Topic outline

  • General

  • UNIT 1:APPLICATIONS OF THERMODYNAMICS LAWS

    Mutesi is a parent of two children at a certain school. Before she takes them 
    to school, she first makes sure that she prepares food and drinks for them 
    and packs some in flasks so that her children can eat and drink during lunch 
    time. 
    She then drives them to school before she reports to her working place and 
    then from the school she then diverts to her working place which is about 5 
    km away from the school.
    The parking yard at her work place is a plain place without any shade but she 
    makes sure that her car is parked near a tree that is near the parking yard 
    to prevent it from different damages among which is destruction of tyres of 
    the car.
    a) Explain why Mutesi makes use of flasks not normal utensils like metallic 

    bowels while parking foods and drinks for her children.

    b) Is there heat exchange inside the flasks? Explain your reasoning.
    c) Imagine on a certain day these two children only eat food and leaves, 
    the drink in the flask and by mistake they forget flask in the store and 
    the mother come to pick it the next day. Do you think the contents in the 
    flask will be at the same temperatures? Explain all scientific phenomena 
    that may lead to either loss or gain in energy of the contents in the flask.
    d) Explain why in most cases the outer covering of a flask is always made 
    of a poor conductor? Explain how quality and efficiency of these flasks 
    can be improved by manufactures.
    e) Based on statements above, Mutesi normally parks her car under a 
    shade to prevent her car from being exposed to sunshine. Explain how 
    during hot days the tyres of a car may burst.
    f) Her Car uses petrol in operation. During operation of her car, the engine 
    draws fuel (Petrol) air mixture from the tank into the engine, explain 

    all the processes that take place in the engine.

    Thermodynamics refers to the study of heat and its transformation into 
    mechanical energy.
    In thermodynamics, the internal energy is one of the two extremely important 
    state functions of the variables of a thermodynamic system. It refers to total 
    energy contained within the system excluding the kinetic energy of motion of 
    the system and the potential energy of the system due to external forces. It 

    keeps account of the gains and losses of energy of the system.

    The internal energy of a system may be changed by 
    i) heating the system
    ii) doing work on it, 
    iii) adding or taking away matter.
    The thermal energy is the portion of internal energy that changes when the 
    temperature of the system changes. Sometimes the term thermal energy is 
    used to mean internal energy. Heat is defined as the transfer of energy across 
    the boundary of a system due to a temperature difference between the system 
    and its surroundings. 
    When you heat a substance, you are transferring energy into it by placing it 
    in contact with surroundings that have a higher temperature. For example, 
    when you place a pan of cold water on a stove burner, the burner is at a higher 
    temperature than the water, and so the water gains energy. 
    In daily life, we recognize the difference between internal energy and heat. The 
    heat transfer is caused by a temperature difference between the system and its 
    surroundings. However, in some systems there are no temperature and pressure 

    gradients, such systems are said to be in thermodynamic equilibrium.



    Consider a gas contained in a cylinder fitted with a movable piston. At 
    equilibrium, the gas occupies a volume V and exerts a uniform pressure P on 
    the cylinder’s walls and on the piston. If the piston has a cross-sectional area 
    A, the force exerted by the gas on the piston is F = PA. Now let us assume that 
    we push the piston inward and compress slowly to allow the system to remain 

    essentially in thermal equilibrium.


    With work done by the force due to pressure, we find the same relation but 
    having a negative sign. The force is exerted in opposite direction and the final 

    volume is less than the initial one.

    The total work done on the gas as its volume changes from initial volume (Vi ) 
    to final volume (Vf ) is given by the above equation.
    If the gas is compressed, ΔV is negative and the work done on the gas is positive 
    (Work done by the gas is positive) and if the gas expands, ΔV is positive and 
    the work done on the gas is negative (Work done on the gas is negative). If 
    the volume remains constant, the work done on the gas is zero. Thus, no work 
    done. To evaluate this relation, one must know how the pressure varies with 
    volume during the process.
    The work done on a gas in a quasi-static process that takes the gas from an 
    initial state to a final state is the negative of the area under the curve on a PV 
    diagram, evaluated between the initial and final states.
    Based on the processes of compressing a gas in the cylinder indicated in figure 
    1.1, the work done depends on the path taken between the initial and final 

    states

    1.3.1. First law of Thermodynamics
    It states that the change in internal energy of a system is equal to the heat added 
    to the system minus the work done by the system. Therefore, the law stated 
    gives mathematical treatment of internal energy of a system shown below.

    Hence the first law of thermodynamics.

    Note: 
    - The first law of thermodynamics is a special case of the law of conservation 
    of energy that encompasses changes in internal energy and energy 
    transfer by heat and work. 
    - It is a law that can be applied to many processes. It is noticed that energy 
    can be transferred between a system and its surroundings. 
    - One is work done on the system, which requires that there be a macroscopic 
    displacement of the point of application of a force. 
    - The other is heat, which occurs on a molecular level whenever a 
    temperature difference exists across the boundary of the system.
    - Both mechanisms result in a change in the internal energy of the system 
    and therefore usually result in measurable changes in the macroscopic 
    variables of the system, such as the pressure, temperature, and volume 
    of a gas.
    - The increase in internal energy of a system is the sum of the work done on 
    the system and the heat supplied to the system.
    - One of the important consequences of the first law of thermodynamics 
    is that there exists a quantity known as internal energy whose value is 
    determined by the state of the system. The internal energy is therefore a 
    state variable like pressure, volume, and temperature.
    - The first law of thermodynamics is an energy conservation equation 
    specifying that the only type of energy that changes in the system is the 

    internal energy ΔU.


    1.3.3. Applications of first law of Thermodynamics
    The first law of thermodynamics that we discussed relates the changes in 
    internal energy of a system to transfers of energy by work or heat. In this case 
    , we consider applications of the first law in processes through which a gas is 

    taken as a model.

    ISOBARIC PROCESS
    A process that occurs at constant pressure is called an isobaric process. In such 
    processes, the values of the heat and the work are both usually nonzero. The 

    work done during isobaric process is simply

     

    Since the first law of thermodynamics states that energy is conserved. There 
    are, however, many processes we can imagine that conserve energy but are not 
    observed to occur in nature. Lets consider an example below of the first law to 
    introduce the second law.
    For example, when a hot object is placed in contact with a cold object, heat 
    flows from the hotter one to the colder one, never spontaneously the reverse. 
    If heat were to leave the colder object and pass to the hotter one, energy could 
    still be conserved. Yet it doesn’t happen spontaneously the reverse.
    There are many other examples of processes that occur in nature but whose 
    reverse does not. To explain this lack of reversibility, scientists in the latter half 
    of the nineteenth century formulated a new principle known as the second 

    law of thermodynamics. 

    The second law of thermodynamics is a statement about which processes occur 
    in nature and which do not. It can be stated in a variety of ways, all of which are 
    equivalent. One statement is that: “Heat can flow spontaneously from a hot 
    object to cold object; heat will not flow spontaneously from a cold object 
    to a hot object”. 
    The development of a general statement of the second law of thermodynamics 
    was based partly on the study of heat engines. A heat engine is any device 
    that changes thermal energy into mechanical work, such as steam engines and 

    automobile engines.

    1.4.2.3. Impact of heat engines on climate
    Most of air pollution is caused by the burning of fuels such as oil, natural gas 
    etc. The air pollution has an adverse effect on the climate. Climate change is the 
    greatest environmental threat of our time endangering our health. When a heat 
    engine is running, several different types of gases and particles are emitted that 
    can have detrimental effects on the environment.
    Of concern to the environment are carbon dioxide, a greenhouse gas; and 
    hydrocarbons. Engines emit greenhouse gases, such as carbon dioxide, which 
    contribute to global warming. Fuels used in heat engines contain carbon. The 
    carbon burns in air to form carbon dioxide. 
    The Carbon dioxide and other global warming pollutants collect in the 
    atmosphere and act like a thickening blanket and destroy the ozone layer. 
    Therefore, the sun’s heat from the sun is received direct on the earth surface 
    and causes the planet to warm up.
    As a result of global warming, the vegetation is destroyed, ice melts and water 
    tables are reduced. Heat engines especially diesel engines produce Soot which 
    contributes to global warming and its influence on climate. 
    The findings show that soot, also called black carbon, has a warming effect. 
    It contains black carbon particles which affect atmospheric temperatures in a 
    variety of ways. The dark particles absorb incoming and scattered heat from the 
    sun; they can promote the formation of clouds that can have either cooling or 
    warming impact.Therefore soot emissions have significant impact on climate 
    change.
     Similarly, some engines leak, for example, old car engines and oil spills all over. 
    When it rains, this oil is transported by rain water to lakes and rivers. The oils 
    then create a layer on top of the water and prevent free evaporation of the water.
    1.4.3. Carnot cycle and Carnot engine
    In 1824 a French engineer named Sadi Carnot described a theoretical engine, 
    now called a Carnot engine, which is of great importance from both practical 
    and theoretical viewpoints. He showed that a heat engine operating in an ideal, 
    reversible cycle—called a Carnot cycle—between two energy reservoirs is the 
    most efficient engine possible.
    An ideal engine establishes an upper limit on the efficiencies of all other engines. 
    That is, the net work done by a working substance taken through the Carnot 
    cycle is the greatest amount of work possible for a given amount of energy 
    supplied to the substance at the higher temperature. 
    Carnot’s theorem can be stated that no real heat engine operating between 
    two energy reservoirs can be more efficient than a Carnot engine operating 
    between the same two reservoirs.
    Note: No Carnot engine actually exists, but as a theoretical idea it played an 
    important role in the development of thermodynamics.
    The idealized Carnot engine consisted of four processes done in a cycle, two of 
    which are adiabatic (Q = 0) and two are isothermal (ΔT = 0). This idealized cycle 
    is shown in figure 1.8.

    From P-V diagram for the Ideal Diesel cycle, the cycle follows the numbers 1-4 
    in clockwise direction. The image on the top shows a P-V diagram for the ideal 
    Diesel cycle; where P is pressure and V is specific volume. The ideal Diesel cycle 
    follows the following four distinct processes (the color references refers to the 
    color of the line on the diagram.
    • Process 1-2 is isentropic (adiabatic) compression of the fluid (blue 
    color). 
    • Process 2-3 is reversible (isobaric constant pressure heating (red). 
    • Process 3-4 is isentropic (adiabatic) expansion (yellow). 
    • Process 4-1 is reversible constant volume cooling (green). 
    The Diesel is a heat engine; it converts heat into work. The isentropic processes 
    are impermeable to heat; heat flows into the loop through the left expanding 
    isobaric process and some of it flows back out through the right depressurizing 
    process, and the heat that remains does the work. 













  • UNIT 2:WAVE AND PARTICLE NATURE OF LIGHT

    Observe the pictures A and B, and answer with scientific explanations the 
    following questions:
    1) a) Who will absorb more heat/radiations?
    b) In the dried clothes, which cloth will dry faster? 
    c) Basing on observations made, explain why in most schools white 
    shirts and blouses are preferred instead of other colours.
    2) a) In packaging silvered foils are used to wrap most of fished products. 
    Explain why these foils are preferred instead of darkened foils.
    b) Explain why it’s not recommended to paint inside one’s room with a 
    black paint? 
    c) Explain the variations in temperatures inside a house that is roofed 
    using black coloured iron sheets and one roofed using white iron 

    sheets.

