# Relativistic rolling tank

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

1. ### imaplanck.BannedBanned

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It seems to me he is.

I doubt anyone would argue that the ground in the tanks rest frame is effectually travelling at 0.866c, therefor the ground would be both length contracted and time dilated in line with gamma. Yet the bottom of the track never moves with regard to the ground, it is effectually the ground.

3. ### DaleSpamTANSTAAFLRegistered Senior Member

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Certainly not. Where did I ever say such an absurd thing? They are at rest wrt each other so there is no length contraction.

I know that I am talking about marks on the ground made by tank tracks, but you are trying to pretend that those marks can be considered to be a single clock at rest in the ground frame and they cannot.

-Dale

5. ### DaleSpamTANSTAAFLRegistered Senior Member

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How are you guys getting this? I must have worded something very poorly because you are both way off.

If the tank is traveling at .866c in the ground's rest frame then, by definition, the ground is traveling at .866c in the opposite direction in the tank's rest frame.

-Dale

7. ### imaplanck.BannedBanned

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Yeah I think I may have missed something.

Last edited: Jul 23, 2006
8. ### 2inquisitiveThe Devil is in the detailsRegistered Senior Member

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If the tank track and the ground are at rest wrt each other, then a clock will tick at the same rate whether located on the tank track or the ground, correct Dale? But a clock in the tank is not at rest wrt a clock on the ground. I stated the marks made by the track could be considered a clock. An observer in the tank would 'see' the tank thread and the ground clock ticking half as fast as his own clock. A stationary observer on the ground would 'see' the tank thread and tank clock ticking half as fast as his own clock. According to Albert. An observer in the tank would 'see' the ground and the tank thread contracted to half their rest measurements. An observer on the ground would 'see' the tank and tank track contracted by half their rest measurements. According to Albert. Each observer would 'see' the other as travelling half the distance in half the clock ticks. No true 'time dilation' or 'length contraction' would occur. According to 2inquisitive.

DaleSpam,
Would you like to reconsider which frame the clock is 'plainly stationary' in? The confusion is because the tank track cleats and the ground are not moving relative to each other, but the bottom of the tank track is moving along the ground at .866c, or vice-versa. There is no problem if Newtonian clocks and distances are used (no time dilation or length contraction), but if Special Theory is correct.....?

9. ### imaplanck.BannedBanned

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Yeah, I believe I failed to study the animations properly. I now see they are indeed correct. The cleats being equally spaced on both the top and bottom of the track in the first animation threw me off. I missed the obvious that the top of the track would also be travelling at 0.866c wrt to the tank in the tank rest frame(in the opposite direction).

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

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You are left with the paradox that, according to an observer inside the tank, the length of the tank tracks (top and bottom) have contracted by one half, but the distance between the axles that the tracks turn around has not changed.

11. ### PeteIt's not rocket surgeryRegistered Senior Member

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Correct - unless the tracks are physically stretched. If they are not able to stretch, and the axles are not able to move closer, then something breaks.

It is clear by looking at the ground frame that the track is indeed stretched.

12. ### imaplanck.BannedBanned

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Yes agreed, but what about simultanity. According to SR things that happen simultaneously in one frame aren't simultaneous in a different frame.

13. ### MacMRegistered Senior Member

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DaleSpam,

Interesting how you can get so deep in the trees that you don't see the forest. Nothing gets stretched and will break because nothing physically contracts. SR (as I have claimed numerous times) in nothing more than a useful mathematical construct but is only an illusion of motion measurement and not consistant with any physical reality.

Given your scenario when the tank is at rest to the earth and where the axles are 30 feet apart and the drive wheels are 3 feet in diameter:

1 - In the resting case the total length of the track is 69.4248 feet in the tank frame and earth frame. The circumference of the wheels are 9.4248 feet. You can take my word for it or calculate it yourself it is straight forward.

2 - Tank in motion at 0.866c relative to earth:

a - Earth frame: The ground track is 30 foot long. The distance between axles is only 15 feet and the upper track by velocity addition is 0.98974c and gamma would be 7.0 such that the track is only 4.28486 feet long. The circumference of the wheel is that of an ellipse with a 2/1 aspect ratio which has a 7.54094 foot circumference.

Total track length is 41.8258 feet; however it physical doesn't fit since the lower track is 15 feet longer than the axles driving it and the upper track is 10.71514 feet to short to reach the driving wheels since the axles are 15 feet apart.

b - Tank Frame: In the tank frame both the upper and lower track have a relative velocity of 0.866c and hence are both only 15 foot long sections but the axles are still 30 foot apart.

