Merged DDWFTTW in a “Real” Wind

[windgrins]

Since the "X" is accelerated in the frame you are using, and the "X" is painted on the belt, the BELT is accelerated in the frame. There is no way out of that for you.
Now, since the belt is a continuous loop, and it undergoes acceleration in some places, how can it not undergo acceleration in all places? Is it because the acceleration takes place only at the ends, where it goes around the cylinders?
The motor is only at one end of the belt, yet when it accelerates the belt, the entire belt must accelerate, or do you not agree with this?
Since the ends of the belt going around the cylinders undergo acceleration, that acceleration must be transmitted along the entire belt, in the same way the motor transmits motion along the entire belt.
There is no way you can talk around this with your babble! You cannot isolate the top of the belt from the forces acting on the belt elsewhere. You cannot "attach" an IFOR to a belt that is rotating in that frame, as the "X" would definitely be doing. You cannot base a FOR on a projection. Give it up; the treadmill is dead.

Sorry PPG, you are still confused.

For the purpose of discussion let's assume the following are the axis of our reference frame:

x axis=origin is associated with the location with the first pass of one of your X's (once the TM is rolling, it is only valid for one rotation. From the point of view of the IFOR, when the X appears again, it will be effectively a different X moved the length of the belt in the IFOR. +x direction is up TM. (If you don't get this, ask or give it some thought!)

ETA: I see that Jadebox just expressed the same idea in the post above about the painted "X".

y axis=origin-the center of the belt's upper surface. +y direction is away from the observer on the right side of the TM with upTM being in the direction of the observer's right hand.

z axis=origin-the upper surface of the belt TM. +z direction is towards the ceiling.

The IFOR is in space as a mathematical entity moving (smoothly translating only in the direction of down TM at belt speed wrt earth) It's not attached to the belt.

Now, this is definitive. While smoothly operating, the belt's upper and lower surface is unaccelerated and when the X appears there, it is unaccelerated in both the IFOR just defined and an IFOR indexed to the earth. The part of the belt that moves around the roller is accelerated in the x and z direction as it moves around the roller. (x because it changes direction and z because it goes from top to bottom on one end and bottom to top on the other.) The top and bottom of the belt in a smoothly running TM are never accelerated in the x axis. The belt is only operating under a constant tension in these areas.

Any object that remains stationary (wrt earth-like the cart) on the top of the TM is unaccelerated (don't confuse this with not moving) in the IFOR that has been defined above and one indexed to the earth. Why do we know this: because no false forces exist in either IFOR defined and they are smoothly translating wrt to each other. Galilean relativity holds and physics is completely valid in both.

The TM is alive and well (figuratively, of course.)!

PS, just because you can't understand a clear explanation, that the other posters do, does not make it babble (a derogatory term which you say you are never guilty of!) simply because you don't understand. All IFORs are based on projections of their axis into three space. I'm sorry you are having a problem understanding this concept but it is a fact.

WindGrins

 

[profpangloss]

Sorry PPG, you are still confused.

For the purpose of discussion let's assume the following are the axis of our reference frame:

x axis=origin is associated with the location with the first pass of one of your X's (once the TM is rolling, it is only valid for one rotation. From the point of view of the IFOR, when the X appears again, it will be effectively a different X moved the length of the belt in the IFOR. +x direction is up TM. (If you don't get this, ask or give it some thought!)

ETA: I see that Jadebox just expressed the same idea in the post above about the painted "X".

y axis=origin-the center of the belt's upper surface. +y direction is away from the observer on the right side of the TM with upTM being in the direction of the observer's right hand.

z axis=origin-the upper surface of the belt TM. +z direction is towards the ceiling.

The IFOR is in space as a mathematical entity moving (smoothly translating only in the direction of down TM at belt speed wrt earth) It's not attached to the belt.

Now, this is definitive. While smoothly operating, the belt's upper and lower surface is unaccelerated and when the X appears there, it is unaccelerated in both the IFOR just defined and an IFOR indexed to the earth. The part of the belt that moves around the roller is accelerated in the x and z direction as it moves around the roller. (x because it changes direction and z because it goes from top to bottom on one end and bottom to top on the other.) The top and bottom of the belt in a smoothly running TM are never accelerated in the x axis. The belt is only operating under a constant tension in these areas.

