QUOTE (Raphie Frank+Jan 11 2011, 11:02 AM)
A somewhat frivolous question, perhaps, but what happens to the plane if the conveyor belt suddenly stops for whatever reason?
Besides a massive amount of energy stored in the wheels having basically nowhere to go?
Once the forces on the plane are no longer a net zero, the plane would begin to accelerate.
Besides a massive amount of energy stored in the wheels having basically nowhere to go?
Once the forces on the plane are no longer a net zero, the plane would begin to accelerate.
Maybe it's just me, but this discussion seems to have gotten quite a bit off topic from the original question (or maybe i missed something in the 672 pages of responses).
As I understand it, an CTOL aeroplane's ability to fly is an effect of lift, which is a product of the surface force (in this case, that of air) on it, and specifically, the perpendicular (in relation to the flow direction) component of that force as it acts on the plane (mostly/obviously, on the wings).
A plane's take off is the result of creating enough of the perpendicular component of surface force in relation to the plane's mass/volume, i.e.: the heavier the plane the more surface force is needed to create the necessary lift for take off.
This can be achieved by several means: increased surface flow (which can be achieved by the speed of the plane or the air), increased surface (for the flow to act upon) or increased resistance (specifically, resistance that would gain in the perpendicular aspect of the surface force).
Modern planes use all three principles to make the most of it: jet engines to achieve greater speeds, large "flat" wings to create more surface for the force to act upon, and slats and flaps to direct the flow (and thus more of the energy of the force) towards the perpendicular. As it is mos commercial planes have to have high-lift devices because they can't generate enough lift during their relatively slow takeoff speeds they can achieve (safely).
Hypothetically, If the plane was set up so that no (or even insufficient) forward momentum could be gained, and assuming the air around it was completely still, it would be unable to generate sufficient speed to create the necessary surface force that would allow lift.
So: a plane with even the most powerful rocket engines, riding magical unbreakable/unmeltable wheels on an fantastical, unbreakable conveyor belt which could generate the same speeds as the plane (but obviously in the opposite direction and in direct proportion to the speed of the plane at any given millisecond), in an extraordinary bubble of totally still air, could not generate the necessary lift for take off.
Aerospace engineering tests deal with this in part (literally). Wheels are tested on conveyors for efficiency, stability, and of course, resilience. Wings and housing are tested in wind tunnels, etc etc. It may in fact be possible to do this experiment, given a small plane that needs the least amount of perpendicular surface force to create the necessary lift.
Practically speaking, there's so many components that would likely break down before any real results could be ascertained that it'd be funny to see.
A possible experiment with models: calculating a set acceleration and necessary take off speed of an rc plane with set conditions (air density, air speed, aircraft weight and volume and configuration, pitch, etc.) and then setting up a conveyor to match it (in acceleration as well as eventual takeoff and top speed).
Caveat: if you had propellers (likely magical ones) mounted in front of the flaps that could generate enough air flow towards them, or flaps that could withstand the heat and pressure generated by jets directed at them, maybe you could still do a take off, but it would probably also take high-lift devices and much more froce, since it'd be directed specifically and the lift devices and not the whole wing/plane.
P.S.: VTOL planes, like the harrier series and v22, can circumvent this by methods like a) using directed jets to propel the plane upwards, or B) using directed rotors for the same effect, in that order.
Anyone really in doubt should ask a pilot, and don't be surprised if you are mocked, scoffed and or laughed at, and possibly looked at as if you're a) an idiot, or B) from another planet, where the physics we know don't apply.
As I understand it, an CTOL aeroplane's ability to fly is an effect of lift, which is a product of the surface force (in this case, that of air) on it, and specifically, the perpendicular (in relation to the flow direction) component of that force as it acts on the plane (mostly/obviously, on the wings).
A plane's take off is the result of creating enough of the perpendicular component of surface force in relation to the plane's mass/volume, i.e.: the heavier the plane the more surface force is needed to create the necessary lift for take off.
This can be achieved by several means: increased surface flow (which can be achieved by the speed of the plane or the air), increased surface (for the flow to act upon) or increased resistance (specifically, resistance that would gain in the perpendicular aspect of the surface force).
Modern planes use all three principles to make the most of it: jet engines to achieve greater speeds, large "flat" wings to create more surface for the force to act upon, and slats and flaps to direct the flow (and thus more of the energy of the force) towards the perpendicular. As it is mos commercial planes have to have high-lift devices because they can't generate enough lift during their relatively slow takeoff speeds they can achieve (safely).
Hypothetically, If the plane was set up so that no (or even insufficient) forward momentum could be gained, and assuming the air around it was completely still, it would be unable to generate sufficient speed to create the necessary surface force that would allow lift.
So: a plane with even the most powerful rocket engines, riding magical unbreakable/unmeltable wheels on an fantastical, unbreakable conveyor belt which could generate the same speeds as the plane (but obviously in the opposite direction and in direct proportion to the speed of the plane at any given millisecond), in an extraordinary bubble of totally still air, could not generate the necessary lift for take off.
Aerospace engineering tests deal with this in part (literally). Wheels are tested on conveyors for efficiency, stability, and of course, resilience. Wings and housing are tested in wind tunnels, etc etc. It may in fact be possible to do this experiment, given a small plane that needs the least amount of perpendicular surface force to create the necessary lift.
Practically speaking, there's so many components that would likely break down before any real results could be ascertained that it'd be funny to see.
A possible experiment with models: calculating a set acceleration and necessary take off speed of an rc plane with set conditions (air density, air speed, aircraft weight and volume and configuration, pitch, etc.) and then setting up a conveyor to match it (in acceleration as well as eventual takeoff and top speed).
Caveat: if you had propellers (likely magical ones) mounted in front of the flaps that could generate enough air flow towards them, or flaps that could withstand the heat and pressure generated by jets directed at them, maybe you could still do a take off, but it would probably also take high-lift devices and much more froce, since it'd be directed specifically and the lift devices and not the whole wing/plane.
P.S.: VTOL planes, like the harrier series and v22, can circumvent this by methods like a) using directed jets to propel the plane upwards, or B) using directed rotors for the same effect, in that order.
Anyone really in doubt should ask a pilot, and don't be surprised if you are mocked, scoffed and or laughed at, and possibly looked at as if you're a) an idiot, or B) from another planet, where the physics we know don't apply.
Sith...whatever: I did not bother to look to deeply into your so-called "work balance" derivation because your initial equation is entirely false if it is your intention that the plane does not move. In particular, you switch frames of reference incorrectly with the term "F_thrust*X" since distance "X" must be in the frame of the observer ... NOT the amount of conveyor rolling under the wheels. If the conveyor has any effect whatsoever on the final motion of the plane in the frame of the observer, then distance "X" is in fact not achieved so your work balance is false.
Suppose X=rpm*ΠD and not the plane. Would you take another look into the equatio?
QUOTE
Sith...whatever: I did not bother to look to deeply into your so-called "work balance" derivation because your initial equation is entirely false if it is your intention that the plane does not move. In particular, you switch frames of reference incorrectly with the term "F_thrust*X" since distance "X" must be in the frame of the observer ... NOT the amount of conveyor rolling under the wheels. If the conveyor has any effect whatsoever on the final motion of the plane in the frame of the observer, then distance "X" is in fact not achieved so your work balance is false.
1) The equation is not wrong. If X where actually zero, and X is the amount of belt that has gone under the plane, then everything else would be zero.
2) I did not switch frames I staid entirely in the rest frame of the belt.
3) The distance X must not be in the frame of the observer it can be in any frame you like as long as when switching to another frame, which I didn't do, you do the proper conversions.
4) Since I did the whole thing from the rest frame of the belt the amount of belt going under the wheel is exactly what X should be.
5) The amount of work being done should always be calculated verses the surface the object is rolling on. Doing it any other way introduces a lot of complexity. It is always simplest to go with the rest frame of whatever the object is moving across. Although you could do it from the rest frame of the observer but now instead of the plane doing work it would be the belt doing work but everything would work out the same in the end.
6) The end equation is completely general and works in any frame of reference because it no longer contains any terms regarding the motion of the object.
7) I got the same answer using Lagrangian mechanics.
8) My classical mechanics text book via the YoYo example starts with the same exact equation.
9) It is consistent with the laws of Newton. That is to say the net force is the sum of all the external forces acting on the wheel.
And here I thought the whole point of the conveyor was that it accelerated to match the plane ... rest frame indeed. 
I am not about to read thru the last 20 or so pages to see what you guys are babbling about amongst yourselves. I saw a reference to some "equations" which no doubt purportedly justify the plane not moving under some circumstance or another. I spent about a minute looking at it and it's clear that it is in error ... as are all such equations that claim to show the plane can't move. Either everything is in the frame of the observer or your work is in error ... because it is the observer who judges the action of the plane on the conveyor and you are not presenting any evidence to said observer. As it is, only your "thrust" force seems to be in the proper frame, the others are in other frames subject to pseudo forces.
I am not about to read thru the last 20 or so pages to see what you guys are babbling about amongst yourselves. I saw a reference to some "equations" which no doubt purportedly justify the plane not moving under some circumstance or another. I spent about a minute looking at it and it's clear that it is in error ... as are all such equations that claim to show the plane can't move. Either everything is in the frame of the observer or your work is in error ... because it is the observer who judges the action of the plane on the conveyor and you are not presenting any evidence to said observer. As it is, only your "thrust" force seems to be in the proper frame, the others are in other frames subject to pseudo forces.
QUOTE (NoCleverName+Jan 12 2011, 12:02 AM)
And here I thought the whole point of the conveyor was that it accelerated to match the plane ... rest frame indeed.
I am not about to read thru the last 20 or so pages to see what you guys are babbling about amongst yourselves. I saw a reference to some "equations" which no doubt purportedly justify the plane not moving under some circumstance or another. I spent about a minute looking at it and it's clear that it is in error ... as are all such equations that claim to show the plane can't move. Either everything is in the frame of the observer or your work is in error ... because it is the observer who judges the action of the plane on the conveyor and you are not presenting any evidence to said observer. As it is, only your "thrust" force seems to be in the proper frame, the others are in other frames subject to pseudo forces.
I still don't know what the question here is.
"If the plane can't fly, can it fly?"
I am not about to read thru the last 20 or so pages to see what you guys are babbling about amongst yourselves. I saw a reference to some "equations" which no doubt purportedly justify the plane not moving under some circumstance or another. I spent about a minute looking at it and it's clear that it is in error ... as are all such equations that claim to show the plane can't move. Either everything is in the frame of the observer or your work is in error ... because it is the observer who judges the action of the plane on the conveyor and you are not presenting any evidence to said observer. As it is, only your "thrust" force seems to be in the proper frame, the others are in other frames subject to pseudo forces.
I still don't know what the question here is.
"If the plane can't fly, can it fly?"
Wow - I can't believe this thread is still on the go! Brilliant!
For all the idiocy of "no flier" ATL5P - or what ever that guy was called way back when - I have to admit that Sithdarth is right.
Making all the assumptions of mechanical strength and rigidity of components, frames of reference etc, blah de blah, there will be an acceleration rate of the conveyor belt which will match the thrust of the plane and stop it taking off.
I just wonder how long - for any given aircraft - can the plane be held back before the conveyor belt accelerates to the speed of light?
For all the idiocy of "no flier" ATL5P - or what ever that guy was called way back when - I have to admit that Sithdarth is right.
Making all the assumptions of mechanical strength and rigidity of components, frames of reference etc, blah de blah, there will be an acceleration rate of the conveyor belt which will match the thrust of the plane and stop it taking off.
I just wonder how long - for any given aircraft - can the plane be held back before the conveyor belt accelerates to the speed of light?
QUOTE (swimmer+Jan 12 2011, 02:38 AM)
I just wonder how long - for any given aircraft - can the plane be held back before the conveyor belt accelerates to the speed of light?
Doesn't matter... as it reaches relativistic speeds, the mass of the wheels will increase, reducing the acceleration required to exert the appropriate thrust on the plane and keep it from moving.
Doesn't matter... as it reaches relativistic speeds, the mass of the wheels will increase, reducing the acceleration required to exert the appropriate thrust on the plane and keep it from moving.
QUOTE
I am not about to read thru the last 20 or so pages to see what you guys are babbling about amongst yourselves.
Then leave the discussion and concede the point. If you aren't willing to put in the time to understand the topic of discussion then you have no right to be part of the discussion.
QUOTE (->
| QUOTE |
| I am not about to read thru the last 20 or so pages to see what you guys are babbling about amongst yourselves. |
Then leave the discussion and concede the point. If you aren't willing to put in the time to understand the topic of discussion then you have no right to be part of the discussion.
I spent about a minute looking at it and it's clear that it is in error ... as are all such equations that claim to show the plane can't move. Either everything is in the frame of the observer or your work is in error ... because it is the observer who judges the action of the plane on the conveyor and you are not presenting any evidence to said observer.
Prove it. I've given the math, the video I made proving my point has been posted, the page from my classical mechanics text book has been posted. The simple fact of the matter is that the sum of all forces includes all forces even the ones that act on different parts of a body. Further, you apparently have no conception of how to handle reference frames. You can do work in any reference frame you want as long as all your work is done in the same reference frame as mine was done. That is why reference frames are useful because you can always choose the one that simplifies the math.
In fact lets see if I can link:
Classical Mechanics Text book
Video of rolling on an accelerating surface
And before you go saying that neither of those are the same physics as the plane I suggest you draw a free body diagram. Ignoring the normal force since it doesn't impact us at the moment in each case you have a force acting on the center of mass of the object and another force acting on the outside edge of said object causing rotation in addition to translation. You'll not that the YoYo derivation is exactly the same step for step as one of my derivation with the minor difference that the relationship between the angular and linear quantities are slightly different. So either my Classical Mechanics text book is wrong or I am right. Now before you go thinking it might just be my Classical Mechanics text book the exact same problem with the exact same solution can be found on various internet sites as well as both of the Physics 201 text books I have in my possession as well. So if my Classical Mechanics text book is wrong so is basically every basic physics text book ever printed.
QUOTE
As it is, only your "thrust" force seems to be in the proper frame, the others are in other frames subject to pseudo forces.
If you actually had bothered to grasp the matter under discussion you would realize we are discussion an accelerating belt. The wheels being in contact with said accelerating belt are in an accelerating reference frame and thereby so is the rest of the plane. This acceleration is best handled in any frame by the use of a pseudo force acting on the wheel. Well technically in the stationary observer frame the equation:
F_net = F_thrust - T/r
still holds it is just that
T = I*α
and in the observer frame because the plane is rolling without slipping
0 = a_net = α*r - a_belt
so that
α = a_belt/r
in the observer frame and we can see by the equations of constraint that the apparent torque on the wheel in this special case comes from the belt.
QUOTE (->
| QUOTE |
| As it is, only your "thrust" force seems to be in the proper frame, the others are in other frames subject to pseudo forces. |
If you actually had bothered to grasp the matter under discussion you would realize we are discussion an accelerating belt. The wheels being in contact with said accelerating belt are in an accelerating reference frame and thereby so is the rest of the plane. This acceleration is best handled in any frame by the use of a pseudo force acting on the wheel. Well technically in the stationary observer frame the equation:
F_net = F_thrust - T/r
still holds it is just that
T = I*α
and in the observer frame because the plane is rolling without slipping
0 = a_net = α*r - a_belt
so that
α = a_belt/r
in the observer frame and we can see by the equations of constraint that the apparent torque on the wheel in this special case comes from the belt.
I just wonder how long - for any given aircraft - can the plane be held back before the conveyor belt accelerates to the speed of light?
The wonderful thing about special relativity is that no matter how fast the belt gets someone sitting in the rest frame of the belt will always feel the same acceleration. Just like there are Lorentz transformations for position and even velocity there are Lorentz transformations for acceleration as well. The end result of which is that even though the person standing still next to the belt sees the acceleration decreasing as it reaches relativistic speeds the wheels themselves continue to feel the same exact acceleration they have always felt.
QUOTE
I still don't know what the question here is.
"If the plane can't fly, can it fly?"
"If the plane can't fly, can it fly?"
I'll give you the wording is rather bad but if you get past that there is interesting and counter intuitive physics buried in the problem.
QUOTE (Sithdarth+Jan 12 2011, 02:49 AM)
I'll give you the wording is rather bad but if you get past that there is interesting and counter intuitive physics buried in the problem.
Isn't the real question, could a conveyor belt (moving in the opposite direction of take off) prevent the plane from taking off? If wheels were attached to a rocket and laid on a conveyor belt, do you believe the rocket would have the ability to move forward regardless of the speed of conveyor belt in the opposite direction?
Isn't the real question, could a conveyor belt (moving in the opposite direction of take off) prevent the plane from taking off? If wheels were attached to a rocket and laid on a conveyor belt, do you believe the rocket would have the ability to move forward regardless of the speed of conveyor belt in the opposite direction?
QUOTE
Isn't the real question, could a conveyor belt (moving in the opposite direction of take off) prevent the plane from taking off? If wheels were attached to a rocket and laid on a conveyor belt, do you believe the rocket would have the ability to move forward regardless of the speed of conveyor belt in the opposite direction?
The speed isn't important it is the acceleration that is important. If the belt was accelerating such that:
a_belt = F_thrust*r^2/I
then the rocket powered wheels would be unable to move forward.
If a_belt was any less than that then the rocket wheels would move forward. If a_belt was any more than that the rocket wheels would be pulled backwards.
QUOTE (Sithdarth+Jan 12 2011, 03:18 AM)
If a_belt was any less than that then the rocket wheels would move forward.
Don't take this wrong, but isn't that obvious? That was my original problem your scenario. There is no need for a knowledge of physics, or even imagination. "The conveyor belt prevents the plane from taking off, can it take off?"
Don't take this wrong, but isn't that obvious? That was my original problem your scenario. There is no need for a knowledge of physics, or even imagination. "The conveyor belt prevents the plane from taking off, can it take off?"
QUOTE
Don't take this wrong, but isn't that obvious? That was my original problem your scenario. There is no need for a knowledge of physics, or even imagination. "The conveyor belt prevents the plane from taking off, can it take off?"
Obvious to you and me maybe. As well as anyone that has followed the derivations. However, it isn't obvious to everyone exactly what is going on physically. Reality Check again being the most ready example.
Also, it does take a little bit of physics to calculate exactly what acceleration the belt has to undergo to counter act the thrust of the plane.
By the way, relative to the rocket, don't you believe in the "real world" that the wheels on the rocket would begin to slip due to increased friction and the rocket would move forward. (But we're in "fanatasy land".)
QUOTE
By the way, relative to the rocket, don't you believe in the "real world" that the wheels on the rocket would begin to slip due to increased friction and the rocket would move forward. (But we're in "fanatasy land".)
Increased friction would reduce the tendency of the wheels to slip. The traction between the tires and the surface is what keeps them from slipping and this is nothing but the static frictional force. So as long as the thrust of the rocket wheels is less than the maximum static friction between the wheels in the surface there will be no slipping. Of course if you could lock the breaks of the rocket wheels on a stationary surface and the rockets still had enough thrust to pull the contraption forward then nothing you can do is going to stop it from going forward. The wheels would simply start slipping. But as I mentioned earlier if you increased the friction it would only make it easier for the wheels to roll without slipping. Wheels slip because of a lack of friction.
As usual, the proponents of the magical conveyor belt forget about inconvenient factors such as "conservation of energy" let alone the third law. For the plane to be stopped the belt must deliver just as much force against the plane as the plane is delivering to the belt. In simpler terms, the belt needs just as much (or more) horsepower to run itself as does the plane.
In the pathological case, the belt is freewheeling and the plane's brakes are set. As the "takeoff run" starts, the plane and belt move as a whole (the plane powering both) ... when the system reaches "takeoff speed", the plane flies away --- its wheels never moving at all. Now, add to the belt "brakes" (or an opposing motor), so it can resist the plane's force to some extent. At some point of braking the belt could halt the plane (the plane's brakes are still on) and the problem becomes one of static equilibrium. Upto that point the plane's energy is being dumped as heat as well as converted to kinetic energy. In any event, you can see the energy balance is one of the plane's motive energy on one side and total system motion and heat loss in the belt brakes on the other.
Gradual reduction in the plane's brake setting converts the problem to the classic "plane on a conveyor" but the energy balance (in general) doesn't change form.
I should also point out that if you allow any motion at all for the plane, then you have to account for "lift" which reduces the normal force on the belt and thus any rolling resistance.
I'll also note in passing that real life belts are somewhat limited to rather low speeds because materials capable of being flexed around the drive wheels don't have enough strength to handle a lot of tension.
The plane on a conveyor can also be modeled by a car and a moving runway of paper both driven by pulleys and weights. In this case the symmetry of the situation leaves one to the conclusion that if the plane can't move, neither can the paper runway so you are left with the picture of the plane and the paper not moving yet both have weights hanging from them via pulleys. A bit nonsensical.
And the situation is indeed symmetric because neither the plane nor belt is "favored" in anyway ... you can arrange for the masses of both objects to be the same and for the paper to be on a air bearing if you wish so that all we have is the forces generated at the wheels plus the gravity driven pull on each object.
By the way, you seem to have failed to notice in your referenced example from the "classical textbook" that tension T is constant and has no effect on the cylinder's acceleration ... that is, there is not "constant" or "zero" velocity but an increase. This is not really that different from the problem at hand. And there is NO buildup of opposing force with increased velocity. So much for the"theory" you have drawn from this example.
In the pathological case, the belt is freewheeling and the plane's brakes are set. As the "takeoff run" starts, the plane and belt move as a whole (the plane powering both) ... when the system reaches "takeoff speed", the plane flies away --- its wheels never moving at all. Now, add to the belt "brakes" (or an opposing motor), so it can resist the plane's force to some extent. At some point of braking the belt could halt the plane (the plane's brakes are still on) and the problem becomes one of static equilibrium. Upto that point the plane's energy is being dumped as heat as well as converted to kinetic energy. In any event, you can see the energy balance is one of the plane's motive energy on one side and total system motion and heat loss in the belt brakes on the other.
Gradual reduction in the plane's brake setting converts the problem to the classic "plane on a conveyor" but the energy balance (in general) doesn't change form.
I should also point out that if you allow any motion at all for the plane, then you have to account for "lift" which reduces the normal force on the belt and thus any rolling resistance.
I'll also note in passing that real life belts are somewhat limited to rather low speeds because materials capable of being flexed around the drive wheels don't have enough strength to handle a lot of tension.
The plane on a conveyor can also be modeled by a car and a moving runway of paper both driven by pulleys and weights. In this case the symmetry of the situation leaves one to the conclusion that if the plane can't move, neither can the paper runway so you are left with the picture of the plane and the paper not moving yet both have weights hanging from them via pulleys. A bit nonsensical.
And the situation is indeed symmetric because neither the plane nor belt is "favored" in anyway ... you can arrange for the masses of both objects to be the same and for the paper to be on a air bearing if you wish so that all we have is the forces generated at the wheels plus the gravity driven pull on each object.
By the way, you seem to have failed to notice in your referenced example from the "classical textbook" that tension T is constant and has no effect on the cylinder's acceleration ... that is, there is not "constant" or "zero" velocity but an increase. This is not really that different from the problem at hand. And there is NO buildup of opposing force with increased velocity. So much for the"theory" you have drawn from this example.
I don't know what's worse. People like Derek who was terribly insulting and was against the idea until he realized that we were right, and now it is obvious. Or people like NoCleverName who can't get it and refuse to look at the equations.
ETA: Cross posted with NCN. Now he is taking the word salad approach. Trying to justify his views with words, but no physics. Short response, wrong, try again.
ETA: Cross posted with NCN. Now he is taking the word salad approach. Trying to justify his views with words, but no physics. Short response, wrong, try again.
