# Relativistic rolling tank

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

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

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Mac, the proper length of the track is not frame dependent. Nor is the physical stretching. If you attach a strain gauge and digital read-out to the track, it will read the same in all frames.
When the tank is rolling at 0.866c, the proper length of the track is 138.8 feet.

In the tank's rest frame, the track is moving at 0.866c, and is contracted by 2.

Got a reading problem? Which part of the figures didn't you understand?

You're very sure of yourself for someone who hasn't tried working it through. Not scientific at all.

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

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Hi, Mac. By freeze frame, I certainly didn't mean a high speed snapshot of the moving tank. That would be stupid.
I meant a freeze frame of the first animation in the first post.

5. ### MacMRegistered Senior Member

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10,104
So then how do you justify your initial response saying the assumption that the chain wouldn't break was in error. Now you have flipped and want to claim different proper lengths of track in different frames and no stress nor breaking chain.

In the Tank resting relative to earth view track length is 69.4248 feet in all frames. The track length gets shorter in either view while moving, not longer to 138 feet.

From that length to the Earth view the length is 41.8258 feet which is not 2/1 as you claim.

From the tank view the length is 34.7124 feet which is 2/1 but it is inadequate track to reach the driving wheels of your tank. Streteching is irrelevant here.

You fool yourself for convience. If you mark the cleats every 30 feet such that a cleat is simultaneously at the tops and bottoms of both wheels at rest, you will find that those marks do not orient 180 degrees across the wheels in your stretched track view because the wheels have a different geometry and circumference.

Can you decide what it is you believe or is this all sort of by braile?

Ditto.

Like I said your unsupported claims don't change the facts. Now try it again using common sense and correct velocities in each frames view.

Do you still assert that in the earth view of the moving tank tha the lower track is 30 feet, the upper track is 4.2848 feet and the wheel circumference is 7.54094 feet?

If so you are lost.

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

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How many mistakes can you put in one paragraph?

• I never said anything about a chain, or about an assumption of the track not breaking.

The assumption you made in error was this: "Nothing gets stretched and will break because nothing physically contracts."

According to SR, the track must either stretch or break. If the tank is rolling at 0.866c relative to the ground, and the axle supporting structure is comparatively strong, then the track must either stretch by a factor of two or break.
• I never claimed different proper lengths of track in different frames and no stress or breaking on the chain. I'm sorry if you misunderstood my meaning - this may be my fault. Let me spell it out for you:

When the tank is at rest relative to the ground, the proper length of the track is 69.4 feet. This is the same in all frames.

When the tank is rolling at 0.866c relative to the ground, the proper length of the track is 138.8 feet. This is also the same in all frames.

The length of the track in the ground frame gets shorter.
The length of the track in the tank frame stays the same.
The proper length of the track doubles.

Look at the animation, Mac. Think about what SR says about simultaneity.

Ditto

That was your incorrect assertion of what SR predicts.

Here (again) is what I assert that SR predicts:

In the ground frame:
The upper track is 15 feet long (length contracted from a proper length of 105 feet).
The lower track is 15 feet long.
The track around the wheels is 7.54 feet long (length contracted from a proper length of 18.8 feet).

Last edited: Jul 27, 2006
8. ### MacMRegistered Senior Member

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10,104

• And you here want to imply that it will stretch and not break? I don't think so.

9. ### imaplanck.BannedBanned

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2,237
It will do neither because according to general relativity a clock at the front of the tank will tick faster than a clock at the rear of the tank therefor there is no damn simultaneity between the front and rear axels.

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

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10,167
You don't object to a tank rolling along at 0.866c. Why should you object to elastic tracks?

But, it doesn't matter either way. I don't have a problem with the track breaking.

Specify the Young's modulus and yield strength of the track, and I'll tell you how fast SR says the tank can roll before the track breaks. I'll even do it both frames for you.

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

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Hi imaplanck,
The tank isn't accelerating, it's cruising at 0.866c.

12. ### imaplanck.BannedBanned

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2,237
..........Ah you are right.

Can you tell me is this belt breaking generally accepted do you know? because I dont see that as acceptable myself. Strictly for the reason that it wouldn't be stretched in the ground rest frame so therefor why would it break in that frame, yet both frames are just two view points of the same event.

Last edited: Jul 26, 2006
13. ### imaplanck.BannedBanned

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2,237
Never mind.
Who was the asshole who said that track was only stretched in the tank frame?

Ground
track contracts x4 axles x2 = track stretch x2

tank
track contracts x2 axles 0 = track stretches x2

Last edited: Jul 26, 2006
14. ### MacMRegistered Senior Member

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10,104
That wouldn't accomplish anything since you erroneously have claimed stress is the same in both frames. My claim is that you are not properly describing each frames view of the track velocity and the wheel geometry, hence calculating the total perimeter of the track.

I am getting two different lengths or contraction factors which would mean two different stresses hence track failure in one frame before the other a physics no no even for relativity.

You don't need to do calculations using yield or tensil strength for me, in case you have forgotten my background and experiences I have engineering training and designed a traction CVT for NASA which computes hertzian pressure based on contact patch size and aspect ratio for deformation of two cylindrical metal components pressed together under high pressure hence ultra high normal force. It also involves computing power slip in the traction fluid in the junction and power transfer based on shear of the fluid in the junction.

