Temat 16: Perception of colors

The human eye
The human eye is a so-called camera eye. Like a photographic camera, and in contrast to insect eyes and other compound eyes, the vertebrate camera eye works by producing an image of the outer world on a surface consisting of light sensors, the retina. The retina covers more than half of the inside of the eye ball, whose typical diameter in an adult is about 16.7mm. The pupil has a diameter between 2mm – below which one gets problems with diffraction – and 7mm – for which lens aberrations are just acceptable. The image on the retina has low image distortion, low chromatic aberrations (about 1 dioptre between red and blue) and low coma; the eye achieves this performance by using an deformable aspheric gradient-index lens and a cornea whose shape is always near the ideal shape within 30 μm – an extremely good value for a deformable body.The eye, together with the brain, also has a powerful autofocus – still not fully understood – and an excellent motion compensation and image stabilization system built in. A section of this amazing device is shown in Figure.

The retina is an outgrowth of the brain. It contains 120 million rods, or black and white pixels, and 6 million cones, or colour pixels. Each pixel can detect around 300 to 500 intensity levels (9 bit). The eye works over an intensity range of 8 to 10 orders of magnitude; the involved mechanism is incredibly complex, takes place already inside the receptors, involves calcium ions, and is fully known only since a few years.The region of highest resolution, the fovea, has an angular size of about 1°. The resolution of the eye is about 1'.The integration time of the retina is about 100ms – despite this, nothing is seen during the saccades.The retina itself is 200μm thick and is transparent: this means that all cables leading to the receptors are transparent as well.
The retina has very low energy consumption and uses a different type of neurons that usual nerves: instead of using spikes, the neurons in it use electrotonic potentials, not the action potentials or spikes used in most other nerves,which would generate interferences that would make seeing impossible. In the fovea, every pixel has a connection to the brain.
At the borders of the retina, around 10 000 pixels are combined to one signal channel. (If all pixels were connected 1 to 1 to the brain, the brain would need to be as large as a typical classroom.) As a result, the signals of the fovea, whose area is only about 0.3% of the retina, use about 50% of the processing in the brain’s cortex.
To avoid chromatic aberrations, the fovea has no blue receptors.The retina is also a graphic preprocessor: it contains three neuronal layers that end up as 1.3 million channels to the cortex, where they feed 5 million axons that in turn connect to 500 million neurons.
The compression methods between the 125 million pixel in the retina and the 1.3 million channels to the cortex is still subject of research. It is known that the signals do not transport pixel data, but data streams processed in about a dozen different ways. The streams do not carry brightness values, but only contrasts, and they do not transmit RGB values, but colour differences.The streams carry motion signals in a compressed way and the spatial frequency data is simplified.
Explorations have shown how the ganglions in the retina provide a navigational horizon, how they detect objects moving against the background of the visual field, and how they subtract the motion of the head. The coming years and decades will provide many additional results; several data channels between the eye and the brain are still unknown.
Apart from rods and cones, human eyes also contain a third type of receptor.This receptor type, the photosensitive ganglion cell or intrinsically photosensitive retinal ganglion cell, has only been discovered in the early 1990s, sparking Ref. 136 a whole new research field.
Photosensitive ganglion cells are sensitive mainly to blue light, use melanopsin as photopigment and are extremely slow.They are connected to the suprachiasmatic nucleus in the brain, a small structure of the size of a grain of rice that controls our circadian hormone cycle. For this reason you should walk a lot outside, where a lot of blue light is available, in order to reset the body’s clock and get rid of jet-lag. Photosensitive ganglion cells also produce the signals that control the diameter of the pupil.

Temat 15: What is light?

The nature of light has fascinated explorers of nature since at least the time of he ancient Greeks. The answer appeared in 1848, when Gustav Kirchhoff noted hat the experimental values on both sides of the equation

agreed within measurement errors. This suggested the answer to the question asked two thousand years earlier:
⊳ Light is an electromagnetic wave.
Ten years later, in 1858, Bernhard Riemann* proved mathematically that any electromagnetic wave must propagate with a speed c given by the above equation. Note that the right-hand side contains electric and magnetic quantities, and the left-hand side is an optical quantity.The expression of Kirchhoff and Riemann thus unifies electromagnetism and optics. The modern value for the speed of electromagnetic waves, usually called c from Latin celeritas, is
c = 299 792 458 m/s .
The value for c is an integer number, because the meter is nowadays defined in such a way as to exactly achieve this number.
In 1865, Maxwell summarized all data on electricity and magnetism collected in the 2500 years in his equations. Almost nobody read his papers, because he wrote them using quaternions. The equations were then simplified independently by Heinrich Hertz and Oliver Heaviside.They deduced the original result of Riemann: in the case of empty space, the equations of the electromagnetic potentials can be written as

Experiments in empty space confirm that the phase velocity c is independent of the frequency of the wave.This phase velocity thus characterizes electromagnetic waves, and distinguishes them from all other types of waves in everyday life.


What are electromagnetic waves? To get a clearer idea of electromagnetic waves, we explore their properties. The wave equation for the electromagnetic field is linear in the field; this means that the sum of two allowed situations is itself an allowed situation. Mathematically speaking, any superposition of two solutions is also a solution. We therefore know that electromagnetic waves must show interference, as all linear waves do.

FIGURE 50 The general structure of a plane, monochromatic and linearly polarized electromagnetic wave at a specific instant of time.

Linearity also implies that two waves can cross each other without disturbing each other, and that electromagnetic waves can travel undisturbed across static electromagnetic fields.
Linearity also means that every electromagnetic wave can be described as a superposition of harmonic, or pure sine waves, each of which is described by expression. The simplest possible electromagnetic wave, the harmonic plane wave with linear polarization, is illustrated in Figure 50. Note that for this simplest type of waves, the electric and the magnetic field are in phase. (Can you prove this experimentally and by calculation?) The surfaces formed by all points of maximal field intensity are parallel planes, spaced by (half the) wavelength; these planes move along the direction of the propagation with the phase velocity.
After Riemann and Maxwell predicted the existence of electromagnetic waves, in the years between 1885 and 1889, Heinrich Hertz* discovered and studied them. He fabricated a very simple transmitter and receiver for 2GHz waves, shown in Figure 53. Such waves are still used today: cordless telephones and the last generation of mobile phones work at this frequency – though the transmitters and the receivers look somewhat differently nowadays. Such waves are now also called radio waves, since physicists tend to call all moving force fields radiation, recycling somewhat incorrectly a Greek term that originally meant ‘light emission.’