It is clear that math in itself is ineffective as an argument since it is evident that the wrong math cannot be seen as such by its proponents.
NoCleverName, I will give a longer response to your last post.
No we didn't. As far as energy goes the fact that the conveyor belt must have more power than the plane has already been brought up on this thread. The third law is specifically covered by the increasing rotational momentum of the wheels. It is a case of balanced forces and therefore no forward movement.
No we didn't. As far as energy goes the fact that the conveyor belt must have more power than the plane has already been brought up on this thread. The third law is specifically covered by the increasing rotational momentum of the wheels. It is a case of balanced forces and therefore no forward movement.
In the pathological case,
The what?
Then you go on to some nonsense about setting the brakes. Why would you want to do that? And then you spew a bunch of unsupported nonsense.
Lastly you said:
Not what we claimed. It is not velocity but acceleration that matters. If you don't know the difference between the two then you are hardly qualified to comment.
Yeah except for that pesky part where I actually did a conservation of energy calculation. And that part where I've been saying repeatedly that the belt is producing a force that must be taken into account by virtue of accelerating. I am forced to repeat the point that if you do not want to make yourself aware of the arguments being presented by the opposing side you have no right to be here. What you are doing is not debate it is pontification.
Yeah except for that pesky part where I actually did a conservation of energy calculation. And that part where I've been saying repeatedly that the belt is producing a force that must be taken into account by virtue of accelerating. I am forced to repeat the point that if you do not want to make yourself aware of the arguments being presented by the opposing side you have no right to be here. What you are doing is not debate it is pontification.
In the pathological case, the belt is freewheeling and the plane's brakes are set. As the "takeoff run" starts, the plane and belt move as a whole (the plane powering both) ... when the system reaches "takeoff speed", the plane flies away --- its wheels never moving at all. Now, add to the belt "brakes" (or an opposing motor), so it can resist the plane's force to some extent. At some point of braking the belt could halt the plane (the plane's brakes are still on) and the problem becomes one of static equilibrium. Upto that point the plane's energy is being dumped as heat as well as converted to kinetic energy. In any event, you can see the energy balance is one of the plane's motive energy on one side and total system motion and heat loss in the belt brakes on the other.
Actually if the plane is strong enough to cause the wheels with breaks locked over the surface it is sitting on then the plane will take off. Since kinetic friction is essentially constant with speed unless the tires fail changing the surfaces that are in contact once the plane starts sliding it will in fact take off.
I should also point out that once again there was not a single part of my derivation that introduced rolling resistance at all. Everything was considered ideal with no rolling resistance.
I should also point out that once again there was not a single part of my derivation that introduced rolling resistance at all. Everything was considered ideal with no rolling resistance.
I'll also note in passing that real life belts are somewhat limited to rather low speeds because materials capable of being flexed around the drive wheels don't have enough strength to handle a lot of tension.
Irrelevant. We are in the realm of a thought problem here. To borrow Subduction Zone's favorite analogy I can't dig a hole through the center of the planet but I can still calculate what would happen if I jumped in one. Likewise I can't build a belt or a plane that wouldn't break under full thrust conditions but that doesn't prevent me from calculating what would happen if I could.
Only if you're working from a version of the thought problem that is not currently under discussion.
Only if you're working from a version of the thought problem that is not currently under discussion.
And the situation is indeed symmetric because neither the plane nor belt is "favored" in anyway ... you can arrange for the masses of both objects to be the same and for the paper to be on a air bearing if you wish so that all we have is the forces generated at the wheels plus the gravity driven pull on each object.
And if you set everything up so that the acceleration of your piece of paper was given by:
a_paper = F_car*r^2/I
where F_car is the weight pulling on the car, r is the radius of the car's wheels, and I is the moment of inertia of the car's wheels then the car would not move relative to a stationary observer. This exact scenario except with a battery for the car and me standing in for the weight pulling the paper is demonstrated right here:
Rolling on an accelerating surface.
Gravity is pulling the battery down the slope creating both linear motion and rotational motion exactly as your weight pulling on the car does. I pull the paper up the ramp exactly as your mass attached to the paper would pull it in the opposite direction of your car. The result is very clear that when the acceleration of the paper is just right the battery stops its linear motion down the ramp but continues to increase its angular velocity. Exactly as predicted.
Now if you would actually like to try to understand the arguments that have actually been made and not the strawman arguments you have constructed then you are welcome to stay. However, if you insist, as you have clearly stated before, on not actually ever reading anything the opposition types then you can leave now because we are not having a debate.
In fact I think I will steal this from Rpenner
Your potentially guilty of several things on that list so I have no idea why I am bothering to continue to discuss this with you. If you don't correct that I don't see much reason to continue to attempt to debate you.
Prove that it is the wrong math. I've given you a page from a text book on classical mechanics that says it is right. I've done the physical testing that proves that it is right. Surely you can come up without something other than your word that it is wrong. But again you've demonstrated that you are absolutely unwilling to actually follow the proper decorum of a debate so there isn't much point in my saying this.
I would add to Derek that this is exactly what I mean when I say that there is interesting and non-intuitive physics inherent in the accelerating belt scenario that people just do not get.
There is no screwed up frames of reference in my derivation. Again I point you to the Classical Mechanics text book which does the derivation starting with the exact same equation I used and using the exact same steps I used.
There is no screwed up frames of reference in my derivation. Again I point you to the Classical Mechanics text book which does the derivation starting with the exact same equation I used and using the exact same steps I used.
I invite you to attempt the car and paper runway experiment I propose as it is a practical model of the plane-on-a-conveyor that anyone can try. Both objects are powered by separate, non-interlinked supplies. The connecting point is just the putative wheels, and, true to the problem, the velocity of each is roughly the same at any time (with suitable powering weights).
You once again aren't paying attention. I did that experiment long before you even suggested it to me. I have further linked you to it twice now. Here it is again. Yes it is a battery and not a car but that makes no difference to the underlying physics.
I won't have to because I have done it and it worked precisely how I predicted it would.
Once again you construct a strawman argument. The derivations have shown many times that the acceleration of the paper or the belt will be much higher than the acceleration the plane would undergo via its thrust normally.
Once again you construct a strawman argument. The derivations have shown many times that the acceleration of the paper or the belt will be much higher than the acceleration the plane would undergo via its thrust normally.
You chose an arbitrary speed ..
I simply pulled roughly as hard as I could in a controllable manner. There was no set speed but I did try to maintain as even an acceleration as possible.
What do you mean starting with an impulse rather than a ramp up? All I did was let the battery go at the top of the ramp and pulled the paper.
What do you mean starting with an impulse rather than a ramp up? All I did was let the battery go at the top of the ramp and pulled the paper.
Rolling resistance IS a factor as it will result in a "terminal velocity" to any object given an upper bound on available power. Failure to include it is an error.
Rolling resistance is a constant that never changes with speed. Go look it up. Well ok realistically there is a very small linear increase of rolling resistance with speed but the wheels would be destroyed long before that became an issue if they weren't assumed ideal. A plane not subject to aerodynamic drag can roll more than fast enough to cause its wheels to fly apart. If its wheels where idea and could not fly apart and it never ran out of fuel it could accelerate forever against rolling resistance. Also, I point out once again that we are making assumptions of ideal wheels and an ideal belt so ignoring rolling resistance is not an error.
But I think you've made it clear you have no interest in actual discussion here. You refused to read my initial explanations, you deny the experimental results, you won't even address the evidence from the text book, you will not provide evidence for your position. In short you are not currently part of this discussion. You have in fact broken the rules that make a discussion a discussion and have thus forfeited your side of the argument until such a time as you can abide by the rules that make a discussion a discussion. Here I'll post them again.
QUOTE
As usual, the proponents of the magical conveyor belt forget about inconvenient factors such as "conservation of energy" let alone the third law. For the plane to be stopped the belt must deliver just as much force against the plane as the plane is delivering to the belt. In simpler terms, the belt needs just as much (or more) horsepower to run itself as does the plane.
No we didn't. As far as energy goes the fact that the conveyor belt must have more power than the plane has already been brought up on this thread. The third law is specifically covered by the increasing rotational momentum of the wheels. It is a case of balanced forces and therefore no forward movement.
QUOTE (->
| QUOTE |
| As usual, the proponents of the magical conveyor belt forget about inconvenient factors such as "conservation of energy" let alone the third law. For the plane to be stopped the belt must deliver just as much force against the plane as the plane is delivering to the belt. In simpler terms, the belt needs just as much (or more) horsepower to run itself as does the plane. |
No we didn't. As far as energy goes the fact that the conveyor belt must have more power than the plane has already been brought up on this thread. The third law is specifically covered by the increasing rotational momentum of the wheels. It is a case of balanced forces and therefore no forward movement.
In the pathological case,
The what?
Then you go on to some nonsense about setting the brakes. Why would you want to do that? And then you spew a bunch of unsupported nonsense.
Lastly you said:
QUOTE
And there is NO buildup of opposing force with increased velocity.
Not what we claimed. It is not velocity but acceleration that matters. If you don't know the difference between the two then you are hardly qualified to comment.
QUOTE
As usual, the proponents of the magical conveyor belt forget about inconvenient factors such as "conservation of energy" let alone the third law. For the plane to be stopped the belt must deliver just as much force against the plane as the plane is delivering to the belt. In simpler terms, the belt needs just as much (or more) horsepower to run itself as does the plane.
Yeah except for that pesky part where I actually did a conservation of energy calculation. And that part where I've been saying repeatedly that the belt is producing a force that must be taken into account by virtue of accelerating. I am forced to repeat the point that if you do not want to make yourself aware of the arguments being presented by the opposing side you have no right to be here. What you are doing is not debate it is pontification.
QUOTE (->
| QUOTE |
| As usual, the proponents of the magical conveyor belt forget about inconvenient factors such as "conservation of energy" let alone the third law. For the plane to be stopped the belt must deliver just as much force against the plane as the plane is delivering to the belt. In simpler terms, the belt needs just as much (or more) horsepower to run itself as does the plane. |
Yeah except for that pesky part where I actually did a conservation of energy calculation. And that part where I've been saying repeatedly that the belt is producing a force that must be taken into account by virtue of accelerating. I am forced to repeat the point that if you do not want to make yourself aware of the arguments being presented by the opposing side you have no right to be here. What you are doing is not debate it is pontification.
In the pathological case, the belt is freewheeling and the plane's brakes are set. As the "takeoff run" starts, the plane and belt move as a whole (the plane powering both) ... when the system reaches "takeoff speed", the plane flies away --- its wheels never moving at all. Now, add to the belt "brakes" (or an opposing motor), so it can resist the plane's force to some extent. At some point of braking the belt could halt the plane (the plane's brakes are still on) and the problem becomes one of static equilibrium. Upto that point the plane's energy is being dumped as heat as well as converted to kinetic energy. In any event, you can see the energy balance is one of the plane's motive energy on one side and total system motion and heat loss in the belt brakes on the other.
Actually if the plane is strong enough to cause the wheels with breaks locked over the surface it is sitting on then the plane will take off. Since kinetic friction is essentially constant with speed unless the tires fail changing the surfaces that are in contact once the plane starts sliding it will in fact take off.
QUOTE
I should also point out that if you allow any motion at all for the plane, then you have to account for "lift" which reduces the normal force on the belt and thus any rolling resistance.
I should also point out that once again there was not a single part of my derivation that introduced rolling resistance at all. Everything was considered ideal with no rolling resistance.
QUOTE (->
| QUOTE |
| I should also point out that if you allow any motion at all for the plane, then you have to account for "lift" which reduces the normal force on the belt and thus any rolling resistance. |
I should also point out that once again there was not a single part of my derivation that introduced rolling resistance at all. Everything was considered ideal with no rolling resistance.
I'll also note in passing that real life belts are somewhat limited to rather low speeds because materials capable of being flexed around the drive wheels don't have enough strength to handle a lot of tension.
Irrelevant. We are in the realm of a thought problem here. To borrow Subduction Zone's favorite analogy I can't dig a hole through the center of the planet but I can still calculate what would happen if I jumped in one. Likewise I can't build a belt or a plane that wouldn't break under full thrust conditions but that doesn't prevent me from calculating what would happen if I could.
QUOTE
The plane on a conveyor can also be modeled by a car and a moving runway of paper both driven by pulleys and weights. In this case the symmetry of the situation leaves one to the conclusion that if the plane can't move, neither can the paper runway so you are left with the picture of the plane and the paper not moving yet both have weights hanging from them via pulleys. A bit nonsensical.
Only if you're working from a version of the thought problem that is not currently under discussion.
QUOTE (->
| QUOTE |
| The plane on a conveyor can also be modeled by a car and a moving runway of paper both driven by pulleys and weights. In this case the symmetry of the situation leaves one to the conclusion that if the plane can't move, neither can the paper runway so you are left with the picture of the plane and the paper not moving yet both have weights hanging from them via pulleys. A bit nonsensical. |
Only if you're working from a version of the thought problem that is not currently under discussion.
And the situation is indeed symmetric because neither the plane nor belt is "favored" in anyway ... you can arrange for the masses of both objects to be the same and for the paper to be on a air bearing if you wish so that all we have is the forces generated at the wheels plus the gravity driven pull on each object.
And if you set everything up so that the acceleration of your piece of paper was given by:
a_paper = F_car*r^2/I
where F_car is the weight pulling on the car, r is the radius of the car's wheels, and I is the moment of inertia of the car's wheels then the car would not move relative to a stationary observer. This exact scenario except with a battery for the car and me standing in for the weight pulling the paper is demonstrated right here:
Rolling on an accelerating surface.
Gravity is pulling the battery down the slope creating both linear motion and rotational motion exactly as your weight pulling on the car does. I pull the paper up the ramp exactly as your mass attached to the paper would pull it in the opposite direction of your car. The result is very clear that when the acceleration of the paper is just right the battery stops its linear motion down the ramp but continues to increase its angular velocity. Exactly as predicted.
Now if you would actually like to try to understand the arguments that have actually been made and not the strawman arguments you have constructed then you are welcome to stay. However, if you insist, as you have clearly stated before, on not actually ever reading anything the opposition types then you can leave now because we are not having a debate.
In fact I think I will steal this from Rpenner
Your potentially guilty of several things on that list so I have no idea why I am bothering to continue to discuss this with you. If you don't correct that I don't see much reason to continue to attempt to debate you.
QUOTE
It is clear that math in itself is ineffective as an argument since it is evident that the wrong math cannot be seen as such by its proponents.
Prove that it is the wrong math. I've given you a page from a text book on classical mechanics that says it is right. I've done the physical testing that proves that it is right. Surely you can come up without something other than your word that it is wrong. But again you've demonstrated that you are absolutely unwilling to actually follow the proper decorum of a debate so there isn't much point in my saying this.
I would add to Derek that this is exactly what I mean when I say that there is interesting and non-intuitive physics inherent in the accelerating belt scenario that people just do not get.
QUOTE (NoCleverName+Jan 12 2011, 04:34 AM)
It is clear that math in itself is ineffective as an argument since it is evident that the wrong math cannot be seen as such by its proponents.
Try us. Show the error, show the correct math, find a link that supports you. All you seem to have done is to misunderstand the given links and math. Oh, and one more thing, a proof of concept video would be nice too.
Try us. Show the error, show the correct math, find a link that supports you. All you seem to have done is to misunderstand the given links and math. Oh, and one more thing, a proof of concept video would be nice too.
QUOTE (Subduction Zone+Jan 12 2011, 12:39 AM)
It is not velocity but acceleration that matters.
Yes, I know ... this is where the screwed up frames of reference occur.
I invite you to attempt the car and paper runway experiment I propose as it is a practical model of the plane-on-a-conveyor that anyone can try. Both objects are powered by separate, non-interlinked supplies. The connecting point is just the putative wheels, and, true to the problem, the velocity of each is roughly the same at any time (with suitable powering weights).
It will be interesting to see how you explain the car moving forward unabated by the runway.
Yes, I know ... this is where the screwed up frames of reference occur.
I invite you to attempt the car and paper runway experiment I propose as it is a practical model of the plane-on-a-conveyor that anyone can try. Both objects are powered by separate, non-interlinked supplies. The connecting point is just the putative wheels, and, true to the problem, the velocity of each is roughly the same at any time (with suitable powering weights).
It will be interesting to see how you explain the car moving forward unabated by the runway.
QUOTE
Yes, I know ... this is where the screwed up frames of reference occur.
There is no screwed up frames of reference in my derivation. Again I point you to the Classical Mechanics text book which does the derivation starting with the exact same equation I used and using the exact same steps I used.
QUOTE (->
| QUOTE |
| Yes, I know ... this is where the screwed up frames of reference occur. |
There is no screwed up frames of reference in my derivation. Again I point you to the Classical Mechanics text book which does the derivation starting with the exact same equation I used and using the exact same steps I used.
I invite you to attempt the car and paper runway experiment I propose as it is a practical model of the plane-on-a-conveyor that anyone can try. Both objects are powered by separate, non-interlinked supplies. The connecting point is just the putative wheels, and, true to the problem, the velocity of each is roughly the same at any time (with suitable powering weights).
You once again aren't paying attention. I did that experiment long before you even suggested it to me. I have further linked you to it twice now. Here it is again. Yes it is a battery and not a car but that makes no difference to the underlying physics.
QUOTE
It will be interesting to see how you explain the car moving forward unabated by the runway.
I won't have to because I have done it and it worked precisely how I predicted it would.
Oh, and your video experiment is totally false since you did not pull out the paper at an acceleration equivalent to the gravity on the battery. You chose an arbitrary speed ... also starting with an impulse rather than a ramp up ... I have little doubt the battery could be made to do whatever you wanted it to do under these circumstances. Get yourself two ramps, attach the paper to a weighted car on a second ramp via a spindle. Release battery and car simultaneously.
Rolling resistance IS a factor as it will result in a "terminal velocity" to any object given an upper bound on available power. Failure to include it is an error.
Rolling resistance IS a factor as it will result in a "terminal velocity" to any object given an upper bound on available power. Failure to include it is an error.
QUOTE
Oh, and you video experiment is totally false since you did not pull out the paper at an acceleration equivalent to the gravity on the battery.
Once again you construct a strawman argument. The derivations have shown many times that the acceleration of the paper or the belt will be much higher than the acceleration the plane would undergo via its thrust normally.
QUOTE (->
| QUOTE |
| Oh, and you video experiment is totally false since you did not pull out the paper at an acceleration equivalent to the gravity on the battery. |
Once again you construct a strawman argument. The derivations have shown many times that the acceleration of the paper or the belt will be much higher than the acceleration the plane would undergo via its thrust normally.
You chose an arbitrary speed ..
I simply pulled roughly as hard as I could in a controllable manner. There was no set speed but I did try to maintain as even an acceleration as possible.
QUOTE
also starting with an impulse rather than a ramp up
What do you mean starting with an impulse rather than a ramp up? All I did was let the battery go at the top of the ramp and pulled the paper.
QUOTE (->
| QUOTE |
| also starting with an impulse rather than a ramp up |
What do you mean starting with an impulse rather than a ramp up? All I did was let the battery go at the top of the ramp and pulled the paper.
Rolling resistance IS a factor as it will result in a "terminal velocity" to any object given an upper bound on available power. Failure to include it is an error.
Rolling resistance is a constant that never changes with speed. Go look it up. Well ok realistically there is a very small linear increase of rolling resistance with speed but the wheels would be destroyed long before that became an issue if they weren't assumed ideal. A plane not subject to aerodynamic drag can roll more than fast enough to cause its wheels to fly apart. If its wheels where idea and could not fly apart and it never ran out of fuel it could accelerate forever against rolling resistance. Also, I point out once again that we are making assumptions of ideal wheels and an ideal belt so ignoring rolling resistance is not an error.
But I think you've made it clear you have no interest in actual discussion here. You refused to read my initial explanations, you deny the experimental results, you won't even address the evidence from the text book, you will not provide evidence for your position. In short you are not currently part of this discussion. You have in fact broken the rules that make a discussion a discussion and have thus forfeited your side of the argument until such a time as you can abide by the rules that make a discussion a discussion. Here I'll post them again.
Okay, those who deny that the theoretical treadmill can keep the plane in place and refuse to do the math are worse, my apologies Derek. We are still waiting for the math NoCleverName.
QUOTE (Subduction Zone+Jan 12 2011, 04:27 AM)
I don't know what's worse. People like Derek who was terribly insulting and was against the idea until he realized that we were right, and now it is obvious.
Look I was trying to be nice. I was neither insulting nor have I "realized" you ("we" as in one person singular with multiple personalities) were right. Your scenario is absurd. The wheels (and tires) would disintegrate and the plane (or rocket) would move forward (although with possible catastrophic results). And anyone with even the basic understanding of physics knows you're wrong.
Look I was trying to be nice. I was neither insulting nor have I "realized" you ("we" as in one person singular with multiple personalities) were right. Your scenario is absurd. The wheels (and tires) would disintegrate and the plane (or rocket) would move forward (although with possible catastrophic results). And anyone with even the basic understanding of physics knows you're wrong.
QUOTE (Derek1148+Jan 12 2011, 05:23 AM)
Look I was trying to be nice. I was neither insulting nor have I "realized" you ("we" as in one person singular with multiple personalities) were right. Your scenario is absurd. The wheels (and tires) would disintegrate and the plane (or rocket) would move forward (although with possible catastrophic results). And anyone with even the basic understanding of physics knows you're wrong.
Of course they would, but that is not the point. Once again, do you not understand the concept of a thought problem? They very often use one or more impossible scenarios in the real world to teach you some aspect of physics.
For being "wrong" it is amazing how no one has been able to successfully argue against the solution that you have been given. Sorry, but anyone who knows basic physics would see that we are right.
ETA: And you weren't being nice. At best you were being snarky. Being nice would be to realize that you were mistaken and apologize. It seems that you haven't learned either.
Of course they would, but that is not the point. Once again, do you not understand the concept of a thought problem? They very often use one or more impossible scenarios in the real world to teach you some aspect of physics.
For being "wrong" it is amazing how no one has been able to successfully argue against the solution that you have been given. Sorry, but anyone who knows basic physics would see that we are right.
ETA: And you weren't being nice. At best you were being snarky. Being nice would be to realize that you were mistaken and apologize. It seems that you haven't learned either.
To add further evidence that I am right here are three pages from one of my Physics 201 text books:
Page 1
Page 2
Page 3
Passage that might be of interest:
In other words:
F_net = F_thrust - T/r
In other words:
F_net = F_thrust - T/r
Look I was trying to be nice. I was neither insulting nor have I "realized" you ("we" as in one person singular with multiple personalities) were right.
And here I thought we were making progress. I am not him and it is clearly the case. Just because he got less than congenial with you is no reason to start insulting me again, or was I right and are you truly not happy unless you are putting someone else down?
To echo Subduction Zone because repeating it isn't a bad idea, this is purely a thought experiment. Such objections are irrelevant.
To echo Subduction Zone because repeating it isn't a bad idea, this is purely a thought experiment. Such objections are irrelevant.
And anyone with even the basic understanding of physics knows you're wrong.
Two text books I have in my possession disagree with you.
Oh and here is a video showing the same thing from someone that is not me.
Prove it. Cite a source, an actual source, that contradicts the physics I have used. I've got two different text books and a that video of a Physics professor working out the YoYo problem saying that I am right. I've got the video I made demonstrating that I am right. I derived my result in two different ways demonstrating that I am right. I derived the equation I started with, which is the correct one as confirmed by the text books and the professors, in two different ways once again demonstrating that I am right. I have what any sane person would call a preponderance of evidence. Surely you can come up with a single source of equal weight to any of the sources I have provided to support your position.