Any object that remains stationary (wrt earth-like the cart) on the top of the TM is unaccelerated (don't confuse this with not moving) in the IFOR that has been defined above and one indexed to the earth. Why do we know this: because no false forces exist in either IFOR defined and they are smoothly translating wrt to each other. Galilean relativity holds and physics is completely valid in both.

The TM is alive and well (figuratively, of course.)!

PS, just because you can't understand a clear explanation, that the other posters do, does not make it babble (a derogatory term which you say you are never guilty of!) simply because you don't understand. All IFORs are based on projections of their axis into three space. I'm sorry you are having a problem understanding this concept but it is a fact.

WindGrins

I am so sorry that you are so wrong and you still do not understand why the belt is not in uniform motion and a cart running on it cannot be compared with a cart in the wind.

Since you seem to like facts, let's look at a few:

You cannot "attach" an IFOR to an “X” painted on the top of the treadmill belt. That is a fact. Any frame of reference in which the “X” appears to be stationary would need to follow the “X” around the ends and would undergo acceleration. Any such frame would be non-inertial. Undeniable fact.

You can attach an IFOR to a projection of the belt, but the belt itself will be seen to be rotating in such an IFOR, meaning the belt is undergoing acceleration in that IFOR and it is not in uniform motion. Or as Llyricist said: “An IFOR that is based on the motion of the upper belt surface, will continue to move in that direction even as the belt changes direction.” A change in direction is acceleration.

Your problem is focusing on the projection, as if the cart is riding on that when in fact the cart is riding on the belt. The belt is not inertial as it is undergoing acceleration at both ends and it is not in constant uniform motion. Since the belt is clearly rotating in your chosen IFOR, the rotational energy of the belt is frame invariant, totally unlike the energy of the wind which is frame dependent.

There can be no equivalency between the cart on the treadmill and the cart in the wind.

Oh, and just because you can't understand a clear explanation, does not mean I am confused. It means you are confused.

 

[windgrins]

I am so sorry that you are so wrong and you still do not understand why the belt is not in uniform motion and a cart running on it cannot be compared with a cart in the wind.

Since you seem to like facts, let's look at a few:

You cannot "attach" an IFOR to an “X” painted on the top of the treadmill belt. That is a fact. Any frame of reference in which the “X” appears to be stationary would need to follow the “X” around the ends and would undergo acceleration. Any such frame would be non-inertial. Undeniable fact.

You can attach an IFOR to a projection of the belt, but the belt itself will be seen to be rotating in such an IFOR, meaning the belt is undergoing acceleration in that IFOR and it is not in uniform motion. Or as Llyricist said: “An IFOR that is based on the motion of the upper belt surface, will continue to move in that direction even as the belt changes direction.” A change in direction is acceleration.

Your problem is focusing on the projection, as if the cart is riding on that when in fact the cart is riding on the belt. The belt is not inertial as it is undergoing acceleration at both ends and it is not in constant uniform motion. Since the belt is clearly rotating in your chosen IFOR, the rotational energy of the belt is frame invariant, totally unlike the energy of the wind which is frame dependent.

There can be no equivalency between the cart on the treadmill and the cart in the wind.

Oh, and just because you can't understand a clear explanation, does not mean I am confused. It means you are confused.

OK, Have it your way. I'm very happy for my post to stand as my record of my understanding for any interested third parties.

I just have one minor question for you:

How is it that the earth's surface can act as IRF today at noon when the same point on it will be going at 2000 miles/hour (roughly) in the opposite direction at midnight (12 hours later)? That's quite an acceleration! Almost as if the surface of the earth is on one big giant 8000 mile diameter roller! I guess it can't be an IRF either by your argument.

Please continue to reason as you see fit!

WindGrins

 

[tobermoryphil]

I am so sorry that you are so wrong and you still do not understand why the belt is not in uniform motion and a cart running on it cannot be compared with a cart in the wind.

Since you seem to like facts, let's look at a few:

You cannot "attach" an IFOR to an “X” painted on the top of the treadmill belt. That is a fact. Any frame of reference in which the “X” appears to be stationary would need to follow the “X” around the ends and would undergo acceleration. Any such frame would be non-inertial. Undeniable fact.

