Page 8

First Form Physics

Studying Physics in the1950’s filled one with excitement; Calder Hall was starting to harness Nuclear Power, the structure of DNA had been determined, Lasers and Masers were being talked about, transistors were replacing valves in electronic circuits and Space was emerging as the final frontier. As early as 1945, Arthur C Clarke (Extra-Terrestrial Relays, page 305, Wireless World, October 1945) had given us the elements of satellite communication and, by 6th October 1957, Sputnik 1 led the way for countless other space vehicles- what new challenges lay ahead?

Well, more than five decades on, this wonderful subject called Physics is not held in such high regard but we still need to have an appreciation of the natural world so here is just a short section which may engender some enthusiasm for a subject rich in history and diversity.

What makes things “tick” has always excited the curiosity of Homo sapiens and man does appear to be distinguished from other animals by his great store of imaginative gifts. He makes plans, inventions, new discoveries, by putting different talents together. Discoveries become more subtle and penetrating as human beings learn to combine their individual talents in more complex and intimate ways and society has built on what previous generations have bequeathed, to build an ever-increasing store of knowledge and artefacts.

From early history only two important “discoveries” will be listed to show the time scale of the development of the human race.

Mankind has used fire for about 400,000 years and this has allowed changes from Stone Age to Bronze Age to Iron Age.

The wheel is thought to date back to about 3,000 BC (5,000 years ago) in the form of solid wooden structure attached to a raft or sledge. It was soon to be used on carts for conveyance of goods and pulleys for lifting objects and further developed as grinding wheels for producing flour from wheat.

Both the above have played a crucial role in the emergence of man and must be woven into a tapestry of life where war and conflict were, perhaps, the most overriding issues of the day and curiosity was in second place to survival.

Without trying to belittle the inventions of fire or the wheel, it is likely that both would have been man copying nature. There would have been many times when cave dwellers would have watched stones cascading down mountains and it would have been obvious that round stones roll with more agility than square ones. Similarly, forests near volcanoes would catch fire and this would lead to the idea that certain materials could be made to ignite and these were just the materials that could be used in fires. Science can be like this but IT CAN BE FAR MORE- it is the ability of mankind to reach out to a virtual world - Newton gazing at the solar system from afar or Einstein riding on a light beam - science is that wonderful link between mind and matter.

Science, or natural philosophy as it is often called, seems to have started a few hundred years BC with names like Archimedes (287 – 212 BC), Aristotle (384 – 322 BC), Pythagoras (570 – 500 BC) Eratosthenes (276 – 194 BC) and Hipparchus (170 – 113 BC) asking questions as to the nature and role of the universe.

To get our first glimpse of science/ Physics ( some would call it mathematics!) we can follow the reasoning that results in every school pupil’s delight, namely, the Pythagoras Theorem.

There is an experimental stage where, perhaps, lengths of wood are placed in a triangular form and the angles at the vertices measured. Every so often a right angle appears and we can make a note of the lengths. For instance, lengths of 3, 4, and 5 will give a right angle; equally 8, 15 and 17 gives a right angled triangle. This experimantal stage presents us with facts , that is, selected groups of three lengths out of all the billions of possible groups give us triangles that contain a right angle.

It would be possible to leave our scientific endeavour after this experimental stage and we would have made a contribution to science. However, for a more complete finishing point a theoretical stage is needed.

It will now be noticed, that by the addition of the red line, the area is composed of squares for the other two sides.( if it is not obvious that two squares are formed then the dimensions of the small coloured square can be used to to calculate dimensions v and w.

-------- v = b + (a-b) = a

-------- w = a - (a-b) = b

(the original position of triangle A is shown in green)

An equation may now be written in the form    c²  =  b² +  a²      and, of course, we see that a our  3-4-5 triangle satisfies the Pythagoras Theorem since

 9 + 16 gives 25 

( In algebraec terms, the proof may be directly determined from the composite square, originally drawn on the hypotenuse, given above. This square has area c² since the hypotenuse has length c. The area can also be determined from the separate objects, namely, one small coloured square (a-b)²  and four triangles with total area 4ab/2, that is 2ab. This gives c² = 2ab + (a-b)² which again gives the result above. )

We see here that Nature had yielded up a secret and, in 550 BC or thereabouts, Pythagoras wrote this secret in a concise mathematical form for the benefit of all future generations.

Another great step forward in Physics came from the studies of heavenly bodies.

Mapping celestial objects in the night sky had started mainly in Egypt and by the time that Copernicus started his work in the 1400's many star charts existed with precise data about the characterisitic of stars visible to the naked eye. Though most stars carried out their diurnal rotation in an orderly fashon, there were a few bright objects (planets or wanderers) which had a more irratic movement, the so called retrograde motion.

