2inq said:

Length contraction of the tread when beginning in the ground frame is what I am questioning. In the ground frame, both **the total length of the bottom tread** and the axels are contracted by a factor of two, but the top tread is contracted by a factor of seven.

These don't go together... You have either two factors of two, or a factor of one and a factor of seven, depending on exactly what you mean:

In the ground frame, both the track on top and the track on bottom are half the tank's proper length.

In the ground frame, the track on the bottom is not length contracted, and the track on top is length contracted by a factor of seven.

I don't see where either the top or bottom of the tread is 'stretched by a factor of two'.

If the track is stretchable and under tension, then it will be stretched, right? I suggest that it is, in fact, under tension.

The top of the tread would have to stretch 3 1/2 times the axel spacing, or break.

I don't think so... let's see why.

The spacing between the 'cleats' or measuring marks would have to be their proper rest length on the bottom...

Their proper

*stretched* length, if the track is under tension.

... and contracted by a factor of seven on the top,

Contracted by a factor of seven from their

*stretched* length, if the track is under tension.

while the total length of the tread would be contracted by a factor of two on the bottom and seven on the top.

The

*stretched* track (if it is under tension) would be uncontracted on the bottom, and contracted by a factor of seven on the top.

Let's say the track's proper length when not under tension is 8 metres, with 8 cleats, one every metre. Say the wheels are very small, and the tank is 4 metres long.

So when the tank is sitting still, there are 4 cleats on the bottom and 4 and top, one every metre, right?

Now, let's look at the tank rolling at 0.866c in the ground frame. The question is

*Is the track stretched, and by what factor?* Let's call this factor

**S**. If the track is not stretched, then

**S** will be one.

The proper length of the track will be 8

**S** metres, with one cleat every

**S** metres.

In the ground frame:

The tank will be 2 metres long.

There is 2 metres track on the ground, not length contracted. There will be 2/

**S** cleats in this section.

There is 2 meters of track not on the ground, length contracted from 14 metres. There will be 14/

**S** cleats in this section.

So, the total proper length of track (working from the ground frame) must be 16 metres, containing 2/

**S** + 14/

**S** cleats. This gives us to ways to work out

**S**:

Total length of track = 8

**S** metres = 16 metres, therefore

**S** = 2.

Total number of cleats = 8 = 2/

**S** + 14/

**S** = 16/

**S**, therefore

**S** = 2.

So working from the ground frame, we find that the track must be under enough stress to stretch it by a factor of 2.