Gravity and Weightlessnes

[Howard LewisParticipant @howardlewis46836]

Just to take the thread off course a little.

Re The cage in the mine shaft when the haulage rope breaks and the safety brakes fail to operate.

The cage, and everything in it will begin to accelerate under gravity, at a rate of 32.18 f/p/s/s, until friction and air resistance limit it to a terminal velocity.

BUT, if the shaft is deep, so that the cage goes closer to the centre of the earth, and gravitational force is subject to the inverse square law, will it not actually reach a terminal velocity, until it eventually hits the bottom?

IF the shaft were infinitely deep, possibly the cage could reach the speed of light, in which case, presumably, no one would see the demise of the cage and its occupants.

The speed is unlikely to kill you, just the forces involved in decelerating to Zero in a VERY short distance.

Howard

[Tim StevensParticipant @timstevens64731]

Not quite, Howard. With no air resistance, first. As it approached the centre of the earth, it would accelerate more slowly, until when it was exactly central, there would be no acceleration, but it would still be going fast (too early in the morning to work it out). This is not terminal velocity unless the shaft ends here. If so it really is terminal. If the shaft continues, as the cage went further it would be slowed by gravity until at the surface in New Zealand (say) it would stop, only to fall back down again …

With air resistance there would be a reduction in speed proportional to the square of the speed (double the speed and there is four times the resistance), so the oscillations would be damped and the cage would come to rest at the centre.

You might like to think about the job of the cage winder if the cage goes past the centre of the earth.

With an infinitely deep hole, you would also have an infinitely large earth, with infinite mass, so infinite gravity. Digging holes in such a place would be impossible so the shaft cannot exist.

If the cage speed were to approach the speed of light (there is not enough room, though) it would become heavier, and the effect of gravity would increase in proportion. But its mass would also increase, so I leave you to think about whether it speeds up, slows down, or what.

And as the centre of the earth is a molten iron alloy, the miners in the cage would be toasted, then the cage would melt.

Happy thoughts

Tim

[SillyOldDufferModerator @sillyoldduffer]

Posted by Howard Lewis on 19/03/2021 08:01:32:

Just to take the thread off course a little.

Re The cage in the mine shaft when the haulage rope breaks and the safety brakes fail to operate.

…

Howard

I've been pondering JA's question too, but from a different angle.

I don't know if Davy Lamps depend on gravity or not. I think not, because the fuel is fed through a wick first by capillary action and then by the flame acting as a heat pump. As the lamp is shielded, I think it would burn despite the draught caused by dropping one down the shaft, provided it fell base first. The lamp would be even better protected in a cage.

Takes about 10 seconds to fall to the bottom of a 500 metre deep mine shaft, and the speed on impact will be about 100m/s (220mph). This compares with a car (not mine) capable of 0-60mph in 6 seconds, which accelerates about 4.5 times faster than the falling Davy Lamp, and I can't imagine the car effecting the lamp either?

The deepest coal mine in the UK was about 1400m deep. I don't know what average depth was, but I'd guess iless than 500m. Bet there's someone on the forum who knows.

I vaguely remember a nasty accident in the early 1970s at a South Wales Colliery where a rod in the braking system broke as a cage full of men approached the surface, causing them to smash into the winding gear and fall back down the shaft, I think about 15 dead and 10 seriously injured. Anyone know what the incident was?

It demonstrated accidents are often caused by combinations of circumstances. The rod was 40 years old and a single point of failure. Although designed with a 6x safety factor, bending forces hadn't been taken into account and these were significant each time the brake was operated, eventually causing fatigue cracks. The rod was hidden inside a spring assembly and couldn't be inspected easily. As well as a mechanical braking system, the cage was fitted with electric regenerative braking, which would have reduced the impact considerably. Unfortunately, faced with a run-away, the operator hit the emergency off button (as he was trained to do) and disconnected the entire electrical system, including the regenerative brake. Then there was nothing to slow the cage's fall.

As is often the case, the accident revealed a bunch of other problems. Due to unaffected underground workers trying to find out what was going on the mine's phone system overloaded and broke communication between the rescue party and the surface. In the confusion a number of key managers weren't contacted, which further delayed the response, including not enough ambulances when the injured reached the surface.

Which is a long-winded way of me not answering JA's question. Perhaps I should be a politician…

Dave

[Frances IoMParticipant @francesiom58905]

“Perhaps I should be a politician…” do you really want readers to lose all trust in your answers?

[John HaineParticipant @johnhaine32865]

I noticed that if I went round a sharp corner in my car with the windows closed and a/c on and recirculating one felt a sudden draft. I realised after a little thought that this is because the air just blown out doesn't "feel" the angular acceleration of taking the corner so in effect I'm rotating into the draught. In the case of the Davy lamp in free fall, I suspect that the fuel would carry on feeding along the wick but go faster as it doesn't have to lift against gravity, but the flame wouldn't know which was is "up", convection would stop, and it might go out as it burns all the nearby oxygen.