I have shouldered my burden of proof far above and beyond any reasonable level. It is now your turn to take up your burden of proof. If you cannot or will not then like NoCleverName you no longer have any right to participate in this discussion.
Prove it. Cite a source, an actual source, that contradicts the physics I have used. I've got two different text books and a that video of a Physics professor working out the YoYo problem saying that I am right. I've got the video I made demonstrating that I am right. I derived my result in two different ways demonstrating that I am right. I derived the equation I started with, which is the correct one as confirmed by the text books and the professors, in two different ways once again demonstrating that I am right. I have what any sane person would call a preponderance of evidence. Surely you can come up with a single source of equal weight to any of the sources I have provided to support your position.
I have shouldered my burden of proof far above and beyond any reasonable level. It is now your turn to take up your burden of proof. If you cannot or will not then like NoCleverName you no longer have any right to participate in this discussion.
What happens when kinetic friction increases?
1) As long as the wheels do not slip there is no kinetic friction at all.
2) Kinetic friction can only increase by increasing the coefficient of friction or by increasing the weight of the object. Melting the tires would only cause a decrease in the coefficient of friction. So how exactly is it supposed to increase? Ok it might for a little bit as the tires warm up should they be sliding but the tires will melt and it will drop. Of course there is no need to worry about any of that this being a thought experiment.
It is quite easy to make anything sound absurd when you construct an argument that has nothing to do with the argument that is being presented and is designed to sound absurd.
Yup. Unless you want to bring the friction between the axle and the wheel into this. Of course whether or not that is actually kinetic friction depends entirely on how the wheel axle interface is set up. If there are bearings between the axle and the wheel than it is rolling resistance that acts between the axle in the wheel. If the axle is just a pipe stuck through the wheel with grease around it then you have something that might be called kinetic friction.
As for between the wheel and the surface it is rolling on there is rolling resistance, which has its origins in the deformation of the surface and/or the wheel, and the static frictional force between the bottom of the wheel in the surface it is rolling on because they wheel is rolling without slipping and therefor the bottom of the wheel is at rest with respect to the surface on which it is rolling.
Hey man no hard feelings. You are certainly allowed to have any opinion that you want.
Absolutely absurd. The bearings do no such thing. Rolling is rolling is rolling. The wing walker can't effect the speed of the plane by turning the wheel because he has to push against the plane in order to turn the wheel. It doesn't matter if there are axles or not the equations of rolling do not change.
You'll notice from here that both bicycle wheels and train wheels are used as examples because they obey the same rules of rolling as a cylinder or disk.
I also point you again to one of the pages from one of my Physics 201 books.
The passage of interest in this case is:
Absolutely absurd. The bearings do no such thing. Rolling is rolling is rolling. The wing walker can't effect the speed of the plane by turning the wheel because he has to push against the plane in order to turn the wheel. It doesn't matter if there are axles or not the equations of rolling do not change.
You'll notice from here that both bicycle wheels and train wheels are used as examples because they obey the same rules of rolling as a cylinder or disk.
I also point you again to one of the pages from one of my Physics 201 books.
The passage of interest in this case is:
We begin our discussion of complex rotations by considering motions that are combinations of translation and rotation. For example, when a bicycle moves along a straight track, the center of each wheel moves forward with a translational speed v_com. At any given instant if the wheel is rolling without slipping, the top point of the wheel is moving forward at twice v_com relative to the track, and the bottom point on the wheel is not moving. However, every point on the wheel also rotates about the center with rotational speed "w". Hence, the rolling motion of the wheel is a combination of purely translational and purely rotational motions.
In short a wheel obeys the same rules for rolling as anything else.
Oh and one other thing. You assertion that a force on the outside of a wheel with an axle cannot effect the linear motion means that nothing could coast to a stop. Things coast to a stop because of rolling resistance which occurs between the wheel and the surface and acts on the edge of the wheel to slow it. So if wheels with axles where truly different then coasting to a stop would be impossible on a bicycle.
Also, if the physics of the two cases are different surely you can go find a source somewhere that isn't you that is at least as reputable as a text book that not only says that an axle changes things but also the exact way the physics is different.
Who said anything about breaks. I said coasting to a stop. Last time I checked you don't coast with the breaks on.
Oh and nice try ignoring all of the other points I made.
Who said anything about breaks. I said coasting to a stop. Last time I checked you don't coast with the breaks on.
Oh and nice try ignoring all of the other points I made.
Do you need a physics book reference for that?
You do when you make a claim like this:
I've given a reference from a website as well as a physics text book that indicates that this is in error. I've given a physical example in the form of a coasting bicycle, which could just as easily be a match box car pushed across a floor or a plane that just shut its engines off, that indicates that your statement is in error.
Rolling resistance. So explain to me again how a force on the outside of a wheel with an axle can't impact the linear speed of said wheel and axle even though this would mean that rolling resistance could never slow down say a match box car pushed across a floor. Said car would roll forever if what you claim was true.
Wrong and has already been addressed. Might I suggest some reading on Special Relativity and accelerations. The gist of it is that from the point of view of the belt it can accelerate forever at whatever acceleration you care to give it because of the effects of special relativity.
Wrong and has already been addressed. Might I suggest some reading on Special Relativity and accelerations. The gist of it is that from the point of view of the belt it can accelerate forever at whatever acceleration you care to give it because of the effects of special relativity.
In the best case scenario, the wheels and the belt reach their relativistic limits and can no longer accelerate, thus allowing the plane to move forward on 1% thrust. What I think is more likely is that the mass of the conveyor designed to support and counter an entire plane is very much greater than the mass of the wheels, and so reaches its limit of possible acceleration long before the wheels do.
1) You ignore the fact that as the mass of the wheels increases it also effects the ability of the thrust of the plane to accelerate the plane.
2) We're assuming an ideal belt that can always maintain any acceleration we desire indefinitely.
This shows nothing because it is rife with several errors. You applied only some of the effects of special relativity and not others. You also introduce non-ideal considerations into an idealized problem.
Page 1
Page 2
Page 3
Passage that might be of interest:
QUOTE
The Forces of Rolling
The simultaneous application of Newton's Second Law in both its translational and rotational forms allows us to calculate the acceleration of an object in situations where the motion combines rotation and translation.
The simultaneous application of Newton's Second Law in both its translational and rotational forms allows us to calculate the acceleration of an object in situations where the motion combines rotation and translation.
In other words:
F_net = F_thrust - T/r
QUOTE (->
| QUOTE |
| The Forces of Rolling The simultaneous application of Newton's Second Law in both its translational and rotational forms allows us to calculate the acceleration of an object in situations where the motion combines rotation and translation. |
In other words:
F_net = F_thrust - T/r
Look I was trying to be nice. I was neither insulting nor have I "realized" you ("we" as in one person singular with multiple personalities) were right.
And here I thought we were making progress. I am not him and it is clearly the case. Just because he got less than congenial with you is no reason to start insulting me again, or was I right and are you truly not happy unless you are putting someone else down?
QUOTE
Your scenario is absurd. The wheels (and tires) would disintegrate and the plane (or rocket) would move forward (although with possible catastrophic results).
To echo Subduction Zone because repeating it isn't a bad idea, this is purely a thought experiment. Such objections are irrelevant.
QUOTE (->
| QUOTE |
| Your scenario is absurd. The wheels (and tires) would disintegrate and the plane (or rocket) would move forward (although with possible catastrophic results). |
To echo Subduction Zone because repeating it isn't a bad idea, this is purely a thought experiment. Such objections are irrelevant.
And anyone with even the basic understanding of physics knows you're wrong.
Two text books I have in my possession disagree with you.
Oh and here is a video showing the same thing from someone that is not me.
QUOTE (Sithdarth+Jan 12 2011, 05:53 AM)
...this is purely a thought experiment.
Okay,... I thought about it. It's absurd.
Okay,... I thought about it. It's absurd.
QUOTE (Derek1148+Jan 12 2011, 06:39 AM)
Okay,... I thought about it. It's absurd.
A typical excuse by those who can't do, or understand the physics.
Once again thought experiments are teaching devices. Some people can't be taught.
A typical excuse by those who can't do, or understand the physics.
Once again thought experiments are teaching devices. Some people can't be taught.
QUOTE (Subduction Zone+Jan 12 2011, 06:53 AM)
A typical excuse by those who can't do, or understand the physics.
Once again thought experiments are teaching devices. Some people can't be taught.
What happens when kinetic friction increases? Do the surfaces get colder or hotter? Like I said, I thought about your scenario... and it is absurd.
Once again thought experiments are teaching devices. Some people can't be taught.
What happens when kinetic friction increases? Do the surfaces get colder or hotter? Like I said, I thought about your scenario... and it is absurd.
QUOTE
Okay,... I thought about it. It's absurd.
Prove it. Cite a source, an actual source, that contradicts the physics I have used. I've got two different text books and a that video of a Physics professor working out the YoYo problem saying that I am right. I've got the video I made demonstrating that I am right. I derived my result in two different ways demonstrating that I am right. I derived the equation I started with, which is the correct one as confirmed by the text books and the professors, in two different ways once again demonstrating that I am right. I have what any sane person would call a preponderance of evidence. Surely you can come up with a single source of equal weight to any of the sources I have provided to support your position.
I have shouldered my burden of proof far above and beyond any reasonable level. It is now your turn to take up your burden of proof. If you cannot or will not then like NoCleverName you no longer have any right to participate in this discussion.
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| QUOTE |
| Okay,... I thought about it. It's absurd. |
Prove it. Cite a source, an actual source, that contradicts the physics I have used. I've got two different text books and a that video of a Physics professor working out the YoYo problem saying that I am right. I've got the video I made demonstrating that I am right. I derived my result in two different ways demonstrating that I am right. I derived the equation I started with, which is the correct one as confirmed by the text books and the professors, in two different ways once again demonstrating that I am right. I have what any sane person would call a preponderance of evidence. Surely you can come up with a single source of equal weight to any of the sources I have provided to support your position.
I have shouldered my burden of proof far above and beyond any reasonable level. It is now your turn to take up your burden of proof. If you cannot or will not then like NoCleverName you no longer have any right to participate in this discussion.
What happens when kinetic friction increases?
1) As long as the wheels do not slip there is no kinetic friction at all.
2) Kinetic friction can only increase by increasing the coefficient of friction or by increasing the weight of the object. Melting the tires would only cause a decrease in the coefficient of friction. So how exactly is it supposed to increase? Ok it might for a little bit as the tires warm up should they be sliding but the tires will melt and it will drop. Of course there is no need to worry about any of that this being a thought experiment.
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Like I said, I thought about your scenario... and it is absurd.
It is quite easy to make anything sound absurd when you construct an argument that has nothing to do with the argument that is being presented and is designed to sound absurd.
QUOTE (Sithdarth+Jan 12 2011, 07:03 AM)
1) As long as the wheels do not slip there is no kinetic friction at all.
Are you sure about that?
Are you sure about that?
QUOTE
Are you sure about that?
Yup. Unless you want to bring the friction between the axle and the wheel into this. Of course whether or not that is actually kinetic friction depends entirely on how the wheel axle interface is set up. If there are bearings between the axle and the wheel than it is rolling resistance that acts between the axle in the wheel. If the axle is just a pipe stuck through the wheel with grease around it then you have something that might be called kinetic friction.
As for between the wheel and the surface it is rolling on there is rolling resistance, which has its origins in the deformation of the surface and/or the wheel, and the static frictional force between the bottom of the wheel in the surface it is rolling on because they wheel is rolling without slipping and therefor the bottom of the wheel is at rest with respect to the surface on which it is rolling.
QUOTE (Sithdarth+Jan 12 2011, 07:40 AM)
If the axle is just a pipe stuck through the wheel with grease around it then you have something that might be called kinetic friction.
Hey, maybe. At any rate I'll accept that. My feelings about your scenario haven't changed. But I agree with you or the other one, in that I don't accept the logic of your "thought experiment," if you want my opinion in the future, ask, otherwise I'll let you continue without my participation.
Hey, maybe. At any rate I'll accept that. My feelings about your scenario haven't changed. But I agree with you or the other one, in that I don't accept the logic of your "thought experiment," if you want my opinion in the future, ask, otherwise I'll let you continue without my participation.
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Hey, maybe. At any rate I'll accept that. My feelings about your scenario haven't changed. But I agree with you or the other one, in that I don't accept the logic of your "thought experiment," if you my opinion in the future, ask, otherwise I'll let you continue without my participation.
Hey man no hard feelings. You are certainly allowed to have any opinion that you want.
Your video shouldn't be allowed into evidence. When you take a wheel off of the plane and let it roll down a slope (battery) the linear velocity and angular velocity are strictly proportional. In this case a force on the angular velocity affects the linear velocity.
When you put the wheel back on the plane the axle, bearings, and lubricant "isolate" the two. Otherwise you would allow a wing walker to climb down and affect the speed of the plane by turning a wheel. This sure isn't going to happen. The tires are free wheeling. The physics of the two cases are different.
http://en.wikipedia.org/wiki/File:Aerobatics.jpg
When you put the wheel back on the plane the axle, bearings, and lubricant "isolate" the two. Otherwise you would allow a wing walker to climb down and affect the speed of the plane by turning a wheel. This sure isn't going to happen. The tires are free wheeling. The physics of the two cases are different.
http://en.wikipedia.org/wiki/File:Aerobatics.jpg
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Your video shouldn't be allowed into evidence. When you take a wheel off of the plane and let it roll down a slope (battery) the linear velocity and angular velocity are strictly proportional. In this case a force on the angular velocity affects the linear velocity.
When you put the wheel back on the plane the axle, bearings, and lubricant "isolate" the two. Otherwise you would allow a wing walker to climb down and affect the speed of the plane by turning a wheel. This sure isn't going to happen. The tires are free wheeling. The physics of the two cases are different.
When you put the wheel back on the plane the axle, bearings, and lubricant "isolate" the two. Otherwise you would allow a wing walker to climb down and affect the speed of the plane by turning a wheel. This sure isn't going to happen. The tires are free wheeling. The physics of the two cases are different.
Absolutely absurd. The bearings do no such thing. Rolling is rolling is rolling. The wing walker can't effect the speed of the plane by turning the wheel because he has to push against the plane in order to turn the wheel. It doesn't matter if there are axles or not the equations of rolling do not change.
You'll notice from here that both bicycle wheels and train wheels are used as examples because they obey the same rules of rolling as a cylinder or disk.
I also point you again to one of the pages from one of my Physics 201 books.
The passage of interest in this case is:
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| QUOTE |
| Your video shouldn't be allowed into evidence. When you take a wheel off of the plane and let it roll down a slope (battery) the linear velocity and angular velocity are strictly proportional. In this case a force on the angular velocity affects the linear velocity. When you put the wheel back on the plane the axle, bearings, and lubricant "isolate" the two. Otherwise you would allow a wing walker to climb down and affect the speed of the plane by turning a wheel. This sure isn't going to happen. The tires are free wheeling. The physics of the two cases are different. |
Absolutely absurd. The bearings do no such thing. Rolling is rolling is rolling. The wing walker can't effect the speed of the plane by turning the wheel because he has to push against the plane in order to turn the wheel. It doesn't matter if there are axles or not the equations of rolling do not change.
You'll notice from here that both bicycle wheels and train wheels are used as examples because they obey the same rules of rolling as a cylinder or disk.
I also point you again to one of the pages from one of my Physics 201 books.
The passage of interest in this case is:
We begin our discussion of complex rotations by considering motions that are combinations of translation and rotation. For example, when a bicycle moves along a straight track, the center of each wheel moves forward with a translational speed v_com. At any given instant if the wheel is rolling without slipping, the top point of the wheel is moving forward at twice v_com relative to the track, and the bottom point on the wheel is not moving. However, every point on the wheel also rotates about the center with rotational speed "w". Hence, the rolling motion of the wheel is a combination of purely translational and purely rotational motions.
In short a wheel obeys the same rules for rolling as anything else.
Oh and one other thing. You assertion that a force on the outside of a wheel with an axle cannot effect the linear motion means that nothing could coast to a stop. Things coast to a stop because of rolling resistance which occurs between the wheel and the surface and acts on the edge of the wheel to slow it. So if wheels with axles where truly different then coasting to a stop would be impossible on a bicycle.
Also, if the physics of the two cases are different surely you can go find a source somewhere that isn't you that is at least as reputable as a text book that not only says that an axle changes things but also the exact way the physics is different.
When brakes are applied, a free wheeling tire is no longer free wheeling. There is no longer" isolation" between the plane and the tire.
Do you need a physics book reference for that?
Do you need a physics book reference for that?
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When brakes are applied, a free wheeling tire is no longer free wheeling. There is no longer" isolation" between the plane and the tire.
Who said anything about breaks. I said coasting to a stop. Last time I checked you don't coast with the breaks on.
Oh and nice try ignoring all of the other points I made.
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| When brakes are applied, a free wheeling tire is no longer free wheeling. There is no longer" isolation" between the plane and the tire. |
Who said anything about breaks. I said coasting to a stop. Last time I checked you don't coast with the breaks on.
Oh and nice try ignoring all of the other points I made.
Do you need a physics book reference for that?
You do when you make a claim like this:
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When you put the wheel back on the plane the axle, bearings, and lubricant "isolate" the two. Otherwise you would allow a wing walker to climb down and affect the speed of the plane by turning a wheel. This sure isn't going to happen. The tires are free wheeling. The physics of the two cases are different.
I've given a reference from a website as well as a physics text book that indicates that this is in error. I've given a physical example in the form of a coasting bicycle, which could just as easily be a match box car pushed across a floor or a plane that just shut its engines off, that indicates that your statement is in error.
Rolling resistance. So explain to me again how a force on the outside of a wheel with an axle can't impact the linear speed of said wheel and axle even though this would mean that rolling resistance could never slow down say a match box car pushed across a floor. Said car would roll forever if what you claim was true.
Both thrust and acceleration produce force, and can indeed counter each other. So that much is right. The problem, confining myself to the premise forwarded by SZ & SD (indestructible materials and all), is that the balancing forces are not equal in every way. As a thought experiment, we are allowed to greatly exaggerate things in order to reveal what may actually be happening.
Say we initiate a 1% thrust with the plane. This is enough to initiate the countering conveyor belt. So far so good, with enough acceleration of the belt, the force of the thrust CAN possibly be countered by the belt. Now NEVER increase the thrust. What must happen?
Since the countering force is a result of acceleration, that acceleration must continue in order to maintain that force. IOW, the speed of the belt must constantly be increasing just to match the constant force resulting from a stable 1% thrust. So even if the plane only ever reaches 1% of its thrust capacity, the belt must accelerate infinitely to counter that thrust an indefinite length of time.
Nothing can accelerate infinitely, so as time progresses, the belt and wheel will be nearing the speed of light (just to counter 1% thrust). Assuming these can reach relativistic speeds (though experiment-wise), which one, belt or wheel, would reach the limit of finite energy that can be applied to further accelerate it?
In the best case scenario, the wheels and the belt reach their relativistic limits and can no longer accelerate, thus allowing the plane to move forward on 1% thrust. What I think is more likely is that the mass of the conveyor designed to support and counter an entire plane is very much greater than the mass of the wheels, and so reaches its limit of possible acceleration long before the wheels do.
This shows that, because of the fundamental differences in how the forces are generated, in the end, the one that can be stably maintained wins out. Force due to acceleration is at a deficit of already losing energy like mad.
Say we initiate a 1% thrust with the plane. This is enough to initiate the countering conveyor belt. So far so good, with enough acceleration of the belt, the force of the thrust CAN possibly be countered by the belt. Now NEVER increase the thrust. What must happen?
Since the countering force is a result of acceleration, that acceleration must continue in order to maintain that force. IOW, the speed of the belt must constantly be increasing just to match the constant force resulting from a stable 1% thrust. So even if the plane only ever reaches 1% of its thrust capacity, the belt must accelerate infinitely to counter that thrust an indefinite length of time.
Nothing can accelerate infinitely, so as time progresses, the belt and wheel will be nearing the speed of light (just to counter 1% thrust). Assuming these can reach relativistic speeds (though experiment-wise), which one, belt or wheel, would reach the limit of finite energy that can be applied to further accelerate it?
In the best case scenario, the wheels and the belt reach their relativistic limits and can no longer accelerate, thus allowing the plane to move forward on 1% thrust. What I think is more likely is that the mass of the conveyor designed to support and counter an entire plane is very much greater than the mass of the wheels, and so reaches its limit of possible acceleration long before the wheels do.
This shows that, because of the fundamental differences in how the forces are generated, in the end, the one that can be stably maintained wins out. Force due to acceleration is at a deficit of already losing energy like mad.
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Nothing can accelerate infinitely, so as time progresses, the belt and wheel will be nearing the speed of light (just to counter 1% thrust). Assuming these can reach relativistic speeds (though experiment-wise), which one, belt or wheel, would reach the limit of finite energy that can be applied to further accelerate it?
Wrong and has already been addressed. Might I suggest some reading on Special Relativity and accelerations. The gist of it is that from the point of view of the belt it can accelerate forever at whatever acceleration you care to give it because of the effects of special relativity.
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| QUOTE |
| Nothing can accelerate infinitely, so as time progresses, the belt and wheel will be nearing the speed of light (just to counter 1% thrust). Assuming these can reach relativistic speeds (though experiment-wise), which one, belt or wheel, would reach the limit of finite energy that can be applied to further accelerate it? |
Wrong and has already been addressed. Might I suggest some reading on Special Relativity and accelerations. The gist of it is that from the point of view of the belt it can accelerate forever at whatever acceleration you care to give it because of the effects of special relativity.
In the best case scenario, the wheels and the belt reach their relativistic limits and can no longer accelerate, thus allowing the plane to move forward on 1% thrust. What I think is more likely is that the mass of the conveyor designed to support and counter an entire plane is very much greater than the mass of the wheels, and so reaches its limit of possible acceleration long before the wheels do.
1) You ignore the fact that as the mass of the wheels increases it also effects the ability of the thrust of the plane to accelerate the plane.
2) We're assuming an ideal belt that can always maintain any acceleration we desire indefinitely.
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This shows that, because of the fundamental differences in how the forces are generated, in the end, the one that can be stably maintained wins out. Force due to acceleration is at a deficit of already losing energy like mad.
This shows nothing because it is rife with several errors. You applied only some of the effects of special relativity and not others. You also introduce non-ideal considerations into an idealized problem.
QUOTE (Sithdarth+Jan 12 2011, 06:12 PM)
Wrong and has already been addressed. Might I suggest some reading on Special Relativity and accelerations. The gist of it is that from the point of view of the belt it can accelerate forever at whatever acceleration you care to give it because of the effects of special relativity.
You obviously don't get the "gist" of that link you posted.
This doesn't imply, at all, that the accelerated frame can do so indefinitely. Are you assuming this "ideal" conveyor has no mass? And when you are countering an accelerated frame against an inertial one, how the acceleration is measured from the inertial frame is very much the point. I see why others have said you are mixing frames of reference willy-nilly.
This doesn't imply, at all, that the accelerated frame can do so indefinitely. Are you assuming this "ideal" conveyor has no mass? And when you are countering an accelerated frame against an inertial one, how the acceleration is measured from the inertial frame is very much the point. I see why others have said you are mixing frames of reference willy-nilly.
1) You ignore the fact that as the mass of the wheels increases it also effects the ability of the thrust of the plane to accelerate the plane.
2) We're assuming an ideal belt that can always maintain any acceleration we desire indefinitely.
1) Since the wheels mediate the acceleration, it only requires the wheels to make ANY gain on the belt to break the constant acceleration and their mass begins to again approach rest mess. Since the belt reaches the limit of acceleration first, acceleration of the wheel ends. Even if this occurs in a cycle of ups and downs, the plane will make progress.