Today Hertz’s experiment can be repeated in a much simpler way. As shown in Figure 54, a budget of a few euro is sufficient to remotely switch on a light emitting diode with a gas lighter. (After each activation, the coherer has to be gently tapped, in order to get ready for the next activation.) Attaching longer wires as antennas and ground allows this set-up to achieve transmission distances up to 30 m.
Hertz also measured the speed of the waves he produced. In fact, you can also measure the speed at home, with a chocolate bar and a (older) kitchen microwave oven. A microwave oven emits radio waves at 2.5GHz – not far from Hertz’s value. Inside the oven, these waves form standing waves. Just put the chocolate bar (or a piece of cheese) in the oven and switch the power off as soon as melting begins. You will notice that the bar melts at regularly spaced spots. These spots are half a wavelength apart. From the measured wavelength value and the frequency, the speed of light and radio waves simply follows as the product of the two.
If you are not convinced, you can measure the speed directly, by telephoning a friend on another continent, if you can make sure of using a satellite line (choose a low cost provider). There is about half a second additional delay between the end of a sentence and the answer of the friend, compared with normal conversation. In this half second, the signal goes up to the geostationary satellite, down again and returns the same way.
This half second gives a speed of c ≈ 4 ⋅ 36 000 km/0.5 s ≈ 3 ⋅ 105 km/s, which is close to the precise value. Radio amateurs who reflect their signals from the Moon can perform a similar experiment and achieve higher precision.
In summary, electromagnetic waves exist and move with the speed of light.

Temat 14: What is electricity?

The answer to this question is: Electricity is more the name for a field of inquiry, and less the name for any specific observation or effect. Electricity is not a specific term; the term is used to refer to the effects of electric charges, of their motion and their fields. In fact the vocabulary issue hides a deeper question: what is the nature of electric charge? In order to solve this issue, we start with the following question.

Can we detect the inertia of electricity?
If electric charge really is something flowing throughmetals, we should be able to observe the effects shown in Figure 12: electric charge should fall, should have inertia and should be separable from matter. And indeed, each of these effects has been observed.

FIGURE 12 Consequences of the flow of electricity.

For example, when a long metal rod is kept vertically, we can measure an electrical potential difference, a voltage, between the top and the bottom. In other words, we can measure the weight of electricity in this way. Similarly, we can measure the potential difference between the ends of an accelerated rod. Alternatively, we can measure the potential difference between the centre and the rim of a rotating metal disc.The last experiment was, in fact, the way in which the ratio q/m for currents in metals was first measured with precision.
The result is:
q/m ≈ −1.8(2) ⋅ 10¹¹ C/kg (7)
for all metals, with small variations in the second digit. The minus sign is due to the definition of charge. In short, electrical charge in metals has mass, though a very small one.
If electric charge hasmass, whenever we switch on an electrical current, we get a recoil. This simple effect can easily be measured and confirms themass to charge ratio just given. Also, the emission of current into air or into vacuum is observed; in fact, every cathode picture. The emission works best for metal objects with sharp, pointed tips. The rays created this way – we could say that they are ‘free’ electricity – are called cathode rays. Within a few per cent, they show the same mass to charge ratio as expression (7). This correspondence thus shows that charges move almost as freely in metals as in air; this is the reason that metals are such good conductors of electric current.
If electric charge falls inside vertical metal rods, we can make the astonishing deduction that cathode rays should not be able to fall through a vertical metal tube. As we will see later, cathode rays consist of free electrons. The name ‘electron’ is due to George Stoney. Electrons are the smallest and lightest charges moving in metals; they are, usually – but not always – the ‘atoms’ of electricity. In particular, electrons conduct electric current inmetals. The charge of an electron is small, 0.16 aC, so that flows of charge typical of everyday life consist of huge numbers of electrons; as a result, electrical charge effectively behaves like a continuous fluid. The particle itself was discovered and presented in 1897 by Johann Emil Wiechert (b. 1861 Tilsit, d. 1928 Göttingen) and, independently, three months later, by Joseph John Thomson (b. 1856 Cheetham Hill, d. 1940 Cambridge).
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The speed of electricity is too slow for many people. Computer chips could be faster if it were higher. And computers that are connected to stock exchanges are located as near as possible to the stock exchange, because the time advantage the short communication distance (including the delay inside switching chips) provides is essential for getting a good financial performance in certain trading markets.
In summary, experiments show that all charges have mass. And like all massive bodies, charges move slower than light. Charge is a property of matter; images and light have no charge.

Temat 13: Albert Einstein

Albert Einstein (b. 1879 Ulm, d. 1955 Princeton) was one of the greatest physicists ever. (The ‘s’ in his name is pronounced ‘sh’.)
In 1905, he published three important papers: one about Brownian motion, one about special relativity and one about the idea of light quanta.
The first paper showed definitely that matter is made of molecules and atoms;
the second showed the invariance of the speed of light;
and the third paper was one of the starting points of quantum theory.
Each paper was worth a Nobel Prize, but he was awarded the prize only for the last one.
Also in 1905, he proved the famous formula E₀ = mc² (published in early 1906), after a few others also had proposed it.
Although Einstein was one of the founders of quantumtheory, he later turned against it. His famous discussions with his friend Niels Bohr nevertheless helped to clarify quantum theory in its most counter-intuitive aspects.
Later, he explained the Einstein–de Haas effect which proves that magnetism is due to motion inside materials. After many other discoveries, in 1915 and 1916 Einstein published his highest achievement: the general theory of relativity, one of the most beautiful and remarkable works of science. In the remaining forty years of his life, he searched for the unified theory of motion, without success.
Being Jewish and famous, Einstein was a favourite target of attacks and discrimination by theNational Socialist movement; therefore, in 1933 he emigrated from Germany to the USA; since that time, he stopped contact with Germans, except for a few friends, among them Max Planck. Until his death, Einstein kept his Swiss passport in his bedroom. He was not only a great physicist, but also a great thinker; his collection of thoughts about topics outside physics are well worth reading. But his family life was disastrous, and he made each of his family members unhappy.
Anyone interested in emulating Einstein should know first of all that he published many papers.* He was both ambitious and hard-working.
Moreover, many of his papers werewrong; he would then correct themin subsequent papers, and then do so again.
This happened so frequently that hemade fun of himself about it. Einstein indeed realized the well-known definition of a genius as a person who makes the largest possible number of mistakes in the shortest possible time.