[BufferParticipant @buffer]

John I have also noticed the car air con thing. One thing that confuses me is that if my pants have been put away inside out. When I turn them the right way round they somehow turn themselves back to front at the same time. How?

[Another JohnSParticipant @anotherjohns]

"You are decending by vertical lift into a very deep coal mine and the only light is from a safety (Davey/Stephenson) lamp. The rope fails and the cage free falls to the bottom of the shaft. What happens to the light from safety lamp before you die? Comment: This has everything to do with gravity and weightlessness"

In the absence of "gravity induced" air flow, the lamp would go out. Now, how you'd have oxygen and no air flow in a vertical lift in free-fall, *that* is an interesting question!

Another interesting question – if you have liquid fuel, are in free-fall (say, in geostationary orbit) and are "weightless", how do you fire up a rocket engine? I mean, the fuel will just be floating about, not waiting at the bottom of the tank to flow into the engines…

[Tim StevensParticipant @timstevens64731]

Liquid Fuel for weightless conditions would be contained within a diaphragm, and forced out by gas pressure on the other side of the diaphragm.

The original problem is really a more complex version of the question 'What happens if you light a candle in a space ship in orbit?' The answer is that the flame goes out as the combustion products are not cleared away. But in a falling mine cage, there would be a significant draft, and so the lamp should continue to burn, even without gravity. And 10 seconds isn't long enough for any other effect to get in the way. This theory still awaits proof, you realise. Any volunteers?

Cheers, Tim

[Howard LewisParticipant @howardlewis46836]

As Tim rightly says, the shaft would have a finite length on earth, if open ended, the cage would be carried beyond the centre of the earth, and slowed by gravity before falling back.

So another discussion point; Would the oscillations of the cage about the centrepoint be Simple Harmonic Motion?

Acceleration proportional to Displacement.

Seconds out!

Howard

[JAParticipant @ja]

Up until the mid 1970s Tim would have been right. Gravity was needed to remove the burnt products and allow hot wax to build up below the flame so preparing the combustion process. The processes were dominated by free convention which is just another way of saying hot air rises due to buoyancy. This is very different from combustion using forced convection which relies on external energy such as the induced turbulence in an IC engine, the air flow from a gas turbine compressor or the pumps in a liquid fuel rocket engine. The forced convection quickly removes the burnt products with additional air and drives the heat transfer required to keep the flame alight.

By the early 1970s with advances in solving particular examples of the Navier-Stokes Equation (Google it if you want to know more) using rigorous mathematics it appeared that flames could occur to zero gravity. Instead of air and burnt products being transported by free convection they would diffuse through each other. The required heat would be transferred by radiation. The postulated flame would be very different to a candle. It was likely to be spherical, emit very little light and burn very slowly.

The experiment could not be done. There are deep mine shafts used for near zero gravity work but air draughts and time was a problem. Parabolic “flight” was over far too quickly. Naked flames were banned, absolutely, on space stations. However in the late 1990s an experiment was allowed on a space station which confirmed the hypothesis. I remember reading the first reports on the results just before I retired.

JA

Simple Harmonic Motion. (edit)

Edited By JA on 19/03/2021 18:17:04

I apologise for the different font. I wrote most of the above in Word and copied/pasted it. This seems to confuse the website.

Edited By JA on 19/03/2021 18:20:39

[Jim CahillParticipant @jimcahill55556]

The tutorial example with the hole through the centre of the Earth seems to have caused some comment. The simplistic analysis results in a harmonic oscillation of a body which is dropped into a hole through the Earth's axis of rotation.

All sorts of things are ignored, probably because it can only ever be a thought experiment. The analysis uses energy considerations and examines the Potential and Kinetic energies of the object at the surface and compares those to the Potential and Kinetic energies at the centre.

The simplistic Energy analysis leads to the conclusion that the object will oscillate from end to end of the hole.

A competent A Level Physics pupil should find it fairly straightforward to demonstrate that the motion most certainly cannot be Simple Harmonic. Having carried out that analysis it can also be shown that the “University approved solution” could scarcely have been further from reality.

I was fully aware that going underground used the Mass above to balance the attraction of the remaining mass of the Earth. I had only been considering above earth weightlessness, and should have restricted my comments accordingly.

As I recall, there were about 50 of us in that Physics year when the tutorial question was posed. We all bought into the argument and accepted the conclusion. We would not have been the first, or only group of students to be presented with that tutorial problem. The fact that the solution persisted is a fine example of the propagation of ignorance by Academia. I certainly walked right into it. Mea Culpa!

[Howard LewisParticipant @howardlewis46836]

Jim,

You did a good job!

You made us think!

Thanks

Howard

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