2) Why bother to argue special relativity if this "ideal" belt is completely immune to its effects? This is taking the thought experiment well beyond any use in physics.
Well you can "idealize" a problem until it has nothing to do with anything but some self-consistent math, and that appears to be what you've done. You've come up with a mathematical argument and "idealized" the problem to fit, defend, and justify that argument. The mathematical argument is not equivalent to the physical situation. It is here you have failed.
Nope. The speed of the belt and the speed of the outside of the wheels are identical. They would both reach light speed at the same time, if they could.
Nope. The speed of the belt and the speed of the outside of the wheels are identical. They would both reach light speed at the same time, if they could.
2) Why bother to argue special relativity if this "ideal" belt is completely immune to its effects? This is taking the thought experiment well beyond any use in physics.
But the belt isn't immune to SR and it does not violate it in any way.
It wasn't idealized to a fault. We analyzed and answered the question as it was originally asked.
We'll see about that.
We'll see about that.
This doesn't imply, at all, that the accelerated frame can do so indefinitely. Are you assuming this "ideal" conveyor has no mass? And when you are countering an accelerated frame against an inertial one, how the acceleration is measured from the inertial frame is very much the point. I see why others have said you are mixing frames of reference willy-nilly.
Really than explain to me these phrases:
If it was a rocket and you were on board you would experience a constant G force.
You should have also followed the link at the bottom.
You might also want to take a look at this as well.
Specifically pay attention to the last equation in the acceleration section. If we set u=0, that is to say if we are measuring the acceleration of something in the rest frame of whatever is accelerating or in other words an astronaut standing in a rocket, and assume a to be a constant we can see that as v approaches the speed of light a' approaches zero. In other words even though the person standing in the rocket always experiences a constant a from his perspective from our perspective his acceleration decreases.
You've made the further mistake of assuming the plane is in an inertial frame just because it isn't moving relative to someone standing still. The wheels of the plane are in the frame of reference of the belt because the bottoms of the wheels are stationary with respect to the belt. Further, if you removed the thrust of the plane the plane would be pulled backwards by the belt. All indicating that the proper frame from the plane is that of the belt. Further indicating that the acceleration that is important is the acceleration felt by someone sitting at rest on the belt which can in fact be precisely constant forever irrespective of how fast the belt seems to be going from the perspective of someone outside the belt.
1) If the plane begins to move forward against the belt this requires that the wheels accelerate faster than the belt. This would make there mass increase further from rest mass not the other way around.
2) There is no limit to the acceleration as previously demonstrated. To further drive home this point I point you to the equivalency principle. According to relativity someone in an accelerating rocket that cannot see outside cannot determine if he is in a rocket or standing on a planet with a matching gravitational acceleration. If what you said were true and such a constant acceleration were not possible it would only be because relativistic effects where leaking into the rest frame of the rocket for the person in the rocket to measure. This obviously violates the equivalency principle.
1) If the plane begins to move forward against the belt this requires that the wheels accelerate faster than the belt. This would make there mass increase further from rest mass not the other way around.
2) There is no limit to the acceleration as previously demonstrated. To further drive home this point I point you to the equivalency principle. According to relativity someone in an accelerating rocket that cannot see outside cannot determine if he is in a rocket or standing on a planet with a matching gravitational acceleration. If what you said were true and such a constant acceleration were not possible it would only be because relativistic effects where leaking into the rest frame of the rocket for the person in the rocket to measure. This obviously violates the equivalency principle.
2) Why bother to argue special relativity if this "ideal" belt is completely immune to its effects? This is taking the thought experiment well beyond any use in physics.
The belt isn't immune to its effects. It simply is said to maintain a constant acceleration as measured by the force felt by someone sitting on the belt. This might mean we need a motor with unreasonable amounts of power but that is irrelevant because we already have wheels that are infinitely strong with no rolling resistance which is a much bigger assumption.
Wrong. Clearly demonstrated to be wrong. Not only did I do an experiment that verified the physicality of the math I posted a video from a guy who did a related experiment that used the same math that also validated the physicality of the math. You on the other hand have failed to take into account all of the consequences of Relativity and have instead picked and choose that which would make your point. This is not how science is done. If you want to bring in a theory you must accept all the consequences of the theory.
Wrong. Clearly demonstrated to be wrong. Not only did I do an experiment that verified the physicality of the math I posted a video from a guy who did a related experiment that used the same math that also validated the physicality of the math. You on the other hand have failed to take into account all of the consequences of Relativity and have instead picked and choose that which would make your point. This is not how science is done. If you want to bring in a theory you must accept all the consequences of the theory.
The limit at which an approach to the speed of light would require infinite energy to continue the approach is based on the object's mass. There being a not insignificant difference in the two masses, they would not reach this limit simultaneously. There is no possibility of actually reaching the speed of light unless you assume the objects in question to be without mass, in which case you are violating SR and have idealized to a fault.
Absolutely hogwash. The differences in masses is irrelevant. For starters the accelerations are defined to be the same by the problem. But that is neither here not there. The is in fact no point at which an object cannot still increase its velocity closer to the speed of light. The velocity of an object undergoing a constant acceleration as felt by someone in the objects rest frame measured by someone outside that rest frame approaches the speed of light asymptotically. Which is described in one of my links above. Asymptotically means that while the rate decreases it never actually stops growing but at the same time it never reaches the value it is approaching. There is no point in the acceleration of an object at which it requires infinite energy to reach the next infinitesimally higher velocity.
You obviously don't get the "gist" of that link you posted.
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What does this mean? We don't mean that its acceleration as measured by an inertial observer is constant. We mean that it is moving so that the acceleration measured in an inertial frame travelling at the same instantaneous velocity as the object is the same at any moment. If it was a rocket and you were on board you would experience a constant G force.
This doesn't imply, at all, that the accelerated frame can do so indefinitely. Are you assuming this "ideal" conveyor has no mass? And when you are countering an accelerated frame against an inertial one, how the acceleration is measured from the inertial frame is very much the point. I see why others have said you are mixing frames of reference willy-nilly.
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| QUOTE |
| What does this mean? We don't mean that its acceleration as measured by an inertial observer is constant. We mean that it is moving so that the acceleration measured in an inertial frame travelling at the same instantaneous velocity as the object is the same at any moment. If it was a rocket and you were on board you would experience a constant G force. |
This doesn't imply, at all, that the accelerated frame can do so indefinitely. Are you assuming this "ideal" conveyor has no mass? And when you are countering an accelerated frame against an inertial one, how the acceleration is measured from the inertial frame is very much the point. I see why others have said you are mixing frames of reference willy-nilly.
1) You ignore the fact that as the mass of the wheels increases it also effects the ability of the thrust of the plane to accelerate the plane.
2) We're assuming an ideal belt that can always maintain any acceleration we desire indefinitely.
1) Since the wheels mediate the acceleration, it only requires the wheels to make ANY gain on the belt to break the constant acceleration and their mass begins to again approach rest mess. Since the belt reaches the limit of acceleration first, acceleration of the wheel ends. Even if this occurs in a cycle of ups and downs, the plane will make progress.
2) Why bother to argue special relativity if this "ideal" belt is completely immune to its effects? This is taking the thought experiment well beyond any use in physics.
QUOTE
This shows nothing because it is rife with several errors. You applied only some of the effects of special relativity and not others. You also introduce non-ideal considerations into an idealized problem.
Well you can "idealize" a problem until it has nothing to do with anything but some self-consistent math, and that appears to be what you've done. You've come up with a mathematical argument and "idealized" the problem to fit, defend, and justify that argument. The mathematical argument is not equivalent to the physical situation. It is here you have failed.
QUOTE (Argyll+Jan 12 2011, 02:41 AM)
... as it reaches relativistic speeds, the mass of the wheels will increase, reducing the acceleration required to exert the appropriate thrust on the plane and keep it from moving.
Yes indeed - maybe that's the solution we all overlooked in this insanely unrealistic and over interpreted problem...
Yes indeed - maybe that's the solution we all overlooked in this insanely unrealistic and over interpreted problem...
QUOTE (dirak+Jul 19 2005, 09:53 AM)
... conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in opposite direction).
back to numero uno Dirak - as opposed to Dirac...
back to numero uno Dirak - as opposed to Dirac...
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1) Since the wheels mediate the acceleration, it only requires the wheels to make ANY gain on the belt to break the constant acceleration and their mass begins to again approach rest mess. Since the belt reaches the limit of acceleration first, acceleration of the wheel ends. Even if this occurs in a cycle of ups and downs, the plane will make progress.
Nope. The speed of the belt and the speed of the outside of the wheels are identical. They would both reach light speed at the same time, if they could.
QUOTE (->
| QUOTE |
| 1) Since the wheels mediate the acceleration, it only requires the wheels to make ANY gain on the belt to break the constant acceleration and their mass begins to again approach rest mess. Since the belt reaches the limit of acceleration first, acceleration of the wheel ends. Even if this occurs in a cycle of ups and downs, the plane will make progress. |
Nope. The speed of the belt and the speed of the outside of the wheels are identical. They would both reach light speed at the same time, if they could.
2) Why bother to argue special relativity if this "ideal" belt is completely immune to its effects? This is taking the thought experiment well beyond any use in physics.
But the belt isn't immune to SR and it does not violate it in any way.
QUOTE
Well you can "idealize" a problem until it has nothing to do with anything but some self-consistent math, and that appears to be what you've done. You've come up with a mathematical argument and "idealized" the problem to fit, defend, and justify that argument. The mathematical argument is not equivalent to the physical situation. It is here you have failed.
It wasn't idealized to a fault. We analyzed and answered the question as it was originally asked.
QUOTE (Subduction Zone+Jan 12 2011, 07:19 PM)
Nope. The speed of the belt and the speed of the outside of the wheels are identical. They would both reach light speed at the same time, if they could.
The limit at which an approach to the speed of light would require infinite energy to continue the approach is based on the object's mass. There being a not insignificant difference in the two masses, they would not reach this limit simultaneously. There is no possibility of actually reaching the speed of light unless you assume the objects in question to be without mass, in which case you are violating SR and have idealized to a fault.
The limit at which an approach to the speed of light would require infinite energy to continue the approach is based on the object's mass. There being a not insignificant difference in the two masses, they would not reach this limit simultaneously. There is no possibility of actually reaching the speed of light unless you assume the objects in question to be without mass, in which case you are violating SR and have idealized to a fault.
QUOTE (synthsin75+Jan 13 2011, 01:25 AM)
The limit at which an approach to the speed of light would require infinite energy to continue the approach is based on the object's mass. There being a not insignificant difference in the two masses, they would not reach this limit simultaneously. There is no possibility of actually reaching the speed of light unless you assume the objects in question to be without mass, in which case you are violating SR and have idealized to a fault.
The point is that since the speed of the belt is identical to the speed of the outside of the wheels neither would ever reach the speed of light. SR is not a problem for this approach.
And Dirak's, or Dirac's, version of this problem is a no brainer. If you analyze the forces on the plane they are almost identical to the forces it feels on a runway, in that case the plane takes off.
The point is that since the speed of the belt is identical to the speed of the outside of the wheels neither would ever reach the speed of light. SR is not a problem for this approach.
And Dirak's, or Dirac's, version of this problem is a no brainer. If you analyze the forces on the plane they are almost identical to the forces it feels on a runway, in that case the plane takes off.
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You obviously don't get the "gist" of that link you posted.
We'll see about that.
QUOTE (->
| QUOTE |
| You obviously don't get the "gist" of that link you posted. |
We'll see about that.
This doesn't imply, at all, that the accelerated frame can do so indefinitely. Are you assuming this "ideal" conveyor has no mass? And when you are countering an accelerated frame against an inertial one, how the acceleration is measured from the inertial frame is very much the point. I see why others have said you are mixing frames of reference willy-nilly.
Really than explain to me these phrases:
QUOTE
We mean that it is moving so that the acceleration measured in an inertial frame traveling at the same instantaneous velocity as the object is the same at any moment.
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| QUOTE |
| We mean that it is moving so that the acceleration measured in an inertial frame traveling at the same instantaneous velocity as the object is the same at any moment. |
If it was a rocket and you were on board you would experience a constant G force.
You should have also followed the link at the bottom.
You might also want to take a look at this as well.
Specifically pay attention to the last equation in the acceleration section. If we set u=0, that is to say if we are measuring the acceleration of something in the rest frame of whatever is accelerating or in other words an astronaut standing in a rocket, and assume a to be a constant we can see that as v approaches the speed of light a' approaches zero. In other words even though the person standing in the rocket always experiences a constant a from his perspective from our perspective his acceleration decreases.
You've made the further mistake of assuming the plane is in an inertial frame just because it isn't moving relative to someone standing still. The wheels of the plane are in the frame of reference of the belt because the bottoms of the wheels are stationary with respect to the belt. Further, if you removed the thrust of the plane the plane would be pulled backwards by the belt. All indicating that the proper frame from the plane is that of the belt. Further indicating that the acceleration that is important is the acceleration felt by someone sitting at rest on the belt which can in fact be precisely constant forever irrespective of how fast the belt seems to be going from the perspective of someone outside the belt.
QUOTE
1) Since the wheels mediate the acceleration, it only requires the wheels to make ANY gain on the belt to break the constant acceleration and their mass begins to again approach rest mess. Since the belt reaches the limit of acceleration first, acceleration of the wheel ends. Even if this occurs in a cycle of ups and downs, the plane will make progress.
1) If the plane begins to move forward against the belt this requires that the wheels accelerate faster than the belt. This would make there mass increase further from rest mass not the other way around.
2) There is no limit to the acceleration as previously demonstrated. To further drive home this point I point you to the equivalency principle. According to relativity someone in an accelerating rocket that cannot see outside cannot determine if he is in a rocket or standing on a planet with a matching gravitational acceleration. If what you said were true and such a constant acceleration were not possible it would only be because relativistic effects where leaking into the rest frame of the rocket for the person in the rocket to measure. This obviously violates the equivalency principle.
QUOTE (->
| QUOTE |
| 1) Since the wheels mediate the acceleration, it only requires the wheels to make ANY gain on the belt to break the constant acceleration and their mass begins to again approach rest mess. Since the belt reaches the limit of acceleration first, acceleration of the wheel ends. Even if this occurs in a cycle of ups and downs, the plane will make progress. |
1) If the plane begins to move forward against the belt this requires that the wheels accelerate faster than the belt. This would make there mass increase further from rest mass not the other way around.
2) There is no limit to the acceleration as previously demonstrated. To further drive home this point I point you to the equivalency principle. According to relativity someone in an accelerating rocket that cannot see outside cannot determine if he is in a rocket or standing on a planet with a matching gravitational acceleration. If what you said were true and such a constant acceleration were not possible it would only be because relativistic effects where leaking into the rest frame of the rocket for the person in the rocket to measure. This obviously violates the equivalency principle.
2) Why bother to argue special relativity if this "ideal" belt is completely immune to its effects? This is taking the thought experiment well beyond any use in physics.
The belt isn't immune to its effects. It simply is said to maintain a constant acceleration as measured by the force felt by someone sitting on the belt. This might mean we need a motor with unreasonable amounts of power but that is irrelevant because we already have wheels that are infinitely strong with no rolling resistance which is a much bigger assumption.
QUOTE
Well you can "idealize" a problem until it has nothing to do with anything but some self-consistent math, and that appears to be what you've done. You've come up with a mathematical argument and "idealized" the problem to fit, defend, and justify that argument. The mathematical argument is not equivalent to the physical situation. It is here you have failed.
Wrong. Clearly demonstrated to be wrong. Not only did I do an experiment that verified the physicality of the math I posted a video from a guy who did a related experiment that used the same math that also validated the physicality of the math. You on the other hand have failed to take into account all of the consequences of Relativity and have instead picked and choose that which would make your point. This is not how science is done. If you want to bring in a theory you must accept all the consequences of the theory.
QUOTE (->
| QUOTE |
| Well you can "idealize" a problem until it has nothing to do with anything but some self-consistent math, and that appears to be what you've done. You've come up with a mathematical argument and "idealized" the problem to fit, defend, and justify that argument. The mathematical argument is not equivalent to the physical situation. It is here you have failed. |
Wrong. Clearly demonstrated to be wrong. Not only did I do an experiment that verified the physicality of the math I posted a video from a guy who did a related experiment that used the same math that also validated the physicality of the math. You on the other hand have failed to take into account all of the consequences of Relativity and have instead picked and choose that which would make your point. This is not how science is done. If you want to bring in a theory you must accept all the consequences of the theory.
The limit at which an approach to the speed of light would require infinite energy to continue the approach is based on the object's mass. There being a not insignificant difference in the two masses, they would not reach this limit simultaneously. There is no possibility of actually reaching the speed of light unless you assume the objects in question to be without mass, in which case you are violating SR and have idealized to a fault.
Absolutely hogwash. The differences in masses is irrelevant. For starters the accelerations are defined to be the same by the problem. But that is neither here not there. The is in fact no point at which an object cannot still increase its velocity closer to the speed of light. The velocity of an object undergoing a constant acceleration as felt by someone in the objects rest frame measured by someone outside that rest frame approaches the speed of light asymptotically. Which is described in one of my links above. Asymptotically means that while the rate decreases it never actually stops growing but at the same time it never reaches the value it is approaching. There is no point in the acceleration of an object at which it requires infinite energy to reach the next infinitesimally higher velocity.
I just remembered I had this bookmarked. If you wish to learn how to properly apply special relativity I suggest you read from the beginning. If you just want to know about Uniform accelerations the discussion begins around page 121. You'll note that in the discussion of "proper acceleration" it is made clear that the "proper acceleration" is the acceleration felt by anyone inside say a rocket undergoing said "proper acceleration" and can go on indefinitely without the rocket ever reaching the speed of light in any reference frame.
QUOTE (Sithdarth+Jan 12 2011, 07:55 PM)
I just remembered I had this bookmarked. If you wish to learn how to properly apply special relativity I suggest you read from the beginning. If you just want to know about Uniform accelerations the discussion begins around page 121. You'll note that in the discussion of "proper acceleration" it is made clear that the "proper acceleration" is the acceleration felt by anyone inside say a rocket undergoing said "proper acceleration" and can go on indefinitely without the rocket ever reaching the speed of light in any reference frame.
From your reference:
This example, which you seem to have based a very large part of you argument on, doesn't include gravity, other than that produced by a rocket's acceleration. In space, where gravity is negligible, "burning fuel at a constant rate" does indeed maintain a constant acceleration. There is no force countering the inertial motion of the rocket other than the thrust accelerating it.
But within gravity, which very much applies to wheels remaining in sufficient contact with the belt, acceleration cannot be maintained by "burning fuel at a constant rate". The energy expenditure must be increasing, which would be the equivalent of the rocket's thrust increasing. In this case, a "constant acceleration" is not uniform.
This example, which you seem to have based a very large part of you argument on, doesn't include gravity, other than that produced by a rocket's acceleration. In space, where gravity is negligible, "burning fuel at a constant rate" does indeed maintain a constant acceleration. There is no force countering the inertial motion of the rocket other than the thrust accelerating it.
But within gravity, which very much applies to wheels remaining in sufficient contact with the belt, acceleration cannot be maintained by "burning fuel at a constant rate". The energy expenditure must be increasing, which would be the equivalent of the rocket's thrust increasing. In this case, a "constant acceleration" is not uniform.
You've made the further mistake of assuming the plane is in an inertial frame just because it isn't moving relative to someone standing still. The wheels of the plane are in the frame of reference of the belt because the bottoms of the wheels are stationary with respect to the belt. Further, if you removed the thrust of the plane the plane would be pulled backwards by the belt. All indicating that the proper frame from the plane is that of the belt. Further indicating that the acceleration that is important is the acceleration felt by someone sitting at rest on the belt which can in fact be precisely constant forever irrespective of how fast the belt seems to be going from the perspective of someone outside the belt.
First, the bottoms of the wheels are not stationary relative to the belt. This only seems to be the case using "momentarily co-moving inertial frames". Second, just like you can remove the thrust of the plane, you can just as equally remove the acceleration of the belt, the belt then being "pulled backward" by and in respect to the plane. You are favoring a frame that is in no way preferred.
Sorry about that, I miss-worded that bit. The wheels never need to gain on the belt, only falter in their acceleration.
Sorry about that, I miss-worded that bit. The wheels never need to gain on the belt, only falter in their acceleration.
2) There is no limit to the acceleration as previously demonstrated. To further drive home this point I point you to the equivalency principle. According to relativity someone in an accelerating rocket that cannot see outside cannot determine if he is in a rocket or standing on a planet with a matching gravitational acceleration. If what you said were true and such a constant acceleration were not possible it would only be because relativistic effects where leaking into the rest frame of the rocket for the person in the rocket to measure. This obviously violates the equivalency principle.
Once again, you're assuming a situation without gravity. Let's take two very specific frames. The accelerating belt and the stationary axle. Each will view the other as accelerating and potentially succumbing to relativistic effects. To the belt, the axle (and by extension, the plane) will become "heavier" (but since you negate friction, this is irrelevant). To the axle, the wheels become part of the belt's frame and also become "heavier", but with the difference, mentioned above, of the effect being more pronounced on the belt.
Please explain how the differing masses of belt and wheel are irrelevant, and please move this thought experiment "indoors" gravity-wise.
Nonsense. Gravity has no effect on the belts ability to accelerate because it is perpendicular to the direction of the force that is accelerating the belt. Anyone with a knowledge of vector addition knows this. Gravity is acting perpendicular to the direction of motion and therefore cannot do any work on the belt. Therefore it cannot effect the expenditure of energy by the belt.
Further, since the bottom of the wheel is at rest with respect to the belt the ability of the belt to accelerated the bottom of the wheel is unaffected by Relativity. Of course if anyone of this wasn't true we are still left with the fact that the set up of the problem specifically states that the belt is designed to match the speed of wheel which leads to the accelerations matching. Our ideal belt is assumed to be able to accomplish this feat no matter what which even if it requires an infinite amount of power from the motor driving the belt is still less unrealistic then a wheel that won't fly apart at a few hundred miles an hours. Which by the way you have no problem with.
Nonsense. Gravity has no effect on the belts ability to accelerate because it is perpendicular to the direction of the force that is accelerating the belt. Anyone with a knowledge of vector addition knows this. Gravity is acting perpendicular to the direction of motion and therefore cannot do any work on the belt. Therefore it cannot effect the expenditure of energy by the belt.
Further, since the bottom of the wheel is at rest with respect to the belt the ability of the belt to accelerated the bottom of the wheel is unaffected by Relativity. Of course if anyone of this wasn't true we are still left with the fact that the set up of the problem specifically states that the belt is designed to match the speed of wheel which leads to the accelerations matching. Our ideal belt is assumed to be able to accomplish this feat no matter what which even if it requires an infinite amount of power from the motor driving the belt is still less unrealistic then a wheel that won't fly apart at a few hundred miles an hours. Which by the way you have no problem with.
First, the bottoms of the wheels are not stationary relative to the belt. This only seems to be the case using "momentarily co-moving inertial frames".
Really now?
This source disagrees with you.
This source disagrees with you as well.
Find me one source that says the part of an an object rolling without slipping in contact with the surface it is rolling on isn't moving at the same speed as said surface.
The fact that the bottom of a wheel rolling without slipping is stationary with respect to what it is rolling on has nothing to do with special relativity or any of the links I have given about special relativity. It is nothing more than the most basic fact about an object that rolls without slipping.
