# Relativistic rolling tank

Discussion in 'Physics & Math' started by Pete, Jul 20, 2006.

1. ### Neddy BateValued Senior Member

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Hi Pete, I have been using rotating disks and tank-tracks fairly interchangeably. They are both forms of a wheel, and the idea (I thought) was that the length of the outer perimeter changes when they are rolling, regardless of the shape of the wheel.

You are free to claim that, since you created the animations, but they can also be considered ruler marks, similar to the ones on the embankment.* In that sense, my picture demonstrates that the length is different when the track is not turning (69.4 feet versus 128.8 feet).

Okay, I think I get it now. Using rulers on the track itself, there are 128.8 feet, and that is what determines how much track "unrolls" per cycle.

I think we essentially agree on everything, but we might be looking at it slightly differently. I thought that the length of the track increased naturally, but now I can fully accept the idea that it occurs as a result of stretching. We both agree that it does increase when rolling, correct?

I am willing to concede that my drawing is not correct with regards to the marks around the outside being spikes. Would you say that the drawing is correct if the marks are considered attached-ruler-marks?

* Edit:
Since the ruler-marks on the tank were originally meant to be spikes, they do not necessarily mark off length in the same units on the tank as they do on the embankment. From my picture it appears that the units are twice as large on the tank.

Last edited: Jul 27, 2006

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3. ### imaplanck.BannedBanned

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Dont you mean the top track not the bottom?

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The track would also have to stretch in that frame (not go loose) for the whole proposition to hold water, wouldn't you say? My immediate estimate would be that it will also stretch.

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5. ### 2inquisitiveThe Devil is in the detailsRegistered Senior Member

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No, you can use either top or bottom of the track. The track is a flat 'band' that an observer could sit on (for a limited time

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) the top surface or the bottom surface. By using the bottom of the track (but the top part of the bottom thread), the ground and the tank will both be passing at .866c in this rest frame. However, the top of the thread will be moving at .866c in the opposite direction.

Come to think of it, an observer sitting on the bottom part of the thread would be at rest wrt the ground, but not with the top thread or the tank. There are actually three frames of reference in this gedanken.
(1) an observer at rest inside the tank
(2) an observer at rest on the ground
(2) an observer at rest on the inside part of the bottom thread
(3) an observer at rest on the top of thread

Both no. (2) observers would see the top of the thread and the tank contracted in her rest frame. Notice an observer on the ground would be at rest wrt an observer sitting on the bottom thread (but NOT wrt the observer inside the tank), they would both 'see' the same contractions. The bottom of the thread would not be contracted according to observer (2), but the top of the thread and the tank (and its axels) would be contracted.

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7. ### imaplanck.BannedBanned

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Yes exactly, so how could you have meant that then? We have already established that the tread will streach in the ground frame.

.......That is wrong.

Last edited: Jul 27, 2006
8. ### 2inquisitiveThe Devil is in the detailsRegistered Senior Member

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Threads don't 'stretch' in their rest frames. The bottom of the thread is 'at rest' wrt a ground observer (no. 2 in my example). Only the top part of the thread and the tank will contract in the ground frame.

9. ### imaplanck.BannedBanned

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....Yes so this is wrong:

Ill say it slow so you can understand.
THE TANK AND THE GROUND WILL ONLY BOTH CONTRACT IN THE REST FRAME OF THE TOP OF THE TRACK

10. ### 2inquisitiveThe Devil is in the detailsRegistered Senior Member

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imaplanck,
I've already conceeded that is made a mistake in the earlier post regarding the ground contracting in the bottom track frame. Now, suppose you tell me in which frame a thread 'stretches' in.

11. ### imaplanck.BannedBanned

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If you mean tread, it stretches by 2 in all frames.

Edit: actually what do you mean by thread?

12. ### 2inquisitiveThe Devil is in the detailsRegistered Senior Member

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Incorrect. The bottom of the tread does not stretch in the ground frame, or the rest frame of an observer sitting on the bottom track. There is no 'Lorentz extension', only proper length in the rest frame and lorentz contraction in relatively moving frames.

13. ### imaplanck.BannedBanned

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Jesus. Look I dont know what planet your on but the track does indeed stretch by a factor of 2 in ALL frames. Why correct me when Im correct?

14. ### 2inquisitiveThe Devil is in the detailsRegistered Senior Member

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No, you're not correct. The tread does not slide along the ground, the bottom of the tread is at rest with respect to the ground. The bottom of the tread is in contact with, and at rest wrt, the ground in all frames. The tank, the axels and the top part of the tread move wrt the ground. You seemed to be confused because the top of the tread and the bottom of the tread move in opposite directions. They are not in the same frame of reference while the tank is in motion wrt a ground observer, or according to an observer located on either part of the tread.

15. ### imaplanck.BannedBanned

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No you are confused. YOU ARE GROSSLY CONFUSED! You are correcting things I havent said for one thing.
The frigging track has to stretch to 2x its length in every frame for the whole proposition to work. And it indeed does. I AM CORRECT!
Get a lobotomy.

The tank tread does NOT loosen and fly off in any frame you care to mention! you are incorrect. You are also incorrect in saying a man on the bottom tread would experience the ground contracted and tank at the same time for the reason that you have just told to me. I corrected YOU on the bottom of the track not moving in respect with the ground, NOT the other way round you complete twonk.

16. ### 2inquisitiveThe Devil is in the detailsRegistered Senior Member

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You should have left the 'c' out of planck, moron. You are a plank. One last time, please read slooowly. The bottom of the track cannot contract in the ground frame. The top of the track does contract in the ground frame, it is moving wrt the ground along with the tank. You, and others, construed a false scenario to make things work, by incorrectly assuming the bottom and top of the track are contracted by the same amount in the ground frame.