    2.1.1. Concept of light
    Particle theory of light
    The nature and properties of light have been a subject of great interest and 
    speculation since ancient times. Until the time of Isaac Newton (1642–1727), 
    the Greeks believed that light consisted of tiny particles that either were 
    emitted by a light source or emanated from the eyes of the viewer. 
    Newton the chief architect of the particle theory of light held that light consisted 
    of tiny particles that were emitted from a light source and that these particles 
    stimulated the sense of sight upon entering the eye. By particle theory, he was 
    able to explain reflection and refraction of light. 
    However , derivation of the law of refraction depend on the assumption that 
    light travels faster in water and in glass than in air, an assumption later shown 
    to be false. Most scientists accepted Newton’s particle theory. 
    Wave theory of light
    In the mid-seventeenth century, the Jesuit priest Francesco Grimaldi (1618–
    1663) had observed that when sunlight entered a darkened room through a 
    tiny hole in a screen, the spot on the opposite wall was larger than would be 
    expected from geometric rays. He also observed that the border of the image 
    was not clear but was surrounded by colored fringes. Grimaldi attributed this 
    to the diffraction of light. 
    In 1678, one of Newton’s contemporaries, the Dutch physicist and astronomer 
    Christian Huygens (1629–1695), was able to explain many other properties of 

    light by proposing that light is a wave.

    By wave theory of light, Huygens was able to explain reflection and refraction 
    of light by assuming that light travels more slowly in water and in glass than in 
    air. Huygens’ Principle is particularly useful for analyzing what happens when 
    waves run into an obstacle. 
    The bending of waves behind obstacles into the “shadow region” is known as 
    diffraction. Since diffraction occurs for waves, but not for particles, it can serve 
    as one means for distinguishing the nature of light. 
    In 1801, the Englishman Thomas Young (1773–1829) provided the first clear 
    demonstration of the wave nature of light and showed that light beams can 
    interfere with one another, giving strong support to the wave theory. Young 
    showed that, under appropriate conditions, light rays interfere with each other. 
    Such behaviour could not be explained at that time by a particle theory because 
    there was no conceivable way in which two or more particles could come 
    together and cancel one another. 
    The general acceptance of wave theory was due to the French physicist 
    AugustinFresnell (1788-1827), who performed extensive experiments on 
    interference and diffraction and put the wave theory on a mathematical basis. 
    In 1850, Jean Foucault measured the speed of light in water and showed that 

    it is less than in air, thus ruling out Newton’s particle theory.





    be explained by wave theory and not by particle nature of light. 
    • Energy distribution in perfect black body radiation, photoelectric effect 
    and Compton Effect can be explained by particle nature of light and not 
    by wave theory. The concept of quantum mechanics is applied even to 
    the motion of electrons in an atom in Bohr’s atomic model.
    Principle of complementarities
    Some experiments indicate that light behaves like a wave; others indicate 
    that it behaves like a stream of particles. These two theories seem to be 
    incompatible, but both have been shown to have validity. Physicists finally 
    came to the conclusion that this duality of light must be accepted as a fact of life. 
    It is referred to as the wave particle duality. To clarify the situation, the great 
    Danish physicist Niels Bohr (1885–1962) proposed his famous principle of 
    complementarity. It states that: 
    “To understand an experiment, sometimes we find an explanation using 
    wave theory and sometimes using particle theory. Yet we must be aware 
    of both the wave and particle aspects of light if we are to have a full 
    understanding of light.” 
    We need both to complete our model of nature, but we will never need to use 
    both at the same time to describe a single part of an occurrence. Therefore 
    these two aspects of light complement one another. We cannot readily picture 
    a combination of wave and particle. Instead, we must recognize that the two 
    aspects of light are different “faces” that light shows to experimenters.
    2.1.4. Wave Nature of Matter
    In 1924, Louis de Broglie (1892–1987) extended the idea of the wave–particle 
    duality. He formulated the hypothesis, claiming that all matter, not just light 
    only, has a wave like nature. He related the wavelength (λ ) and the momentum 
    (p) by the equation.



    2.1.5. Types of photon Interactions
    When a photon passes through matter, it interacts with the atoms and electrons. 
    There are four important types of interactions that a photon can undergo:
    1. The photoelectric effect: A photon may knock an electron out of an atom 
    and in the process the photon disappears. To escape from the surface, an 
    electron must absorb enough energy from the incident light to overcome 
    the attraction of positive ions in the material. These attractions constitute 
    a potential-energy barrier; the light supplies the “kick” that enables the 
    electron to escape. The photoelectric effect provides convincing evidence 
    that light is absorbed in the form of photons. 
    2. The photon may knock an atomic electron to a higher energy state in the 
    atom if its energy is not sufficient to knock the electron out altogether. In 
    this process the photon also disappears, and all its energy is given to the 
    atom. Such an atom is then said to be in an excited state.
    3. Compton Effect: The photon can be scattered from an electron (or a nucleus) 
    and in the process lose some energy; this is the Compton Effect(Fig. 2.1). 
    But notice that the photon is not slowed down. It still travels with speed c, 

    but its frequency will be lower because it has lost some energy.

    A single photon of wavelength strikes an electron in some material, 
    knocking it out of its atom. The scattered photon has less energy (some 
    energy is given to the electron) and hence has a longer wavelength (shown 
    exaggerated). 
    4. Pair production: If a gamma-ray photon of sufficiently short wavelength 
    is fired at a target, it may not scatter. Instead, as depicted in Fig.2.2, it may 
    disappear completely and be replaced by two new particles: an electron
    and a positron (a particle that has the same rest mass as an electron but 
    has a positive charge rather than the negative charge of the electron). 
    This process, called pair production, was first observed by the physicists 
    (Patrick Blackett and Giuseppe Occhialini). The electron and positron have 

    to be produced in pairs in order to conserve electric charge.

    The inverse process, electron–positron pair annihilation, occurs when a 
    positron and an electron collide. 
    In pair production, the photon disappears in the process of creating the 
    electron–positron pair. This is an example of mass being created from pure 

    energy, and it occurs in accord with Einstein’s equation.

            

    2.2.1. Concept of blackbody
    A blackbody is a body that, when cool, would absorb all the radiation falling 
    on it (and so would appear black under reflection when illuminated by other 
    sources). 
    A good approximation to a blackbody is a hollow box with a small aperture in 
    one wall (Fig. 2.2). Light that enters the aperture will eventually be absorbed 
    by the walls of the box, so the box is a nearly perfect absorber. Conversely, 
    when we heat the box, the light that emanates from the aperture is nearly ideal 

    blackbody radiation with a continuous spectrum.

    Note: When the box is heated, the electromagnetic radiation that emerges from 
    the aperture has a blackbody spectrum.
    Our sun, which has a surface temperature of about 6000K, appears yellow, while 
    the cooler star Betelgeuse has a red-orange appearance due to its lower surface 
    temperature of 2900 K. Our body at 310 K emit electromagnetic radiation in 
    the infra-red region of the spectrum, and these can be detected with infra-red 

    sensitive devices.

    The experimental value of the constant in expression above is 2.90 x 10-3 m.K. 
    The spectrum of radiation depends on the temperature and the properties of 
    the object. 
    At normal temperatures , we are not aware of this electromagnetic radiation 
    because of its low intensity. At higher temperatures, there is sufficient infrared 
    radiation that we can feel heat if we are close to the object. 
    At still higher temperatures (on the order of 1000 K), objects actually glow, 
    such as a red-hot electric stove burner or the heating element in a toaster. At 
    temperatures above 2000 K, objects glow with a yellow or whitish color, such 

    as white-hot iron and the filament of a light bulb.

    The spectrum of light emitted by a hot dense object is shown in Fig. 2.3 for an 
    idealized blackbody. The radiation such an idealized blackbody would emit 
    when hot and luminous, called blackbody radiation (though not necessarily 
    black in color), and approximates that from many real objects. 
    The 6000 K curve in Fig. 2.3, corresponding to the temperature of the surface of 
    the Sun, peaks in the visible part of the spectrum. For lower temperatures, the 
    total intensity drops considerably and the peak occurs at longer wavelengths 
    (or lower frequencies). 
    This is why objects glow with a red color at around 1000 K. Measured spectra 
    of wavelengths and frequencies emitted by a blackbody at three different 

    temperatures.

     

    In 1920, Arthur Holly Compton investigated the scattering of monochromatic 
    x-rays (electromagnetic radiation) from various materials. In his experiment 
    Compton aimed a beam of x rays at a solid target and measured the wavelength 
    of the radiation scattered from the target (Fig. 2.4). The incident photon would 
    give up part of its energy and momentum to the electron, which recoils as a 

    result of this impact.

    The scattered photon that remains can fly off at a variety of angles θ with 
    respect to the incident direction, but it has less energy and less momentum 
    than the incident photon (Fig.2.4). 
    Therefore, in the photon model, the scattered light has a lower frequency and 
    longer wavelength than the incident light. This is precisely what the photon 
    model predicts for light scattered from electrons in the target, a process that is 

    now called Compton scattering.













  • UNIT 3:SIMPLE HARMONIC MOTION

    a) Based on your observation,describe the motion of pupils in 
    i). Child’s swing
    ii). Merry-Go-Round.
    b) How is the kinds of motion described in a) above differ from linear 
    motion?
    c) By using the situation above, state and explain all the energy changes 
    before and after undergoing motion.
    d) How is the study of such kinds of motion in physics significant in real 

    life situations?

    a) Examine the type of motion undergone by the bob in the pendulum.
    b) Can you guess a point where the bob moves fast. Explain to support 
    your decision.
    c) Discuss some of the factors that can make the bob to move faster or 
    slower while in the swing.
    d) Would the bob continue oscillating indefinitely if displaced? If yes 

    explain why? If not, explain why not?

    In simple harmonic motion a body moves periodically such that its acceleration 
    is directed towards a fixed point and directly proportional to the displacement 
    of the body from the fixed point, we say that a body has executed simple 
    harmonic motion.
    Simple Harmonic motion can be defined as a special type of periodic motion in 
    which acceleration is directed towards a fixed point and directly proportional 
    to the displacement of the body from that fixed point.
    CHARACTERISTICS OF SIMPLE HARMONIC MOTION 
    i) It is classified under periodic motion. Periodic motion is the motion of 
    the body which continuously retraces its paths in equal intervals of time.
    ii) Its acceleration is directly proportional to the displacement from a fixed 

    point

    iii) Its acceleration is always directed towards a fixed point
    iv) Mechanical energy is always conserved
    Note: The motions, which all repeat in a regular cycle, are examples of periodic 
    motion. Whenever the object is pulled away from its equilibrium position, the 
    net force on the system becomes nonzero and pulls the object back toward 

    equilibrium.

    Example 3.2


    One day you went to a picnic on a certain hotel .In the compound, there 
    is a swinging chair that is suspended on a string. When you sit down 
    on the chair, it oscillates vertically. After the oscillations have stopped, 
    you stand up slowly, and the chair rises up a small distance. Your friend 
    also sits in the chair, and you find that the rate at which the chair is 
    oscillating is different.
    a) Basing on the scenario above,can you predict the kind of oscillator 
    shown above? What other examples of oscillators do you know?
    b) Explain any two factors you think affects the number of oscillations 
    made by the swinging seat.
    c) Imagine, the springs are replaced by an elastic rope. Do you think the 
    seat can swing the same way as when there were springs? Explain 
    your reasoning.
    d) When your friend sat on the same seat, it oscillated with different 
    oscillations. Explain what you think caused the difference?
    The following are some of examples of harmonic oscillators that will be 
    discussed in this unit.
    a) Simple Pendulum,
    b) Mass on a helical spring (Helical Spring mass system)/ Stretched Spring

    c) Water in a U-tube

    3.2.1. Simple Pendulum
    A pendulum consists of a small mass m attached to the end of wire/thread of 
    length l and the other end is attached to the fixed-point p. 
    If we displace the mass slightly and release it, we have the oscillation. The arc of 
    a circle of center P and radius l whose o is the equilibrium point.