The circumference of the wheels is pi*d/gamma = 4.7124 feet.

The total track length is 34.7124 feet.

Again the problem is obvious in that the moving track sections are to short to fit the fixed distance between the axles.

Giving SR the maximum benefit of doubt and wraping excess track from the bottom and around the drive wheels to the upper track space, in case 2a above, you have 49.7124 feet of track now being contracted by a gamma of 7 or an upper track section of 7.1 feet.

Still 7.898 feet short of reaching the drive wheels.

This is a clear explanation as to why SR is simply crap. Tension in the track is not the same in every frame as claimed by SR's equality of frames physics. The track breaks in one frame but not the other.

I would like to thank you for posting such a clear explanation as to why SR is simply crap.

Last edited: Jul 26, 2006
14. ### PeteIt's not rocket surgeryRegistered Senior Member

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I see that you're assuming that SR is invalid before you begin. Do you think anyone else will accept that premise?

The bolded sentence is a mistake. Can you figure out why?

You've made a similar mistake here.

But how much track is on the wheel? Is it length contracted? Is it physically stretched?

This is where your assumptions comes back to bite you. If you assume that the track can't stretch or break, then you find that SR is invalid. So what?

Try again, Mac. First try it without the wheels - ie use wheels with a tiny radius.

In the tank frame, the upper and lower tracks are both contracted by a factor of two, and under enough tension to be stretched by a factor two. Total length = 60 feet.

In the earth frame, the lower track is 15 feet long when stretched from axle to axle. Its unstretched rest length is therefore 7.5 feet.
The upper track is 15 feet long when stretched by a factor of two and length contracted by a factor of seven. Its unstretched rest length is therefore 52.5 feet.
Total length = 60 feet.

Conclusion: According to SR, in both frame the track reaches perfectly around both axles when under enough tension to be stretched by a factor of two.

15. ### imaplanck.BannedBanned

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Jesus how do you produce such idiots? The reason the track doesn't snap is due to simultaneity. In the tanks frame of reference the axles would not be present simultaniously as in the ground reference frame. I refer the reader to the 'TRAIN PARADOX' where the doors shut simultaniously in one frame but not the other. I can see how my esteemed colleges could overlook such an obvious thing, but you obviously haven't understood relativity at all and need reeducation.

16. ### MacMRegistered Senior Member

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Pete,

“ Originally Posted by MacM
Nothing gets stretched and will break because nothing physically contracts. SR (as I have claimed numerous times) in nothing more than a useful mathematical construct but is only an illusion of motion measurement and not consistant with any physical reality. ”

“ Originally Posted by MacM
2 - Tank in motion at 0.866c relative to earth:

a - Earth frame: The ground track is 30 foot long.

Sorry Pete but you are flat wrong. I said in the earth frame. In the earth frame neither the earth nor the lower track in contact with the earth has any velocity and hence is not contracted. It remains 30 foot long. If you can't get past this you surely won't be able to make viable comments to the rest.

“Originally Posted by MacM - The distance between axles is only 15 feet and the upper track by velocity addition is 0.98974c and gamma would be 7.0 such that the track is only 4.28486 feet long. ”

The mistake I am afraid is yours. In the earth frame the upper track has a velocity of 0.9897c and has a gamma factor = 7.00. Your statements to the contrary does not alter that fact. It only makes you wrong.

“ Originally Posted by MacM - The circumference of the wheel is that of an ellipse with a 2/1 aspect ratio which has a 7.54094 foot circumference. ”

What don't you understand about the term aspect ratio of 2 for an ellipse? The circumference is calculated for the contracted geometry of the wheel. That geometry is less than the resting geometry. There is no stretch there.

“ Originally Posted by MacM - b - Tank Frame: In the tank frame both the upper and lower track have a relative velocity of 0.866c and hence are both only 15 foot long sections but the axles are still 30 foot apart. ”

So this scenario hasn't bit me it has bit you. I made no such assumption. I made a statement and this analysis proves it. It it does contract enough to maintain the total track length rquired then it damn sure would break and if it does break it can do so in one frame and not the other because they have different contraction factors.. THATS WHAT.

“ Originally Posted by MacM - This is a clear explanation as to why SR is simply crap. Tension in the track is not the same in every frame as claimed by SR's equality of frames physics. The track breaks in one frame but not the other. ”

Wonderful. Now please post the Rpm of the axle in your case. Try infinity.

