded (agreed to) ANY change of the OP question. So, having determined the OP question to be trivial, all subsequent discussions are OFF-TOPIC.
Sorry, I missed this because I was responding to NCN. I have no problem with this version of the problem:
I will try to follow your rules of posting here, but since this is an open forum you may find your task to be more difficult than herding cats.
Also, as far as things already discussed a bit, I am not fond of the use of the term "paradox" since that indicates that a judgement has been made. Tautological might be a better term since the plane is self defined to stay in place on the belt. We can still argue whether that tautology will hold or not.
NO one has seconded (agreed to) ANY change of the OP question. So, having determined the OP question to be trivial, all subsequent discussions are OFF-TOPIC.
Sorry, I missed this because I was responding to NCN. I have no problem with this version of the problem:
QUOTE
An aircraft (jet or propeller) sits on a conveyor belt runway. The belt monitors and adjusts its speed to that of the wheels, but in the opposite direction to that of the attempt to take off. Can the plane take off?
I will try to follow your rules of posting here, but since this is an open forum you may find your task to be more difficult than herding cats.
Also, as far as things already discussed a bit, I am not fond of the use of the term "paradox" since that indicates that a judgement has been made. Tautological might be a better term since the plane is self defined to stay in place on the belt. We can still argue whether that tautology will hold or not.
QUOTE
QUOTE (->
| QUOTE |
An aircraft (jet or propeller) sits on a conveyor belt runway. The belt monitors and adjusts its speed to that of the wheels, but in the opposite direction to that of the attempt to take off. Can the plane take off? Also, as far as things already discussed a bit, I am not fond of the use of the term "paradox" since that indicates that a judgement has been made. Tautological might be a better term since the plane is self defined to stay in place on the belt. We can still argue whether that tautology will hold or not. |
Do you have a rebuttal to RTS' mathematical assertion that this wording defines the plane as unable to translate? If not, there is no discussion of this wording, as the answer is trivial.
Please show how the current wording can be interpreted (leading to a possibly less ambiguous wording) that allows anything but a trivial answer. I have already forwarded such:
"We have a hydraulic cylinder with wheels on one end attached to a solid support on the other. The wheels rest on a conveyor belt. Given a specified force by the hydraulic cylinder, what would the belt have to do to counter it? What would be the relation between the force and wheel's angular velocity/acceleration?"
Would this be equivalent to your interpretation of the spirit of the question, at least physics-wise? If so, would you agree that it is less ambiguous?
Without an illustration I would say that is more ambiguous since I don't see exactly what you are asking.
And yes, I do agree with RTS' analysis that with the original wording the wheels are free to roll but do not move relative to the ground. And I will let the word "paradox" alone for now, it is a minor point. Though I may request a minor point in the future.
One point, when there is possible motion to relative to the belt, the ground, or both it might be helpful if people specified what the motion was relative to.
And yes, I do agree with RTS' analysis that with the original wording the wheels are free to roll but do not move relative to the ground. And I will let the word "paradox" alone for now, it is a minor point. Though I may request a minor point in the future.
One point, when there is possible motion to relative to the belt, the ground, or both it might be helpful if people specified what the motion was relative to.
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