     

                      

            

        

              

               

       

              

              

  • UNIT 4:PROPAGATION OF MECHANICAL WAVES

    Materials: Two torches of the same intensity, Screen, material with two 
    small slits and material with big slits.
    Procedures:
    Arrange the materials as shown in the illustration above following the 
    procedures to complete the investigation:
    a) The first student at position A switched on the torch and light passed 
    through one slit. What do you think is the nature of image(s) observed on 
    the screen by second student at position B or C?
    b) Explain what causes the nature of the image(s) observed on the screen.
    c) Assuming the first Student at position A used two torches giving light of 
    same intensities torching on two slits simultaneously, would image(s) on 
    the screen be identical as observed in (a) above. Explain to justify your 

    observation.

    d) Now, if small slits are replaced with ones of big holes (widened slits). 
    Explain what this change will have on the images formed on the screen.
    e) Explain why do we not ordinarily observe wave behaviour for light, such 
    as observed in Young’s double slit experiment?

    f) Explain how this experiment is significant in real life

    4.1.1. Coherent sources
    Coherent sources are those which emit light waves of the same wavelength or 
    frequency which are always in phase with each other or have a constant phase 
    difference. Two coherent and monochromatic sources can together produce 
    the phenomenon of interference. 
    When light passes through a slit with a size that is close to the light’s wavelength, 

    the light will diffract, or spread out in waves. 

    Interference is a phenomenon in which two waves superpose(meet) to form a 
    resultant wave of greater, lower, or the same amplitude.
    Young’s method for producing two coherent light sources involves illuminating 
    a pair of slits with a single source. Another arrangement for producing an 

    interference pattern with a single light source is known as Lloyd’s mirror.


    A point light source is placed at point S close to a mirror, and a viewing screen 
    is positioned some distance away and perpendicular to the mirror. Light waves 
    can reach point P on the screen either directly from S to P or by the path 
    involving reflection from the mirror.
    An interference pattern is produced at point P on the screen as a result of the 
    combination of the direct ray (blue) and the reflected ray (brown). The reflected 
    ray undergoes a phase change of 180°.
    In order to observe interference in light waves, the following conditions must 
    be met:
    • The sources must be coherent—that is, they must maintain a constant 
    phase with respect to each other.
    • The sources should be monochromatic—that is, of a single wavelength.
    • The interfering waves Must Obey the Principal of superposition.
    As an example, single-frequency sound waves emitted by two side-by-side 
    loudspeakers driven by a single amplifier can interfere with each other because 
    the two speakers are coherent—that is, they respond to the amplifier in the 
    same way at the same time.
    If two light bulbs are placed side by side, no interference effects are observed 
    because the light waves from one bulb are emitted independently of those 
    from the other bulb. The emissions from the two light bulbs do not maintain 
    a constant phase relationship with each other over time. Light waves from an 
    ordinary source such as a light bulb undergo random phase changes in time
    intervals less than a nanosecond. Such light sources are said to be incoherent.
    When light passes through two or slits, the waves from one slit will interfere
    with the waves from the other: 
    • Constructive interference occurs when two crests or two troughs meet 
    forming a wave with a larger crest or lower trough. 
    • Destructive interference occurs when a crest meets a trough cancelling 
    each other to produce a smaller wave or no wave at all.
    4.1.2. Principle of superposition
    The principle of superposition states that when two or more waves meet at a 
    point, the resultant displacement at that point is the vector sum of the individual 
    displacement of each wave













      



    4.2.1. Concept of stationary wave
    Standing wave also known as a stationary wave, is wave pattern that results 
    when two waves of the same frequency; wavelength and amplitude travelling in 
    opposite directions in the same medium interfere or meet. 
    The point at which the two waves cancel are called node. There is no motion 
    in the string at the nodes, but midway between two adjacent nodes, the string 
    vibrates with the largest amplitude. These points are called antinodes. At 

    points between successive nodes the vibrations are in phase.


     

          

  • UNIT 5:FOSSIL, NON FOSSIL FUEL AND POWER PRODUCTION


    Most of the energy that we consume comes from fossil fuels. Coal, petroleum and 
    natural gas are called fossil fuels. Millions of years ago, during the carboniferous 
    age, due to the change in atmospheric conditions and other changes, the forests 
    were destroyed and they were fossilized. 
    With the action of bacteria and other microorganisms on the surface of the 
    earth, these trees and other vegetations were decayed and disintegrated. Years 
    after these trees were available in solid, liquid and gaseous state. The solid 

    form is coal. It is the most widely used form of fossil fuel for domestic purposes.


    5.1.1. Fossil fuel
    History of usage of Fossil Fuel
    Before steam engines were invented, heavy industry depended on mechanical 
    water power to grind flour, saw wood, and so forth. Industrialization led to a 
    higher rate of energy usage. Fossil fuel led to development and it played a crucial 
    rule as energy sources, inputs for agriculture, and feed stocks for chemical 
    manufacture. The Industrial Revolution marked a big change for people of the 
    world. 
    Many of the agriculture based societies that used human and animal labor forces 
    switched to use machines to do work. Coal was commonly used in the early era 
    of industrialization until internal combustion engine and the automobile were 

    invented. Oil and gas became the most common fossil fuel people used. 

    Fossil fuels are hydrocarbons, primarily coal, fuel oil or natural gas, formed 
    from the remains of dead plants and animals. In common dialogue, the term 
    ‘fossil fuel’ also includes hydrocarbon-containing natural resources that are not 
    derived from animal or plant sources.
    Coal, oil and natural gas are called ‘fossil fuels’ because they have been formed 
    from the fossilized remains of prehistoric plants and animals. Fossil fuels are 
    non-renewable energy source since they take millions of years to form. They 
    ultimately get their energy from the sun.
    Types of Fossil Fuels 
    • Coal 
    Coal is a hard, black colored rock-like substance formed when dead plants were 
    subjected to extreme heat and pressure for millions of years. Coal is formed 
    through coalification. Coal is made of decomposed plant matter in conditions 
    of high temperature and pressure. Its formation is similar to oil’s but it takes 
    less time to form.
    It is made up of carbon, hydrogen, oxygen, nitrogen and varying amounts of 
    sulphur. There are two ways to mine coal: surface mining and underground 
    mining. 
    • Natural Gas 
    Natural gas is formed from the remains of tiny sea animals and plants that 
    died millions of years ago. The gas then became trapped in layers of rock-like 
    water in a wet sponge. Raw natural gas is a mixture of different gases. Its main 
    ingredient is methane. The strange smell of natural gas (like rotten eggs) comes 
    from a chemical added by the companies. 
    • Oil (Petroleum) 
    Oil is formed from the remains of animals and plants that died millions of years 
    ago. The organic material was then broken down into hydrogen and carbon 
    atoms and a sponge-like rock was formed, full of oil. 
    Oil cannot be used as it is when it is drawn from the ground. Oil refineries clean 
    and separate the oil into various fuels and by products. The most important of 

    these is gasoline.

    Uses of Fossil Fuels 
    The main systems of fossil fuels are the steam cycle and the gas turbine 
    cycle. Fossil fuels are used to generate electrical energy in a series of energy 

    transformations. The following is an example:


    Advantages of Fossil Fuels
    1. Can be easily transported via pipelines, railroads, trucks and ships.
    2. They are easily available. More and more extractions are occurring all over 
    the world and therefore resulting in a large amount of readily available 
    energy sources.
    3. Oil refineries close to the sea have easy access to shipping.
    4. Fossil fuels are easily combustible. In other words, they produce larger 
    amounts of energy.
    5. Creates infrastructure jobs for the surrounding communities.
    6. Much of our infrastructure is designed to run using fossil fuels.
    7. Although fossil fuels are considered as a relatively new energy source, in 
    reality they have been around for hundreds of years.
    8. Every machine that is not run by electricity uses fossil fuels. Vehicles, 
    machines, devices, etc. are powered by coal, petroleum or natural gas.
    9. They are considered to be very stable.
    10. They are easy to set up. Since fossil fuels are easily available, their power 
    plants can be constructed anywhere in the world. They are also easier 
    to extract and process, as well as capable of producing large amounts of 
    energy at a single location.
    11. Fossil fuels are easy to store and transport because they are so stable. They 
    are easily distributed.
    12. Easy transportation allows countries around the world to enjoy affordable 
    power.

    13. The price of fossil fuels is inexpensive compared to other sources of energy.

    Disadvantages of Fossil Fuels
    Fossil fuels, for all their pros, have many cons that have major concerns for 
    human being, animals and the environment.
    The biggest disadvantage of fossil fuels is the air pollution that many are 
    claiming is causing global warming.It is claimed that with global warming, the 
    Earth’s climates are changing. Below is a list of the disadvantages of fossil fuels.
    1. Air Pollution and its effects on the Earth and environment. This includes the 
    concepts of global warming and climate change.
    2. They are non-renewable sources of energy. As fossil fuels are extracted to an 
    unlimited level, they would surely deplete one day. They are non-renewable, 
    so it is likely that when fuel reserves have been completely used up, there is 
    nothing more left. It wouldtake millions of years to replace them. They are 
    on a limited amount, and we are not actually sure where that limit is.
    3. Pipelines transporting fossil fuels spoil the natural beauty.
    4. They affect marine life through oil spills. Fossil fuels, being needed to be 
    transported to their processing plants via land, air and water poses a threat 
    to the environment. The process can involve leaks in oil tankers or ships 
    getting drowned deep under the sea. The crude oil contains some toxic 
    substances that, when mixed up with water, pose serious hazards to marine 
    life. 
    5. Risk of political issues and terrorism
    6. Most facilities that are powered by coal require large quantities of coal to 
    have on hand for use. Storage facilities for the coal are required, this can be 
    pricey.
    7. Coal mining is a very dangerous and many workers have been killed in the 
    mines as well as becoming ill with lung diseases after working the coal 
    mines.
    8. While fossil fuels are relatively inexpensive, the prices are rising due to 
    Middle Eastern countries holding large reserves of oil such as petroleum.
    9. Coal mining has created destroyed lands and the mines are creating hazards 
    in the event of natural disasters.
    10. They need huge amounts of reserves. Coal power plants for example need 
    regular and huge supply of resources to produce large amounts of electricity 
    on a constant basis, which means they need reserves to carry out their 
    operations.
    11. The extraction of natural gas is leaving large craters within the Earth’s 

    surface.

    5.1.2. Non fossil fuel
    Non fossil fuels are alternative sources of energy or renewable source of energy 
    that do not rely on burning up limited supply of coal, oil or natural gas. They 
    should generate power that can be utilized indefinitely. They include sun light, 
    wind, hydro, tidal and waves from water, geothermal all of them generate 

    energy.


    Non-fossil fuels are considered to be extremely important for power creation. 
    This is because they are usually renewable energy sources that could be tapped 
    for hundreds of years and not run out. In addition, energy production using 
    non fossil-based fuels usually generates much less pollution than fossil-based 

    energy sources.