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* All his papers and letters are now freely available online, at einsteinpapers.press.princeton.edu .


Check your knowledge: Special relativity
1. Which of the following has not been observed to change due to motion?
- Time
- Length
- Speed of light in a vacuum
2. An astronaut takes a long space journey at close to light speed. The astronaut's twin sister remained on Earth. On a return to Earth, what is the astronaut's age compared to her earthbound twin?
- Older
- The same
- Younger
3. As it approaches the speed of light, what will happen to the length of a spacecraft as observed by a passenger inside? - It will increase
- It will remain constant
- It will decrease
4. A spacecraft of length 780 meters is travelling at a constant speed of 0,95 c . The spacecraft travels at this speed for 10 years, as measured by a clock on the Earth.
Calculate the time elapsed, in years, as measured by a clock in the spacecraft.
- 2.23 years
- 3.12 years
- 32.0 years
5. A spacecraft of length 780 meters is travelling at a constant speed of 0,95 c. The spacecraft travels at this speed for 10 years, as measured by a clock on the Earth. If the spacecraft passes Earth at this speed what length would an observer on Earth measure for the spacecraft?
- 174 m
- 244 m
- 2500 m
6. Imagine a train travelling at 100 m/s with a passenger who throws a ball ahead of the train at 5 m/s . What is the resultant velocity of the ball?
- 5 m/s
- 100 m/s
- 105 m/s
7. Imagine a train is travelling at 2,9 x 108 m/s . A passenger shines a torch from the front of the train. What speed does the passenger see the light from the torch move at?
- 0,1 x 108 m/s
- 3 x 108 m/s
- 5,9 x 108 m/s
8. Imagine a train is travelling at 2,9 x 108 m/s . A passenger shines a torch from the front of the train. A stationary observer on the train platform measures the speed of light from the torch. How fast does the light appear to move according to the stationary observer?
- 0,1 x 108 m/s
- 3 x 108 m/s
- 5,9 x 108 m/s

Temat 12: The physics of blood and breathing

Fluid motion is of vital importance. There are at least four fluid circulation systems inside the human body.
First, blood flows through the blood system by the heart.
Second, air is circulated inside the lungs by the diaphragm and other chestmuscles.
Third, lymph flows through the lymphatic vessels, moved passively by body muscles.
Fourth, the cerebrospinal fluid circulates around the brain and the spine, moved by motions of the head.
For this reason, medical doctors like the simple statement: every illness is ultimately due to bad circulation.
Why do living beings have circulation systems?
Circulation is necessary because diffusion is too slow. Can you detail the argument?
We now explore the two main circulation systems in the human body.
Blood keeps us alive: it transports most chemicals required for our metabolism to and from the various parts of our body.
The flow of blood is almost always laminar; turbulence only exists in the venae cavae. The heart pumps around 80 ml of blood per heartbeat, about 5 l/min. At rest, a heartbeat consumes about 1.2 J.
The consumption is sizeable, because the dynamic viscosity of blood ranges between 3.5 ⋅ 10 ⁻³ Pa s (3.5 times higher than water) and 10⁻² Pa s, depending on the diameter of the blood vessel; it is highest in the tiny capillaries.
The speed of the blood is highest in the aorta, where it flows with 0.5 m/s, and lowest in the capillaries, where is as low as 0.3 mm/s. As a result, a substance injected in the arm arrives in the feet between 20 and 60 s after the injection. In fact, all animals have similar blood circulation speeds, usually between 0.2 m/s and 0.4 m/s. Why?
To achieve blood circulation, the heart produces a (systolic) pressure of about 16 kPa, corresponding to a height of about 1.6 m of blood. This value is needed by the heart to pump blood through the brain. When the heart relaxes, the elasticity of the arteries keeps the (diastolic) pressure at around 10 kPa.
These values are measured at the height of the heart. The values vary greatly with the position and body orientation at which they are measured: the systolic pressure at the feet of a standing adult reaches 30 kPa, whereas it is 16 kPa in the feet of a lying person.
For a standing human, the pressure in the veins in the foot is 18 kPa, larger than the systolic pressure in the heart. The high pressure values in the feet and legs is one of the reasons that leads to varicose veins. Nature uses many tricks to avoid problems with blood circulation in the legs.
Humans leg veins have valves to avoid that the blood flows downwards; giraffes have extremely thin legs with strong and tight skin in the legs for the same reason. The same happens for other large animals.
At the end of the capillaries, the pressure is only around 2 kPa. The lowest blood pressure is found in veins that lead back from the head to the heart, where the pressure can even be slightly negative. Because of blood pressure, when a patient receives a (intravenous) infusion, the bag must have a minimum height above the infusion point where the needle enters the body; values of about 0.8 to 1m cause no trouble. (Is the height difference also needed for person-to-person transfusions of blood?)
Since arteries have higher blood pressure, for the more rare arterial infusions, hospitals usually use arterial pumps, to avoid the need for unpractical heights of 2m or more.