The belt would be pulled forward for starters. However, the major flaw in your argument is that even if you remove the acceleration of the belt the plane and the belt are still in the same frame exactly has I had indicated. You simply changed that frame by changing the acceleration of the belt. However, changing the thrust of the plane doesn't change the frame of reference it only changes the plane's motion through that frame of reference. The point stands that the plane is in the frame of reference of the belt. Also, there is a preferred frame of reference it is the rest frame of the bottom of the wheels since that is where the force on the bottom of the wheels is being applied.
Beyond that you still must contend with the fact that all observers must agree on what events occur or you have a paradox. Simply put I have demonstrated that in the frame of reference of the belt and therefore the part of the tires in contact with the belt, the acceleration of the belt can be held constant forever without the belt every reaching the speed of light in any reference frame. The physical requirements of the motor that would be needed are irrelevant because we've already made much more physically impossible assumptions in the form of wheels that won't fly apart. Thus the wheels always feel this constant acceleration and thus the force of thrust is always canceled. Changing frames can never change this fact. When you change frames while the acceleration may in fact appear slower to all that matters it was the wheels experience not what you see.
It should be noted that in the rest frame of the belt it is the plane that is moving relativistically and thus the planes acceleration that is approaching zero due to relativistic effects. So going by your logic in the rest frame of the belt the acceleration of the belt should be overwhelming the plane and pulling it backwards. This means that we have one frame that predicts the plane moves "forward" against the belt and another where it is predicted to be dragged "backward" by the belt. This is a paradox. The resolution of said paradox is simple and has been given. It is simply that neither happens and that as the belt reaches relativistic speeds the proper acceleration of the belt never changes.
The belt would be pulled forward for starters. However, the major flaw in your argument is that even if you remove the acceleration of the belt the plane and the belt are still in the same frame exactly has I had indicated. You simply changed that frame by changing the acceleration of the belt. However, changing the thrust of the plane doesn't change the frame of reference it only changes the plane's motion through that frame of reference. The point stands that the plane is in the frame of reference of the belt. Also, there is a preferred frame of reference it is the rest frame of the bottom of the wheels since that is where the force on the bottom of the wheels is being applied.
Beyond that you still must contend with the fact that all observers must agree on what events occur or you have a paradox. Simply put I have demonstrated that in the frame of reference of the belt and therefore the part of the tires in contact with the belt, the acceleration of the belt can be held constant forever without the belt every reaching the speed of light in any reference frame. The physical requirements of the motor that would be needed are irrelevant because we've already made much more physically impossible assumptions in the form of wheels that won't fly apart. Thus the wheels always feel this constant acceleration and thus the force of thrust is always canceled. Changing frames can never change this fact. When you change frames while the acceleration may in fact appear slower to all that matters it was the wheels experience not what you see.
It should be noted that in the rest frame of the belt it is the plane that is moving relativistically and thus the planes acceleration that is approaching zero due to relativistic effects. So going by your logic in the rest frame of the belt the acceleration of the belt should be overwhelming the plane and pulling it backwards. This means that we have one frame that predicts the plane moves "forward" against the belt and another where it is predicted to be dragged "backward" by the belt. This is a paradox. The resolution of said paradox is simple and has been given. It is simply that neither happens and that as the belt reaches relativistic speeds the proper acceleration of the belt never changes.
Sorry about that, I miss-worded that bit. The wheels never need to gain on the belt, only falter in their acceleration.
Unfortunately for you, since you are trying to make the point that the plane will take off, in order for the plane to gain any velocity relative to our stationary observer it must do so by causing the angular acceleration of its wheels times their radius to increase beyond the value of the acceleration of the belt thereby causing the wheels to spin faster than the belt. Simply put the plane cannot take off without moving its wheels faster than the surface it is rolling on which should be intuitively obvious.
1) The plane becoming heavier is not irrelevant to the belt. It is right in the equation given to calculate the acceleration of the belt needed in the form of the thrust of the plane and in the moment of inertia of the planes wheels.
2) The effect is identical because the effect of the increasing mass on the forces in acceleration depends only on the percentage increase, or in other words the relativistic correction factor gamma, which is identical for both belt and wheel. The quantity that matters is not the the difference between relativistic and rest mass but instead gamma which is identical in both cases.
For example, as a very simplistic analysis if I apply 10 Newtons to an object weighing 10 kilograms in the initial rest frame of the object it will accelerate at 1 m/s^2. Similarly if I apply that force to 100 kilograms in the initial rest frame of the object it will accelerate at .1 m/s^2. Now if instead I measured those accelerations from a frame of reference moving at .9c the acceleration of the 10 kg object would be .0828 m/s^2 and the acceleration of the 100 kg object would be .00828 m/s^2. The multiplicative factor both changed by being exactly identical. This is because the change in the acceleration from a given force due to relativistic effects depends only upon the factor gamma and gamma depends only on velocity.
1) The plane becoming heavier is not irrelevant to the belt. It is right in the equation given to calculate the acceleration of the belt needed in the form of the thrust of the plane and in the moment of inertia of the planes wheels.
2) The effect is identical because the effect of the increasing mass on the forces in acceleration depends only on the percentage increase, or in other words the relativistic correction factor gamma, which is identical for both belt and wheel. The quantity that matters is not the the difference between relativistic and rest mass but instead gamma which is identical in both cases.
For example, as a very simplistic analysis if I apply 10 Newtons to an object weighing 10 kilograms in the initial rest frame of the object it will accelerate at 1 m/s^2. Similarly if I apply that force to 100 kilograms in the initial rest frame of the object it will accelerate at .1 m/s^2. Now if instead I measured those accelerations from a frame of reference moving at .9c the acceleration of the 10 kg object would be .0828 m/s^2 and the acceleration of the 100 kg object would be .00828 m/s^2. The multiplicative factor both changed by being exactly identical. This is because the change in the acceleration from a given force due to relativistic effects depends only upon the factor gamma and gamma depends only on velocity.
Please explain how the differing masses of belt and wheel are irrelevant
As explained above the relevant factor the governs the magnitude of relativistic effects is the parameter gamma and gamma does not vary with rest mass. There is in fact no term for mass of any kind in gamma. This means that the relativistic effects experienced by something that weighs a billion tons are the same as the relativistic effects experienced by a proton.
There is absolutely no need to include gravity, other than to say that it provides the static friction that keeps the wheel from slipping. It has no other effect on the problem because it acts perpendicularly to the thrust and the acceleration of the belt and therefore by vector addition has absolutely no effect on either.
Ah you're thinking of the various forms of friction which have nothing to do with gravity, except that it provides the force to keep the surfaces together which could be supplied equally well by anything. However, we've already established that we are ignoring all forms of friction aside from the static friction that allows the wheels to roll without slipping and has no effect on the movement of rolling things. Also, kinetic friction and rolling resistance are largely independent of velocity anyway.
Entirely irrelevant. We are assuming ideal wheels that don't deform and don't explode. The belt is also idea an capable of maintaining whatever acceleration we set and the plane might as well be assumed to have infinite power generation as well.
Entirely irrelevant. We are assuming ideal wheels that don't deform and don't explode. The belt is also idea an capable of maintaining whatever acceleration we set and the plane might as well be assumed to have infinite power generation as well.
I should also note that with your brakes fully on, you can't exceed a power setting of about 25% or you'll rip the wheels off. Since one might say that "full brakes on" is pretty much the same as the conveyor "holding the plane in place, it's obvious this plane isn't going to be bothered by no stinkin' belt.
1) This has already been addressed. Please stop bringing up arguments that have already been addressed. The main problem with this is that for every plane you find that can rip its wheels off at full thrust I could probably find 10 that can't. The wording says a plane and not all plane so even one plane that can't is enough.
2) Where is your source for that?
Not only is this irrelevant but if we did take it into consideration it just makes it easier for the belt to stop the plane.
I thought you were leaving the thread. Anyway, there is no slippage because it is in the statement of the problem. The lack of slippage is what allows one to isolate the very non-intuitive bit of physics regarding how the accelerating belt effects the plane and to calculate the acceleration needed by the belt to preform the feat. I repeat to once again that what there is to think about is the exact acceleration that the belt will have to undergo in order from the physical situation described to happen. You might not think that it is very instructive or interesting but that is an opinion and you are welcome to it as long as you acknowledge that it is an opinion and that though mine differs it is just as valid.
I thought you were leaving the thread. Anyway, there is no slippage because it is in the statement of the problem. The lack of slippage is what allows one to isolate the very non-intuitive bit of physics regarding how the accelerating belt effects the plane and to calculate the acceleration needed by the belt to preform the feat. I repeat to once again that what there is to think about is the exact acceleration that the belt will have to undergo in order from the physical situation described to happen. You might not think that it is very instructive or interesting but that is an opinion and you are welcome to it as long as you acknowledge that it is an opinion and that though mine differs it is just as valid.
I thought SZ said that if a plane has enough power to break off its brakes, it will pretty much get off this conveyor. At least that's how i understood it. No contest there.
He did. People just don't seem to listen very well all the time.
I wasn't saying you couldn't participate I was just wondering out loud why you came back after leaving without giving a reason for coming back. It was just my rather clumsy way of asking exactly what brought you back.
Would you please stop doing this. I am not him. It has been clearly demonstrated that I am not him. I have no problem with you currently but if you insist on insulting me along with him every time he is less than nice to you then I am going to have a problem with you.
Entirely irrelevant.
Really?
And here I was using your own equation (essentially ... I just added a time parameter which converts work to power).
I've figured out that you are either Alt5p or a close relative (
) because you and the Zone are in league with those that measure the plane's speed by (in essence) reading it off a speedometer attached to the wheels. This idea has been thoroughly smacked down because it "defines" that the plane doesn't move. This is an attempt to put the plane-on-a-conveyor into the same class as car-on-a-conveyor. To boot, your own little battery video doesn't even do that since it is clear from the video that the angular velocity of the battery is far too large for its linear velocity (both measured by the observer, I might add). The plane's speed is measured relative to the ground, as is the belt's opposing speed. (What other choice makes sense?) Wheel speed is not a consideration.
That the wheels, slip, skid, or roll faster than the plane is moving has little to do with the problem ... except that whatever regime holds forth determines the maximum retarding force the belt can deliver. But because the engines have enough power to overcome a lot of the braking action of the tires (in the example I provide above the max resistive force with brakes fully on is about 2,400,000 newtons) the plane advances under realistic considerations.
There is no other way to transmit a retarding force to the plane than through the tires. The tire interface with the belt is its rubber tread. That tread has an ultimate holding strength based on its coefficient of friction (u) and the normal force loading them (weight of the plane in newtons). For this strength to be tested the brakes have to be substantially on. That provides a lot more resistance the simple free-wheeling (which is the whole point, after all, of having wheels in the first place).
Using the power balance equation (above) it was shown that rolling resistance alone can't transmit resistance to the plane to keep it from lifting off. (Ultimately, if the plane didn't try to lift off, its engines can make it go only so fast down the runway ... due to rolling resistance and aero drag ... but that ultimate speed is far in excess of takeoff speed). You need some additional braking action or another way to sap power from the engines. And you're going to have to come up with something really big ... equivalent to having your foot on the brakes.
No you didn't.
No you didn't.
I've figured out that you are either Alt5p or a close relative because you and the Zone are in league with those that measure the plane's speed by (in essence) reading it off a speedometer attached to the wheels. This idea has been thoroughly smacked down because it "defines" that the plane doesn't move. This is an attempt to put the plane-on-a-conveyor into the same class as car-on-a-conveyor. To boot, your own little battery video doesn't even do that since it is clear from the video that the angular velocity of the battery is far too large for its linear velocity (both measured by the observer, I might add). The plane's speed is measured relative to the ground, as is the belt's opposing speed. (What other choice makes sense?) Wheel speed is not a consideration.
1) The point is that even though it defines the plane as not moving it is still possible to calculate the physical parameters needed for it to happen. That is to say the acceleration of the belt.
2) The angular velocity of the battery was much greater than its linear velocity for the exact reason I have been describing. The accelerating belt changed the linear velocity of the rolling battery.
Not in all planes. One example, which you can't even source apparently, does not apply to all planes.
Not in all planes. One example, which you can't even source apparently, does not apply to all planes.
There is no other way to transmit a retarding force to the plane than through the tires. The tire interface with the belt is its rubber tread. That tread has an ultimate holding strength based on its coefficient of friction (u) and the normal force loading them (weight of the plane in newtons). For this strength to be tested the brakes have to be substantially on. That provides a lot more resistance the simple free-wheeling (which is the whole point, after all, of having wheels in the first place).
Absolutely wrong. The accelerating belt can provide exactly as much backward force as the wheels when the brakes are on because the wheels will roll without slipping until the point where the force exceeds the maximum of static friction which is also exactly when the plane with the brakes on will start to move. This much I have conclusively proven several times.
1) You proven the exact opposite. You've proven that in our ideal thought experiment where there are no maximum speeds it is quite trivial to stop the plane.
2) As I have proven several times the acceleration of the belt constitutes a backward force on anything rolling on the belt. You continue to deny this despite the mountain of evidence provided and without putting up any evidence of your own which is hardly an effective means of debate.
1) You proven the exact opposite. You've proven that in our ideal thought experiment where there are no maximum speeds it is quite trivial to stop the plane.
2) As I have proven several times the acceleration of the belt constitutes a backward force on anything rolling on the belt. You continue to deny this despite the mountain of evidence provided and without putting up any evidence of your own which is hardly an effective means of debate.
That version, if that is what it is, is "car-on-a-conveyor" and holds no interest whatsoever because it defines the plane as not moving since the relative motion between the moving parts is zero. Same as walking-on-a-treadmill or boat-moving-upstream ... all trivial and boring. What's the point?
The point as I am saying now for the third or fourth time is getting people to realize that an accelerating belt puts a backwards force on something rolling on that belt.
Really not getting the point that when something rolls its angular and linear velocity as well as the velocity of the surface it rolls on are all linked and one cannot be changed without affecting the others.
Really not getting the point that when something rolls its angular and linear velocity as well as the velocity of the surface it rolls on are all linked and one cannot be changed without affecting the others.
One should also note that the wheel speed is not just a function of the plane driving forward but it is also being powered by the belt itself. Effectively, the belt is providing the energy needed to overcome any "magical resistance" proponents claim it is adding to the wheel.
No it rather clearly isn't. Without the thrust of the plane the wheel and plane would be pulled backwards by the accelerating belt. This does constitute work by the belt but it is the negative of work done by the thrust. So if the plane is to move forward it must do more work than if it where on a stationary runway.
No they aren't. That has been conclusively proven. The rolling resistance between the battery and the paper was not great enough to cause it to stop. How do I know this you ask? I know this because the battery accelerated down the paper when it was stationary. Thus the force of gravity on the battery was greater than any rolling resistance. Also, as you stated up there yourself rolling resistance is largely constant over velocity. Certainly it is constant over the velocities I can attain by pulling. Thus if it was just rolling resistance, which couldn't change with me pulling the paper, the battery's motion would not have changed in the second round of testing.
No they aren't. That has been conclusively proven. The rolling resistance between the battery and the paper was not great enough to cause it to stop. How do I know this you ask? I know this because the battery accelerated down the paper when it was stationary. Thus the force of gravity on the battery was greater than any rolling resistance. Also, as you stated up there yourself rolling resistance is largely constant over velocity. Certainly it is constant over the velocities I can attain by pulling. Thus if it was just rolling resistance, which couldn't change with me pulling the paper, the battery's motion would not have changed in the second round of testing.
For example, a steel ball bearing heading down an upward moving metal slide would show little propensity to slow down (that is why bearing races are made from ball bearings and metal rings). There is no perpendicular torque that results in linear motion. (Imagine a bicyclist floating free in the space shuttle. If he start pedaling, does he start to move forward? Or backward, for that matter?)
1) Is the upward slide accelerating?
2) Is the slide angled so that the force of gravity isn't enough to cause slipping?
If the answer is yes to both those questions than the steel ball bearing will in fact slow as demonstrated quite clearly in my video and via the math that I have done.
To bad we've been ignoring it.
To bad we've been ignoring it.
Of course, rolling friction is always required to get the wheel to roll at all ... if it were constructed along the lines of the frictionless air puck then it would merely slide without rotating.
Wrong. It is static friction between the bottom of the rolling object and the surface that is required to get the wheel to roll. This can exist without rolling friction because it does not depend on deformation. The static friction keeps the bottom of the wheel from moving allowing a force at the center of mass to create a torque around that point and causing the wheel to turn. This occurs regardless of any deformation leading to rolling resistance.
Wrong. As you said yourself rolling resistance is largely constant with speed. This is especially true over the speeds I can obtain with my hands pulling on a sheet of paper. Thus whatever rolling resistance existed when the paper wasn't moving is virtually identical to whatever rolling resistance existed when I pulled the paper. Since the force of gravity over came the rolling resistance when the paper was stationary it also overcame the rolling resistance when the paper wasn't stationary. The only way for the motion of the battery to change is for the forces on it to change. That is basic physics and since the rolling resistance didn't change it cannot be the explanation.
Wrong. As you said yourself rolling resistance is largely constant with speed. This is especially true over the speeds I can obtain with my hands pulling on a sheet of paper. Thus whatever rolling resistance existed when the paper wasn't moving is virtually identical to whatever rolling resistance existed when I pulled the paper. Since the force of gravity over came the rolling resistance when the paper was stationary it also overcame the rolling resistance when the paper wasn't stationary. The only way for the motion of the battery to change is for the forces on it to change. That is basic physics and since the rolling resistance didn't change it cannot be the explanation.
The work-balance equations presented by SD merely show what the resulting motion will be when a force is exerted on a rolling wheel. The geometry and mass of the wheel plays a role ... obviously you could build a big, massive wheel that you don't provide sufficient force to move.
So in other words it is the right equation to use.
Skidding results from exceeding the traction of the tire which has the same maximum as the static friction of the tire. It is quite different than rolling resistance.
Here is a link that might be educational.
You will note that there is no rolling resistance what soever. Everything happens in that example because of static friction.
Skidding results from exceeding the traction of the tire which has the same maximum as the static friction of the tire. It is quite different than rolling resistance.
Here is a link that might be educational.
You will note that there is no rolling resistance what soever. Everything happens in that example because of static friction.
This effect is observed with billiard and bowling balls which, when first struck or thrown, skid across the surface before rolling resistance is capable of extracting enough translational motion to get the angular velocity up to non-slipping speed.
Wrong. It would be the kinetic friction which is doing most of the work there.
This point has already been addressed several times. Please stop bringing it up.
This point has already been addressed several times. Please stop bringing it up.
Did I not state that ... essentially? The plane only has so much power and at some point it can't go any faster due to rolling resistance, aero drag, whatever else you can think of. All it is necessary to do is bump any of these factors up to some particular value and the plane has limited speed. For example, you could construct the belt out of some sort of gravel surface such that the rolling resistance becomes really high (think runaway truck ramps). The poor old plane might not even get up to 40-50 mph before its engines are gassed.
Or as has been repeatedly demonstrated you could just accelerate the belt assuming the static friction between the bottoms of the wheels and the belt is high enough.
You mean what I learned at MIT wasn't enough?
If you got a degree in physics I'd ask for your money back.
If you got a degree in physics I'd ask for your money back.
I used SD's equation (a power version) ... what more do you want?
No you didn't and then you went and made several errors.
As boit pointed out before we accept the result for a non-accelerating belt. The only person here unwilling to accept another solution to a slightly altered problem is you.
As boit pointed out before we accept the result for a non-accelerating belt. The only person here unwilling to accept another solution to a slightly altered problem is you.
Of course I can make the plane stop ... or fly ... at will by just varying the physical parameters. But this has nothing to do with EITHER version of the problem ... which by the way were word problems that sited no numbers ... because it was just an effort to get you to see the difference between motive power that depended on the belt versus power that didn't.
The acceleration of the belt is quite important to the other version of the thought problem. Also be careful there is sounds like you are falling into the old trap of thinking that the car can be held back on the constant speed treadmill because it can't push off from a moving surface. The only reason it is easier to hold a car back is because of the rpm of its engine and the rpm of its wheels are linked and the torque the engine can produce after a certain amount of rpm starts to decrease. If this limitation where removed the car would behave identically to the plane.
If it is the wrong position then why is it I have two text books, and two YouTube videos that support my analysis and you have absolutely no evidence at all?
If it is the wrong position then why is it I have two text books, and two YouTube videos that support my analysis and you have absolutely no evidence at all?
... Off hand I believe you are right ... I had in mind the steel-steel versus paper-battery interface ... difference in rolling friction values ... not sliding versus rolling. But, good catch.
Wrong. Difference between rolling and sliding entirely. It has nothing to do with rolling friction.
Difference between rolling and sliding.
Maybe later I'll copy some other pages out of one of my Physics 201 text books dealing with rolling down an inclined plane that demonstrate it has nothing to do with rolling resistance.
I do try to make it as clear as possible to anyone entering the debate what point I am arguing in the first response I make to them. The problem is that they don't always listen and sometimes even when they do listen they don't understand the consequences of an accelerating belt. You are correct that some of the continued discussion comes from not understanding what situation is being advocated. However, no all of the continued discussion stems from there. NoCleverName for example who made it rather clear that he thinks the acceleration of the belt has no effect on the motion of the plane despite the evidence to the contrary.
From your reference:
QUOTE
In particular, it turns
out to answer the question “Why can’t an object go faster than the speed of
light?” to which I promised we would return. Here, we have considered the
simple case of a rocket that tries to continually accelerate by burning fuel at
a constant rate. What we see is that it gains equal boost parameter in every
interval of proper time. So, will it ever reach the speed of light? No. After a
very long (but finite) proper time has elapsed the rocket will merely have a large
(but finite) boost parameter. Since any finite boost parameter (no matter how
large) corresponds to some v less than c, the rocket never reaches the speed of
light.
Similarly, it turns out that whether or not the acceleration is uniform, any
rocket must burn an infinite amount of fuel to reach the speed of light. Thus,
the speed of light (infinite boost parameter) plays the same role in relativity
that was played by infinite velocity in Newtonian physics.
out to answer the question “Why can’t an object go faster than the speed of
light?” to which I promised we would return. Here, we have considered the
simple case of a rocket that tries to continually accelerate by burning fuel at
a constant rate. What we see is that it gains equal boost parameter in every
interval of proper time. So, will it ever reach the speed of light? No. After a
very long (but finite) proper time has elapsed the rocket will merely have a large
(but finite) boost parameter. Since any finite boost parameter (no matter how
large) corresponds to some v less than c, the rocket never reaches the speed of
light.
Similarly, it turns out that whether or not the acceleration is uniform, any
rocket must burn an infinite amount of fuel to reach the speed of light. Thus,
the speed of light (infinite boost parameter) plays the same role in relativity
that was played by infinite velocity in Newtonian physics.
This example, which you seem to have based a very large part of you argument on, doesn't include gravity, other than that produced by a rocket's acceleration. In space, where gravity is negligible, "burning fuel at a constant rate" does indeed maintain a constant acceleration. There is no force countering the inertial motion of the rocket other than the thrust accelerating it.
But within gravity, which very much applies to wheels remaining in sufficient contact with the belt, acceleration cannot be maintained by "burning fuel at a constant rate". The energy expenditure must be increasing, which would be the equivalent of the rocket's thrust increasing. In this case, a "constant acceleration" is not uniform.