You can attach an IFOR to a projection of the belt, but the belt itself will be seen to be rotating in such an IFOR, meaning the belt is undergoing acceleration in that IFOR and it is not in uniform motion. Or as Llyricist said: “An IFOR that is based on the motion of the upper belt surface, will continue to move in that direction even as the belt changes direction.” A change in direction is acceleration.

Your problem is focusing on the projection, as if the cart is riding on that when in fact the cart is riding on the belt. The belt is not inertial as it is undergoing acceleration at both ends and it is not in constant uniform motion. Since the belt is clearly rotating in your chosen IFOR, the rotational energy of the belt is frame invariant, totally unlike the energy of the wind which is frame dependent.

There can be no equivalency between the cart on the treadmill and the cart in the wind.

Oh, and just because you can't understand a clear explanation, does not mean I am confused. It means you are confused.

Not to put too fine a point on it, what absolute and utter rubbish!

Stop thinking treadmill- how about a half mile long mining conveyor belt? Does it matter if it goes round a drum at either end? if the belt is running at 15 mph, you have two minutes of constant uniform motion on top of it.

The treadmill may only have a few seconds where one section of the the belt is on top, with constant motion, but it is an endless belt, and apart from the length, no different to the mining conveyor belt as far as anything running on it can tell.

But I doubt you could even comprehend the concept; please prove me wrong.

 

[profpangloss]

OK, Have it your way. I'm very happy for my post to stand as my record of my understanding for any interested third parties.

I just have one minor question for you:

How is it that the earth's surface can act as IRF today at noon when the same point on it will be going at 2000 miles/hour (roughly) in the opposite direction at midnight (12 hours later)? That's quite an acceleration! Almost as if the surface of the earth is on one big giant 8000 mile diameter roller! I guess it can't be an IRF either by your argument.

Please continue to reason as you see fit!

WindGrins

I have already answered that question several times. Here is the answer again:

When applying the equations of motion for problems on earth, it is common practice to “attach” a coordinate system to the ground and assume that this is an inertial reference frame. However, it is not quite, since the earth itself rotates and the earth in turn revolves around the sun, etc. However, the rotation rate of a (ground) reference frame attached to the earth is very small, and its acceleration is also very small, so for practical purposes it can be treated as an inertial reference frame.
To show this, let’s determine the rotation rate and acceleration of a ground reference frame attached to the earth (so that it moves with the earth).
The rotation rate of the earth is one full revolution (2π rad) every 24 hours. The angular velocity (rotation rate) of the earth is therefore w = 7.3x10-5 rad/s. This is equal to the rotation rate of the ground reference frame. As you can see, it is very small.
Therefore, a ground reference frame attached to earth can be treated (with a high degree of accuracy) as an inertial reference frame.

Here is the source: http://www.real-world-physics-problems.com/inertial-reference-frame.html

Compare that angular velocity of 7.3x10-5 rad/s to the angular velocity of 80 rad/s as the belt goes around the end cylinders! How many orders of magnitude greater is the angular velocity on the belt?

Face it, there is no comparison and the treadmill is indeed dead.

 

[profpangloss]

Not to put too fine a point on it, what absolute and utter rubbish!

Stop thinking treadmill- how about a half mile long mining conveyor belt? Does it matter if it goes round a drum at either end? if the belt is running at 15 mph, you have two minutes of constant uniform motion on top of it.

The treadmill may only have a few seconds where one section of the the belt is on top, with constant motion, but it is an endless belt, and apart from the length, no different to the mining conveyor belt as far as anything running on it can tell.

But I doubt you could even comprehend the concept; please prove me wrong.

Why should I stop thinking treadmill, when that is what the cart is running on? Show me a cart running on a half-mile long conveyor and I might consider it, but all I see is a cart running on a treadmill that has high angular velocity and acceleration. It is absolute and utter rubbish to show one thing and claim it is something else! A cart running on a treadmill is exactly equivalent to a cart running on a treadmill and nothing else!

 

[windgrins]

I have already answered that question several times. Here is the answer again:



Here is the source: http://www.real-world-physics-problems.com/inertial-reference-frame.html

Compare that angular velocity of 7.3x10-5 rad/s to the angular velocity of 80 rad/s as the belt goes around the end cylinders! How many orders of magnitude greater is the angular velocity on the belt?