The physics of breathing is equally interesting. A human cannot breathe at any depth under water, even if he has a tube going to the surface, as shown in Figure 242 (right):

At a few metres of depth, trying to do so is inevitably fatal!
Even at a depth of 50 cm only, the human body can only breathe in this way for a few minutes, and can get badly hurt for life.Why?
Inside the lungs, the gas exchange with the blood occurs in around 300 millions of little spheres, the alveoli, with a diameter between 0.2 and 0.6 mm. To avoid that the large one grow and the small ones collapse,  the alveoli are covered with a phospholipid surfactant that reduces their surface tension. In newborns, the small radius of the alveoli and the low level of surfactant is the reason that the first breaths, and sometimes also the subsequent ones, require a large effort.
We need around 2% of our energy for breathing alone.The speed of air in the throat is 10 km/h for normal breathing; when coughing, it can be as high as 160 km/h. The flow of air in the bronchi is turbulent; the noise can be heard in a quiet invironment. In normal breathing, the breathingmuscles, in the thorax and in the belly, exchange 0.5 l of air; in a deep breath, the volume can reach 4 l.
Breathing is especially tricky in unusual situations. After scuba diving* at larger
depths than a few meters for more than a few minutes, it is important to rise slowly, to avoid a potentially fatal embolism.Why?
The same can happen to participants in high altitude flights with balloons or aeroplanes, to high altitude parachutists and to cosmonauts

*The blood pressure values measured on the two upper arms also differ; for right handed people, the pressure in the right arm is higher

How blood pressure works


Understanding Blood Pressure
Human Anatomy and Physiology video 3D animation

This is a biology/anatomy video for Grade 10-11 students about Blood Pressure, its causes and effects. The pressure with which blood flows in the blood vessels is called Blood Pressure or BP. BP is measured using a special device called Sphygmomanometer

Temat 11: Fluids and their MOTION

Fluids can be liquids or gases, including plasmas. And the motion of fluids can be exceedingly intricate, as Figure 233 shows.
In fact, fluid motion is so common – think about breathing, blood circulation or the weather – that exploring is worthwhile.

F IGURE 233 Examples of fluid motion: a vertical water jet striking a horizontal impactor, two jets of a glycerol–water mixture colliding at an oblique angle, a water jet impinging on a reservoir (all © John Bush, MIT) and a dripping water tap (© Andrew Davidhazy).

The state of a fluid
To describe motion means to describe the state of a system. For most fluids, the state at every point in space is described by composition, velocity, temperature and pressure. We will explore temperature below. We thus have one new observable: The pressure at a point in a fluid is the force per area that a body of negligible size feels at that point. Pressure is measured with the help of barometers or similar instruments. The unit of pressure is the pascal: 1 Pa is 1N/m2.
Pressure is not a simple property. Can you explain the observations of Figure 235?

F IGURE 235 The hydrostatic and the hydrodynamic paradox (© IFE).

If the hydrostatic paradox – an effect of the so-called communicating vases – would not be valid, it would be easy to make perpetuum mobiles. Can you think about an example?
Another puzzle about pressure is given in Figure 236.

FIGURE 236 A puzzle: Challenge 545 s Which method of emptying a container is fastest? Does the method at the right hand side work at all?

Air has a considerable pressure, of the order of 100 kPa. As a result, it is not easy to make a vacuum; indeed, everyday forces are often too weak to overcome air pressure. This is known since several centuries, as Figure 237 shows. Your favorite physics laboratory should posess a vacuum pump and a pair of (smaller) Magdeburg hemispheres; enjoy performing the experiment yourself.

F IGURE 237 The pressure of air leads to surprisingly large forces, especially for large objects that enclose a vacuum. This was regularly demonstrated in the years from 1654 onwards by Otto von Guericke with the help of his so-called Magdeburg hemispheres and, above all, the various vacuum pumps that he invented (© Deutsche Post, Otto-von-Guericke-Gesellschaft, Deutsche Fotothek).

Laminar and turbulent flow
Like all motion, fluid motion obeys energy conservation. In the case that no energy is transformed into heat, the conservation of energy is particularly simple. Motion that does not generate heat is motion without vortices; such fluid motion is called laminar. If, in addition, the speed of the fluid does not depend on time at all positions, it is called stationary.
For motion that is both laminar and stationary, energy conservation can be expressed with the help of speed v and pressure p:
½ pv² + p + qgh = const
where h is the height above ground. This is called Bernoulli’s equation. *

* Daniel Bernoulli (b. 1700 Bale, d. 1782 Bale), important mathematician and physicist. His father Johann and his uncle Jakob were famous mathematicians, as were his brothers and some of his nephews. Daniel Bernoulli published many mathematical and physical results. In physics, he studied the separation of compound motion into translation and rotation. In 1738 he published the Hydrodynamique, in which he deduced all results from a single principle, namely the conservation of energy.The so-called Bernoulli equation states that (and how) the pressure of a fluid decreases when its speed increases. He studied the tides and many complex mechanical problems, and explained the Boyle–Mariotte gas ‘law’. For his publications he won the prestigious prize of the French Academy of Sciences – a forerunner of the Nobel Prize – ten times.

F IGURE 234 Daniel Bernoulli (1700–1782)

In this equation, the last term is only important if the fluid rises against ground. The first term is the kinetic energy (per volume) of the fluid, and the other two terms are potential energies (per volume). Indeed, the second term is the potential energy (per volume) resulting from the compression of the fluid.This is due to a second way to define pressure:
Pressure is potential energy per volume
Energy conservation implies that the lower the pressure is, the larger the speed of a fluid becomes.
We can use this relation to measure the speed of a stationary water flow in a tube. We just have to narrow the tube somewhat at one location along the tube, and measure the pressure difference before and at the tube restriction.The speedv far from the constriction is then given as

(What is the constant k?)
A device using this method is called a Venturi gauge. If the geometry of a system is kept fixed and the fluid speed is increased – or the relative speed of a body in fluid – at a certain speed we observe a transition: the liquid loses its clarity, the flow is not laminar anymore. We can observe the transition whenever we open a water tap: at a certain speed, the flow changes from laminar to turbulent. At this point, Bernoulli’s equation is not valid any more.
The description of turbulence might be the toughest of all problems in physics. When the young Werner Heisenberg was asked to continue research on turbulence, he refused – rightly so – saying it was too difficult; he turned to something easier and he discovered and developed quantum mechanics instead. Turbulence is such a vast topic, with many of its concepts still not settled, that despite the number and importance of its applications, only now, at the beginning of the twenty-first century, are its secrets beginning to be unravelled.
It is thought that the equations of motion describing fluids, the so called Navier–Stokes equations, are sufficient to understand turbulence.** But the mathematics behind them is mind-boggling. There is even a prize of one million dollars offered by the Clay Mathematics Institute for the completion of certain steps on the way to solving the equations.
** They are named after Claude Navier (b. 1785 Dijon, d. 1836 Paris), important engineer and bridge builder, and Georges Gabriel Stokes (b. 1819 Skreen, d. 1903 Cambridge), important physicist and mathematician.