QUOTE (->
| QUOTE |
| In particular, it turns out to answer the question “Why can’t an object go faster than the speed of light?” to which I promised we would return. Here, we have considered the simple case of a rocket that tries to continually accelerate by burning fuel at a constant rate. What we see is that it gains equal boost parameter in every interval of proper time. So, will it ever reach the speed of light? No. After a very long (but finite) proper time has elapsed the rocket will merely have a large (but finite) boost parameter. Since any finite boost parameter (no matter how large) corresponds to some v less than c, the rocket never reaches the speed of light. Similarly, it turns out that whether or not the acceleration is uniform, any rocket must burn an infinite amount of fuel to reach the speed of light. Thus, the speed of light (infinite boost parameter) plays the same role in relativity that was played by infinite velocity in Newtonian physics. |
This example, which you seem to have based a very large part of you argument on, doesn't include gravity, other than that produced by a rocket's acceleration. In space, where gravity is negligible, "burning fuel at a constant rate" does indeed maintain a constant acceleration. There is no force countering the inertial motion of the rocket other than the thrust accelerating it.
But within gravity, which very much applies to wheels remaining in sufficient contact with the belt, acceleration cannot be maintained by "burning fuel at a constant rate". The energy expenditure must be increasing, which would be the equivalent of the rocket's thrust increasing. In this case, a "constant acceleration" is not uniform.
You've made the further mistake of assuming the plane is in an inertial frame just because it isn't moving relative to someone standing still. The wheels of the plane are in the frame of reference of the belt because the bottoms of the wheels are stationary with respect to the belt. Further, if you removed the thrust of the plane the plane would be pulled backwards by the belt. All indicating that the proper frame from the plane is that of the belt. Further indicating that the acceleration that is important is the acceleration felt by someone sitting at rest on the belt which can in fact be precisely constant forever irrespective of how fast the belt seems to be going from the perspective of someone outside the belt.
First, the bottoms of the wheels are not stationary relative to the belt. This only seems to be the case using "momentarily co-moving inertial frames". Second, just like you can remove the thrust of the plane, you can just as equally remove the acceleration of the belt, the belt then being "pulled backward" by and in respect to the plane. You are favoring a frame that is in no way preferred.
QUOTE
1) If the plane begins to move forward against the belt this requires that the wheels accelerate faster than the belt. This would make there mass increase further from rest mass not the other way around.
Sorry about that, I miss-worded that bit. The wheels never need to gain on the belt, only falter in their acceleration.
QUOTE (->
| QUOTE |
| 1) If the plane begins to move forward against the belt this requires that the wheels accelerate faster than the belt. This would make there mass increase further from rest mass not the other way around. |
Sorry about that, I miss-worded that bit. The wheels never need to gain on the belt, only falter in their acceleration.
2) There is no limit to the acceleration as previously demonstrated. To further drive home this point I point you to the equivalency principle. According to relativity someone in an accelerating rocket that cannot see outside cannot determine if he is in a rocket or standing on a planet with a matching gravitational acceleration. If what you said were true and such a constant acceleration were not possible it would only be because relativistic effects where leaking into the rest frame of the rocket for the person in the rocket to measure. This obviously violates the equivalency principle.
Once again, you're assuming a situation without gravity. Let's take two very specific frames. The accelerating belt and the stationary axle. Each will view the other as accelerating and potentially succumbing to relativistic effects. To the belt, the axle (and by extension, the plane) will become "heavier" (but since you negate friction, this is irrelevant). To the axle, the wheels become part of the belt's frame and also become "heavier", but with the difference, mentioned above, of the effect being more pronounced on the belt.
Please explain how the differing masses of belt and wheel are irrelevant, and please move this thought experiment "indoors" gravity-wise.
there is no gravity acting in the horizontal direction therefore i can't appreciate synth's convention. about the bottom of the wheel being at rest relative to the surface, i was about to argue that this is only true in a translating wheel rolling on a stationary (even relative stationary surface). in the case of a wheel on a belt that are in constant 'mesh' and speed, zero speed will be measured at 3 and 9 o'clock. but on an accelerating surface and by extension also the rotating wheel, i agree the bottom will be at rest relative to the belt. bottom being at 6 o'block. thanks synths for waking me up.
QUOTE
This example, which you seem to have based a very large part of you argument on, doesn't include gravity, other than that produced by a rocket's acceleration. In space, where gravity is negligible, "burning fuel at a constant rate" does indeed maintain a constant acceleration. There is no force countering the inertial motion of the rocket other than the thrust accelerating it.
But within gravity, which very much applies to wheels remaining in sufficient contact with the belt, acceleration cannot be maintained by "burning fuel at a constant rate". The energy expenditure must be increasing, which would be the equivalent of the rocket's thrust increasing. In this case, a "constant acceleration" is not uniform.
But within gravity, which very much applies to wheels remaining in sufficient contact with the belt, acceleration cannot be maintained by "burning fuel at a constant rate". The energy expenditure must be increasing, which would be the equivalent of the rocket's thrust increasing. In this case, a "constant acceleration" is not uniform.
Nonsense. Gravity has no effect on the belts ability to accelerate because it is perpendicular to the direction of the force that is accelerating the belt. Anyone with a knowledge of vector addition knows this. Gravity is acting perpendicular to the direction of motion and therefore cannot do any work on the belt. Therefore it cannot effect the expenditure of energy by the belt.
Further, since the bottom of the wheel is at rest with respect to the belt the ability of the belt to accelerated the bottom of the wheel is unaffected by Relativity. Of course if anyone of this wasn't true we are still left with the fact that the set up of the problem specifically states that the belt is designed to match the speed of wheel which leads to the accelerations matching. Our ideal belt is assumed to be able to accomplish this feat no matter what which even if it requires an infinite amount of power from the motor driving the belt is still less unrealistic then a wheel that won't fly apart at a few hundred miles an hours. Which by the way you have no problem with.
QUOTE (->
| QUOTE |
| This example, which you seem to have based a very large part of you argument on, doesn't include gravity, other than that produced by a rocket's acceleration. In space, where gravity is negligible, "burning fuel at a constant rate" does indeed maintain a constant acceleration. There is no force countering the inertial motion of the rocket other than the thrust accelerating it. But within gravity, which very much applies to wheels remaining in sufficient contact with the belt, acceleration cannot be maintained by "burning fuel at a constant rate". The energy expenditure must be increasing, which would be the equivalent of the rocket's thrust increasing. In this case, a "constant acceleration" is not uniform. |
Nonsense. Gravity has no effect on the belts ability to accelerate because it is perpendicular to the direction of the force that is accelerating the belt. Anyone with a knowledge of vector addition knows this. Gravity is acting perpendicular to the direction of motion and therefore cannot do any work on the belt. Therefore it cannot effect the expenditure of energy by the belt.
Further, since the bottom of the wheel is at rest with respect to the belt the ability of the belt to accelerated the bottom of the wheel is unaffected by Relativity. Of course if anyone of this wasn't true we are still left with the fact that the set up of the problem specifically states that the belt is designed to match the speed of wheel which leads to the accelerations matching. Our ideal belt is assumed to be able to accomplish this feat no matter what which even if it requires an infinite amount of power from the motor driving the belt is still less unrealistic then a wheel that won't fly apart at a few hundred miles an hours. Which by the way you have no problem with.
First, the bottoms of the wheels are not stationary relative to the belt. This only seems to be the case using "momentarily co-moving inertial frames".
Really now?
This source disagrees with you.
This source disagrees with you as well.
Find me one source that says the part of an an object rolling without slipping in contact with the surface it is rolling on isn't moving at the same speed as said surface.
The fact that the bottom of a wheel rolling without slipping is stationary with respect to what it is rolling on has nothing to do with special relativity or any of the links I have given about special relativity. It is nothing more than the most basic fact about an object that rolls without slipping.
QUOTE
Second, just like you can remove the thrust of the plane, you can just as equally remove the acceleration of the belt, the belt then being "pulled backward" by and in respect to the plane. You are favoring a frame that is in no way preferred.
The belt would be pulled forward for starters. However, the major flaw in your argument is that even if you remove the acceleration of the belt the plane and the belt are still in the same frame exactly has I had indicated. You simply changed that frame by changing the acceleration of the belt. However, changing the thrust of the plane doesn't change the frame of reference it only changes the plane's motion through that frame of reference. The point stands that the plane is in the frame of reference of the belt. Also, there is a preferred frame of reference it is the rest frame of the bottom of the wheels since that is where the force on the bottom of the wheels is being applied.
Beyond that you still must contend with the fact that all observers must agree on what events occur or you have a paradox. Simply put I have demonstrated that in the frame of reference of the belt and therefore the part of the tires in contact with the belt, the acceleration of the belt can be held constant forever without the belt every reaching the speed of light in any reference frame. The physical requirements of the motor that would be needed are irrelevant because we've already made much more physically impossible assumptions in the form of wheels that won't fly apart. Thus the wheels always feel this constant acceleration and thus the force of thrust is always canceled. Changing frames can never change this fact. When you change frames while the acceleration may in fact appear slower to all that matters it was the wheels experience not what you see.
It should be noted that in the rest frame of the belt it is the plane that is moving relativistically and thus the planes acceleration that is approaching zero due to relativistic effects. So going by your logic in the rest frame of the belt the acceleration of the belt should be overwhelming the plane and pulling it backwards. This means that we have one frame that predicts the plane moves "forward" against the belt and another where it is predicted to be dragged "backward" by the belt. This is a paradox. The resolution of said paradox is simple and has been given. It is simply that neither happens and that as the belt reaches relativistic speeds the proper acceleration of the belt never changes.
QUOTE (->
| QUOTE |
| Second, just like you can remove the thrust of the plane, you can just as equally remove the acceleration of the belt, the belt then being "pulled backward" by and in respect to the plane. You are favoring a frame that is in no way preferred. |
The belt would be pulled forward for starters. However, the major flaw in your argument is that even if you remove the acceleration of the belt the plane and the belt are still in the same frame exactly has I had indicated. You simply changed that frame by changing the acceleration of the belt. However, changing the thrust of the plane doesn't change the frame of reference it only changes the plane's motion through that frame of reference. The point stands that the plane is in the frame of reference of the belt. Also, there is a preferred frame of reference it is the rest frame of the bottom of the wheels since that is where the force on the bottom of the wheels is being applied.
Beyond that you still must contend with the fact that all observers must agree on what events occur or you have a paradox. Simply put I have demonstrated that in the frame of reference of the belt and therefore the part of the tires in contact with the belt, the acceleration of the belt can be held constant forever without the belt every reaching the speed of light in any reference frame. The physical requirements of the motor that would be needed are irrelevant because we've already made much more physically impossible assumptions in the form of wheels that won't fly apart. Thus the wheels always feel this constant acceleration and thus the force of thrust is always canceled. Changing frames can never change this fact. When you change frames while the acceleration may in fact appear slower to all that matters it was the wheels experience not what you see.
It should be noted that in the rest frame of the belt it is the plane that is moving relativistically and thus the planes acceleration that is approaching zero due to relativistic effects. So going by your logic in the rest frame of the belt the acceleration of the belt should be overwhelming the plane and pulling it backwards. This means that we have one frame that predicts the plane moves "forward" against the belt and another where it is predicted to be dragged "backward" by the belt. This is a paradox. The resolution of said paradox is simple and has been given. It is simply that neither happens and that as the belt reaches relativistic speeds the proper acceleration of the belt never changes.
Sorry about that, I miss-worded that bit. The wheels never need to gain on the belt, only falter in their acceleration.
Unfortunately for you, since you are trying to make the point that the plane will take off, in order for the plane to gain any velocity relative to our stationary observer it must do so by causing the angular acceleration of its wheels times their radius to increase beyond the value of the acceleration of the belt thereby causing the wheels to spin faster than the belt. Simply put the plane cannot take off without moving its wheels faster than the surface it is rolling on which should be intuitively obvious.
QUOTE
Once again, you're assuming a situation without gravity. Let's take two very specific frames. The accelerating belt and the stationary axle. Each will view the other as accelerating and potentially succumbing to relativistic effects. To the belt, the axle (and by extension, the plane) will become "heavier" (but since you negate friction, this is irrelevant). To the axle, the wheels become part of the belt's frame and also become "heavier", but with the difference, mentioned above, of the effect being more pronounced on the belt.
1) The plane becoming heavier is not irrelevant to the belt. It is right in the equation given to calculate the acceleration of the belt needed in the form of the thrust of the plane and in the moment of inertia of the planes wheels.
2) The effect is identical because the effect of the increasing mass on the forces in acceleration depends only on the percentage increase, or in other words the relativistic correction factor gamma, which is identical for both belt and wheel. The quantity that matters is not the the difference between relativistic and rest mass but instead gamma which is identical in both cases.
For example, as a very simplistic analysis if I apply 10 Newtons to an object weighing 10 kilograms in the initial rest frame of the object it will accelerate at 1 m/s^2. Similarly if I apply that force to 100 kilograms in the initial rest frame of the object it will accelerate at .1 m/s^2. Now if instead I measured those accelerations from a frame of reference moving at .9c the acceleration of the 10 kg object would be .0828 m/s^2 and the acceleration of the 100 kg object would be .00828 m/s^2. The multiplicative factor both changed by being exactly identical. This is because the change in the acceleration from a given force due to relativistic effects depends only upon the factor gamma and gamma depends only on velocity.
QUOTE (->
| QUOTE |
| Once again, you're assuming a situation without gravity. Let's take two very specific frames. The accelerating belt and the stationary axle. Each will view the other as accelerating and potentially succumbing to relativistic effects. To the belt, the axle (and by extension, the plane) will become "heavier" (but since you negate friction, this is irrelevant). To the axle, the wheels become part of the belt's frame and also become "heavier", but with the difference, mentioned above, of the effect being more pronounced on the belt. |
1) The plane becoming heavier is not irrelevant to the belt. It is right in the equation given to calculate the acceleration of the belt needed in the form of the thrust of the plane and in the moment of inertia of the planes wheels.
2) The effect is identical because the effect of the increasing mass on the forces in acceleration depends only on the percentage increase, or in other words the relativistic correction factor gamma, which is identical for both belt and wheel. The quantity that matters is not the the difference between relativistic and rest mass but instead gamma which is identical in both cases.
For example, as a very simplistic analysis if I apply 10 Newtons to an object weighing 10 kilograms in the initial rest frame of the object it will accelerate at 1 m/s^2. Similarly if I apply that force to 100 kilograms in the initial rest frame of the object it will accelerate at .1 m/s^2. Now if instead I measured those accelerations from a frame of reference moving at .9c the acceleration of the 10 kg object would be .0828 m/s^2 and the acceleration of the 100 kg object would be .00828 m/s^2. The multiplicative factor both changed by being exactly identical. This is because the change in the acceleration from a given force due to relativistic effects depends only upon the factor gamma and gamma depends only on velocity.
Please explain how the differing masses of belt and wheel are irrelevant
As explained above the relevant factor the governs the magnitude of relativistic effects is the parameter gamma and gamma does not vary with rest mass. There is in fact no term for mass of any kind in gamma. This means that the relativistic effects experienced by something that weighs a billion tons are the same as the relativistic effects experienced by a proton.
QUOTE
and please move this thought experiment "indoors" gravity-wise.
There is absolutely no need to include gravity, other than to say that it provides the static friction that keeps the wheel from slipping. It has no other effect on the problem because it acts perpendicularly to the thrust and the acceleration of the belt and therefore by vector addition has absolutely no effect on either.
QUOTE (boit+Jan 12 2011, 10:42 PM)
there is no gravity acting in the horizontal direction therefore i can't appreciate synth's convention.
Could someone please explain how something, other than a rocket in space, can be made to constantly accelerate with a constant thrust. Acceleration is a change of velocity, whether of speed and/or direction. The belt isn't changing direction is it? Is it just by neglecting friction that you've ignored how anything on the surface of earth losses energy and must provide constant thrust to maintain a single velocity?
Could someone please explain how something, other than a rocket in space, can be made to constantly accelerate with a constant thrust. Acceleration is a change of velocity, whether of speed and/or direction. The belt isn't changing direction is it? Is it just by neglecting friction that you've ignored how anything on the surface of earth losses energy and must provide constant thrust to maintain a single velocity?
QUOTE
Could someone please explain how something, other than a rocket in space, can be made to constantly accelerate with a constant thrust. Acceleration is a change of velocity, whether of speed and/or direction. The belt isn't changing direction is it? Is it just by neglecting friction that you've ignored how anything on the surface of earth losses energy and must provide constant thrust to maintain a single velocity?
Ah you're thinking of the various forms of friction which have nothing to do with gravity, except that it provides the force to keep the surfaces together which could be supplied equally well by anything. However, we've already established that we are ignoring all forms of friction aside from the static friction that allows the wheels to roll without slipping and has no effect on the movement of rolling things. Also, kinetic friction and rolling resistance are largely independent of velocity anyway.
A few years ago I posted this semi-practical example:
The B-777 has 300,000 kg mass, two really nice GE-90 engines that develop some 836,000 Newtons thrust, and 12 main wheels that (as was figured earlier) have a rolling resistance of 0.03 that results in 88,000 Newtons of resistance.
If we fire-wall our throttles for takeoff we get all the thrust so by F = ma we have:
(836,000-88,000) = 300,000 * a
or acceleration = 2.5 m/s (about 1/4 g). (Note: that would get us to take-off speed of about 185mph in 33 sec in about 4100 feet of runway.) (NOTE ADDED: Actual takeoff distance in practice is at least twice this figure).
(NOTE ADDED: The following computes the fastest possible runway speed for the plane given the power of its engines and the rolling resistance ... aero drag is ignored)
Using both this take-off performance data and engine exhaust data (of 200 mph about 100 feet behind the engines) I get a horsepower estimate of some 82,000-90,000 hp (calcs not shown here). I'm going to use 63,000,000 watts, which is about in the middle of these figures.
Using Power = Force * velocity with the opposing power being the 88,000 N provided by the tires, we get a "terminal velocity" of:
63,000,000 = 88,000 * v
or 715 m/s or about 1,600 mph. This exceeds the plane's tire speed limit of 235.
END OF EXAMPLE.
I should also note that with your brakes fully on, you can't exceed a power setting of about 25% or you'll rip the wheels off. Since one might say that "full brakes on" is pretty much the same as the conveyor "holding the plane in place, it's obvious this plane isn't going to be bothered by no stinkin' belt.
No doubt you'll want to whine about the power it takes to spin up the wheels (separate from rolling resistance). Needless to say, the power needed to get a few hundred kg of rubber spinning up to 185 mph pales in comparison to the power needed to get the other 300,000 kg to that speed.
The B-777 has 300,000 kg mass, two really nice GE-90 engines that develop some 836,000 Newtons thrust, and 12 main wheels that (as was figured earlier) have a rolling resistance of 0.03 that results in 88,000 Newtons of resistance.
If we fire-wall our throttles for takeoff we get all the thrust so by F = ma we have:
(836,000-88,000) = 300,000 * a
or acceleration = 2.5 m/s (about 1/4 g). (Note: that would get us to take-off speed of about 185mph in 33 sec in about 4100 feet of runway.) (NOTE ADDED: Actual takeoff distance in practice is at least twice this figure).
(NOTE ADDED: The following computes the fastest possible runway speed for the plane given the power of its engines and the rolling resistance ... aero drag is ignored)
Using both this take-off performance data and engine exhaust data (of 200 mph about 100 feet behind the engines) I get a horsepower estimate of some 82,000-90,000 hp (calcs not shown here). I'm going to use 63,000,000 watts, which is about in the middle of these figures.
Using Power = Force * velocity with the opposing power being the 88,000 N provided by the tires, we get a "terminal velocity" of:
63,000,000 = 88,000 * v
or 715 m/s or about 1,600 mph. This exceeds the plane's tire speed limit of 235.
END OF EXAMPLE.
I should also note that with your brakes fully on, you can't exceed a power setting of about 25% or you'll rip the wheels off. Since one might say that "full brakes on" is pretty much the same as the conveyor "holding the plane in place, it's obvious this plane isn't going to be bothered by no stinkin' belt.
No doubt you'll want to whine about the power it takes to spin up the wheels (separate from rolling resistance). Needless to say, the power needed to get a few hundred kg of rubber spinning up to 185 mph pales in comparison to the power needed to get the other 300,000 kg to that speed.
Sithdarth,
You are stating there would be no kinetic friction because there would no slippage. Is that right? Are you saying there would be no slippage because your equations prove that? Or are you saying there would be no slippage because your "thought" exercise won't allow it? If there is no slippage, what is there to think about?
You are stating there would be no kinetic friction because there would no slippage. Is that right? Are you saying there would be no slippage because your equations prove that? Or are you saying there would be no slippage because your "thought" exercise won't allow it? If there is no slippage, what is there to think about?
I thought SZ said that if a plane has enough power to break off its brakes, it will pretty much get off this conveyor. At least that's how i understood it. No contest there.
QUOTE
A few years ago I posted this semi-practical example:
The B-777 has 300,000 kg mass, two really nice GE-90 engines that develop some 836,000 Newtons thrust, and 12 main wheels that (as was figured earlier) have a rolling resistance of 0.03 that results in 88,000 Newtons of resistance.
If we fire-wall our throttles for takeoff we get all the thrust so by F = ma we have:
(836,000-88,000) = 300,000 * a
or acceleration = 2.5 m/s (about 1/4 g). (Note: that would get us to take-off speed of about 185mph in 33 sec in about 4100 feet of runway.) (NOTE ADDED: Actual takeoff distance in practice is at least twice this figure).
(NOTE ADDED: The following computes the fastest possible runway speed for the plane given the power of its engines and the rolling resistance ... aero drag is ignored)
Using both this take-off performance data and engine exhaust data (of 200 mph about 100 feet behind the engines) I get a horsepower estimate of some 82,000-90,000 hp (calcs not shown here). I'm going to use 63,000,000 watts, which is about in the middle of these figures.
Using Power = Force * velocity with the opposing power being the 88,000 N provided by the tires, we get a "terminal velocity" of:
63,000,000 = 88,000 * v
or 715 m/s or about 1,600 mph. This exceeds the plane's tire speed limit of 235.
END OF EXAMPLE.
The B-777 has 300,000 kg mass, two really nice GE-90 engines that develop some 836,000 Newtons thrust, and 12 main wheels that (as was figured earlier) have a rolling resistance of 0.03 that results in 88,000 Newtons of resistance.
If we fire-wall our throttles for takeoff we get all the thrust so by F = ma we have:
(836,000-88,000) = 300,000 * a
or acceleration = 2.5 m/s (about 1/4 g). (Note: that would get us to take-off speed of about 185mph in 33 sec in about 4100 feet of runway.) (NOTE ADDED: Actual takeoff distance in practice is at least twice this figure).
(NOTE ADDED: The following computes the fastest possible runway speed for the plane given the power of its engines and the rolling resistance ... aero drag is ignored)
Using both this take-off performance data and engine exhaust data (of 200 mph about 100 feet behind the engines) I get a horsepower estimate of some 82,000-90,000 hp (calcs not shown here). I'm going to use 63,000,000 watts, which is about in the middle of these figures.
Using Power = Force * velocity with the opposing power being the 88,000 N provided by the tires, we get a "terminal velocity" of:
63,000,000 = 88,000 * v
or 715 m/s or about 1,600 mph. This exceeds the plane's tire speed limit of 235.
END OF EXAMPLE.
Entirely irrelevant. We are assuming ideal wheels that don't deform and don't explode. The belt is also idea an capable of maintaining whatever acceleration we set and the plane might as well be assumed to have infinite power generation as well.