Face it, there is no comparison and the treadmill is indeed dead.

OK, I'll bite, now I'll give you a thought problem:

Suppose if we could we built a TM with the belt going entirely around the world and we run it a 10 mph over the earth's surface. (yes, I know we don't have the engineering and money to do this but that's why we call it a thought experiment.)

Question 1. Since the accelerations are all the same on the TM roller as the earth, can this be a valid platform for this discussion. If not, why not?

Question 2. If it is a valid platform, can a small portion of it be simulated by our TM moving at 10 mph? If not, why not?

Your turn!

WindGrins

 

[Llyricist]

The shoes on the bottom of those treads aren't really motionless wrt the ground for 25 seconds at a time while the crawler moves at .45 m/s.

They must be accelerating, because they are connected to other shoes that are experiencing both angular and linear acceleration. /ppg

 

[Subduction Zone]

ppg, your misunderstanding showed when you altered the copy and paste you did of the article you quoted. The reason they put the word attach in quotes is because you cannot attach a frame of reference to anything. A frame of reference may have a zero relative velocity to an object, but it cannot be the object. For example, you can have an IFOR that has the a zero relative velocity to the top of the treadmill. That means that the bottom of the treadmill would have a velocity of twice the relative velocity of the top of the treadmill to the ground but in the opposite direction in that IFOR. And yes, the ends are accelerating, but that does not matter. The belt is not the frame of reference. The cart is only interacting with the flat top portion of the belt. If a scraper is taking off the pavement of a road ten miles away from you does it affect the road where you are right now? I don't think so.

Another way to look at it is to put the treadmill outside on a calm day. Let's orient it North/South and have the top moving South at ten mph. If a flatbed truck is driving south at ten mph both a person on the truck bed and a person standing on the treadmill will feel a "wind" of ten mph. The cart cannot see that it is on a belt and will react the same as a cart on the truck bed, or a cart in a ten mph wind would react.

Did you see that three different people or groups that made carts have tested them on treadmills independently of each other? They were spork and JB of course, Mr. Goodman, and the last was from an article recently quoted by someone that I forgot, sorry. None of these people were aware of the others treadmill tests, yet they all did them. It is time to wonder why ppg.

 

[phunk]

Since the "X" is accelerated in the frame you are using, and the "X" is painted on the belt, the BELT is accelerated in the frame. There is no way out of that for you.
Now, since the belt is a continuous loop, and it undergoes acceleration in some places, how can it not undergo acceleration in all places? Is it because the acceleration takes place only at the ends, where it goes around the cylinders?
The motor is only at one end of the belt, yet when it accelerates the belt, the entire belt must accelerate, or do you not agree with this?
Since the ends of the belt going around the cylinders undergo acceleration, that acceleration must be transmitted along the entire belt, in the same way the motor transmits motion along the entire belt.
There is no way you can talk around this with your babble! You cannot isolate the top of the belt from the forces acting on the belt elsewhere. You cannot "attach" an IFOR to a belt that is rotating in that frame, as the "X" would definitely be doing. You cannot base a FOR on a projection. Give it up; the treadmill is dead.

You might want to go back to high school physics. Acceleration is a change in speed OR direction. Different parts of the belt can undergo different accelerations. For example, the top of the belt can be at a constant velocity while the end is accelerating around the roller to the other direction.

 

[jadebox]

You might want to go back to high school physics. Acceleration is a change in speed OR direction. Different parts of the belt can undergo different accelerations. For example, the top of the belt can be at a constant velocity while the end is accelerating around the roller to the other direction.

That's right. It's obvious that, from any inertial frame of reference, the "X" is moving at a constant speed and direction while on the top of the treadmill and interacting with the cart. It is not accelerating.

-- Roger

 

[windgrins]

Did you see that three different people or groups that made carts have tested them on treadmills independently of each other? They were spork and JB of course, Mr. Goodman, and the last was from an article recently quoted by someone that I forgot, sorry. None of these people were aware of the others treadmill tests, yet they all did them. It is time to wonder why ppg.