FIGURE 238 Left: non-stationary and stationary laminar flows; right: an example of turbulent flow (© Martin Thum, Steve Butler).

Temat 10: Forces and Motion

Forces and Motion - REVISION PODCAST

This revision podcast is for Edexcel IGCSE physics (4PH0 or 4SC0), and covers all of topic 1 - forces and motion. It is also suitable for other GCSEs.
There's no hard and fast rule about what to plot on each axis of a graph - I have plotted Force on the y-axis and Extension on the x-axis so that the gradient of the graph is k - the spring constant. (Consider the equation F=kx and the general equation for a straight line, y=mx).
I know that generally, students at GCSE are taught that the independent variable (what you change) goes on the x-axis, and the dependent variable (what you measure) goes on the y-axis, but sometimes it dies make sense to swap the axes, if the gradient is more meaningful. 

Temat 9: Sanjay Limaye and Akatsuki 6 - 8 December 2015

Live from Sagamihara: Akatsuki in Orbit, The Planetary Society
Posted by Sanjay Limaye

December 8
One day after closest approach, Akatsuki is now speeding away from Venus at 4.09 kilometers per second and is 180,000 kilometers from the planet. I am still thinking about the higher-than-expected delta-V achieved yesterday. One possible answer is that closest approach could have been a little bit nearer to Venus than the planned 550 km distance. This would induce extra velocity due to more bending of the trajectory and result in a larger change in velocity than what would result from the actual thrust for the planned miss-distance. The apoapsis distance will now determine the orbit period which is of some concern due to the time Akatsuki will spend in eclipse and need to draw upon the battery power.
In the press conference yesterday, we learned that the amount of fuel used for orbit insertion was close to what was expected. The insertion sequence occurred while the spacecraft was in shadow cast by the planet. Battery capacity, charging and discharging rates will be checked out in the coming days. The fuel left after the orbit insertion burn will also determine operations. Once the orbit is determined in the next day or so, the team will streamline the command generation process.
more: Blog by Sanjay Limaye on The Planetary Society

A Blog by Nadia Drake
Now Orbiting Cloud-Shrouded Venus, Akatsuki Sends New Images
POSTED WED, 12/9/2015

It’s not every day you hear about a troubled spacecraft making a desperate attempt to cling to a planet — for the second time. After missing its first chance to orbit Venus, Japan’s Akatsuki spacecraft circled the sun for five long years, waiting for the right time to try again. That moment came on Dec. 7, a half-decade to the day after a broken nozzle sent Akatsuki hurtling toward the sun instead of falling into the gravitational clutches of Earth’s sister planet. But with its large, main engine crippled, the spacecraft needed another way to slip into orbit. That responsibility went to four smaller thrusters that are normally used to adjust where the spacecraft is pointing; for 20 minutes they fired, nudging Akatsuki onto a course for capture as it skimmed the Venusian cloud tops.
And then the team commanding the spacecraft, at the Japan Aerospace Exploration Agency, waited. Shifts in the radio waves Akatsuki uses to communicate with Earth would indicate whether the spacecraft had changed course. If it hadn’t, there was a small window in which the team could try again, using an alternate set of thrusters. And if that didn’t work? Well, no one wanted to think about that. The third time might be the charm on Earth, but in space, getting even a second chance is exceedingly rare.
An hour later, scientists shared the exciting news: “It is in orbit!!” reported Sanjay Limaye, of the University of Wisconsin-Madison, who was with the team in Sagamihara, Japan. The question was, which orbit? Was it stable? Could the team talk with the spacecraft? Is Akatsuki healthy?
more: Phenomena, National Geographic

Temat 8: Kepler's Law

Gravitation in the sky
The expression a = GM/r² for the acceleration due to universal gravity also describes the motion of all the planets across the sky.We usually imagine to be located at the centre of the Sun and say that the planets ‘orbit the Sun’. How can we check this?
First of all, looking at the sky at night, we can check that the planets always stay within the zodiac, a narrow stripe across the sky. The centre line of the zodiac gives the path of the Sun and is called the ecliptic, since the Moon must be located on it to produce an eclipse.This shows that planets move (approximately) in a single, common plane.*
The detailedmotion of the planets is not easy to describe. As Figure 129 shows, observing a planet or star requires measuring various angles.

F IGURE 129 Some important concepts when observing the stars at night.

For a planet, these angles change every night. From the way the angles change, one can deduce the motion of the planets. A few generations before Hooke, using the observations of Tycho Brahe, the Swabian astronomer Johannes Kepler, in his painstaking research on the movements of the planets in the zodiac, had deduced several ‘laws’.The three main ones are as follows:
1. Planets move on ellipses with the Sun located at one focus (1609).
2. Planets sweep out equal areas in equal times (1609).
3. All planets have the same ratio T²/R³ between the orbit duration T and the semimajor axis R (1619).
Kepler’s results are illustrated in Figure 130.

F IGURE 130 The motion of a planet around the Sun, showing its semimajor axis d, which is also the spatial average of its distance from the Sun.

The sheer work required to deduce the three ‘laws’ was enormous. Kepler had no calculating machine available. The calculation technology he used was the recently discovered logarithms. Anyone who has used tables of logarithms to performcalculations can get a feeling for the amount of work behind these three discoveries.
Now comes the central point.The huge volume of work by Brahe and Kepler can be summarized in the expression
a = GM/r²
as Hooke and a few others had stated. Let us see why.

Temat 7: Free fall

Galileo was the first to state an important result about free fall: the motions in the horizontal and vertical directions are independent. He showed that the time it takes for a cannon ball that is shot exactly horizontally to fall is independent of the strength of the gunpowder, as shown in Figure 44.Many great thinkers did not agree with this statement even after his death: in 1658 the Academia del Cimento even organized an experiment to check this assertion, by comparing the flying cannon ball with one that simply fell vertically. Can you imagine how they checked the simultaneity?
Figure 44 also shows how you can check this at home. In this experiment, whatever the spring load of the cannon, the two bodies will always collide in mid-air (if the table is high enough), thus proving the assertion.