1 - You cannot dodge a realistic case given actual rational dimensions for a tank and substitute an irrational example where there are NO wheels, hence no possible velocity of the tank, and think for one split second that you have somehow resolved the failure of the example I gave with your irrational example given a tank going 0.866c using zero diameter wheels.

Conclusion changing scenarios does not rebut the scenario given. Try again. Put wheels on your tank this time. The title of this thread is a bout "Rotating Cylinders" claiming cyulinders with no radius is the same as claiming singularities. Infinite mathematical results are meaningless.

Last edited: Jul 26, 2006
17. ### PeteIt's not rocket surgeryRegistered Senior Member

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Think it through, Mac. I know you can do it. Looking at the animations might help.

According to SR, how many treads are in contact with the ground at the same time in the tank frame?
According to SR, how many treads are in contact with the ground at the same time in the earth frame?
Why are these two numbers different? (Hint - the italicised phrase is important)

In the simplified case, the wheel rpm is very large, because the wheels are very tiny. So what?

Like I said, this is a simplified case to make it easier for you. If you can't properly apply SR to the straight track sections, you haven't a hope of handling the wheels.

18. ### PeteIt's not rocket surgeryRegistered Senior Member

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Ah, why not. I've nothing better to do anyway. 30 foot tank (axle to axle), 3 foot wheels.

When not rolling, the track is not stretched and has a total proper length of 69.4 feet.

When rolling at 0.866c, the track is stretched by a factor of two. Its total proper length is now 138.8 feet.

In the tank frame, this 138.8 feet is distributed like so:
• 60 feet on top, contracted by factor of two for a tank-frame length of 30 feet. This matches the tank-frame axle-to-axle length, as it should.
• 60 feet on the bottom, contracted by factor of two for a tank-frame length of 30 feet. Again, this matches the tank-frame axle-to-axle length.
• 18.8 feet around the wheels, contracted by a factor of two for a tank-frame length of 9.4 feet. This matches the tank-frame wheel circumference, as it should.

No problems so far!

In the ground frame, the 138.8 feet of stretched track is distributed like so:
• 105 feet on top, contracted by factor of seven for a ground-frame length of 15 feet. This matches the ground-frame axle-to-axle length, as it should.
• 15 feet on the bottom, not contracted, for a ground-frame length of 15 feet. Again, this matches the ground-frame axle-to-axle length.
• 18.8 feet around the wheels, contracted by a factor varying from 1 to 7. I haven't worked out the average length contraction (feel free!), but it needs to be a factor 2.53 if it is to match the ground-frame wheel circumference of 7.45 feet.

Here's your chance, Mac. If SR is consistent, then the average length contraction in the tank frame of the track around the wheel needs to be 2.53. Care to check?

Last edited: Jul 26, 2006
19. ### PeteIt's not rocket surgeryRegistered Senior Member

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We could also run the scenario where the tank is squashed rather than the axle stretched if you like. Or, pick a maximum stretch factor for the track and we'll figure out the speed where it breaks. Or go the whole hog and specify the Young's modulus and yield strength for the track and tank and we'll graph the proper tank length against speed up to breaking point if you like (assuming linear materials - I'm not up to anything too nasty!)

Last edited: Jul 26, 2006
20. ### PeteIt's not rocket surgeryRegistered Senior Member

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I've just noticed a mistake earlier in the thread.

Neddy's picture of the tank at rest is not correct. The tank at rest will look like a freeze-frame of the rolling tank in the tank frame.

21. ### MacMRegistered Senior Member

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10,104
Stop right here. No need to go further. In what frame do you conclude the tract is stretched by a factor of two? NONE. There is no frame where the tracks contract by 2.

Post each frame view of each track section just as I did.

Frame View:
Upper velocity
Axle Velocity
Lower track Velocity
Wheel Geometry hence circumference
collective perimeter of the track

Now do it correctly and stop making false statements.

22. ### MacMRegistered Senior Member

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10,104
Go ahead. If you do it properly and you will find that the track breaks in one frame before it would break in another. That falsifies SR.

23. ### MacMRegistered Senior Member

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10,104
So you want to claim that in a freeze frame view of the moving tank the circumference in once again pi * D? But in the actual tank frame it is pi * D / gamma.

I love it. So you claim that if we have a quick enough camera and take an instaneous snap shot of the tank there is no contracted track or alter wheel geometry where pi * D describes the circumference. But without the snap shot there is physical contraction, stress and the track breaks.

So all we need to do to resolve this conundrum is attach flash bulbs all around the tank and have them operate at a frequency high enough to release the track stress by reducing the contraction.

Nice theory.