Andrew Bauer apparently did it also for a private demonstration in the offices of Aerovironment for Dr. Paul MacCready on a TM he purpose built for the demonstration.

 

[Subduction Zone]

Oh my, the third example may have come from humber himself

But then humber does have a tendency to shoot himself in the foot. Here is a link to humber's post:http://www.internationalskeptics.com/forums/showpost.php?p=7288781&postcount=9610

Did humber get that article from someone else here or did he actually find an article that supported everything the "carteers" claim and post it for some strange humberian reason?

 

[Subduction Zone]

Andrew Bauer apparently did it also for a private demonstration in the offices of Aerovironment for Dr. Paul MacCready on a TM he purpose built for the demonstration.

Yes, humber may have copied an article of Bauer's and not given him the credit due. That is typical of him.

 

[windgrins]

Def Bods is asking a lot here Phunk!

You cannot "attach" an IFOR to an “X” painted on the top of the treadmill belt. That is a fact. Any frame of reference in which the “X” appears to be stationary would need to follow the “X” around the ends and would undergo acceleration. Any such frame would be non-inertial. Undeniable fact.

You can attach an IFOR to a projection of the belt, but the belt itself will be seen to be rotating in such an IFOR, meaning the belt is undergoing acceleration in that IFOR and it is not in uniform motion. Or as Llyricist said: “An IFOR that is based on the motion of the upper belt surface, will continue to move in that direction even as the belt changes direction.” A change in direction is acceleration.

Your problem is focusing on the projection, as if the cart is riding on that when in fact the cart is riding on the belt. The belt is not inertial as it is undergoing acceleration at both ends and it is not in constant uniform motion. Since the belt is clearly rotating in your chosen IFOR, the rotational energy of the belt is frame invariant, totally unlike the energy of the wind which is frame dependent.

You might want to go back to high school physics. Acceleration is a change in speed OR direction. Different parts of the belt can undergo different accelerations. For example, the top of the belt can be at a constant velocity while the end is accelerating around the roller to the other direction.

I thought it might be asking a lot for someone who doesn't understand IRFs to understand Deformable Bodies also!

WindGrins

 

[jadebox]

ETA: I see that Jadebox just expressed the same idea in the post above about the painted "X".

You actually said it earlier. I just translated what you said into terms someone not familiar with physics should be able to understand.

-- Roger

 

[windgrins]

Yes, humber may have copied an article of Bauer's and not given him the credit due. That is typical of him.

I don't remember who originally supplied it but there is a picture of the TM Bauer used in a personal letter to Paul MacCready below.

ETA: It was Bauer's son who originally posted the letter from his father's files.

I think this may be another but maybe not.

 

[Subduction Zone]

At any rate, we have three independent groups who all thought that DDWFTTW was possible. They all made working models. And they all tested them on a treadmill.

Of course those are not too believable. It must be a conspiracy of some sort I tell ya. The next thing you that will happen is that people will claim you can test airplanes by holding them still and use moving air to simulate flight

 

[tobermoryphil]

[qimg]http://www.nasa.gov/images/content/140911main_crawler1.jpg[/qimg]

The shoes on the bottom of those treads aren't really motionless wrt the ground for 25 seconds at a time while the crawler moves at .45 m/s.

They must be accelerating, because they are connected to other shoes that are experiencing both angular and linear acceleration. /ppg

Likewise the shoes on the horizontal top of the track could never be doing a constant 0.9 m/sec with respect to the ground either. Mind you, if the tracks were half a mile long, it would be different.

 

[Llyricist]

Or as Llyricist said: “An IFOR that is based on the motion of the upper belt surface, will continue to move in that direction even as the belt changes direction.” A change in direction is acceleration.

I wrote a little sloppily. Though what I wrote was true, your interpretation was not.

The belt, as a whole, does not change direction unless someone moves the treadmill. If someone did, then the belt would change direction.

The issue here is that parts of the belt change direction while the tread mill is in operation, not the whole belt.

Specifically, the parts of the belt with which the cart is interacting do not change direction or speed, and in an IFOR based on those parts, they have no velocity, acceleration, or power. (to speak of, small variations aside).

And if you claim the cart harnesses those small variations, you really have to define a mechanism by which the carts actually harness them, not vague hints and links to things that bare no relationship to the actual carts.