FIGURE 44 Two ways to test that the time of free fall does not depend on horizontal velocity.

Temat 6: Earth's Magnetic Field

Origin of Earth's magnetic field, new discoveries and new concepts, published in world-class scientific literature and explained here:



The earths magnetic field can be explained by a variable speed core that oscillates its volume between stretched in the N_S axis to stretched in the equatorial axis. See also:

Temat 5: The rotation of the EARTH

Is the Earth rotating?
The search for definite answers to this question gives an interesting cross section of the history of classical physics. Around the year 265 bce, Samos, the Greek thinker Aristarchus maintained that the Earth rotates.
He had measured the parallax of theMoon (today known to be up to 0.95°) and of the Sun (today known to be 8.8').**
The parallax is an interesting effect; it is the angle describing the difference between the directions of a body in the sky when seen by an observer on the surface of the Earth and when seen by a hypothetical observer at the Earth’s centre. (See Figure 89.)

FIGURE 89 The parallax – not drawn to scale
Aristarchus noticed that the Moon and the Sun wobble across the sky, and this wobble has a period of 24 hours. He concluded that the Earth rotates. It seems that Aristarchus received death threats for his result.
Aristarchus’ observation yields an evenmore powerful argument than the trails of the stars shown in Figure 90. Can you explain why? (And how do the trails look at the most populated places on Earth?)

FIGURE 90 The motion of the stars during the night, observed on 1 May 2012 from the South Pole, together with the green light of an aurora australis (© Robert Schwartz).

Measurements of the aberration of light also show the rotation of the Earth; it can be detected with a telescope while looking at the stars.The aberration is a change of the expected light direction, which we will discuss shortly. At the Equator, Earth rotation adds an angular deviation of 0.32' , changing sign every 12 hours, to the aberration due to the motion of the Earth around the Sun, about 20.5' . In modern times, astronomers have found a number of additional proofs, but none is accessible to theman on the street.
Furthermore, the measurements showing that the Earth is not a sphere, but is flattened at the poles, confirmed the rotation of the Earth. Figure 91 illustrates the situation.

FIGURE 91 Earth’s deviation from spherical shape due to its rotation (exaggerated).

Again, however, this eighteenth centurymeasurement byMaupertuis*** is not accessible to everyday observation.
Then, in the years 1790 to 1792 in Bologna, Giovanni Battista Guglielmini (1763–1817) finally succeeded in measuring what Galileo and Newton had predicted to be the simplest proof for the Earth’s rotation. On the Earth, objects do not fall vertically, but are slightly deviated to the east. This deviation appears because an object keeps the larger horizontal velocity it had at the height fromwhich it started falling, as shown in Figure 92.

FIGURE 92 The deviations of free fall towards the east and towards the Equator due to the rotation of the Earth.

Guglielmini’s result was the first non-astronomical proof of the Earth’s rotation. The experiments were repeated in 1802 by Johann Friedrich Benzenberg (1777–1846). Using metal balls which he dropped from theMichaelis tower in Hamburg – a height of 76m – Benzenberg found that the deviation to the east was 9.6mm. Can you confirm that the value measured by Benzenberg almost agrees with the assumption that the Earth turns once every 24 hours? There is also a much smaller deviation towards the Equator, not measured by Guglielmini, Benzenberg or anybody after them up to this day; however, it completes the list of effects on free fall by the rotation of the Earth.
Both deviations from vertical fall are easily understood if we use the result (described Page 180 below) that falling objects describe an ellipse around the centre of the rotating Earth. The elliptical shape shows that the path of a thrown stone does not lie on a plane for an observer standing on Earth; for such an observer, the exact path thus cannot be drawn on a piece of paper.
In 1798, Pierre Simon Laplace explained how bodies move on the rotating Earth and showed that they feel an apparent force. In 1835, Gustave-Gaspard Coriolis then reformulated the description. Imagine a ball that rolls over a table. For a person on the floor, the ball rolls in a straight line. Now imagine that the table rotates. For the person on the floor, the ball still rolls in a straight line. But for a person on the rotating table, the ball traces a curved path. In short, any object that travels in a rotating background is subject to a transversal acceleration.The acceleration, discovered by Laplace, is nowadays called Coriolis acceleration or Coriolis effect. On a rotating background, travelling objects deviate from the straight line.The best way to understand the Coriolis effect is to experience it yourself; this can be done on a carousel, as shown in Figure 93.

FIGURE 93 A typical carousel allows observing the Coriolis effect in its most striking appearance: if a person lets a ball roll with the proper speed and direction, the ball is deflected so strongly that it comes back to her.
Watching films on the internet on the topic is also helpful. You will notice that on a rotating carousel it is not easy to hit a target by throwing or rolling a ball.
Also the Earth is a rotating background. On the northern hemisphere, the rotation is anticlockwise. As the result, any moving object is slightly deviated to the right (while the magnitude of its velocity stays constant). On Earth, like on all rotating backgrounds, the Coriolis acceleration a results from the change of distance to the rotation axis. Can you deduce the analytical expression for the Coriolis effect?

* ‘And yet she moves’ is the sentence about the Earth attributed, most probably incorrectly, to Galileo since the 1640s. It is true, however, that at his trial he was forced to publicly retract the statement of a moving Earth to save his life. For more details of this famous story, see the section on page 311.
** For the definition of the concept of angle, see page 66, and for the definition of the measurement units for angle see Appendix B.
*** Pierre LouisMoreau deMaupertuis (1698–1759), French physicist andmathematician.He was one of the key figures in the quest for the principle of least action, which he named in this way. He was also founding president of the Berlin Academy of Sciences.Maupertuis thought that the principle reflected the maximization of goodness in the universe.This idea was thoroughly ridiculed by Voltaire in this Histoire du Docteur Akakia et du natif de Saint-Malo, 1753.Maupertuis (www.voltaire-integral.com/Html/23/08DIAL.htm) performed his measurement of the Earth to distinguish between the theory of gravitation of Newton and that of Descartes, who had predicted that the Earth is elongated at the poles, instead of flattened.

