MOKE UP A GUM TREE
Mechanics – Class 7 – Main Lesson
“What did you do at school today children?” asked Mother of her twins, Tan and Lily.
“We hung Nyyl’s Mini Moke up in a tree.” Answered Tan carelessly as he colored in a drawing on his home assignment.
“No seriously; you know your father and I are interested in your education (it costs enough!) – what did Tan mean Lily?”
“That’s right;” said tan’s blond 13-year-old sister “using a pulley we lifted the car right up the big gum tree – about 4 meters high! It sure looked funny; the whole school came to have a look. ‘How did you get it up there?!’ they all said. We showed them that just a couple of children could pull the chains – it took a fair bit of time but – and move the Moke up and down as we liked.”
“Good heavens, and what was that lesson supposed to be, vehicle transport?” Tan stopped for a moment, a puzzled frown crossing his dark features. “Um, it’s a kind of toss-up between science – physics in particular – and maths. Nyyl told us it could be programmed in either, depending on the emphasis; and as his emphasis was going to be the expression of The 7 Mechanical Principles in equation form, with lots of problem-solving, it would be maths.
We’re doing it as a middle lesson, in the Numeracy stream – the Applied Number (Will) stand actually. Nyyl said there’d be a lot of hands-on stuff right through the three weeks.” Tan went back to the mechanical device he was making; again something to do with cars, but only a model car this time. He was tying a rubber band to the tow-bar and sliding it down a tilted painted board.
Lily came back from the bookshelf with an encyclopedia and began looking up the word ‘quoin’!? Mother went on with her needlework. “A needle’s a wedge.” Remarked Tan, but she ignored it as she considered the spiritual implications of this 7 Mechanical Principles unit.
Even though there was a particularly evident cerebral element in Mechanics Maths, this was still a middle lesson, with its heart/art imperatives. Numeracy is the 2nd stream of the 4 middle lessons, calling on the astral forces in the child’s soul – especially as these impress upon the diaphragm. “I wonder if Nyyl will explain how the diaphragm functions as a mechanical principle – physically at least?”
Mother pondered on the miracle of diaphragmatic breathing; of how the ‘fence across’ works according to mechanical principles – based on low and high pressure. More important though are the two alternating forms the diaphragm assumes with each breath cycle.
On the in-breath, it is an astral form, a kind of weight-bearing lunette – when we breath out, this remarkable organ becomes rather a wedge. This presses up between the lungs forcing exhalation – the wedge is of course a triangular – etheric – form. So, astral/lunette/abdomen/in-breath – etheric/triangle/thorax/out-breath. What synchronicity, what living mechanics!!
Numeracy is the Taurus subject of the 12-fold Subject Zodiac. Of the 12-fold Philosophical Zodiac, Rudolf Steiner ascribes Rationalism to The Bull – and by inference to mathematics. There are few subjects where the power of the rational is better expressed than in Mechanics.
There is an unambiguous logic, a transparent rationale, which creates the various ‘mechanical advantages’. The children find this inwardly gratifying – empowering even. When we look across to its complement, Scorpio, we find the aspect of the 12-fold Ego to be Dynamism – in both a human and mechanical sense!
This infers raw, non-rational power, as perceived in things like magnetism and gravity. These powers (as the word dynamic means) cannot be rationally explained; yet they form an intrinsic part of the study of Mechanics. Mother watched son Tan with his car and rubber band on an inclined plane. The will ‘quality’ of Taurus can certainly be exploited with enthusiastic 13-year-olds.
“We had a story about the 7 Mechanical Principles, didn’t we Lily.” Said Tan looking up at his adoring mum “It wasn’t a baby-type story, more a real-life tale about people who got out of tight spots by using one or other of the 7 Systems.”
“And what are they?” asked Mother curiously.