The above illustration is a modern explanation of this erratic motion in which the celestial object (in this case Mars) normally moves forward in the star field but, for several nights, will move backwards. The stationary points S and S1 indicate times when Mars exactly follows the diurnal motion of the stars and the intervals 1-2, 2-3, 3-4 etc are equal intervals of time.To explain this motion with a geocentic model of the Universe ( SUN MOVING ROUND THE EARTH) was extremely daunting and Nicholas Kopernik, better known as Copernicus, (1473 - 1543) suggested that a heliocentric view of the Universe ( EARTH MOVING ROUND THE SUN ) explained retrograde motion in a simpler manner, as illustrated above. Tycho Brahe (1546 - 1601) carried out more painstaking measurements on the orbits of all the planets and this allowed Johanus Kepler (1571 - 1630) to summarise this observational data into three laws:-

1. Each planet travels in an elliptical orbit with the sun at one focus of the ellipse.

2. If one imagines a line drawn from the sun to the planet, this line sweeps out equal areas in equal periods of time.

3. The distance,d, of the planet from the sun uniquely determines the length of time required by the planet to complete one orbital revolution or period t. A concise statement is given where d³ is proportional to t².

The arrival of Galileo Galilei (1564 - 1642) onto the scientific scene brought fresh confirmation to a heliocentric model. With observations of Jupiter through a telescope, four moons were seen to be revolving round the planet. So the long held idea that earth was special - created by God - and was at the centre of things in the Universe was probably an illusion. The moons of Jupiter had little regard for Earth being at the centre of all things and were happy to revolve round a different centre, namely, planet Jupiter. Galileo reiterated the heliocentric theory but brought down the wrath of the Church who, in the end, banned him from working on anything concerning motion in the Universe.

Isaac Newton, (1642 - 1727), the father of modern science, now made a momentous leap.

He used all the facts that had been accumulated from astromomical observations (like Pythagoras with his sets of three special numbers) and developed his theory of gravitational attraction.

He showed that planetary motion was caused by the mutual attraction of the planet to the sun by a gravitational force FG                                               where                  FG = G (M_sun m_planet) / d²

                                                   M_sun and m_planet are masses of the sun and planet respectively

                                                    d is the separation

                                                     and G is the gravitational constant - ----    6.67 x 10^-11 Nm²kg^-2

Perhaps we could follow this through a bit further and, for the sake of simplicity, assume the orbits of the planets are circular. Kepler's Laws would now read :  1 the planets travel round the sun in circular orbits with the sun at the centre : 2 Equal areas are swept out in equal times -- this means that the planets have constant speeds : 3 we substitute Newton's gravitational formula into the second of Newton's motional laws ie force=mass x acceleration

                                         G (M_sun m_planet) / d²      =   m_planet  x  acceleration

                                          Now acceleration for circular motion is v² / d

   On substitution we find that the mass of the planet cancels out so v²  = constant / d

    Now the time for a planet to complete an orbit is 2 x PI x d / v and we call this the period t.

So eventually we reach Kepler's third law that    t^{2   =}   constant x   d^{3 .} 

No longer could there be any doubt that the sun was, indeed, at the centre of the solar system and earth was a pretty run of the mill planet.

Later Henry Cavendish (1731-1810) determined the Gravitational constant on earth by measuring the force of attraction between metal spheres. His value commpared well with Newton's values thus showing the universality of Physics - it explains nature on earth or in the vast reaches of the universe .

Newton showed how science was to be carried out - experimental observations ( for this case of planetary observations the experiments covered many centuries) - marshalling facts into an orderly form, these so called laws are a short hand or concise way in which to express accumulated data ( for planetary motion we have Kepler's three laws) - and finally the establishment of a theory to provide an greater understanding of nature.

The scientific method has not changed since Newton's days and it has been accepted as the one true method for studying the Natural world.

*************************************************************************************************

There is not space here to cover  all the many and varied aspects of Physics that have developed since the days of Newton but we can be very grateful to Professor Crowell who has put a complete text on the internet.  If you visit www.lightandmatter.com the whole evolution of Physics can be studied in depth or you can "dip in and out" for any particular topic. For a more leisurely read I would suggest The Ascent of Man by Jacob Bronowski. It is an almost word for word transcript of the original TV series from the 1970's. Youtube has done a video clip which does say quite a lot about science from the back drop of Auschwitz - any scientist should never play at being God!

Well, good luck and good hunting .