    It is easy to think that the advantages of fossil fuels outweigh their disadvantages. 
    All over the World, Fossil fuels are gaining popularity as energy sources because 
    they are relatively inexpensive and look like clean. Remember that fossil fuels 
    are comprised of three substances: coal, oil and gas. In the following lines we 
    are going to discuss some of the common advantages and disadvantages of 
    fossil fuels transportation and storage.
    5.2.1. Advantages associated with transportation and storage of 
    fossil fuels
    - The majority of oil transported by maritime means reaches their 
    destination. Normally there are no serious oil spillages. In fact, as soon as 
    the pipeline is damaged by accident or sabotage, pumping is stopped and 
    pollution remains limited. 
    - Oil depots are usually situated close to oil refineries or in locations where 
    marine tankers containing products can discharge their cargo.
    - The long life of the permanent assets, relatively trouble-free operation 
    with minimum maintenance, the large-volume shipments that are 
    possible, the high mechanical efficiencies that are obtained with low 
    rolling resistances. 
    - The total costs of moving slurry during the life of the line do not increase
    in proportion to inflation. The advantage over rail and truck transport is 
    clear, as the costs of these latter modes escalate with inflation.
    - Taller and wider stockpiles reduce the land area required to store a set 
    tonnage of coal. Larger coal stockpiles have a reduced rate of heat lost, 
    leading to a higher risk of spontaneous combustion.
    - Waterways are usually circuitous, resulting in slow delivery times. 
    However, transport of coal on barges is highly cost-efficient.
    - Transportation by gas pipelines are less costly and are thus more common.
    5.2.2. Disadvantages associated with transportation of fossil fuels
    - At sea, the relative disadvantages derive from the possibilities of oil spills 
    and discharging of polluting products such as the residue from tank and 
    bilge cleaning.
    - Oil is always corrosive to a greater or lesser extent, because it contains 
    acidic gases. The pipes deteriorate from the inside and if they are not 
    changed in time, they finish by leaking. 
    - The construction of major pipelines crossing several countries requires 
    intense negotiation.
    - On the other hand, slurry pipelines involve potential environmental 
    problems. Water requirements are substantial: almost one ton of water is 
    needed to move one ton of coal.
    - Even though pipelines are useful, in certain cases the construction of gas 

    pipelines is technically impossible or too expensive.



    Fossil fuels have been formed from the organic matter: these are remains of 
    long-dead plants and animals. They contain a high percentage of carbon and 
    hydrocarbons. Primary sources of energy we are using in our country and 
    around the world in particular include petroleum, coal, and natural gas, all 
    fossil fuels. With the needs increase of energy, the production and use of these 
    fossil fuels create serious environmental concerns. Until a global movement for 
    renewable energy is successful, the negative effects of fossil fuel will continue.
    5.3.1. Climate Change and Global Warming
    Global warming occurs when carbon dioxide is accumulated in the atmosphere. 
    Carbon monoxide is produced by the combustion of fossil fuels and converted 
    into carbon dioxide. These gases trap more sunlight; therefore, less light is 
    reflected back into space. They are called Greenhouse Gases, because the 
    effect is like being in a plant glasshouse, or in a car with the windows wound 
    up. As a result, the surface temperature of the earth is increasing drastically.
     If the increase is enough it will distress the ecological systems. The 
    consequences are: severe weather, droughts, floods, drastic temperature 
    changes, heat waves, and more severe wildfires. Food and water supplies 
    are also threatened. Tropical regions will expand; allowing disease-carrying 
    insects to expand their ranges.
    5.3.2. Hole in the Ozone Layer
    Ozone is a gas in the Earth’s upper atmosphere whose chemical formula is O3
    Ozone acts to block out much of the sun’s ultraviolet radiation which causes 
    skin cancer and contributes to the fluctuations of global climatic conditions 
    that affect the environment. 
    However, the World is facing a serious confrontation as the emissions of 
    chlorofluorocarbons and other destructive gases are causing ozone holes to 
    appear in the stratospheric ozone layer. As a consequence, the concentration of 
    detrimental ultraviolet radiation is increasing at ground level and jeopardizing 
    humans, crops and ecosystems.
    5.3.3. Acid rain
    Acidic rain, which is made up of several acidic compounds, forms when sulfur 
    dioxide and nitrogen dioxide react in the air with water, oxygen and other 
    chemicals. The wind carries the acidic compounds into the air, and they later 
    fall to the ground in either dry or wet form.
    They form an acidic ‘rain’ which can destroy vegetation. Some of these gases 
    are from natural sources, such as lightning, decomposing plants and volcanoes. 
    However, much of these gases are the result of emissions from cars, power 
    stations, smelters and factories.
    The effects of acid rain are as follows :
    - Acidification of lakes, streams, and soils .
    - Direct and indirect effects (release of metals, for example: Aluminum 
    which washes away plant nutrients).
    - Killing of wildlife (trees, crops, aquatic plants, and animals).
    - Decay of building materials and paints, statues, and sculptures .

    - Health problems (respiratory, burning- skin and eyes)

    5.3.4. Air Pollution
    Air pollution is the release of excessive amounts of harmful gases (e.g. methane, 
    carbon dioxide, sulphur dioxide, nitrogen oxides) as well as particles (e.g. dust 
    of tyre, rubber, and lead from car exhausts) into the atmosphere. Areas of 
    high air pollution indexes have populations with higher rates of asthma than 
    cleaner environments do. 
    5.3.5. Changes in Food Supply
    Changing weather affects the agricultural industry and the human food supply. 
    Carbon emissions contribute to increasing temperatures and decreasing 
    precipitation, changing the growing conditions for food crops in many areas. 
    Major changes in crop yield will cause food prices to rise around the world.
     In addition, climate change influenced by carbon emissions forces animals, 
    many of which are hunted as food, to migrate to higher altitudes or northern 
    habitats as the climate warms.
    5.3.6. Water Pollution
    1. Sewage is the household waste water. Many detergents contain phosphates 
    which act as plant fertilizers. When these phosphates and the sewerage reach 
    rivers, they help water plants to grow in abundance, reducing the dissolved 
    oxygen in the river water. 
    2. Biodegradable detergents are more environment-friendly because they are 
    readily broken down to harmless substances by decomposing bacteria.
    3. Suspended solids in water, such as silt reduce the amount of light that reaches 
    the depths of the water in lakes and rivers. This reduces the ability of aquatic 
    plants to photosynthesise and reduce the plant and animal life. Turbidity is 
    the measure of ‘cloudiness’ or the depth to which light can reach in water.
    5.3.7. Population Explosion
    It is the rapid increase in population in developing countries causing famine, 
    and also in developed countries causing more demand for energy and with 

    that, it increases pollution and destruction of the environment.



    Study the figure 5.3 and try to respond to the following questions: 
    i) Predict and write down what is observed in the picture above
    ii) Do you think that the picture above produces food? Explain your 
    reasoning.
    iii) The power Plant ejects big amount of smoke in the atmosphere. 
    What kind of combustibles do you think are used there?
    iv) Apart from the gaseous smoke ejected, discuss other problems 

    met during the production of energy using fossil fuel.

    5.4.1. Nuclear fuel and nuclear fission
    Nuclear fuel is any material that can be consumed to derive nuclear energy. 
    The nuclear fuel can be made to undergo nuclear fission chain reactions in a 
    nuclear reactor. The most common nuclear fuels are 235U (uranium 235) and 
    239Pu (plutonium 239). Not all nuclear fuels are used in fission chain reactions.
    Nuclear fission is a process, by which a heavy nucleus splits into two or more 

    simpler pieces. This process releases a lot of energy.


    When a neutron strikes an atom of uranium, the uranium nucleus splits into 
    two lighter atoms and releases heat simultaneously. Fission of heavy elements 
    is an exothermic reaction which can release large amounts of energy both as 
    electromagnetic radiation and as kinetic energy of the fragments.
    A chain reaction refers to a process in which neutrons released in fission 
    produce an additional fission in at least one further nucleus. This nucleus in 
    turn produces neutrons, and the process continues. If the process is controlled 

    it is used for nuclear power or if uncontrolled it is used for nuclear weapons. 


    5.4.2. Controlled fission (power production) and uncontrolled fission 
    (nuclear weapons)
    Nuclear fission is based upon the release of neutrons during the reaction. If 
    more than one neutron is released for every fission reaction it will accelerate, 
    less than one it will decelerate. 
    Of the three neutrons, liberated during a fission reaction, only one triggers a 
    new reaction and the others are simply captured. The system is in equilibrium. 
    One fission reaction leads to one new fission reaction, which leads to one 

    more, and so on. This is known as controlled fission.

    In an uncontrolled fission reaction (weaponry) the appropriate amount of 235U 
    is simply mixed with a moderator, making the reaction go out of control. As the 
    reaction is out of control, the exponential acceleration of the reactions creates 
    massive amounts of energy.
     This can be kept from going off by keeping the moderator and the 235U separate, 
    both below critical mass, until the desired time of explosion. In a controlled 
    reaction there is a higher proportion of 238U to ease the reaction. 
    However, this is difficult to control as the reaction becomes faster or slower. To 
    counteract this, control rods, made of neutron absorbing materials (i.e. Boron) 
    are added or removed between each fuel rod.
    5.4.3. Problems associated with the production of nuclear power
    - The problem of radioactive waste is still unsolved. The waste from nuclear 
    energy is extremely dangerous and it has to be carefully looked after for 
    several thousand years. 
    - High risks: Despite a generally high security standard, accidents can still 
    happen. It is technically impossible to build a plant with 100% security. 
    A small probability of failure will always last. The consequences of an 
    accident would be absolutely devastating both for human beings and the 
    nature. 
    - The more nuclear power plants (and nuclear waste storage shelters) are 
    built, the higher is the probability of a disastrous failure somewhere in 
    the world. 
    - During the operation of nuclear power plants, radioactive waste is 
    produced, which, in turn, can be used for the production of nuclear 
    weapons.
    - Nuclear power plants could be preferred targets for terrorist attacks. 
    Such a terrorist act would have catastrophic effects for the whole world. 
    - The energy source for nuclear energy is Uranium. Uranium is a scarce 
    resource; its supply is estimated to last only for the next 30 to 60 years 
    depending on the actual demand.
    - The timeframe needed for formalities, planning and building of a new 
    nuclear power generation plant, is in the range of 20 to 30 years in the 
    western democracies. In other words, it is an illusion to build new 

    nuclear power plants in a short time.


    5.5.1. Nuclear Meltdown
    A nuclear meltdown is an informal term for a severe nuclear reactor accident 
    that results in core damage from overheating.
    A nuclear meltdown occurs when a nuclear power plant system or component 
    fails so the reactor core becomes overheat and melts. Usually, this occurs due to 
    the lack of coolant that decreases the temperature of the reactor. The commonly 
    used coolant is water but sometimes a liquid metal, which is circulated past the 
    reactor core to absorb the heat, is also used.
    In another case, a sudden power surge that exceeds the coolant’s cooling 
    capabilities causes an extreme increase in temperature which leads to a 
    meltdown. A meltdown releases the core’s highly radioactive and toxic elements 

    into the atmosphere and environment.