QUOTE (->
| QUOTE |
| A few years ago I posted this semi-practical example: The B-777 has 300,000 kg mass, two really nice GE-90 engines that develop some 836,000 Newtons thrust, and 12 main wheels that (as was figured earlier) have a rolling resistance of 0.03 that results in 88,000 Newtons of resistance. If we fire-wall our throttles for takeoff we get all the thrust so by F = ma we have: (836,000-88,000) = 300,000 * a or acceleration = 2.5 m/s (about 1/4 g). (Note: that would get us to take-off speed of about 185mph in 33 sec in about 4100 feet of runway.) (NOTE ADDED: Actual takeoff distance in practice is at least twice this figure). (NOTE ADDED: The following computes the fastest possible runway speed for the plane given the power of its engines and the rolling resistance ... aero drag is ignored) Using both this take-off performance data and engine exhaust data (of 200 mph about 100 feet behind the engines) I get a horsepower estimate of some 82,000-90,000 hp (calcs not shown here). I'm going to use 63,000,000 watts, which is about in the middle of these figures. Using Power = Force * velocity with the opposing power being the 88,000 N provided by the tires, we get a "terminal velocity" of: 63,000,000 = 88,000 * v or 715 m/s or about 1,600 mph. This exceeds the plane's tire speed limit of 235. END OF EXAMPLE. |
Entirely irrelevant. We are assuming ideal wheels that don't deform and don't explode. The belt is also idea an capable of maintaining whatever acceleration we set and the plane might as well be assumed to have infinite power generation as well.
I should also note that with your brakes fully on, you can't exceed a power setting of about 25% or you'll rip the wheels off. Since one might say that "full brakes on" is pretty much the same as the conveyor "holding the plane in place, it's obvious this plane isn't going to be bothered by no stinkin' belt.
1) This has already been addressed. Please stop bringing up arguments that have already been addressed. The main problem with this is that for every plane you find that can rip its wheels off at full thrust I could probably find 10 that can't. The wording says a plane and not all plane so even one plane that can't is enough.
2) Where is your source for that?
QUOTE
No doubt you'll want to whine about the power it takes to spin up the wheels (separate from rolling resistance). Needless to say, the power needed to get a few hundred kg of rubber spinning up to 185 mph pales in comparison to the power needed to get the other 300,000 kg to that speed.
Not only is this irrelevant but if we did take it into consideration it just makes it easier for the belt to stop the plane.
I still don't think that you are getting it NoCleverName.
Rolling resistance plays a very small role in this problem. And do you have any links that support your claims of only one quarter thrust with the brakes set or you will rip the wheels off. There have been a couple of Muthbusters episodes where they used a jet planes engines to produce thrust to flip cars and mimic hurricane force winds. The inside shots made it look like they were using a lot more than quarter throttle, it looked like they were at about full throttle to me, but that isn't the strongest evidence.
Rolling resistance plays a very small role in this problem. And do you have any links that support your claims of only one quarter thrust with the brakes set or you will rip the wheels off. There have been a couple of Muthbusters episodes where they used a jet planes engines to produce thrust to flip cars and mimic hurricane force winds. The inside shots made it look like they were using a lot more than quarter throttle, it looked like they were at about full throttle to me, but that isn't the strongest evidence.
QUOTE
Sithdarth,
You are stating there would be no kinetic friction because there would no slippage. Is that right? Are you saying there would be no slippage because your equations prove that? Or are you saying there would be no slippage because your "thought" exercise won't allow it? If there is no slippage, what is there to think about?
You are stating there would be no kinetic friction because there would no slippage. Is that right? Are you saying there would be no slippage because your equations prove that? Or are you saying there would be no slippage because your "thought" exercise won't allow it? If there is no slippage, what is there to think about?
I thought you were leaving the thread. Anyway, there is no slippage because it is in the statement of the problem. The lack of slippage is what allows one to isolate the very non-intuitive bit of physics regarding how the accelerating belt effects the plane and to calculate the acceleration needed by the belt to preform the feat. I repeat to once again that what there is to think about is the exact acceleration that the belt will have to undergo in order from the physical situation described to happen. You might not think that it is very instructive or interesting but that is an opinion and you are welcome to it as long as you acknowledge that it is an opinion and that though mine differs it is just as valid.
QUOTE (->
| QUOTE |
| Sithdarth, You are stating there would be no kinetic friction because there would no slippage. Is that right? Are you saying there would be no slippage because your equations prove that? Or are you saying there would be no slippage because your "thought" exercise won't allow it? If there is no slippage, what is there to think about? |
I thought you were leaving the thread. Anyway, there is no slippage because it is in the statement of the problem. The lack of slippage is what allows one to isolate the very non-intuitive bit of physics regarding how the accelerating belt effects the plane and to calculate the acceleration needed by the belt to preform the feat. I repeat to once again that what there is to think about is the exact acceleration that the belt will have to undergo in order from the physical situation described to happen. You might not think that it is very instructive or interesting but that is an opinion and you are welcome to it as long as you acknowledge that it is an opinion and that though mine differs it is just as valid.
I thought SZ said that if a plane has enough power to break off its brakes, it will pretty much get off this conveyor. At least that's how i understood it. No contest there.
He did. People just don't seem to listen very well all the time.
QUOTE (Sithdarth+Jan 13 2011, 06:57 AM)
I thought you were leaving the thread... You might not think that it is very instructive or interesting but that is an opinion and you are welcome to it as long as you acknowledge that it is an opinion and that though mine differs it is just as valid.
Actually, I just wanted to clarify that one point.
If you find this discussion "instructive or interesting" that is fine. And further, not being a physicist myself, maybe this discussion is in fact instructive and interesting. Just not to me. But in that this not your forum and it is not within your prerogative to restrict anyone from participating in anyway they may seem fit, I may return or I may not.
Actually, I just wanted to clarify that one point.
If you find this discussion "instructive or interesting" that is fine. And further, not being a physicist myself, maybe this discussion is in fact instructive and interesting. Just not to me. But in that this not your forum and it is not within your prerogative to restrict anyone from participating in anyway they may seem fit, I may return or I may not.
QUOTE
But in that this not your forum and it is not within your prerogative to restrict anyone from participating in anyway they may seem fit, I may return or I may not.
I wasn't saying you couldn't participate I was just wondering out loud why you came back after leaving without giving a reason for coming back. It was just my rather clumsy way of asking exactly what brought you back.
Derek, yesterday you said this:
Though you didn't come right out and say it the implication is fairly clear that you were leaving this discussion. sithdarth was not trying to ban you from this topic, he was merely pointing out that you were being a hypocrite by coming back. You can probably lie on this forum and get away with it, but you shouldn't complain when others point out that you were lying.
QUOTE
Hey, maybe. At any rate I'll accept that. My feelings about your scenario haven't changed. But I agree with you or the other one, in that I don't accept the logic of your "thought experiment," if you want my opinion in the future, ask, otherwise I'll let you continue without my participation.
Though you didn't come right out and say it the implication is fairly clear that you were leaving this discussion. sithdarth was not trying to ban you from this topic, he was merely pointing out that you were being a hypocrite by coming back. You can probably lie on this forum and get away with it, but you shouldn't complain when others point out that you were lying.
QUOTE (Subduction Zone+Jan 13 2011, 07:38 AM)
Derek, yesterday you said this:
Though you didn't come right out and say it the implication is fairly clear that you were leaving this discussion. sithdarth was not trying to ban you from this topic, he was merely pointing out that you were being a hypocrite by coming back. You can probably lie on this forum and get away with it, but you shouldn't complain when others point out that you were lying.
Hey Slick,
I merely asked your alter ego a question. I didn't view it as participating. But, to be honest, I really don't give a damn what you and your imaginary friend think.
Though you didn't come right out and say it the implication is fairly clear that you were leaving this discussion. sithdarth was not trying to ban you from this topic, he was merely pointing out that you were being a hypocrite by coming back. You can probably lie on this forum and get away with it, but you shouldn't complain when others point out that you were lying.
Hey Slick,
I merely asked your alter ego a question. I didn't view it as participating. But, to be honest, I really don't give a damn what you and your imaginary friend think.
QUOTE
Hey Slick,
I merely asked your alter ego a question. I didn't view it as participating. But, to be honest, I really don't give a damn what you and your imaginary friend think.
I merely asked your alter ego a question. I didn't view it as participating. But, to be honest, I really don't give a damn what you and your imaginary friend think.
Would you please stop doing this. I am not him. It has been clearly demonstrated that I am not him. I have no problem with you currently but if you insist on insulting me along with him every time he is less than nice to you then I am going to have a problem with you.
sithdarth has more patience than I have. I am exposed to trolls regularly on a site that I visit and he doesn't. As a result I do get a bit testy sometimes.
By the way, you should be able to tell by my user name that I was not a physics major. I did recruit sithdarth because this is a topic we both have posted on and I needed his expertise in physics. He is also quite a bit younger than I am. My user name is probably older than he is. Let me check.
Hey sith, are you younger than thirty?
By the way, you should be able to tell by my user name that I was not a physics major. I did recruit sithdarth because this is a topic we both have posted on and I needed his expertise in physics. He is also quite a bit younger than I am. My user name is probably older than he is. Let me check.
Hey sith, are you younger than thirty?
Yeah by a few years but not many. I'll by 27 in almost exactly 6 months.
I didn't use it for many years, but I came up with my user name over thirty years ago when I was in college.
QUOTE (Sithdarth+Jan 13 2011, 02:49 AM)
Entirely irrelevant.
Really?
And here I was using your own equation (essentially ... I just added a time parameter which converts work to power).I've figured out that you are either Alt5p or a close relative (
) because you and the Zone are in league with those that measure the plane's speed by (in essence) reading it off a speedometer attached to the wheels. This idea has been thoroughly smacked down because it "defines" that the plane doesn't move. This is an attempt to put the plane-on-a-conveyor into the same class as car-on-a-conveyor. To boot, your own little battery video doesn't even do that since it is clear from the video that the angular velocity of the battery is far too large for its linear velocity (both measured by the observer, I might add). The plane's speed is measured relative to the ground, as is the belt's opposing speed. (What other choice makes sense?) Wheel speed is not a consideration.That the wheels, slip, skid, or roll faster than the plane is moving has little to do with the problem ... except that whatever regime holds forth determines the maximum retarding force the belt can deliver. But because the engines have enough power to overcome a lot of the braking action of the tires (in the example I provide above the max resistive force with brakes fully on is about 2,400,000 newtons) the plane advances under realistic considerations.
There is no other way to transmit a retarding force to the plane than through the tires. The tire interface with the belt is its rubber tread. That tread has an ultimate holding strength based on its coefficient of friction (u) and the normal force loading them (weight of the plane in newtons). For this strength to be tested the brakes have to be substantially on. That provides a lot more resistance the simple free-wheeling (which is the whole point, after all, of having wheels in the first place).
Using the power balance equation (above) it was shown that rolling resistance alone can't transmit resistance to the plane to keep it from lifting off. (Ultimately, if the plane didn't try to lift off, its engines can make it go only so fast down the runway ... due to rolling resistance and aero drag ... but that ultimate speed is far in excess of takeoff speed). You need some additional braking action or another way to sap power from the engines. And you're going to have to come up with something really big ... equivalent to having your foot on the brakes.
QUOTE (boit+Jan 4 2011, 07:25 PM)
I think it is a good idea to start with a preamble: We agree that the airplane flys in this version of the OP. What we are now debating is the oldest version of the riddle hereby called the Russian version. In this version the speed of the convayor belt matches the speed of wheel. No slipping is allowed. Speed need not be constant either. Please familiarize yourself with this version before responding. Thank you very much. PS. Put physics first, intuition a distant second.
I know NCN's physics is always sound and the only thing that explain his stance on the other side of the debate can only be the OP under discussion. Apparently there is an original version before the original post. Plane is not moving in this version, only trying to. This version is similar to what A tl5p tried to come up with, the plane on a treadbelt thread below this. He had the right answer but for the wrong reason. Try Cecil Adams for the right reason. Thanks mate.
I know NCN's physics is always sound and the only thing that explain his stance on the other side of the debate can only be the OP under discussion. Apparently there is an original version before the original post. Plane is not moving in this version, only trying to. This version is similar to what A tl5p tried to come up with, the plane on a treadbelt thread below this. He had the right answer but for the wrong reason. Try Cecil Adams for the right reason. Thanks mate.
That version, if that is what it is, is "car-on-a-conveyor" and holds no interest whatsoever because it defines the plane as not moving since the relative motion between the moving parts is zero. Same as walking-on-a-treadmill or boat-moving-upstream ... all trivial and boring. What's the point?
There are this planes I used to read about in war stories, i don't remember if it was Spitfire or another make. For quick take off with minimum runway the pilot had to hold on the brakes(I don't know if they were airbrakes or wheel brakes or both, probably) and rev up the engine. The point of this exercise is to test if we could theoreticaly keep an airplane in place by using a conveyor that is accelerated indefinately. We assume ideal tires and wheels. I know a trully ideal wheel should be mass less but for the sake of this discussion let it have mass. This is because moment of inertia and acceleration plays a big role in this set up. I hope i've presented it clearly. Thanks.
QUOTE (boit+Jan 13 2011, 10:22 AM)
This is because moment of inertia and acceleration plays a big role in this set up.
That is true ... but that contributes only to angular velocity, not linear velocity. The so-called "rolling resistance" is the torque on the wheels and it is (largely) constant over (either) velocity ... in other words the amount of energy needed to get from v to (v + delta v) is the same for all v.
One should also note that the wheel speed is not just a function of the plane driving forward but it is also being powered by the belt itself. Effectively, the belt is providing the energy needed to overcome any "magical resistance" proponents claim it is adding to the wheel.
All the backwards effects proposed by the hold-back crowd are the result of rolling friction ... which is an effect due mostly to surface irregularity and deformation. For example, a steel ball bearing heading down an upward moving metal slide would show little propensity to slow down (that is why bearing races are made from ball bearings and metal rings). There is no perpendicular torque that results in linear motion. (Imagine a bicyclist floating free in the space shuttle. If he start pedaling, does he start to move forward? Or backward, for that matter?)
Surface deformation causes a torque that is no longer perpendicular to the radius lever arm. This unbalanced torque is what causes the retarding action of rolling resistance. Of course, rolling friction is always required to get the wheel to roll at all ... if it were constructed along the lines of the frictionless air puck then it would merely slide without rotating. By the way, this is why the battery video experiment works: because the deformed paper more or less "lifts" the battery higher up the ramp, from which it must fall back down again.
The work-balance equations presented by SD merely show what the resulting motion will be when a force is exerted on a rolling wheel. The geometry and mass of the wheel plays a role ... obviously you could build a big, massive wheel that you don't provide sufficient force to move.
You can provide way more force than rolling resistance can handle and skidding will result. This effect is observed with billiard and bowling balls which, when first struck or thrown, skid across the surface before rolling resistance is capable of extracting enough translational motion to get the angular velocity up to non-slipping speed. The reverse is true, too: you can provide an acceleration to a rolling object than it can't handle and get it to skid.
That is true ... but that contributes only to angular velocity, not linear velocity. The so-called "rolling resistance" is the torque on the wheels and it is (largely) constant over (either) velocity ... in other words the amount of energy needed to get from v to (v + delta v) is the same for all v.
One should also note that the wheel speed is not just a function of the plane driving forward but it is also being powered by the belt itself. Effectively, the belt is providing the energy needed to overcome any "magical resistance" proponents claim it is adding to the wheel.
All the backwards effects proposed by the hold-back crowd are the result of rolling friction ... which is an effect due mostly to surface irregularity and deformation. For example, a steel ball bearing heading down an upward moving metal slide would show little propensity to slow down (that is why bearing races are made from ball bearings and metal rings). There is no perpendicular torque that results in linear motion. (Imagine a bicyclist floating free in the space shuttle. If he start pedaling, does he start to move forward? Or backward, for that matter?)
Surface deformation causes a torque that is no longer perpendicular to the radius lever arm. This unbalanced torque is what causes the retarding action of rolling resistance. Of course, rolling friction is always required to get the wheel to roll at all ... if it were constructed along the lines of the frictionless air puck then it would merely slide without rotating. By the way, this is why the battery video experiment works: because the deformed paper more or less "lifts" the battery higher up the ramp, from which it must fall back down again.
The work-balance equations presented by SD merely show what the resulting motion will be when a force is exerted on a rolling wheel. The geometry and mass of the wheel plays a role ... obviously you could build a big, massive wheel that you don't provide sufficient force to move.
You can provide way more force than rolling resistance can handle and skidding will result. This effect is observed with billiard and bowling balls which, when first struck or thrown, skid across the surface before rolling resistance is capable of extracting enough translational motion to get the angular velocity up to non-slipping speed. The reverse is true, too: you can provide an acceleration to a rolling object than it can't handle and get it to skid.
The force is not only angular, there is also a little linear force when a wheel is set rolling. http://straightdope.com/columns/read/2642/...s-not-heres-why
Did I not state that ... essentially? The plane only has so much power and at some point it can't go any faster due to rolling resistance, aero drag, whatever else you can think of. All it is necessary to do is bump any of these factors up to some particular value and the plane has limited speed. For example, you could construct the belt out of some sort of gravel surface such that the rolling resistance becomes really high (think runaway truck ramps). The poor old plane might not even get up to 40-50 mph before its engines are gassed.
But we are talking reasonable conveyors here, aren't we (yeah, right).
By the way the max braking action of a rolling B-777 is in the 950,000 newton range if you want to do some more interesting calculations.
But we are talking reasonable conveyors here, aren't we (yeah, right).
By the way the max braking action of a rolling B-777 is in the 950,000 newton range if you want to do some more interesting calculations.
Let's use the Spitfire or a plane with less power. Let's also have a sturdy rubber tire and steel surface. In an ideal set up we would like to eliminate rolling friction (I love the steel bearings on a steel railing kind of naked wheel more but I fear we may sacrifice static friction if I in that way). Eliminate axle friction somehow too, super grease on ball bearing etc. Now let's go! . Is moment of inertia and acceleration of the belt enough to hold this small powered plane? The physics seems to be in favour of stopping the plane on its tracks.
. Is moment of inertia and acceleration of the belt enough to hold this small powered plane? The physics seems to be in favour of stopping the plane on its tracks.
NCN, the reason that the plane's speed is measured at the wheels is because that is the way it was measured in the original Russian version of this thought problem. I know that is not the normal way that a planes speed is measured, but it sometimes is. I gave an example when it was measured by ground speed rather than by air speed. Some airplanes do have speedometers in their wheels. So it is not a good idea to deny this on how speed is measured alone. And if you get technical about it a plane's speed is never measured directly relative to the ground either. It is usually measured relative to the air. In the version that the OP uses it is assumed that wind velocity is zero so that in this case air speed does equal speed relative to the ground.
Then you fell back on the old tautological argument. Yes, for the simple minded that does work. If the plane meets the requirements of the Russian myth it will not advance. But that is hardly any fun now. The more important question is "Given the conditions of the Russian myth will there be forces developed by the plane that will keep it in place?" When you do use the tautological argument you force the others to go deeper into the question. The answer is yes.
The rest of your objections are wrong and have been dealt with. Numerous times over in fact. You are trying to use words to describe what your physics is incapable of. Study the physics of rolling some more. SD provided enough links, and equations.
It is strange that all of the physics experts who say that SD's analysis is wrong can neither show mathematically his error, or provide links that support their claim. Since this is in the realm of pure Newtonian mechanics right not you would think, if they were right, that that would not be too hard to do.
Then you fell back on the old tautological argument. Yes, for the simple minded that does work. If the plane meets the requirements of the Russian myth it will not advance. But that is hardly any fun now. The more important question is "Given the conditions of the Russian myth will there be forces developed by the plane that will keep it in place?" When you do use the tautological argument you force the others to go deeper into the question. The answer is yes.
The rest of your objections are wrong and have been dealt with. Numerous times over in fact. You are trying to use words to describe what your physics is incapable of. Study the physics of rolling some more. SD provided enough links, and equations.
It is strange that all of the physics experts who say that SD's analysis is wrong can neither show mathematically his error, or provide links that support their claim. Since this is in the realm of pure Newtonian mechanics right not you would think, if they were right, that that would not be too hard to do.
QUOTE (Subduction Zone+Jan 13 2011, 12:54 PM)
Study the physics of rolling some more. SD provided enough links, and equations.
You mean what I learned at MIT wasn't enough?
I used SD's equation (a power version) ... what more do you want?
Haven't you guys figured out that there is a range of solutions in this problem space ... not just one? Of course I can make the plane stop ... or fly ... at will by just varying the physical parameters. But this has nothing to do with EITHER version of the problem ... which by the way were word problems that sited no numbers ... because it was just an effort to get you to see the difference between motive power that depended on the belt versus power that didn't. Apparently, in an effort to justify what is obviously the wrong position, proponents of no-fly introduce a blizzard of math to something that doesn't need it.
You mean what I learned at MIT wasn't enough?
I used SD's equation (a power version) ... what more do you want?
Haven't you guys figured out that there is a range of solutions in this problem space ... not just one? Of course I can make the plane stop ... or fly ... at will by just varying the physical parameters. But this has nothing to do with EITHER version of the problem ... which by the way were word problems that sited no numbers ... because it was just an effort to get you to see the difference between motive power that depended on the belt versus power that didn't. Apparently, in an effort to justify what is obviously the wrong position, proponents of no-fly introduce a blizzard of math to something that doesn't need it.
QUOTE (Subduction Zone+Jan 13 2011, 08:36 AM)
I didn't use it for many years, but I came up with my user name over thirty years ago when I was in college.
You were active on the internet in about 1980?
You were active on the internet in about 1980?
QUOTE (Derek1148+Jan 13 2011, 05:22 PM)
You were active on the internet in about 1980?
No, it was a user name for a computer game on a system that used time sharing. One mainframe. Perhaps hundreds of users. There was a game that required a user name and I came up with this one. It was played on a CRT monitor with the characters coming in at a blazing 30 cps.
I remember a machine language course that I took once, unfortunately that knowledge is completely gone, where the instructor thought that time sharing was a temporary fad. He was right, but we didn't know why at the time. We thought he was crazy. At that time a college roommate of mine had his own personal computer. It started out with one k of memory. When he fist got it it had no keyboard or monitor. He programmed it by flipping switches on the front if it. And had to interpret the readout of its LED lights. He did upgrade it as time went on, but it was always a kludge. For example sometimes it would freeze due to overheating, at which point we sprayed the offending circuit with freon, straight from the can.
No, it was a user name for a computer game on a system that used time sharing. One mainframe. Perhaps hundreds of users. There was a game that required a user name and I came up with this one. It was played on a CRT monitor with the characters coming in at a blazing 30 cps.
I remember a machine language course that I took once, unfortunately that knowledge is completely gone, where the instructor thought that time sharing was a temporary fad. He was right, but we didn't know why at the time. We thought he was crazy. At that time a college roommate of mine had his own personal computer. It started out with one k of memory. When he fist got it it had no keyboard or monitor. He programmed it by flipping switches on the front if it. And had to interpret the readout of its LED lights. He did upgrade it as time went on, but it was always a kludge. For example sometimes it would freeze due to overheating, at which point we sprayed the offending circuit with freon, straight from the can.
QUOTE (NoCleverName+Jan 13 2011, 04:27 PM)
But we are talking reasonable conveyors here, aren't we (yeah, right).
ROFL! By what definition of "reasonable" do you include a conveyor that can accelerate to c?
ROFL! By what definition of "reasonable" do you include a conveyor that can accelerate to c?
QUOTE (Subduction Zone+Jan 13 2011, 09:16 PM)
No, it was a user name for a computer game on a system that used time sharing. One mainframe. Perhaps hundreds of users. There was a game that required a user name and I came up with this one. It was played on a CRT monitor with the characters coming in at a blazing 30 cps.
I remember a machine language course that I took once, unfortunately that knowledge is completely gone, where the instructor thought that time sharing was a temporary fad. He was right, but we didn't know why at the time. We thought he was crazy. At that time a college roommate of mine had his own personal computer. It started out with one k of memory. When he fist got it it had no keyboard or monitor. He programmed it by flipping switches on the front if it. And had to interpret the readout of its LED lights. He did upgrade it as time went on, but it was always a kludge. For example sometimes it would freeze due to overheating, at which point we sprayed the offending circuit with freon, straight from the can.