Temat 4: A hollow Earth?

Space and straightness pose subtle challenges. Some strange people maintain that all humans live on the inside of a sphere; they (usually) call this the hollow Earth theory. They claim that theMoon, the Sun and the stars are all near the centre of the hollow sphere, as illustrated in Figure 29.
They also explain that light follows curved paths in the sky and that when conventional physicists talk about a distance r from the centre of the Earth,the real hollow Earth distance is r = R² _Earth/r.
Can you show that this model is wrong?
Roman Sexl* used to ask this question to his students and fellow physicists. The answer is simple: if you think you have an argument to show that this view is wrong, you are mistaken!There is no way of showing that such a view is wrong. It is possible to explain the horizon, the appearance of day and night, as well as the satellite photographs of the around Earth, such as Figure 28. To explain what happened during a flight to the Moon is also fun. A consistent hollow Earth view is fully equivalent to the usual picture of an infinitely extended space. We will come back to this problem in the section on general relativity.
**
Another famous exception, unrelated to atomic structures, is the well-known Irish geological formation called the Giant’s Causeway. Other candidates thatmight come tomind, such as certain bacteria which have (almost) square or (almost) triangular shapes are not counter-examples, as the shapes are only approximate.

FIGURE 29 A model illustrating the hollow Earth theory, showing how day and night appear (© Helmut Diehl).

Temat 3: Throwing, jumping and shooting

The kinematic description of motion is useful for answering a whole range of questions.
∗∗
What is the upper limit for the long jump? The running peak speed world record in 2008 was over Ref. 59 12.5m/s ≈ 45 km/h by Usain Bolt, and the 1997 women’s record was 11m/s ≈ 40 km/h. However, male long jumpers never run much faster than about 9.5m/s. How much extra jump distance could they achieve if they could run full speed? How could they achieve that? In addition, long jumpers take off at angles of about 20°, as they are not able to achieve a higher angle at the speed they are running. How much would they gain if they could achieve 45°?
∗∗
What do the athletes Usain Bolt and Michael Johnson, the last two world record holders on the 200m race at time of this writing, have in common?They were tall, athletic, and had many fast twitch fibres in the muscles.These properties made them good sprinters. A last differencemade them world class sprinters: they had a flattened spine, with almost no S-shape.This abnormal condition saves them a little bit of time at every step, because their spine is not as flexible as in usual people. This allows them to excel at short distance races.
∗∗
Athletes continuously improve speed records. Racing horses do not. Why? For racing horses, breathing rhythm is related to gait; for humans, it is not. As a result, racing horses cannot change or improve their technique, and the speed of racing horses is essentially the same since it is measured.
∗∗
How can the speed of falling rain be measured using an umbrella?The answer is important: the same method can also be used to measure the speed of light, as we will find out later. (Can you guess how?) When a dancer jumps in the air, how many times can he or she rotate around his or her vertical axis before arriving back on earth?
∗∗
Numerous species of moth and butterfly caterpillars shoot away their frass – to put it more crudely: their shit – so that its smell does not help predators to locate them. Stanley Caveney and his team took photographs of this process. Figure 46 shows a caterpillar (yellow) of the skipper Calpodes ethlius inside a rolled up green leaf caught in the act. Given that the record distance observed is 1.5m (though by another species, Epargyreus clarus), what is the ejection speed? How do caterpillars achieve it?
∗∗
What is the horizontal distance one can reach by throwing a stone, given the speed and the angle from the horizontal at which it is thrown?
∗∗
What is the maximum numbers of balls that could be juggled at the same time?
∗∗
Is it true that rain drops would kill if it weren’t for the air resistance of the atmosphere? What about hail?
∗∗
Are bullets, fired into the air from a gun, dangerous when they fall back down?
∗∗
Police finds a dead human body at the bottom of cliff with a height of 30m, at a distance of 12m from the cliff. Was it suicide or murder?
∗∗
All land animals, regardless of their size, achieve jumping heights of at most 2.2m, as shown in Figure 47.The explanation of this fact takes only two lines. Can you find it? The last two issues arise because the equation (6) describing free fall does not hold in all cases. For example, leaves or potato crisps do not follow it. As Galileo already knew, this is a consequence of air resistance; we will discuss it shortly. Because of air resistance, the path of a stone is not a parabola. In fact, there are other situations where the path of a falling stone is not a parabola, even without air resistance. Can you find one?

Temat 2: MOTION

Experimentss how that the properties of Galilean time and space are xtracted from the environment both by children and animals. This xtraction has been confirmed for cats, dogs, rats, mice, ants and fish, among others. They all find the same results. First of all, motion is change of position with time. This description is illustrated by rapidly flipping the lower left corners of this book, starting at page 224. Each page simulates an instant of time, and the only change that takes place during motion is in the position of the object, say a stone, represented by the dark spot. The other variations from one picture to the next, which are due to the imperfections of printing techniques, can be taken to simulate the inevitable measurement errors. Stating that ‘motion’ is the change of position with time is neither an explanation nor a definition, since both the concepts of time and position are deduced frommotion itself. It is only a description of motion. Still, the statement is useful, because it allows for high precision, as we will find out by exploring gravitation and electrodynamics. After all, precision is our guiding principle during this promenade.Therefore the detailed description of changes in position has a special name: it is called kinematics. The idea of change of positions implies that the object can be followed during its motion. This is not obvious; in the section on quantum theory we will find examples where this is impossible. But in everyday life, objects can always be tracked.The set of all positions taken by an object over time forms its path or trajectory.The origin of this concept is evident when one watches fireworks or again the flip film in the lower left corners (starting at page 224). In everyday life, animals and humans agree on the Euclidean properties of velocity, space and time. In particular, this implies that a trajectory can be described by specifying three numbers, three coordinates (x, y, z) – one for each dimension – as continuous functions of time t. This is usually written as x = x(t) = (x(t), y(t), z(t))

Temat 1: Fizyka Galileusza

Galilean physics in six interesting statements and movies

Christoph Schiller, MOTION MOUNTAIN, the adventure of physics – vol.I, Fall, flow and heat.