    The causes of a meltdown occur due to:
    Loss of pressure control: The loss of pressure control of confined coolant may 
    be caused by the failure of the pump or having resistance or blockage within 
    the pipes. This causes the coolant to cease flow or insufficiency flow rate to the 
    reactor; thus the heat transfer efficiency decreases.
    Loss of coolant: A physical loss of coolant, due to leakage or insufficient 
    provision, causes a deficit of coolant to decrease the heat of the reactor. A 
    physical loss of coolant can be caused by leakages. In some cases, the loss of 
    pressure control and the loss of coolant are similar because of the systematic 
    failure of the coolant system. 
    Uncontrolled power excursion: A sudden power surge in the reactor is a 
    sudden increase in reactor reactivity. It is caused by an uncontrolled power 
    excursion due to the failure of the moderator or the control that slows down 
    the neutron during chain reaction. A sudden power surge will create a high 
    and abrupt increase of the reactor’s temperature, and will continue to increase 
    due to system failure. Hence, the uncontrollable increase of the reactor’s 
    temperature will ultimately lead to a meltdown. 
    5.5.2. Nuclear (Radioactive) Wastes
    Nuclear wastes are radioactive materials that are produced after the nuclear 
    reaction. Nuclear reactors produce high-level radioactive wastes. The wastes 
    must be isolated from human contact for a very long time in order to prevent 
    radiation.
    Short- and long-term storage of spent nuclear fuel has been a challenge for 
    the industry and policymakers. Spent fuel, if not disposed of properly, could 
    contaminate water supplies or be used by terrorists to create a dirty bomb. In 
    the short-term, spent fuel is stored in pools on-site--but they only need to stay 
    there a few months until they are cool enough to move to dry storage (either on 
    site or in a long-term storage facility). Still, at some plants, fuel rods are packed 
    in pools in numbers well above design specifications and stay in the pools long 
    after they are ready to be moved 
    Efforts to reprocess nuclear waste are expensive and come with associated 
    environmental and security risks. Yet a growing number of countries--including 
    Japan and Russia--have begun fuel recycling projects.
    5.5.3. Security Issues
    Most countries either pursuing nuclear power or currently using it have signed 
    on to the Nuclear Nonproliferation Treaty and have agreed to comply with 
    rules that ensure that they will not use nuclear technologies toward making 
    weapons. However, any country with nuclear technology is considered a 
    proliferation risk.

            

             

    3. Which of the following is true about solar energy?
    a) It is becoming cheaper to produce photovoltaic cells
    b) Solar energy can currently replace all of the energy created by 
    fossil fuels
    c) Most solar panels convert more than 25% of the light that strikes 
    them
    4. Identify three technological challenges that limit the use of solar 
    power in Rwanda.
    a) Weight, cost, toxicity
    b) Aesthetics, toxicity, efficiency
    c) Storage, weight, fragility
    d) Cost, storage, efficiency
    5. Which of the following is NOT utilized in the process of harnessing 
    solar energy?
    a) Gas
    b) Mirrors
    c) Steam
    d) Photovoltaic cells
    6. Which issues would better energy storage technologies help solve?
    a) Inconsistent energy demands
    b) Inconsistent power production
    c) The need to keep inefficient power plants on standby
    d) All of the above
    7. a) Design and explain advantages of non fossil fuel.
    b) Suggest disadvantages of non fuel energy if any.
    8. Evaluate different ways used to eradicate environment pollution in 

    Rwanda.

  • UNIT 6:MOTION IN ORBITS

    People have always enjoyed viewing stars and planets on clear, dark nights. 
    It is not only the beauty and variety of objects in the sky that is so fascinating, 
    but also the search for answers to questions related to the patterns and 
    motions of those objects.
    Until the late 1700s, Jupiter and Saturn were the only outer planets identified 
    in our solar system because they were visible to the naked eye. Combined 
    with the inner planets the solar system was believed to consist of the Sun 
    and six planets, as well as other smaller bodies such as moons. Some of the 
    earliest investigations in physical science started with questions that people 
    asked about the night sky.
    i) Based on the scenario above and the observation from the picture. 
    Briefly summarize what is illustrated in the picture.
    ii) What is the name of belt separating the largest and smallest planets?
    iii) Explain why you think the moon doesn’t fall on the earth.
    iv) Why don’t we fly off into space rather than remaining on the Earth’s 
    surface? Explain your idea.

    v) Explain why planets move across the sky.

    Introduction 
    A natural phenomenon by which all things with mass or energy includingsatellites, 
    planets,stars,galaxies, and even light, are brought toward (or gravitate toward) 
    one another is referred to as gravity or gravitation. On Earth, gravity gives 
    weight to all physical objects around it.
    Gravity is very important to our everyday lives. Without Earth’s gravity we 
    would fly right off it. If you kicked a ball, it would fly off forever. While it might 
    be fun to try for a few minutes, we certainly can’t live without gravity. Gravity 
    also is important on a larger scale. 
    It is the Sun’s gravity that keeps the Earth in orbit around the Sun. Life on Earth 
    needs the Sun’s light and warmth to survive. Gravity helps the Earth to stay at 

    just the right distance from the Sun, so it’s not too hot or too cold.

    a) Discuss the interactions between two stones.
    b) Can the two stones attract one another? Explain your reasoning.
    c) Make a general conclusion about small bodies close to one another
    d) Imagine whether we have two bodies which are massive (too big), 
    explain the difference in interactions of massive bodies and small 

    bodies.Give any examples

    From the time of Aristotle, the circular motions of heavenly bodies were 
    regarded as natural. The ancients believed that the stars, planets, and Moon 
    moved in divine circles, free from any impressed forces. Newton, however, 
    recognized that a force must be acting on the Planets; otherwise, their paths 
    would be straight lines. 
    And whereas others of his time, influenced by Aristotle, said that any such 
    force would be directed along the planets’ motion, Newton reasoned it must 
    be perpendicular to their motion, directed toward the center of their curved 
    paths- toward the sun. This was the force of gravity, the same force that pulls 
    apples off trees.
    The Newton’s law of universal gravitation states that “Every particle in the 
    Universe attracts every other particle with a force that is directly proportional 
    to the product of their masses and inversely proportional to the square of the 
    distance between them”.






    Properties of Gravitational Force
    - It is always attractive in nature while electric and magnetic force can be 
    attractive or repulsive.
    - It is independent of the medium between the particles while electric 
    and magnetic forces depend on the nature of the medium between the 

    particles.

    - It holds well over a wide range of distances. It is found true for 
    interplanetary to inter-atomic distances.
    - It is a central force which means it acts along the line joining the centers 
    of two interacting bodies. 
    - It is a two-body interaction, where gravitational force between two 
    particles is independent of the presence or absence of other particles; so, 
    the principle of superposition is valid, and on the contrary, nuclear force 
    is a many-body interaction. 
    - It is the weakest force in nature. 
    - It is a conservative force,where work done by it is path independent or 
    work done in moving a particle round a closed path under the action of 
    gravitational force is zero. 
    - It is an action reaction pair,where the force with which one body (say, 
    earth) attracts the second body (say, moon) is equal to the force with 
    which moon attracts the earth. This is in accordance with Newton’s third 

    law of motion.

     

    Critically observe the picture above and answer the questions that follow.
    a) Describe the motion of bodies (planets) as indicated in the picture.
    b) Do the different planets pass through the same path? Explain to support your decision.
    c) With clear observations, which body is the largest. Explain to support your selection.
    d) Basing on the knowledge from Newton’s law of gravitation, is there 
    any force of attraction between the body stated in above and other 
    bodies? Explain your reasoning.
    e) If yes, how does the force affect the motion of the bodies as they are 
    in their paths?


    The Sun is not at the center of the ellipse, but is instead at one focus (generally 
    there is nothing at the other focus of the ellipse). 
    The planet then follows the ellipse in its orbit, which means that the Earth-Sun 
    distance is constantly changing as the planet goes around its orbit. 
    For purpose of illustration we have shown the orbit as rather eccentric; 

    remember that the actual orbits are much less eccentric than this. 

    6.2.2. Kepler’s Second Law
    It states that the line joining the planet to the Sun sweeps out equal areas in 

    equal times as the planet travels around the ellipse.

    Kepler’s second law is illustrated in the preceding figure. The line joining the 
    Sun and planet sweeps out equal areas in equal times, so the planet moves 
    faster when it is nearer the Sun. Thus, a planet executes elliptical motion with 
    constantly changing angular speed as it moves about its orbit. 
    What happen is best understood in terms of energy. As the planet moves away 
    from the Sun (or the satellite from Earth), it loses energy by overcoming the 
    pull of gravity, and it slows down, like a stone thrown upwards. And like the 

    stone, it regains its energy as it comes back

    The point of nearest approach of the planet to the Sun is termed perihelion; 
    the point of greatest separation is termed aphelion. Hence, by Kepler’s second 
    law, the planet moves fastest when it is near perihelion and slowest when it is 

    near aphelion. 

    6.2.3. Kepler’s Third Law
    It states that the ratio of the squares of the revolutionary periods for two 
    planets is equal to the ratio of the cubes of their semi major axes .Therefore, 

    the law is summarized in the expression below.

    - In this equation T represents the period of revolution for a planet and R 
    represents the length of its semi major axis. The subscripts “1” and “2” 
    distinguish quantities for planet 1 and 2 respectively. The periods for the 
    two planets are assumed to be in the same time units and the lengths of 
    the semi major axes for the two planets are assumed to be in the same 
    distance units. 
    - Kepler’s Third Law implies that the period for a planet to orbit the Sun 
    increases rapidly with the radius of its orbit. Thus, we find that Mercury, 
    the innermost planet, takes only 88 days to orbit the Sun but the outermost 
    planet (Pluto) requires 248 years to do the same. 
    - Kepler’s 3rd law applies only to objects orbiting the same attracting center. 
    Do not use to compare, say the Moon’s orbit around the Earth to the orbit 
    of Mars around the Sun because they depend on different attracting 

    centers.

    a) Verification of Kepler’s third law
    There is only one speed that a planet can have if the planet is to remain in an 
    orbit with a fixed radius. Since the gravitational force acting on the planet of 
    mass m in the radial direction, it alone provides the centripetal force. Therefore, 

    using Newton’s law of gravitation, we have:

    The mass m of planet does not appear in equation consequently, for a given 
    orbit, a planet with a large mass has exactly the same orbital speed as a planet 
    with a small mass. 
    The radius r of the orbit (distance from the center of planet to the center of the 
    sun) is in the denominator in equation. This means that the closer the planet is 
    to Sun, the smaller is the value for r and the greater the orbital speed must be.
    The period T of a planet is the time required for one orbital revolution. The 

    period is related to the speed of the motion by

    b) Verification of acceleration due to gravity at the surface of the earth
    The force of attraction exerted by the earth on a body is called gravitational pull 
    or gravity. We know that when force acts on a body, it produces acceleration. 
    Therefore, a body under the effect of gravitational pull must accelerate. The 
    acceleration produced in the motion of a body under the effect of gravity is 
    called acceleration due to gravity (g). 

    Consider a body of mass m lying on the surface of earth.

           

    1) Hold a balloon and fill it with air. Then let it go. In which direction 
    does the air come out of the balloon and in which direction does the 
    balloon get propelled?
    2) If you fill the balloon with water and then let the balloon go, does 
    the balloon’s direction change? Explain your answer.
    3) Based on the observations made on (a) and (b) above, analyze the 
    movement of the rocket shown in the figure above.
    4) Artificial satellites are machines launched in the atmosphere to 
    move around the Earth.
    (i) What is the instrument do you think is used to launch them in 
    the atmosphere?

