KBGS Old Boys' Forum

A place to discuss Keighley Boys' Grammar School. 


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Bernard: Summat for nowt

Bernard there is nothing wrong with wanting ‘summat for nowt’. It is after all a Yorkshireman’s credo.
I am going to suggest the possibility of such and to appreciate the idea properly you will need to suspend all arguments of practicality and trivia like the earth not being a perfect sphere since it is an irrelevance in this case and now seize the concept as being potentially realisable.
Imagine a straight tunnel from point A on the surface of the ‘perfectly spherical’ earth to a point B on the same earth and that tunnel being 5000 km long. A and B could be two major cities.
The centre of the Earth, C, is the same distance from A as it is from B. The triangle ABC then is an isosceles and the tunnel is the base of that triangle. AC and BC are radii of that earth and AB is a chord of the circle with centre C.( I say all this so you can draw it.) M is the centre point of the tunnel and MC is the height of the triangle ABC.
As one travels along the tunnel from A to M one approaches the centre of the earth, that is, we become closer to it, and the point M is the closest we can travel to that centre, C. In effect since we are getting closer to the centre of the earth as we travel, we are going ‘downhill’, despite our tunnel being straight in all understood ways. If we are going ‘downhill’ we shall be accelerating due to gravity. That acceleration will continue until we reach the point M at which time we will begin to slow as we go back ‘uphill’ towards B and gravity now acts as a brake.
If we have magnetic suspension giving close to zero friction and ignore for the moment air resistance our train will finish its journey by rolling quietly to rest at the platform in B without the application of mechanical braking.
Now we can judge empirically how much the journey might be slowed due to friction and air resistance and apply sufficient impetus at the commencement of the journey to counter these effects.
The whole journey can be made using only this initial impetus and no further input would be needed. Gravity is virtually, to all intents and purposes, the sole source of energy.
Not exactly ‘summat for nowt’ but a very cheap way,( after the expense of the tunnelling has been met,) of getting from A to B.
It would be a nice exercise if you have the time and inclination to calculate maximum speeds and time taken for the journey. It might surprise you.

Re: Bernard: Summat for nowt

Is this the tunnel?
click here

assuming it is, then the train will try to fall towards C (not M) and you will have to devote a lot of energy towards creating the "zero friction" (overcoming the tendency to move towards C)

so it would not be summat for nowt

Re: Bernard: Summat for nowt

just to add, it's very similar to a funicular railway that has two carriages counter-balancing each other...or a train starting at the top of one mountain falling into a valley then ascending a similar mountain on the other side (the train track looking like a U sideways on)

gravitational potential energy swapping for kinetic energy and back again

Re: Bernard: Summat for nowt

Interesting thought Arthur, but Chris has an excellent response. Your idea is complicated by the constantly changing force vector due to the position of the tunnel relative to the center of mass of the earth. Na then....IF the tunnel was to pass through the center of mass of the earth, gravity would act directly in the line of travel. If we could provide a perfect vacuum there would be no air resistance to overcome (no work). Also friction would not enter the picture since there would be no side loads involved. The result would be simple harmonic motion. I haven't given this a great deal of thought but I suspect that this motion would continue as long as there was no changes to the factors making up the thought experiment. QED perpetual motion. Again though, you don't get summat for nowt because if you try and utilize any of the energy, your vehicle/machine would eventually come to rest at the center of mass and you finish up with a bloody great long tunnel that's blocked up in t'middle.

Years at KBGS e.g. 1958-1964 (optional) 52-57

Current location (optional) USA

Re: Bernard: Summat for nowt

a video demo...kind of

Re: Bernard: Summat for nowt

Wouldn't it have been great to have science demos like this at KBGS?

Re: Bernard: Summat for nowt

Never noticed this thread before - very interesting.
Three lessons to be learnt.
1. You can't get summat for nowt.
2. Never take on Chris in matters scientific.
3. Don't use a dummy in a demonstration when you could have used Clarkson.

Years at KBGS e.g. 1958-1964 (optional) 58-65

Current location (optional) leeds

Re: Bernard: Summat for nowt

Great news,lads! A French computer programmer has cal culated pi to almost 2700 billion decimal places. I'm just checking to see if he's made any mistakes, but it may help you to square the circle in the meantime.

Years at KBGS e.g. 1958-1964 (optional) 55-60

Current location (optional) Harrogate

Re: Bernard: Summat for nowt

Stuff that Napoleonic metricism.

What's that in fractions?

22 over 7 (d'apres Albert AND Beaky) to "almost 2700 billion decimal places" sounds a bit multi-cultural - but that's what we're supposed to be good at.

(Also 2700 billion decimal places looks fractionally imperious.)

Why have the French got so interested in this at such a late date? Beats me. (As usual)

Years at KBGS e.g. 1958-1964 (optional) 1952-60

Current location (optional) Lincoln