“Um, there’s the Lever – actually there are three kinds of lever, 1st, 2nd and 3rd Class. Then there’s the Inclined Plane; that’s what I’m playing with now – er, I mean working on – for my home assignment. After that was the Wheel, which includes the axle; then Gearing – and the Wedge. Hey Lily, is a quoin really a wedge? Yes? Anyway number 6 is the Screw. We learnt about Archimedes’ inventions with that one; how he just turned a big screw to lift water. Finally there’s the Pulley – the Moke in the tree remember!
Some of the stories about Mechanics were from history, other Nyyl made up. They were both good weren’t they Lily? But my favorite thing was going outside and experimenting with different systems.”
“Nyyl said there were for paths to understanding Mechanics,” continued Tan without pause “Story; Description; Experience; and Formulae – in that order of presentation; from Imagination to Conceptualization I think he said? Anyway, with levers we played on a seesaw, and moved rocks with crowbars; even inside there were things to do, like using scissors, a hammer, a spanner – all lever actions!”
“What about how the 7 Principles are found in us Tan? I like it when Nyyl told us we are levers in our limbs, from finger down to leg even. A finger can open a letter, a leg a door! Archimedes came in here too; he was the original Master of Mechanics, in Greece anyway. He said that he could move the whole world (HE knew it was a globe!) if he had a long enough lever, and a fixed base to lever it with.
He was right too, because he worked it out mathematically! I love those formulae; they made complicated things seem so simple. The formula for all the levers in the world is based on just three elements, Effort, Fulcrum and Resistance – E, F, R. The 1st class lever always has the fulcrum in the middle, like a surfboard or a box trailer.
The formula is weight X length = weight X length – WL = WL, so the see-saw is balanced.
The 2nd class lever has the fulcrum at the end, like a bottle opener or a wheelbarrow. We had fun with that one outside, seeing how harder it was to push if someone sat on the handles rather than the wheel. The formula was the same though, WL = WL. An outstretched arm carrying a weight is a 2nd class lever. We balanced an upright broom on our hands for this one!
The 3rd class lever merely reverses the resistance and effort, as in a fishing rod. I did a funny drawing in my book with this one – I had a straining fisherperson complaining in the cartoon bubble about the effort to lift the rod, and the fish obligingly informing us that she was the resistance (before she jumped off the hook that is!!). Then there was a voice in the man’s tummy telling us it was the fulcrum – ha, ha, ha… again it was WL = WL.”
“A front-end loader is also a 3rd class lever; I drew one of those” added Tan helpfully “I didn’t put jokes in mine; Mechanics is a serious subject you know, especially front-end loaders! A straight arm is also a 3rdclass lever, as it the jaw – lever means ‘to raise’.”
Mother smiled and went back to her needlework – or ‘wedgework’! she thought of the Four Laws of Mechanics she had learnt at school, and of how these were an expression of the 4 Elements (she didn’t learn that at school). They apply also to the human being, not only through an embodiment of fire, air, water, and earth, but even as they affect the four temperaments.
This 1st Law is Dynamics, that Scorpio-ego aspect as found in dynamos like Joan of Arc and Alexander the Great. These are the motive forces, or power, which initiates all mechanical activity – powers like gravity and heat. This is naturally the ‘fire’ law, expressing as the choleric temperament.
Law 2 is Kinetics, or how something moves; this is the ‘air’ law, and relates to the sanguine temperament. It is even noticeable how descriptions of these 4 laws are enjoyed differently by children of different ‘humors’.
The blue-eyed cholerics love anything with a dynamics emphasis; as do the hazel-green-yellow eyed with kinetics, like the penetrating power of a turning crew for instance.
The 3rd law is Inertia; this is when something occurs consistently – unchanging. It is the water-phlegmatic law, seen to perfection in a long, low wave, like a tsunami as it travels thousands of miles without abating. When a giraffe runs, its head is in a state of inertia, remaining on the one steady plane as the rest of it rolls along in a slow-motion gallop! Brown-eyed phlegmatic children love inertia descriptions, exercises and activities.