    (ii)Discuss any roles of artificial satellites.

    1) Hold a balloon and fill it with air. Then let it go. In which direction 
    does the air come out of the balloon and in which direction does the 
    balloon get propelled?
    2) If you fill the balloon with water and then let the balloon go, does 
    the balloon’s direction change? Explain your answer.
    3) Based on the observations made on (a) and (b) above, analyze the 
    movement of the rocket shown in the figure above.
    4) Artificial satellites are machines launched in the atmosphere to 
    move around the Earth.
    (i) What is the instrument do you think is used to launch them in 
    the atmosphere?

    (ii)Discuss any roles of artificial satellites.

    6.3.1. Rockets
    A rocket is a missile, spacecraft, aircraft or other vehicle that obtains thrust 
    from a rocket engine. A rocket is a device that produces thrust by ejecting 
    stored matter (fuel). A rocket moves forward when gas expelled from the rear 
    of a rocket pushes it in the opposite direction. From Newton’s laws of motion, 

    for every action, there is an equal and opposite reaction. 

    Basic principle of Rocket propulsion
    Rocket propulsion is based on Newton’s laws of motion:
    - Momentum conservation law
    - Newton’s third law
    In a rocket, fuel is burned to make a hot gas and this hot gas is forced out of 
    narrow nozzles in the back of the rocket, propelling the rocket forward. 
    Factors Affecting a Rocket’s Acceleration
    - The greater the exhaust velocity of the gases relative to the rocket, the 
    greater the acceleration.
    - The faster the rocket burns its fuel, the greater its acceleration.
    - The smaller the rocket’s mass (all other factors being the same), the 
    greater the acceleration.
    Spacecraft Propulsion
    Spacecraft is a vehicle designed to operate, with or without a crew, in a controlled 
    flight pattern above Earth’s lower atmosphere.The spacecraft typically either 
    is placed into an orbit around Earth or, if given sufficient velocity to escape 
    Earth’s gravity, continues toward another destination in space. The spacecraft 
    itself often carries small rocket engines for maneuvering and orienting in space.
    Spacecraft Propulsion is characterized in general by its complete integration 
    within the spacecraft (e.g. satellites). Its function is to provide forces and 
    torques in (empty) space to:
    - Transfer the spacecraft: used for interplanetary travel 
    - Position the spacecraft: used for orbit control
    - Orient the spacecraft: used for altitude control
    The jet propulsion systems for launching rockets are also called primary 
    propulsion systems. Spacecrafts, e.g. satellites, are operated by secondary 
    propulsion systems.
    Characteristics of Spacecraft Propulsion Systems 
    In order to fulfill altitude and orbit operational requirements of spacecraft, 
    spacecraft propulsion systems are characterized by: 
    - Very high velocity increment capability ( km/s) 
    - Low thrust levels (1 mN to 500 N) with low acceleration levels 
    - Continuous operation mode for orbit control 
    - Pulsed operation mode for altitude control 
    - Predictable, accurate and repeatable performance (impulse bits)
    - Reliable, leak-free long time operation (storable propellants) 
    - Minimum and predictable thrust exhaust impingement effects 
    Classification of Propulsion Systems 
    Spacecraft propulsion can be classified according to the source of energy 
    utilized for the ejection of propellant: 
    - Chemical propulsion use heat energy produced by a chemical reaction 
    to generate gases at high temperature and pressure in a combustion 
    chamber. These hot gases are accelerated through a nozzle and ejected 
    from the system at a high exit velocity to produce thrust force.
    - Electric propulsion uses electric or electromagnetic energy to eject 
    matter at high velocity to produce thrust force. 
    - Nuclear propulsion uses energy from a nuclear reactor to heat gases 
    which are then accelerated through a nozzle and ejected from the system 
    at a high exit velocity to produce thrust force. 
    6.3.2. Satellites
    A satellite is an artificial or a natural body placed in orbit round the earth 
    or another planet in order to collect information or for communication. 
    Communication satellites are satellites that are used specifically to communicate. 
    The payload of communication satellite consists of huge collection of powerful 
    radio transmitters and or a big dish, to enable it to exchange information with 
    the ground. We use them to transmit TV signals, to transmit radio signals, and 
    in some cases, it transmits internet signals. 
    There is only one main force acting on a satellite when it is in orbit, and that 
    is the gravitational force exerted on the satellite by the Earth. This force is 
    constantly pulling the satellite towards the centre of the Earth.
    A satellite doesn’t fall straight down to the Earth because of its velocity. 
    Throughout a satellite’s orbit there is a perfect balance between the gravitational 
    force due to the Earth and the centripetal force necessary to maintain the orbit 
    of the satellite.
    Satellites are natural or artificial bodies describing orbit around a planet under 
    its gravitational attraction. Moon is a natural satellite while INSAT-1B is an 
    artificial satellite of the earth. Condition for establishment of artificial satellite 
    is that the centre of orbit of satellite must coincide with centre of earth or 
    satellite must move around great circle of earth.

    Orbital Velocity of Satellite







    6.3.3. Applications of satellites
    Satellites that are launched in to the orbit by using the rockets are called manmade satellites or artificial satellites. Artificial satellites revolve around the 
    earth because of the gravitational force of attraction between the earth and 
    satellites. Unlike the natural satellites (moon), artificial satellites are used in 

    various applications. The various applications of artificial satellites include:

    Weather forecasting, Navigation, Astronomy, Satellite phone, Satellite 
    television, Military satellite, Satellite internet and Satellite radio.
    1. Weather forecasting
    Weather forecasting is the prediction of the future of weather. The satellites that 
    are used to predict the future of weather are called weather satellites. Weather 
    satellites continuously monitor the climate and weather conditions of earth. 
    They use sensors called radiometers for measuring the heat energy released 
    from the earth surface. Weather satellites also predict the most dangerous 
    storms such as hurricanes.
    2. Navigation
    Generally, navigation refers to determining the geographical location of an 
    object. The satellites that are used to determine the geographic location of 
    aircrafts, ships, cars, trains, or any other object are called navigation satellites. 
    GPS (Global Positioning System) is an example of navigation system. It allows 
    the user to determine their exact location at anywhere in the world.
    3. Astronomy
    Astronomy is the study of celestial objects such as stars, planets, galaxies, 
    natural satellites, comets, etc. The satellites that are used to study or observe the 
    distant stars, galaxies, planets, etc. are called astronomical satellites. They are 
    mainly used to find the new stars, planets, and galaxies. Hubble space telescope 
    is an example of astronomical satellite. It captures the high-resolution images 
    of the distant stars, galaxies, planets etc.
    4. Satellite phone
    Satellite phone is a type of mobile phone that uses satellites instead of cell 
    towers for transmitting the signal or information over long distances.
    Mobile phones that use cell towers will work only within the coverage area of 
    a cell tower. If we go beyond the coverage area of a cell tower or if we reach the 
    remote areas, it becomes difficult to make a voice call or send text messages 
    with the mobile phones. Unlike the mobile mobiles, satellite phones have global 
    coverage. Satellites phones uses geostationary satellites and low earth orbit 
    (LEO) satellites for transmitting the information.
    When a person makes a call from the satellite phone, the signal is sent to the 
    satellite. The satellite will receives that signal, processes it, and redirects the 
    signal back to the earth via a gateway. The gateway then send the signal or
    call to the destination by using the regular cellular and landline networks. The 
    usage of satellite phones is illegal in some countries like Cuba, North Korea, 
    Burma, India, and Russia.
    5. Satellite television
    Satellite television or satellite TV is a wireless system that uses communication 
    satellites to deliver the television programs or television signals to the users or 
    viewers.
    TV or television mostly uses geostationary satellites because they look 
    stationary from the earth. Hence, the signal is easily transmitted. When the 
    television signal is send to the satellite, it receives the signal, amplifies it, and 
    retransmits it back to the earth. The first satellite television signal was send 
    from Europe to North America by using the Telstar satellite.
    6. Military satellite
    Military satellite is an artificial satellite used by the army for various purposes 
    such as spying on enemy countries, military communication, and navigation.
    Military satellites obtain the secret information from the enemy countries. 
    These satellites also detect the missiles launched by the other countries in the 
    space.
    Military satellites are used by armed forces to communicate with each other. 
    These satellites also used to determine the exact location of an object.
    7. Satellite internet
    Satellite internet is a wireless system that uses satellites to deliver the internet 
    signals to users. High-speed internet is the main advantage of satellite internet. 
    Satellite internet does not use cable systems, but instead it uses satellites to 
    transmit the information or signal.
    8. Satellite radio
    Satellite radio is a wireless transmission service that uses orbiting satellites 
    to deliver the information or radio signals to the consumers. It is primarily 
    used in the cars. When the ground station transmit signal to the satellite that 
    is revolving around the earth, the satellite receives the signal, amplifies it, and 

    redirects the signal back to the earth (radio receivers in the cars).


    ACROSS
    1. The only natural satellite of Earth. 
    5. An object in orbit around a planet. 
    6. The smallest planet and farthest from the Sun. 
    7. This planet probably got this name due to its red color and is 
    sometimes referred to as the Red Planet. 
    9. This planet’s blue color is the result of absorption of red light by 
    methane in the upper atmosphere.
    10. It is the brightest object in the sky except for the Sun and the 
    Moon.
    DOWN
    2. Named after the Roman god of the sea.
    3. The closest planet to the Sun and the eighth smallest.
    4. A large cloud of dust and gas which escapes from the nucleus of 
    an active comet.
    8. The largest object in the solar system.
    2) (i) Define astronomical satellite
     (ii) What does astronomical satellite used for? Give one example 
    of it.
    3) For a satellite to be in a circular orbit 780 km above the surface of 
    the earth, (a) what orbital speed must it be given, and (b) what is 

    the period of the orbit (in hours)?

             

                    

      


  • UNIT 7: ATOMIC MODELS AND PHOTOELECTRIC EFFECT


    1) Basing on the figure above,
    a) How is the structure/arrangement of balls shown in the figure related 
    to an atom? You can use chemistry knowledge from O’level.
    b) Relate the arrangement of electrons in an atom to how the balls in the 
    figure above are arranged.
    c) Explain how movement of particles in an atom leads to release or 
    absorption of energy
    2) It is important to realise that a lot of what we know about the structure 
    of atoms has been developed over a long period of time. This is often how 
    scientific knowledge develops, with one person building on the ideas of 
    someone else.In attempt to explain an atom, different scientists suggest 
    different models. An atomic model represents what the structure of an 
    atom could look like, based on what we know about how atoms behave. 
    It is not necessarily a true picture of the exact structure of an atom. 
    a) Why did these scientists use the word Model not exact structure of an 
    atom?
    b) Can you explain some of the scientific models that tried to explain the 

    structure of an Atom?

    7.1. Bohr model of the atom and energy levels
    ACTIVITY 7.1 
    In year 1, you discussed about Rutherford model and this was a great 
    step in understanding atomic structure of an atom but it still had some 
    limitations that are listed below.
    - Why doesn’t the electron fall into the nucleus since it revolves 
    around the nucleus
    - Rutherford’s model could not explain the observed line spectra 
    of elements. As electrons spiraled towards the nucleus with 
    increasing speed, they should emit all frequencies of radiation not 
    just one. Thus, the observed spectrum of the element should be a 
    continuous spectrum not a line spectrum.
    - The model did not explain the distribution of electrons outside 
    the nucleus.
    a) Basing on Rutherford’s limitations above, suggest some of corrections 
    that would be made 
    b) Talk about the energy possessed by these electrons as they are in 
    energy levels.
    c) Does an electron remain with same energy if it
    i) Jumps

    ii) Drops from one energy level to another?