The study of everyday motion, Galilean physics, is already worthwhile in itself: we will uncover many results that are in contrast with our usual experience.

For example, if we recall our own past, we all have experienced how important, delightful or unwelcome surprises can be. Nevertheless, the study of everyday motion shows that there are no surprises in nature.

Motion, and thus the world, is predictable or deterministic.

The main surprise of our exploration of motion is that there are no surprises in nature.

Nature is predictable. In fact, we will uncover six aspects of the predictability of everyday motion:

1. Continuity. We know that eyes, cameras and measurement apparatus have a finite resolution.  All have a smallest distance they can observe. We know that clocks have a smallest time they can measure. Despite these limitations, in everyday life all movements, their states, as well as space and time themselves, are continuous.

2. Conservation. We all observe that people, music and many other things in motion stop moving after a while. The study of motion yields the opposite result: motion never stops. In fact, three aspects of motion do not change, but are conserved: momentum, angular momentum and energy (together with mass) are conserved, separately, in all examples of motion. No exception to these three types of conservation has ever been observed. In addition, we will discover that conservation implies that motion and its properties are the same at all places and all times: motion is universal.

3. Relativity.We all know that motion differs from rest. Despite this experience, careful study shows that there is no intrinsic difference between the two. Motion and rest depend on the observer. Motion is relative. And so is rest. This is the first step towards understanding the theory of relativity.

4. Reversibility. We all observe that many processes happen only in one direction. For example, spilled milk never returns into the container by itself. Despite such observations, the study of motion will show us that all everyday motion is reversible. Physicists call this the invariance of everyday motion under motion reversal (or, sloppily, but incorrectly, under ‘time reversal’).

5. Mirror invariance. Most of us find scissors difficult to handle with the left hand, have difficulties to write with the other hand, and have grown with a heart on the left side. Despite such observations, our exploration will show that everyday motion is mirrorinvariant (or parity-invariant). Mirror processes are always possible in everyday life.

 6. Change minimization.We all are astonished by the many observations that the world offers: colours, shapes, sounds, growth, disasters, happiness, friendship, love.The variation, beauty and complexity of nature is amazing. We will confirm that all observations are due to motion. And despite the appearance of complexity, all motion is simple.

Our study will show that all observations can be summarized in a simple way:

Nature is lazy. All motion happens in a way that minimizes change. Change can be measured, using a quantity called ‘action’, and nature keeps it to a minimum. Situations – or states, as physicists like to say – evolve by minimizing change. Nature is lazy.

These six aspects are essential in understanding motion in sport, in music, in animals, in machines or among the stars.This first volume of our adventure will be an exploration of such movements. In particular, we will confirm, against all appearences of the contrary, the mentioned six key properties in all cases of everyday motion.

Galileo Galilei Biography: https://www.youtube.com/watch?v=Rejbk1oJ2xg
Galilean relativity: https://www.youtube.com/watch?v=uJ8l4kh_jto

WSTĘP: Dlaczego uczymy się fizyki po angielsku?

Lekcje fizyki w języku angielskim są realizowane w wymiarze 1 godziny tygodniowo, czyli 30 godzin w całym roku szkolnym w klasie matematyczo-fizycznej II A. W czasie zajęć stosowane są w szerokim zakresie środki technologii informacyjnej, czyli komputer, tablica interaktywna i różnorodne oprogramowanie.

Głównym celem innowacji jest uatrakcyjnienie zajęć, rozwijanie zainteresowań młodzieży, która realizuje program rozszerzony zarówno z fizyki, jak i języka angielskiego. Program fizyki w języku angielskim jest realizowany przy wykorzystaniu bezpłatnego podręcznika (pliku pdf) Christoph’a Schillera MOTION MOUNTAIN - the adventure of physics: http://motionmountain.net/

Uczniowie mają możliwość uzyskać dodatkowe wiadomości i umiejętności z fizyki, dzięki bogatej w grafikę i filmy publikację edukacyjną, wydaną w języku angielskim oraz inne strony edukacyjne oraz materiały dostępne na youtube.com.

Innowacja pedagogiczna „Lekcje fizyki w języku angielskim” pozwoli na osiągnięcie następujących celów edukacyjnych:

-  uczniowie powinni lepiej poznają  słownictwo z j. angielskiego dla potrzeb  studiów przyrodniczych i technicznych (na uczelniach wszystkich krajów UE)

- poprawa wyników nauczania z przedmiotów kierunkowych poprzez utrwalanie praw i zasad fizycznych w języku angielskim

- poprawa wyników egzaminów maturalnych, zarówno z fizyki,  jak i języka angielskiego

- rozwijanie zdolności i zainteresowań przedmiotowych,

- promocja szkoły, zainteresowanie ofertą szkoły, a zwłaszcza klasą matematyczno-fizyczną

- propagowanie realizowanej innowacji w innych szkołach,

- wzrost aktywności i zaangażowania uczniów, 

- poprawa umiejętności korzystania z technik informacyjno-komunikacyjnych (stosowanie tablicy interaktywnej, komputera, zasobów otwartych),

- ukierunkowanie zawodowe, lepsze przygotowanie do ewentualnych studiów (przyrodniczych lub technicznych)

- podniesienie kompetencji  nauczycieli realizujących innowację

.

            Innowacja pedagogiczna programowa utrwala wiedzę z fizyki poprzez definiowanie znanych już praw w języku angielskim. Analiza rysunków i filmów opisujących różnorodne zjawiska fizyczne w języku angielskim da możliwość uczniom formułowania wniosków i spowoduje  rozwijanie wyobraźni oraz poprawi logiczne myślenie.

Nabyte umiejętności językowe ułatwią absolwentom podjęcie studiów na atrakcyjnych kierunkach w całej Europie, a po ich ukończeniu zdobycie ciekawej pracy.

      Zajęcia odbywać się będą w pracowni fizycznej, która jest wyposażona w sprzęt komputerowy, rzutnik i tablicę interaktywną. Dostępne oprogramowanie i środki TIK umożliwią uczniom zrozumienie fizyki w języku angielskim, łatwiejsze tłumaczenie tekstów oraz utrwalanie słownictwa.