The last, the 4th Law of Mechanics, is Statics, or forces of equilibrium, in short, stillness; as achieved when the gold and weights in the balancing scales are equal – static means ‘to stand’. This expresses the mineral element, and by soul extension, the melancholic temperament – as found in black or grey eyed children (adults are different as to the eye color-temperament characteristics).
“After the three levers, we did the Incline Plane.” Said Tan proudly holding up his own inclined plane home assignment. This was on a sloping sheet of Masonite down which the toy car rolled before being stopped by the rubber band. Tan had to measure the changes when the board inclined at a steeper angle off the horizonal.
At 35° the car traveled only 18cm – at 45°, 21cm – 60° it ran down the hill for 36cm – and so on. The inclined plane works on the principle of gravity, the steeper the plane, the more effort to travel up it – and less effort to go down! Examples were given: a road winding up a steep hill; loading a truck with a board; and steps – the two extremes being the horizontal and vertical planes of the treads and risers.
As you lengthen the inclined plane, you reduce the effort proportionately – if I double the height, I double the effort – and so on.
Equilibrium is achieved in the following example – it takes 25 kilograms of effort to maintain a 50-kilo weight on a slope of 10 meters length with a rise of 5 meters:
To find the Mechanical Advantage of the plane (the reason the ball doesn’t roll down), you just divide the length of plane by height.
“What did you do with the 3rd Mechanical Principle, the wheel?” asked Mother, her needlework now static!
“Ah,” replied Lily, brushing back her long, blond hair as she surfaced from her quoin drawing “that was the school wishing well. We experimented with different bucket weights (resistance R) and handle lengths.
We learnt more about Pi here too – you know, Pi is the ratio of a circle diameter to its circumference 1:1.314. Anyway, this wheel thing has the same formula as a 1st class lever. Both the wheels and axle are actually levers of a kind (after all, most levers turn around an invisible axle of some kind) – but the wheel’s mobility, based on many revolutions, seems to demand a principle of its own.
An 8-kilo load can be held by a 4-kilo effort if axle circumference is 1 meter and handle circumference is 4m – WL = WL – 4X2 = 1X8-8 = 8! A detailed exposition of the 7 Mechanical Functions and their formulae is not possible in the scope of this article; this lesson is fact-forwarded by obtaining illustrated (upper primary) books dealing with Maths and Mechanics.
Mother did not know if she could follow her enthusiastic offspring’s’ rather unsteady descriptions of the 4th, 5th, 6th, and 7th Mechanics Principles – wedge, gear, screw and pulley. She was fascinated by Lily’s exhaustive list of wedges, though, many of them colorfully drawn – splitting a log; ice pick; wedge-tailed eagle!?; chisel; tongue; bear’s claw; airplane’s nose; door stop – quoin? “What’s a quoin? She asked, “That’s the block you put under the wheel of a cannon to prevent recoil – everyone knows that!”
Mother didn’t pursue the mysteries of the quoin, because Dad was coming in the front door. “Home is the hunter…” she observed wryly. He was welcomed by an insensibly happy Silence, the family’s mall, black dog. “Hi, everyone, what’s for dinner? What are you drawing Lily? What’s that contraption Tan? Oh, and, er, what are you needleworking dear?” They all answered at once, including Silence, so Dad was none the wiser – but he did hear the word pulley. I know how to make a rope pulley, with no wheels at all – here Lily, pass me your pencil.
See, you just pull that rope, and for every foot or so, the tree, or whatever you’re trying to pull up or along, moves an inch. There’s no way a person could pull the equivalent. Actually it’s more a winch than a pulley, but a similar process, the rope turning on itself being the wheels. Hey, and talking about pulleys; one of the men at work today said that he saw a mob of young delinquents at a school somewhere lift up one of the teacher’s cars – right up into a big gum tree!! I think he said it was a Mini Moke; they did it with a pulley, a proper one but Boy, I’m sure glad we send you two to a decent school!”