    7.1.1. Bohr’s atomic model
    In 1900 Max Planck (1858–1947)investigated the relationship between the 
    intensity and frequency of the radiation emitted by very hot objects. Planck 
    showed that the radiation from a hot body was emitted only in discrete 
    quantities or “packets” called quanta. The energy, E, of each quantum was 

    shown to be proportional to the frequency, f, of the radiation emitted:

    Bohr’s thinking on a new atomic model was also guided by the work that had 
    been done on the spectrum of hydrogen. 
    In 1913 he develops a theory of the atom in which he assumes that: “Electrons
    are arranged in definite shells, or quantum levels, at a considerable distance from 

    the nucleus”. 

    7.1.2. Orbital radii, orbital speed and Energy level
    Starting with these four postulates and using a mixture of Classical and Quantum 
    Physics, Bohr derived equations for: 
    The radii of the various stationary states and the velocity of an electron in 
    a particular stationary state;
    Let’s assume the electron’s orbit is a circular obit with radius r which is 
    approximately the size of the hydrogen atom. Since the electron in Fig.7.2is 

    moving in a circle, there must be a force directed toward the center of the circle.

       

       

    When light coming from a discharge tube containing hydrogen gas is passed 

    through a prism, a series of lines is observed in the visible part of the spectrum: 

    this is termed Balmer series. Some are found in the IR (Infra-Red) and UV 

    (ultraviolet) regions. Those lines detected in the UV are known as Lyman series 

    and those detected in the IR were discovered by Paschen, Brackett, and Pfund. 

    From 1884 to 1886, Johann Balmer, a Swiss school teacher, suggested a 

    mathematical formula to fit the known wavelengths of the hydrogen emission 

    spectrum: 

    When light coming from a discharge tube containing hydrogen gas is passed 
    through a prism, a series of lines is observed in the visible part of the spectrum: 
    this is termed Balmer series. Some are found in the IR (Infra-Red) and UV 
    (ultraviolet) regions. Those lines detected in the UV are known as Lyman series 
    and those detected in the IR were discovered by Paschen, Brackett, and Pfund. 
    From 1884 to 1886, Johann Balmer, a Swiss school teacher, suggested a 
    mathematical formula to fit the known wavelengths of the hydrogen emission 

    spectrum: 

    where
    - m is an integer with a different value for each line (m = 3, 4, 5, 6) 
    - b is a constant with a value of 364.56 nm.
    This formula produces wavelength values for the hydrogen emission spectral 
    lines in excellent agreement with measured values. This series of lines has 
    become known as the Balmer series.
    Balmer predicted that there should be other series of hydrogen spectral lines 
    and that their wavelengths could be found by substituting values higher than 

    the 2 shown on the right hand side of the denominator in his formula. 

    The great success of Bohr’smodel is that:
    - It gives an explanation for why atoms emit line spectra, and accurately 
    predicts the wavelengths of emitted light for hydrogen. 
    - It explains absorption spectra: photons of just the right wavelength can 
    knock an electron from one energy level to a higher one. To conserve 
    energy, only photons that have just the right energy will be absorbed.
    This explains why a continuous spectrum of light entering a gas will 
    emerge with dark (absorption) lines at frequencies that correspond to 
    emission lines. 
    - It ensures the stability of atoms. It establishes stability by decree: the
    ground state is the lowest state for an electron and there is no lower 
    energy level to which it can go and emit more energy. 
    - It accurately predicts the ionization energy of 13.6 eV for hydrogen. 
    However, the Bohr model was not so successful for other atoms
    Limitations of the Bohr model: 
    As with any scientific model, however, there were limitations. The problems 
    with the Bohr model can be summarized as follows: 
    - Bohr used a mixture of classical and quantum physics, mainly the former.
    He assumed that some laws of classical physics worked while others did 
    not.
    - The model could not explain the relative intensities of spectral lines.
    Some lines were more intense than others.
    - It could not explain the hyperfine structure of spectral lines. Some spectral 
    lines actually consist of a series of very fine, closely spaced lines.
    - It could not satisfactorily be extended to atoms with more than one electron 
    in their valence shell because it does not account for the electrostatic 
    force that one electron exerts on another. 
    - It could not explain the “Zeeman splitting” of spectral lines under the 
    influence of a magnetic field.The Zeeman Effect is the splitting of atomic 
    energy levels and the associated spectral lines when the atoms are placed 
    in a magnetic field. 

    - It could not explain the Stark effect (splitting up in electric field).

    The picture above is a section of solar panels that were installed in 
    Rwamagana district to supplement power in the region.
    a) From your experience what do you know about solar panels.
    b) Using the knowledge of black bodies, explain how a solar panel 
    operates.
    c) Explain why the same project may not work well in areas like 
    Musanze and Gicumbi.
    d) Basing on your answers provided in the above questions, does light 

    carry energy?

    7.2.1. Photoelectric Effect
    Photoelectric effect is the emission of electrons from the surface of metal 
    when illuminated with electromagnetic radiation of sufficient frequency. A 

    material that exhibits photoelectric effect is said to be Photosensitive.











    4. Stopping voltage
    The stopping potential does not depend on intensity, but does depend only on 
    frequency. 
    The only effect of increasing the intensity is to increase the number of electrons 
    per second and hence the photocurrent i. If the intensity of light is held constant 
    but the frequency is increased, the stopping potential also increases.
    In other words, Greater intensity at a particular frequency means a greater 
    number of photons per second absorbed, and thus a greater number of electrons 
    emitted per second and a greater photocurrent. The greater the light frequency 

    is, the higher the energy of the ejected photoelectrons is.



    7.2.4. Applications of photoelectric effect
    The photoelectric effect has a number of applications. Digital cameras, studying 
    nuclear processes, chemically analyzing materials based on their emitted 
    electrons, image intensifiers andnight-vision scopes use it to convert light 
    energy into an electric signal that is reconstructed into an image. 
    On the moon, sunlight striking the surface causes surface dust to eject electrons, 
    leaving the dust particles with a positive charge. The mutual electric repulsion 
    of these charged dust particles causes them to rise above the moon’s surface, a 
    phenomenon that was observed from lunar orbit by the Apollo astronauts.
    It led physicists to think about the nature of light and the structure of atoms in 
    an entirely new way
    (a) Photo emissive cells
    These are used in reproduction of sound in a film sound track and also in 
    controlling lift doors. Photo emissive cells are also used in security alarms. The 
    symbol for a photo emissive cell is shown below. Light falling on the cathode 
    ejects electrons which are attracted to the anode and a current flow.

    

     (b) Photovoltaic cells
    In photovoltaic cells, the ejected electron travels through the emitting material 
    to enter a solid electrode in contact with the photo emitter (instead of travelling 
    through a vacuum to the anode) leading to the direct conversion of radiant 
    energy to electrical energy. The more intense the light falling on the photocell, 
    the greater the conductivity of the photocell and the greater the current 
    measured by the ammeter (A).
    Photovoltaic cells are used in calculators and light exposure metres in cameras. 

    They can also drive small machines.

    (c) Photoconductive cells.
    Examples of photoconductive cells are photodiodes, photo resistors (lightdependent resistors, LDR) and phototransistors. These work on the principle that light reduces the resistance of some semiconductor materials such as 

    calcium sulphide.

           

     

    7.3.1. Production of Cathode rays
    Thermoelectric emission is the process by which electrons are emitted from a 
    metal surface when it has been electrically heated. The least energy an electron 
    requires to break away from the surface is called the work function and this 
    value varies from one metal to another. Substance with low work functions 
    emits electrons at lower temperatures compared with metals with higher work 
    function.
    Cathode rays are stream of electrons that are moving at high speed. Cathode 
    rays are produced in a discharge tube which is a long (about 30 cm or more) 
    hard glass tube with two electrodes attached at its two ends. The electrodes 
    are made of any metal which is a good conductor such as copper, aluminium or 
    platinum, and are connected externally to a high voltage source. The discharge 
    tube has a facility to connect it to a vacuum pump. Gaseous discharge takes 
    place between the two electrodes and hence the name of the tube. 
    If the temperature of the metal is raised, the thermal velocities of the electrons 
    will be increased. The chance of electrons escaping from the attraction of the 
    positive ions, fixed in the lattice, will then also be raised. Thus by heating a 
    metal such as tungsten to a high temperature, electrons can be boiled off. This 
    called thermionic emission.

    The electrode connected to the negative terminal is known as the cathode and 
    the terminal connected to the positive terminal is known as the anode. As the 
    discharge tube is evacuated, various changes take place.
    - The air inside the discharge tube is a non-conductor of electricity and 
    therefore initially tube looks intact.
    - As the air pressure inside reduces, the gas starts ionizing. Since a potential 
    difference is maintained inside the tube, when one gas atom is ionized, the 
    electrons escaping from it ionize other gas atoms. This creates a stream 
    of positive ions and negative electrons. These start moving towards the 

    cathode and the anode respectively and generate a current.

    - When the pressure is not very low, the gas movement looks like bluish 
    streaks. As the pressure reduces further, the gas inside looks pink.
    - When the discharge tube is evacuated to a high degree, the inside will 
    start looking black, as there is no gas inside to conduct a current. This 
    dark space is called Faraday’s dark space. A small glow can be observed 
    at the cathode and the anode. This is due to residual gases.
    - As the vacuum is reduced further, there will be a greenish glow behind the 
    anode. The rays or particles come from the cathode towards the anode. 
    Some of them overshoot the anode and reach the inner surface of the 
    tube. This causes the glow. These rays are called cathode rays. Since the 
    cathode rays come towards the anode, they must be negatively charged.
    It has been proved that the cathode rays are nothing but electrons. As the 
    discharge tube is evacuated, the electrons at the cathode get attracted to the 
    anode due to the high potential difference. Cathode rays are not seen when the 
    potential difference is low or if he gas pressure is high.
    7.3.2. Properties of cathode rays.
    Cathode rays are moving electrons and have the following properties:
    - They travel in straight lines and They carry negative charge.
    - They are deflected by electric and magnetic fields.
    - Cathode rays cause fluorescence on striking certain materials.
    - They have energy and momentum.
    - Cathode rays are capable of ionizing gas atoms if the potential difference 
    is large and the gas pressure is not high.
    - Depending on their energy, cathode rays can penetrate thin sheets of 
    paper or metal foils.
    - When cathode rays are stopped suddenly, they produce X-rays.
    - They affect photographic plates.
    7.3.3. Applications of cathode rays
    a) Cathode ray oscilloscope
    A Cathode Ray Oscilloscope (CRO) also called Oscillograph is an instrument 
    generally used in a laboratory to display, measure and analyze various 
    waveforms of electrical circuits. A cathode ray oscilloscope is a very fast X-Y 

    plotters that can display an input signal versus time or other signal.

