OT (?): Lithostatic pressure ...

[The Natural Philosopher]

*Wooden* be straight? Orange juice at lunchtime?

[Robin]

ISTM that is anything but the obvious answer for a straight tunnel bored for a train up a mountain (or for a hydroelectric scheme).

[Robin]

Since you insist on being explicit about assumptions[1] I am surprised you have not made clear if you really mean the Earth as opposed to an idealised, homogeneous sphere.

And if a tunnel is both (a) straight and (b) between 2 points on the surface of a sphere then I don't see the need for any additional condition such as "tangential to the curvature of the earth at that point". At least, not in Euclidean space: I've forgotten what little I learnt of other geometries.

And I am

[1] I had indeed assumed the question was about what would happen to a ball placed in the middle of the tunnel.

[Tim Streater]

Further, since someone mentioned linear accelerators, the one I worked at is 2 miles long and straight and is not between two points on the surface of the Earth.

[Tim Streater]

Tartiflette and a glass of box.

[Tim Streater]

As far as I'm aware, we're talking about linear accelerator tunnels.

[The Natural Philosopher]

That wasn't part of the original questions specification which is why I did see the need..

... then I don't see the need for any additional

[The Natural Philosopher]

I thought it was road and train tunnels meself.

[Tim Streater]

Why is anyone asking about which way a ball would roll then? As I said, a long, straight, tangential in the middle, tunnel is the only interesting one.

[Robin]

I'd assumed 'cos not everyone met the issue in maths/physics. No sin in that: I am ignorant of very many things which others learnt from their O level woodwork, GCSE geography etc etc

[The Natural Philosopher]

Does your wife know this?

[dennis]

8<

The chances of the land at the exits being level is pretty remote. Therefore for a real tunnel, even if straight, the ball would roll towards one end.

Maybe you should call it a straight and level tunnel?

[Tim Streater]

The state of the land at the exits is neither here nor there. It's the tunnel that counts. The Stanford Linear Accelerator is 2 miles long, straight, and visible from space. It's on the surface of the planet, and is really a long building, not a tunnel, although it feels like one when you are inside it.

Actually no I tell a lie, what one is in is the klystron building. The klystrons feed RF power down to the linac, which is a few feet underground. I never went down there. But that will also be straight.

I did. Anyway, I'm officially bored with this thread now.

[Tim+]

True, but asking what effect would it have on a ball kinda implied horizontal dontcha think?

Well again I think most folk would assume I was referring to a theoretical perfect sphere.

See above

Well I didn't state the starting position of the ball (my mistake) but I was wondering if it would roll to the middle from the entrance (which it clearly will).

Tim

[Tim+]

No it wasn't. I forgot to state the starting position. ;-)

Tim

[Tim+]

No, because "level" implies a relation to the direction of gravity. A long level tunnel would curve around the earth. A long straight tunnel wouldn't.

Tim

[RayL12]

Taking into account what has been said here already: Consider a straight tunnel through two points on the Earth. The tunnel will have a centre well below the Earth's surface. Assume the Earth surface to be perfectly formed arc, and, soil density to be homogeneous throughout. The tunnel is straight beyond any physics that say it may be other than straight, including 'line of sight'.

Given that the centre of the tunnel would be the deepest point, it has the greatest force/density of gravity. Meaning, either side of centre, and, each point further from the centre, is a decreasing force of gravity. Which, to my knowledge, only occurs when going 'uphill'?

[Tim Streater]

No. Once you go below the surface of the planet, gravity decreases linearly from surface to centre. So, zero at the centre of the Earth. Above the surface, it decreases in accordance with the inverse sq. law.

[The Natural Philosopher]

Well no, it doesn't.

"The pull of gravity is zero at the center, since the entire planet pulls on you from all directions. It falls off from 1g to 0g (more or less smoothly, but not uniformly) as you go from the surface to the center. *But due to the greater density of the core, it actually increases until you reach the bottom of the mantle.*

So, zero at the centre of the Earth.

And in between, its not simple.

[Tim Streater]

Well yes, but RayL12 was positing uniform density etc for simplicity.