17. ### imaplanck.BannedBanned

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YES that is correct! but I told you that first. You were the one who had to be corrected on that point.

NO! that is wrong it is not moving along with the tank it is moving in its own reference frame.

No we have constructed a true scenario by correctly assuming both the top and bottom tracks are contracted by the same amount in the tank frame.

Last edited: Jul 27, 2006
18. ### PeteIt's not rocket surgeryRegistered Senior Member

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Hi 2inquisitive,
You appear to be misunderstanding something.

Where has anyone said that the bottom of the track contracts in the ground frame?

Where has anyone said that the top and bottom of the track are contracted by the same amount in the ground frame?

Are you confusing stretching with contracting?

Do you understand that imaplanck is maintaining (as I do) that SR predicts that in the ground frame, the bottom of the track is stretched by a factor of two, and not contracted?

Why not? There is tension on the tread... so it stretches (or breaks). Just like a rubber band. Is a stretched rubber band not stretched in its rest frame?

19. ### 2inquisitiveThe Devil is in the detailsRegistered Senior Member

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posted by imaplank,

“ Originally Posted by dickforbrains
The top of the track does contract in the ground frame, it is moving wrt the ground along with the tank. ”

(imaplank>>
Both the tank axels and the top of the tread are moving in both the ground frame and the bottom tread frame. The top of the tread does not move in its own reference (rest)frame, numbnuts.

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posted by imaplank,
Yes, both top and bottom tracks are contracted by the same amount IN THE TANK REST FRAME. Who disagrees that this is what SR predicts? The problem is in the ground frame and the bottom track frame, kapeesh?

Pete,
“ Originally Posted by 2inquisitive
The bottom of the track cannot contract in the ground frame. The top of the track does contract in the ground frame, it is moving wrt the ground along with the tank. You, and others, construed a false scenario to make things work, by incorrectly assuming the bottom and top of the track are contracted by the same amount in the ground frame. ”

That the paradox, Pete. The bottom track does not contract in the ground frame, but the top of the track does. To fix this paradox, you now claim this:
Pete,
Are you claiming that a stationary observer on the ground will see the bottom of the track stretched by a factor of two? Does this same observer see the top of the track stretched by a factor of two? Where are the axels located in this scenario? No, in the ground frame, the bottom of the tread will be its proper rest length, but the axels, top tread, and tank will be contracted, according to Special Theory. Did you read my statement as to what SR predicts? Here it is:
an observer sitting on the bottom part of the tread would be at rest wrt the ground, but not with the top tread or the tank. There are actually three frames of reference in this gedanken.
(1) an observer at rest inside the tank
(2a) an observer at rest on the ground
(2b) an observer at rest on the inside part of the bottom tread
(3) an observer at rest on the top of thread

Both no. (2) observers, a and b, would see the top of the tread and the tank contracted in their rest frame. Notice an observer on the ground would be at rest wrt an observer sitting on the bottom tread (but NOT wrt the observer inside the tank), they would both 'see' the same contractions. The bottom of the tread would not be contracted according to observer (2), but the top of the tread and the tank (and its axels) would be contracted.

20. ### imaplanck.BannedBanned

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No, Both the tank axels and the top of the tread are moving in both the ground frame and the bottom tread frame. The top of the track is moving in the tank rest frame aswell as the ground frame therefor the top of the tread does move in its own reference (rest)frame, numbnuts.

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..........So how do you get that much but then say this:

Last edited: Jul 27, 2006
21. ### PeteIt's not rocket surgeryRegistered Senior Member

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Did you read the first post of the thread, 2inq?
"Notice how the portion of the track in contact with the ground is stretched to twice its proper tread spacing."

Yes - I thought that was clearly stated in the opening post.

Stretched by two, and length contracted by seven.

Come on, 2inq, I've spelled this out with Mac already, and it's clearly shown in the animations. In the ground frame, the axels are half their proper distance apart.

The entire tread is stretched by a factor of two, unless the axles are squeezed together or the tread breaks.

All correct here!

Have you picked up yet that in the ground frame, there is seven times as much track in the upper section as in the lower section at any given instant?

22. ### 2inquisitiveThe Devil is in the detailsRegistered Senior Member

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Pete, I understand what you are doing. You are beginning your exercise in the tank's rest frame, and transforming from that frame to the ground frame. I am beginning in the ground frame. According to Special Theory, there are no preferred frames.
Suppose Stella is driving the tank, and Terence is the observer on the ground. The tank and the axels will be contracted from what they were before Stella began her drive past Terrence. Because the bottom of the tank tread is at rest with the surface of the Earth and Terrence, it is not contracted, but the axels are moving wrt the surface and will be contracted. So, how do you explain this:
Pete:
I understand you are stating the top of the tread is contracted more than the tank axels, so the top of the tread would have to stretch wrt the axel spacing, but I am speaking of the bottom of the tread in the ground (Terrence's) frame, as I have clearly stated all along. According to Terrence in the ground frame, the bottom of the tread is its proper length, the axels of the tank are contracted by 1/2, and the top of the tread is contracted by a factor of seven. You have to use the velocity addition formula for the top of the tread, or else it is travelling faster than light according to the ground observer. The following statement is reversed when beginning the exercise in the ground frame:

23. ### imaplanck.BannedBanned

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Why are you focusing on the track being contracted in either just the top or the bottom of the track? The proper length of the track (overall length) will still be increased by a factor of 2. Why cant you get that?

Last edited: Jul 28, 2006