Ersatz Conjecture

[agor95]

Ersatz needs to be given another review. In honour of Grimer [2013/04] and Sanex [2020/10]

Here is the conjecture :-

Start with a steal ball bearing on a flat steel table [both are hard].

This is a control example were the force of gravity is vertical.

Well the ball is not going anywhere without a push.
If we did then vertical force would not change much.

We could slant the table and then the force against gravity would not be vertical.
The ball starts to move. I wonder if it's vertical pressure [inertia] is less.

So the ball speeds up and drops off the table.

What happens when the ball has a rubber layer. A thin layer of rubber.

The ball pressure due to gravity and the table is in effect a ramp.
That means the rubber is compress more on the uphill side so to speak.

Does this ball roll faster down the table?

Is there anything we can do to increase this effect if it does?

What about a slight step ramp?

Would a ball be pushed off the step with the rubber layer exerting a forward thrust then a vertical one?


All the above we are using gravity to compress the rubber layer.

What about the ball rolling around a circular hoop on the table?

Well the ball is push towards the centre of the hoop. It kind of acts like artificial gravity [Ersatz Gravity].

Hold on the the rubber is compress, but symmetrically. Also work is being done to deform the rubber. A hard steal would roll better!

What would happen if we implement the slight step that move out by a small amount?

If you think about it then a slight spiral out would cause the rubber to be less compressed on the leading side and more so trailing half. Would this cause the ball to roll faster than a hard ball?

Well this spiral can not go for ever. We could use a circle path to direct it back.
That would collide the ball with the existing track?

What about ramping the track down a little so another spiral could be used?

I wonder if this could caused the ball too speed up.

It could be sent up instead of down!

Are there spirals present in the path in the image below some vertical some horizontal.

All the Best