Wow! Interesting time you've lived through. Electronic calculator with black on white display was the most advanced computer (actualy the only computer) that we could have access to. In standard five (elementary school 5th grade) a well to do pupil in our class possessed one. He was an instant celeb
I remember a machine language course that I took once, unfortunately that knowledge is completely gone, where the instructor thought that time sharing was a temporary fad. He was right, but we didn't know why at the time. We thought he was crazy. At that time a college roommate of mine had his own personal computer. It started out with one k of memory. When he fist got it it had no keyboard or monitor. He programmed it by flipping switches on the front if it. And had to interpret the readout of its LED lights. He did upgrade it as time went on, but it was always a kludge. For example sometimes it would freeze due to overheating, at which point we sprayed the offending circuit with freon, straight from the can.
Wow! Interesting time you've lived through. Electronic calculator with black on white display was the most advanced computer (actualy the only computer) that we could have access to. In standard five (elementary school 5th grade) a well to do pupil in our class possessed one. He was an instant celeb
NCN. what did you study at MIT? I doubt it was physics when you post something like this:
The simple ramp test shows this not t be the case. A ball rolling on a ramp goes much slower than the same ball would go sliding frictionlessly on a ramp of the same angle. It has been way too many years since college for me to derive the formula, but if I remember correctly, a rolling solid sphere will have about 2/3's of the acceleration that the sliding ball would have. I think you need to brush up on your physics of rolling as well as I do. Since I have been out too long I will trust SD's physics which I have yet to see be in error, especially on something as simple as this.
QUOTE
All the backwards effects proposed by the hold-back crowd are the result of rolling friction ... which is an effect due mostly to surface irregularity and deformation. For example, a steel ball bearing heading down an upward moving metal slide would show little propensity to slow down
The simple ramp test shows this not t be the case. A ball rolling on a ramp goes much slower than the same ball would go sliding frictionlessly on a ramp of the same angle. It has been way too many years since college for me to derive the formula, but if I remember correctly, a rolling solid sphere will have about 2/3's of the acceleration that the sliding ball would have. I think you need to brush up on your physics of rolling as well as I do. Since I have been out too long I will trust SD's physics which I have yet to see be in error, especially on something as simple as this.
QUOTE (boit+Jan 13 2011, 06:32 PM)
Wow! Interesting time you've lived through. Electronic calculator with black on white display was the most advanced computer (actualy the only computer) that we could have access to. In standard five (elementary school 5th grade) a well to do pupil in our class possessed one. He was an instant celeb
Yeah, well when I was in college we used slide rules. (And super fast conveyor belts.)
Yeah, well when I was in college we used slide rules. (And super fast conveyor belts.)
QUOTE (Subduction Zone+Jan 13 2011, 02:37 PM)
but if I remember correctly, a rolling solid sphere will have about 2/3's of the acceleration that the sliding ball would have.
... Off hand I believe you are right ... I had in mind the steel-steel versus paper-battery interface ... difference in rolling friction values ... not sliding versus rolling. But, good catch.
... Off hand I believe you are right ... I had in mind the steel-steel versus paper-battery interface ... difference in rolling friction values ... not sliding versus rolling. But, good catch.
QUOTE (boit+Jan 13 2011, 06:32 PM)
Wow! Interesting time you've lived through. Electronic calculator with black on white display was the most advanced computer (actualy the only computer) that we could have access to. In standard five (elementary school 5th grade) a well to do pupil in our class possessed one. He was an instant celeb
You are a few years younger than I am. My brother who was a year ahead of me while in high school bought a calculator for $150.00 his senior year. It could add, subtract, multiply, and divide and had one memory. You would pay $5.00 in today's money for one that did the same. I still kick myself because I had a half decent slide rule that I sold when I bought my first scientific calculator. I paid as much for my Texas Insturments 50 (I think) as my brother paid for his. It had trig and exponential functions besides the basic adding, multiplying etc. If you adjusted for inflation you could easily get a desk top or even laptop for that sort of money today.
And I see Derek can't be much older than I am. Yes, slide rules were nice. When the scientific calculators came out I heard more than one prof chastising a student for spouting too many numbers in an answer. That was never a problem with the old slip sticks.
You are a few years younger than I am. My brother who was a year ahead of me while in high school bought a calculator for $150.00 his senior year. It could add, subtract, multiply, and divide and had one memory. You would pay $5.00 in today's money for one that did the same. I still kick myself because I had a half decent slide rule that I sold when I bought my first scientific calculator. I paid as much for my Texas Insturments 50 (I think) as my brother paid for his. It had trig and exponential functions besides the basic adding, multiplying etc. If you adjusted for inflation you could easily get a desk top or even laptop for that sort of money today.
And I see Derek can't be much older than I am. Yes, slide rules were nice. When the scientific calculators came out I heard more than one prof chastising a student for spouting too many numbers in an answer. That was never a problem with the old slip sticks.
Edit. Yeah. Long time ago.
[QUOTE] You are a few years younger that I am.[QUOTE] I would be if I was raised in the same world. The information that I held back is: I belong to neither of the first two worlds. It takes roughly thirty years before 'current' technology trickles down to us.
QUOTE
Really? And here I was using your own equation (essentially ... I just added a time parameter which converts work to power).
No you didn't.
QUOTE (->
| QUOTE |
| Really? And here I was using your own equation (essentially ... I just added a time parameter which converts work to power). |
No you didn't.
I've figured out that you are either Alt5p or a close relative because you and the Zone are in league with those that measure the plane's speed by (in essence) reading it off a speedometer attached to the wheels. This idea has been thoroughly smacked down because it "defines" that the plane doesn't move. This is an attempt to put the plane-on-a-conveyor into the same class as car-on-a-conveyor. To boot, your own little battery video doesn't even do that since it is clear from the video that the angular velocity of the battery is far too large for its linear velocity (both measured by the observer, I might add). The plane's speed is measured relative to the ground, as is the belt's opposing speed. (What other choice makes sense?) Wheel speed is not a consideration.
1) The point is that even though it defines the plane as not moving it is still possible to calculate the physical parameters needed for it to happen. That is to say the acceleration of the belt.
2) The angular velocity of the battery was much greater than its linear velocity for the exact reason I have been describing. The accelerating belt changed the linear velocity of the rolling battery.
QUOTE
That the wheels, slip, skid, or roll faster than the plane is moving has little to do with the problem ... except that whatever regime holds forth determines the maximum retarding force the belt can deliver. But because the engines have enough power to overcome a lot of the braking action of the tires (in the example I provide above the max resistive force with brakes fully on is about 2,400,000 newtons) the plane advances under realistic considerations.
Not in all planes. One example, which you can't even source apparently, does not apply to all planes.
QUOTE (->
| QUOTE |
| That the wheels, slip, skid, or roll faster than the plane is moving has little to do with the problem ... except that whatever regime holds forth determines the maximum retarding force the belt can deliver. But because the engines have enough power to overcome a lot of the braking action of the tires (in the example I provide above the max resistive force with brakes fully on is about 2,400,000 newtons) the plane advances under realistic considerations. |
Not in all planes. One example, which you can't even source apparently, does not apply to all planes.
There is no other way to transmit a retarding force to the plane than through the tires. The tire interface with the belt is its rubber tread. That tread has an ultimate holding strength based on its coefficient of friction (u) and the normal force loading them (weight of the plane in newtons). For this strength to be tested the brakes have to be substantially on. That provides a lot more resistance the simple free-wheeling (which is the whole point, after all, of having wheels in the first place).
Absolutely wrong. The accelerating belt can provide exactly as much backward force as the wheels when the brakes are on because the wheels will roll without slipping until the point where the force exceeds the maximum of static friction which is also exactly when the plane with the brakes on will start to move. This much I have conclusively proven several times.
QUOTE
Using the power balance equation (above) it was shown that rolling resistance alone can't transmit resistance to the plane to keep it from lifting off. (Ultimately, if the plane didn't try to lift off, its engines can make it go only so fast down the runway ... due to rolling resistance and aero drag ... but that ultimate speed is far in excess of takeoff speed). You need some additional braking action or another way to sap power from the engines. And you're going to have to come up with something really big ... equivalent to having your foot on the brakes.
1) You proven the exact opposite. You've proven that in our ideal thought experiment where there are no maximum speeds it is quite trivial to stop the plane.
2) As I have proven several times the acceleration of the belt constitutes a backward force on anything rolling on the belt. You continue to deny this despite the mountain of evidence provided and without putting up any evidence of your own which is hardly an effective means of debate.
QUOTE (->
| QUOTE |
| Using the power balance equation (above) it was shown that rolling resistance alone can't transmit resistance to the plane to keep it from lifting off. (Ultimately, if the plane didn't try to lift off, its engines can make it go only so fast down the runway ... due to rolling resistance and aero drag ... but that ultimate speed is far in excess of takeoff speed). You need some additional braking action or another way to sap power from the engines. And you're going to have to come up with something really big ... equivalent to having your foot on the brakes. |
1) You proven the exact opposite. You've proven that in our ideal thought experiment where there are no maximum speeds it is quite trivial to stop the plane.
2) As I have proven several times the acceleration of the belt constitutes a backward force on anything rolling on the belt. You continue to deny this despite the mountain of evidence provided and without putting up any evidence of your own which is hardly an effective means of debate.
That version, if that is what it is, is "car-on-a-conveyor" and holds no interest whatsoever because it defines the plane as not moving since the relative motion between the moving parts is zero. Same as walking-on-a-treadmill or boat-moving-upstream ... all trivial and boring. What's the point?
The point as I am saying now for the third or fourth time is getting people to realize that an accelerating belt puts a backwards force on something rolling on that belt.
QUOTE
That is true ... but that contributes only to angular velocity, not linear velocity. The so-called "rolling resistance" is the torque on the wheels and it is (largely) constant over (either) velocity ... in other words the amount of energy needed to get from v to (v + delta v) is the same for all v.
Really not getting the point that when something rolls its angular and linear velocity as well as the velocity of the surface it rolls on are all linked and one cannot be changed without affecting the others.
QUOTE (->
| QUOTE |
| That is true ... but that contributes only to angular velocity, not linear velocity. The so-called "rolling resistance" is the torque on the wheels and it is (largely) constant over (either) velocity ... in other words the amount of energy needed to get from v to (v + delta v) is the same for all v. |
Really not getting the point that when something rolls its angular and linear velocity as well as the velocity of the surface it rolls on are all linked and one cannot be changed without affecting the others.
One should also note that the wheel speed is not just a function of the plane driving forward but it is also being powered by the belt itself. Effectively, the belt is providing the energy needed to overcome any "magical resistance" proponents claim it is adding to the wheel.
No it rather clearly isn't. Without the thrust of the plane the wheel and plane would be pulled backwards by the accelerating belt. This does constitute work by the belt but it is the negative of work done by the thrust. So if the plane is to move forward it must do more work than if it where on a stationary runway.
QUOTE
All the backwards effects proposed by the hold-back crowd are the result of rolling friction ... which is an effect due mostly to surface irregularity and deformation.
No they aren't. That has been conclusively proven. The rolling resistance between the battery and the paper was not great enough to cause it to stop. How do I know this you ask? I know this because the battery accelerated down the paper when it was stationary. Thus the force of gravity on the battery was greater than any rolling resistance. Also, as you stated up there yourself rolling resistance is largely constant over velocity. Certainly it is constant over the velocities I can attain by pulling. Thus if it was just rolling resistance, which couldn't change with me pulling the paper, the battery's motion would not have changed in the second round of testing.
QUOTE (->
| QUOTE |
| All the backwards effects proposed by the hold-back crowd are the result of rolling friction ... which is an effect due mostly to surface irregularity and deformation. |
No they aren't. That has been conclusively proven. The rolling resistance between the battery and the paper was not great enough to cause it to stop. How do I know this you ask? I know this because the battery accelerated down the paper when it was stationary. Thus the force of gravity on the battery was greater than any rolling resistance. Also, as you stated up there yourself rolling resistance is largely constant over velocity. Certainly it is constant over the velocities I can attain by pulling. Thus if it was just rolling resistance, which couldn't change with me pulling the paper, the battery's motion would not have changed in the second round of testing.
For example, a steel ball bearing heading down an upward moving metal slide would show little propensity to slow down (that is why bearing races are made from ball bearings and metal rings). There is no perpendicular torque that results in linear motion. (Imagine a bicyclist floating free in the space shuttle. If he start pedaling, does he start to move forward? Or backward, for that matter?)
1) Is the upward slide accelerating?
2) Is the slide angled so that the force of gravity isn't enough to cause slipping?
If the answer is yes to both those questions than the steel ball bearing will in fact slow as demonstrated quite clearly in my video and via the math that I have done.
QUOTE
Surface deformation causes a torque that is no longer perpendicular to the radius lever arm. This unbalanced torque is what causes the retarding action of rolling resistance.
To bad we've been ignoring it.
QUOTE (->
| QUOTE |
| Surface deformation causes a torque that is no longer perpendicular to the radius lever arm. This unbalanced torque is what causes the retarding action of rolling resistance. |
To bad we've been ignoring it.
Of course, rolling friction is always required to get the wheel to roll at all ... if it were constructed along the lines of the frictionless air puck then it would merely slide without rotating.
Wrong. It is static friction between the bottom of the rolling object and the surface that is required to get the wheel to roll. This can exist without rolling friction because it does not depend on deformation. The static friction keeps the bottom of the wheel from moving allowing a force at the center of mass to create a torque around that point and causing the wheel to turn. This occurs regardless of any deformation leading to rolling resistance.
QUOTE
By the way, this is why the battery video experiment works: because the deformed paper more or less "lifts" the battery higher up the ramp, from which it must fall back down again.
Wrong. As you said yourself rolling resistance is largely constant with speed. This is especially true over the speeds I can obtain with my hands pulling on a sheet of paper. Thus whatever rolling resistance existed when the paper wasn't moving is virtually identical to whatever rolling resistance existed when I pulled the paper. Since the force of gravity over came the rolling resistance when the paper was stationary it also overcame the rolling resistance when the paper wasn't stationary. The only way for the motion of the battery to change is for the forces on it to change. That is basic physics and since the rolling resistance didn't change it cannot be the explanation.
QUOTE (->
| QUOTE |
| By the way, this is why the battery video experiment works: because the deformed paper more or less "lifts" the battery higher up the ramp, from which it must fall back down again. |
Wrong. As you said yourself rolling resistance is largely constant with speed. This is especially true over the speeds I can obtain with my hands pulling on a sheet of paper. Thus whatever rolling resistance existed when the paper wasn't moving is virtually identical to whatever rolling resistance existed when I pulled the paper. Since the force of gravity over came the rolling resistance when the paper was stationary it also overcame the rolling resistance when the paper wasn't stationary. The only way for the motion of the battery to change is for the forces on it to change. That is basic physics and since the rolling resistance didn't change it cannot be the explanation.
The work-balance equations presented by SD merely show what the resulting motion will be when a force is exerted on a rolling wheel. The geometry and mass of the wheel plays a role ... obviously you could build a big, massive wheel that you don't provide sufficient force to move.
So in other words it is the right equation to use.
QUOTE
You can provide way more force than rolling resistance can handle and skidding will result.
Skidding results from exceeding the traction of the tire which has the same maximum as the static friction of the tire. It is quite different than rolling resistance.
Here is a link that might be educational.
You will note that there is no rolling resistance what soever. Everything happens in that example because of static friction.
QUOTE (->
| QUOTE |
| You can provide way more force than rolling resistance can handle and skidding will result. |
Skidding results from exceeding the traction of the tire which has the same maximum as the static friction of the tire. It is quite different than rolling resistance.
Here is a link that might be educational.
You will note that there is no rolling resistance what soever. Everything happens in that example because of static friction.
This effect is observed with billiard and bowling balls which, when first struck or thrown, skid across the surface before rolling resistance is capable of extracting enough translational motion to get the angular velocity up to non-slipping speed.
Wrong. It would be the kinetic friction which is doing most of the work there.
QUOTE
The reverse is true, too: you can provide an acceleration to a rolling object than it can't handle and get it to skid.
This point has already been addressed several times. Please stop bringing it up.
QUOTE (->
| QUOTE |
| The reverse is true, too: you can provide an acceleration to a rolling object than it can't handle and get it to skid. |
This point has already been addressed several times. Please stop bringing it up.
Did I not state that ... essentially? The plane only has so much power and at some point it can't go any faster due to rolling resistance, aero drag, whatever else you can think of. All it is necessary to do is bump any of these factors up to some particular value and the plane has limited speed. For example, you could construct the belt out of some sort of gravel surface such that the rolling resistance becomes really high (think runaway truck ramps). The poor old plane might not even get up to 40-50 mph before its engines are gassed.
Or as has been repeatedly demonstrated you could just accelerate the belt assuming the static friction between the bottoms of the wheels and the belt is high enough.
QUOTE
You mean what I learned at MIT wasn't enough?
If you got a degree in physics I'd ask for your money back.
QUOTE (->
| QUOTE |
You mean what I learned at MIT wasn't enough? |
If you got a degree in physics I'd ask for your money back.
I used SD's equation (a power version) ... what more do you want?
No you didn't and then you went and made several errors.
QUOTE
Haven't you guys figured out that there is a range of solutions in this problem space ... not just one?
As boit pointed out before we accept the result for a non-accelerating belt. The only person here unwilling to accept another solution to a slightly altered problem is you.
QUOTE (->
| QUOTE |
| Haven't you guys figured out that there is a range of solutions in this problem space ... not just one? |
As boit pointed out before we accept the result for a non-accelerating belt. The only person here unwilling to accept another solution to a slightly altered problem is you.
Of course I can make the plane stop ... or fly ... at will by just varying the physical parameters. But this has nothing to do with EITHER version of the problem ... which by the way were word problems that sited no numbers ... because it was just an effort to get you to see the difference between motive power that depended on the belt versus power that didn't.
The acceleration of the belt is quite important to the other version of the thought problem. Also be careful there is sounds like you are falling into the old trap of thinking that the car can be held back on the constant speed treadmill because it can't push off from a moving surface. The only reason it is easier to hold a car back is because of the rpm of its engine and the rpm of its wheels are linked and the torque the engine can produce after a certain amount of rpm starts to decrease. If this limitation where removed the car would behave identically to the plane.
QUOTE
Apparently, in an effort to justify what is obviously the wrong position, proponents of no-fly introduce a blizzard of math to something that doesn't need it.
If it is the wrong position then why is it I have two text books, and two YouTube videos that support my analysis and you have absolutely no evidence at all?
QUOTE (->
| QUOTE |
| Apparently, in an effort to justify what is obviously the wrong position, proponents of no-fly introduce a blizzard of math to something that doesn't need it. |
If it is the wrong position then why is it I have two text books, and two YouTube videos that support my analysis and you have absolutely no evidence at all?
... Off hand I believe you are right ... I had in mind the steel-steel versus paper-battery interface ... difference in rolling friction values ... not sliding versus rolling. But, good catch.
Wrong. Difference between rolling and sliding entirely. It has nothing to do with rolling friction.
Difference between rolling and sliding.
Maybe later I'll copy some other pages out of one of my Physics 201 text books dealing with rolling down an inclined plane that demonstrate it has nothing to do with rolling resistance.
QUOTE (Sithdarth+Jan 13 2011, 09:34 PM)
If you got a degree in physics I'd ask for your money back.
How about Cornell?
How about Cornell?
If you got a degree in physics and was saying things as contrary to basic physics as NoCleverName I'd tell you to ask for your money back as well. I mean if he like has a degree in Chemistry or something and only took a little physics while there I could understand how he might have those conception. I don't see how anyone that actually majored in Physics could believe some of the things he's said.
QUOTE (Sithdarth+Jan 13 2011, 09:48 PM)
If you got a degree in physics and was saying things as contrary to basic physics as NoCleverName I'd tell you to ask for your money back as well.
No, I didn't get a degree in Applied Physics from Cornell, but I did date a girl who had her Master's Degree in Hotel Management from Cornell. Does that count?
No, I didn't get a degree in Applied Physics from Cornell, but I did date a girl who had her Master's Degree in Hotel Management from Cornell. Does that count?
They offer management degrees at Cornell? Well I guess when you're that big it makes sense.
Anyway here is that other page from one of my Physics 201 books I was talking about:
Page 4
To point out what should be obvious rolling resistance is being ignored because mechanical energy is being conserved and yet these objects still roll and roll at different velocities. Rolling resistance does not conserve mechanical energy which is of course why things roll to a stop eventually.
Anyway here is that other page from one of my Physics 201 books I was talking about:
Page 4
To point out what should be obvious rolling resistance is being ignored because mechanical energy is being conserved and yet these objects still roll and roll at different velocities. Rolling resistance does not conserve mechanical energy which is of course why things roll to a stop eventually.
QUOTE (Sithdarth+Jan 13 2011, 09:58 PM)
They offer management degrees at Cornell?
QUOTE (boit+Jan 13 2011, 10:20 AM)
http://straightdope.com/columns/read/2642/...s-not-heres-why
This sums it up well enough for me.
SD & SZ have framed the question in such a way that anyone new to the conversation has to surmise the intended premise, constantly stated as "the Russian version", as I guess it's too much to reiterate the premise (even though their post volume should be able to accommodate it easily). Anyone new to the discussion will ad-infinitum spur on more of the same because of the same cross-purpose communication.
This sums it up well enough for me.
QUOTE
Then there's a whole other breed of disputants who, whether or not they've cracked the riddle as originally posed, prefer to reframe it by proposing progressively more esoteric assumptions, refinements, analogies, etc. Often they arrive at a separate question entirely: Is there a way to set up the conveyor so that it overcomes the thrust of the engines and the plane remains stationary and doesn't take off?
SD & SZ have framed the question in such a way that anyone new to the conversation has to surmise the intended premise, constantly stated as "the Russian version", as I guess it's too much to reiterate the premise (even though their post volume should be able to accommodate it easily). Anyone new to the discussion will ad-infinitum spur on more of the same because of the same cross-purpose communication.
QUOTE
SD & SZ have framed the question in such a way that anyone new to the conversation has to surmise the intended premise, constantly stated as "the Russian version", as I guess it's too much to reiterate the premise (even though their post volume should be able to accommodate it easily). Anyone new to the discussion will ad-infinitum spur on more of the same because of the same cross-purpose communication.
I do try to make it as clear as possible to anyone entering the debate what point I am arguing in the first response I make to them. The problem is that they don't always listen and sometimes even when they do listen they don't understand the consequences of an accelerating belt. You are correct that some of the continued discussion comes from not understanding what situation is being advocated. However, no all of the continued discussion stems from there. NoCleverName for example who made it rather clear that he thinks the acceleration of the belt has no effect on the motion of the plane despite the evidence to the contrary.
QUOTE (Sithdarth+Jan 13 2011, 10:58 PM)
NoCleverName for example who made it rather clear that he thinks the acceleration of the belt has no effect on the motion of the plane despite the evidence to the contrary.
What he is arguing is what would actually happen. Short of the catastrophic failure we discussed earlier, the plane would move forward and there would be a high degree of kinetic friction on the wheels, as they slipped.
What you are arguing is if there is no slippage the plane would remain stationary with its wheels spinning. Okay. End of discussion.
What he is arguing is what would actually happen. Short of the catastrophic failure we discussed earlier, the plane would move forward and there would be a high degree of kinetic friction on the wheels, as they slipped.
What you are arguing is if there is no slippage the plane would remain stationary with its wheels spinning. Okay. End of discussion.
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