15. ### Neddy BateValued Senior Member

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2,548
I think you have misunderstood my picture. My picture is supposed to represent the tank and the embankment both at rest together.

Of course, a snapshot of the first animation would represent the tank's own rest frame in which the embankment is moving under it at .866c, but that is not what my picture is meant to represent.

I think that if you accept my picture, you will come to the conclusion that there is no "stretching" -- only length contraction in other frames.

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

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Yes, I realise that.

I know... but a picture of the tank at rest relative to the ground should look the same as a snapshot of the first animation.

There must be 22 spikes on the track no matter how it's moving or what way you look at it.

17. ### Neddy BateValued Senior Member

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2,548
If you look at one frame of the first animation, you will see that the embankment rulers do not match the rulers when the embankment is at rest. In my picture they do match, and they they appear exactly as they do in the second animation where the bottom half of the tread is at rest with the embankment. I know that it seems bizarre, but your animations lead logically and inevitably to my picture (if we want to consider both tank and embankment at rest). Otherwise, your first animation has length contraction applied to the embankment but not to the bottom tread which is moving at the same speed as the embankment it is touching.

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

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Hi Neddy,
When the tank is rolling, the tread is under tension and physically stretched (or broken) - The distance between spikes in the tread's rest frame (ie the tread's proper length) is twice its regular value.

So as the tank rolls faster and faster, the tread is stretched more and more (until it breaks), and there is more and more distance (in the ground frame) between where the spikes touch the earth.

19. ### Neddy BateValued Senior Member

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2,548
Hi Pete,

I do not understand why the bottom half of the tread would physically stretch. As you stated ealier,

so why is there no stretch evident in the rolling tank's frame?

Perhaps your explanation would make more sense if it was based on loss of simultanaety instead of physical stretching. Likewise, perhaps my picture would make more sense if it was based on loss of simultanaety instead of a physical change in the length of the drive-belt. As Dale noted earlier, there is no way to synchronize clocks around the perimeter of a rotating disk, so likewise, clocks around the drive-belt are only synchroinized in places where its velocity is zero, such as the bottom half of the tread in the second animation (where the so-called "stretching" is observed).

I think we have to attribute these changes in distance measurements to changes in space-time (where clocks are only sychronized in one frame). That is the best I can do to explain it, but I still believe in the accuracy of my picture of the tank and embankment both at rest.

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

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Hi Neddy,
That's correct - when rolling, the track is physically stretched by a factor of two in all frames. This must be true - the stretching of the track is a physical fact, and must be agreed on by all observers. We know from the tank frame that be the track is length contracted, it must be stretched to fit around the wheels. Therefore the entire length of track (not just the bottom) must also be stretched by the same amount in the ground frame.

Length contraction! It's spelled out in [post=1100829]this earlier post[/post]. The track stretches by a factor of two, and is length contracted by a factor of two.

I haven't been worrying about clocks moving with the track (I still haven't got around to adding tank clocks and ground clocks to the animations). If we did, we would indeed find that they would stay synchronized with each other in any frame during a cycle (although their average time accumulation would match).

When on the bottom, the track clocks would tick at the same rate as the ground clocks. When on the top, the track clocks would tick at a different rate to both ground clocks and tank clocks.

It can't be correct, because it doesn't have enough spikes on the tread. Where do the extra spikes come from when the tank is rolling?

21. ### Neddy BateValued Senior Member

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2,548
Okay, I think I finally understand that part. You are saying that the length-contracted track would have to stretch in order to fit over the wheels. But then the physical stretching would cancel out the length contraction, and the geometric length would be forced to remain the same as it was when it was at rest with the embankment.

But Einstein says that Euclidean geometery fails for a rotating disk. If the outer edge of the disk is deforming to keep the geometry the same as it was before it started rotating, then that should cancel out the length contraction like it does with the drive-belt.

They were not meant to be spikes, but proper length measurements. If you consider them spikes it creates a paradox.

This what I was trying to say in the first place. The track is longer when it is rolling. That is why there are more ruler-marks on the track in your animations than there are in my picture of the tank and embankmnent at rest. It is not stretched, it is physically longer due to failure of Euclidean geometery to hold. That is why the number 138.8 works in your example, because if we go back to your "stretching" idea, we have this:

69.4 feet of track before the wheels begin turning. With the wheels turning, the track should be length-contracted to 34.7 feet except for the fact that it is stretched to a geometric length of 69.4 feet.

Where am I going wrong?

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

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10,167
Hi Neddy,
That's why I'm focusing mainly on the straight sections. The rotating disk problem is not an issue for the upper and lower track sections.

In the original animations, they were intended to be spikes.

Yes, that's correct... if you measure the length of the track using rulers in the rolling tank's frame, you measure a length of 69.4 feet.

I think we're on slightly different wavelengths - I'm not completely sure what you're thinking?

23. ### 2inquisitiveThe Devil is in the detailsRegistered Senior Member

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3,181
Pete,
What about the frame of an observer sitting on the bottom track? The tank and the ground would be contracted, according to this observer. Would the track fall off the axles in this frame?