    Cathode ray oscilloscopes use luminous spots which are produced by striking 
    the beam of electrons and this luminous spot moves in response variation in 
    the input quantity.
    Nowadays, with the help of transducers it is possible to convert various physical 
    quantities like current, pressure, acceleration etc to voltage thus it enable us 
    to have a visual representations of these various quantities on cathode ray 
    oscilloscope.
    The main part of cathode ray oscilloscope is cathode ray tube (CRT) which is 
    also known as the heart of cathode ray oscilloscope.
     The CRT is a vacuum tube in which a beam of electrons is accelerated and 
    deflected under the influence of electric or magnetic fields. The electron beam 
    is produced by an assembly called an electron gun located in the neck of the 
    tube. These electrons, if left undisturbed, travel in a straight-line path until they 
    strike the front of the CRT, the “screen,” which is coated with a material that 
    emits visible light when bombarded with electrons. Electrons leaving the hot 
    cathode C are accelerated to the anode A. The beam of electrons produced is 
    called Cathode rays. In addition to accelerating electrons, the electron gun is 

    also used to focus the beam of electrons, and the plates deflect the beam.

    This tube is commonly used to obtain a visual display of electronic information 

    in oscilloscopes, radar systems, television receivers, and computer monitors. 

    Functions of a Cathode Ray Oscilloscope
    A cathode ray oscillograph is essentially an electrostatic instrument which 
    consists of a high evacuated glass tube. The features of a CRO (Cathode ray 
    oscilloscope) can be split into 3 main sections: The electron gun, the deflection 
    system and the fluorescent screen.
    - Electron Gun: The role of this section is to produce electrons at a high, 
    fixed, velocity and focus them on the screen. This is done through a process 
    known as thermionic emission. A filament in the cathode is heated to the 
    point where its electrons become loose. 
    An anode with a high voltage applied to it accelerates the electrons towards 
    the screen due to electrostatic attraction. On the way, the electrons pass 
    through a series of control grids which control the brightness of the 
    image produced. The more negative the grid, the darker the image and 
    vice versa.
    - Deflection system: The role of the deflection system is to control the image 
    produced by controlling the position that the electrons hit the screen. 
    It consists of Two perpendicular sets of Electric/Magnetic fields. This 
    allows control over both horizontal and vertical axes. By controlling the 
    Voltage applied to the fields, it is possible to vary the deflection through 
    Electrostatic force/Motor effect.
    - Fluorescent screen: The role of this part is to display where the electrons 
    are hitting the CRT. It is a screen coated with a material that emits light 
    when struck by electrons. Zinc sulfide or Phosphorus are two commonly 
    used materials. The CRO is a perfect voltmeter as its input resistance is 
    very high. It is usually placed in parallel with a component. 
    The voltage is measured on the vertical axis, which is controlled by the 
    Y-plates.It can also be used as an ammeter by placing it across a resistor 
    of known resistance.The CRO is used to analyze waveforms. It can be used 
    to determine the peak voltage of an a.c. waveform and the period, which 
    in turn allows one to work out its frequency.
    b) Televisions
    A CRT TV works by having the electron beam “scan” the screen at a rate faster 
    than our eyes can perceive. This means that it shoots across the screen like a 
    machine gun, and the images we see are actually made from many fluorescent 
    dots.
    The fluorescence caused by the beam striking the screen lasts a bit longer so 
    that the next scan can be made without the previous image disappearing. It
    scans twice each time, first filling in the odd “holes” then the even ones. Each 
    scan is about 1/50 of a second.
    Colour CRT TVs has electron guns rather than a single one, a shadow mask, 
    and a modified fluorescent screen. The 3 electron guns are needed as there are 
    three primary colours (Red, Green and Blue) that can be adjusted in different 
    amounts to create any colour.
    The colours are formed as a result of the shadow mask, which is a layer with 
    holes in it that controls the angle of the incoming electron beams. This is 
    because the fluorescent screen is separated into multi-coloured phosphors 
    that are placed adjacent to each other at small intervals. Thus it isn’t actually a 
    single coloured pixel, but rather 3 very small pixels that join together to form a 
    larger dot.
    The vertical sensitivity defines the voltage associated with each vertical 
    division of the display or the amplitude of the displayed signal. Virtually all 
    oscilloscope screens are cut into a crosshatch pattern of lines separated by 1 
    cm in the vertical and horizontal directions.
     This section carries a Volts-per-Division (Volts/Div) selector knob, an AC/DC/
    Ground selector switch and the vertical (primary) input for the instrument. 
    Additionally, this section is typically equipped with the vertical beam position 
    knob.
    7.3.4. Fluorescence and Phosphorescence
    When an atom is excited from one energy state to a higher one by the absorption 
    of a photon, it may return to the lower level in a series of two (or more) 
    transitions if there is at least one energy level in between. The photons emitted 
    will consequently have lower energy and frequency than the absorbed photon. 
    When the absorbed photon is in the UV and the emitted photons are in the 
    visible region of the spectrum, this phenomenon is called fluorescence.
    The wavelength for which fluorescence will occur depends on the energy levels 
    of the particular atoms. Because the frequencies are different for different 
    substances, and because many substances fluoresce readily, fluorescence is a 
    powerful tool for identification of compounds. It is also used for determining 
    how much of a substance is present and for following substances along a natural 
    metabolic pathway in biological organisms. 
    For detection of a given compound, the stimulating light must be monochromatic, 
    and solvents or other materials present must not fluoresce in the same region 

    of the spectrum.

    Sometimes the observation of fluorescent light being emitted is sufficient to 
    detect a compound. In other cases, spectrometers are used to measure the 
    wavelengths and intensities of the emitted light.
    Fluorescent light bulbs work in a two-step process. The applied voltage 
    accelerates electrons that strike atoms of the gas in the tube and cause them 
    to be excited. When the excited atoms jump down to their normal levels, they 
    emit UV photons which strike a fluorescent coating on the inside of the tube. 
    The light we see is a result of this material fluorescing in response to the UV 
    light striking it.
    Materials such as those used for luminous watch dials, and other glow-in thedark products, are said to be phosphorescent. When an atom is raised to a 
    normal excited state, it drops back down within about .
    In phosphorescent substances, atoms can be excited by photon absorption to 
    energy levels called metastable, which are states that last much longer because 
    to jump down is a “forbidden” transition. Metastable states can last even a few 
    seconds or longer.
    In a collection of such atoms, many of the atoms will descend to the lower state 
    fairly soon, but many will remain in the excited state for over an hour. Hence 

    light will be emitted even after long periods.

         

     

    - Clean a zinc plate with fine emery paper or steel wool.
    - Attach the plate to the top disc on a gold leaf electroscope, so there 
    is good electrical contact.
    - Charge the zinc plate and inner assembly of the electroscope 
    negatively, e.g. by rubbing the zinc plate with a polythene rod 
    which has been rubbed with wool or fur. [Charging by induction 
    using a perspex rod is more reliable, but might be considered too 
    confusing!] 
    - The leaf should now be raised, because the leaf and the back plate 
    are both charged negatively and repel each other. The leaf should 
    temporarily rise further if the charged polythene rod is brought 
    near the zinc plate.
    - Place an ultraviolet lamp near the zinc plate. Switch it on. The leaf 
    should be seen to fall.
    - Safety note: Don’t look at the ultraviolet lamp (when it’s turned 
    on!)] Clearly the plate (and inner assembly of electroscope) is 

    losing charge.

    - Repeat the procedure, but charging the zinc plate and inner 
    assembly of the electroscope positively, e.g. by rubbing the plate 
    with a charged perspex rod.
    - Observe what happen
    This time the ultraviolet does not affect the leaf. Charge is not lost. The 
    simplest explanation is the correct one. The ultraviolet causes electrons 
    to be emitted from the zinc plate. If the plate is charged positively, the 
    electrons are attracted back again. If the plate is charged negatively the 

    emitted electrons are repelled and lost from the plate for ever.

    - A metal plate P made in caesium and a smaller electrode C 
    (collecting electrode) are placed inside an evacuated glass tube, 
    called a photocell. The two electrodes are connected to an 
    ammeter and a source of emf, as shown Fig.7.14. Note the polarity 
    of the power supply.
    - Any electrons emitted from the caesium surface will be collected 
    by the ‘collecting electrode’.
    - If the photocell is covered the current is zero; if light falls on the 

    caesium electrode there is current.

            

           

           

        

  • UNIT 8: ANALOG AND DIGITAL SIGNALS IN TELECOMMUNICATION SYSTEMS


    There has been a move by the government of Rwanda to make her citizens to 
    change from using analog devices to digital devices. Analog devices transmit 
    and receive signals in analog form whereas digital devices transmit and 
    receive signals digitally.
    a) What are different forms of signals you know that you normally use in 
    daily life communication?
    b) Why do you think there is a need to change from analog to digital signal 
    transmission?
    c) Mutesi communicates to her brother Ndayisenga who studies abroad 
    using Facebook. Is the flow of information analog or digital? Explain your 
    argument.
    d) Using information gained in above questions, discuss different signals 
    shown in the illustration.

    8.1.1. Classification of types of Information
    Information is any entity or form that resolves uncertainty or provides the 
    answer to a question of some kind. It is thus related to data and knowledge, 
    as data represents values attributed to parameters, and knowledge signifies 
    understanding of real things or abstract concepts.
    Buck (1983) provides a useful classification of types of information that can 
    be displayed to users. These are: Instructions, Command, Advisory, Answers, 
    Historical, and Predictive.
    Each of these types of information can, in theory, be provided on most types of 
    displays. However, some lend themselves better to one form of display rather 
    than another. The characteristics of each of these types can now be briefly 
    discussed. 
    1. Instructions: Refer to information that guides behavior in a particular way. 
    In other words, it supports performance to carry out a task by prompting 
    on what to do and when to do it. A simple sign telling people to enter or 
    not enter a door would be one example. Other simple cases include the 
    dialogue messages that are provided on automated cash machines (ACM). 
    More complex instructions will appear in printed form on the packaging or 
    the instructional manuals for pieces of equipment.
    2. Command: Messages give a very straightforward statement on what 
    is or what is not permitted. ‘Do not enter’, ‘do not smoke’, ‘do not eat or 
    drink’, are examples of command messages. Sometimes they are similar to 
    instructions, but are much more focused on simple statements that refer to 
    high priority items.
    3. Advisory: Messages are somewhat watered down versions of command 
    messages. In some cases, these will be recommendations to avoid a situation, 
    at other times they would be information allowing for the preparation or 
    planning of particular activities. For example, we might be advised that 
    our train is late by a spoken message and we might, possibly, be given an 
    accurate time estimate for when the train will be available.
    4. Answers: Information may be provided in response to a particular enquiry 
    that has been made. This is typical of an interactive information-handling 
    situation, where we have a particular question in mind or degree of 
    uncertainty and we seek information from a source with regard to removing 
    that uncertainty.
    It turns out that most of the information that is sought from displays is of 
    the answer kind. If we want to know what the time of day is, we look at our 
    watches and clocks to find the answer.
    5. Historical: Displays are used to look back at the state of a variable over a 
    period of minutes, hours, days or even years. A graphical representation 
    of road accidents over the last century would be a historical display of 
    information. If we want to know what the temperature fluctuation has 
    been in an office on a daily basis, then specialist devices can be brought in 
    and placed in the office that will give a pen recording over a fixed period of 
    time.
     It is much easier to see if there is a trend in information if it is displayed in 
    this way; the alternative is to hold in memory a general impression of what
    the temperature readings have been at a number of points during the day 
    or record them manually on a chart. Gauging the temperature in an office 
    concerns a relatively low risk situation.
     However, if the concern is with the temperature in a critical vessel in a 
    chemical process, then the temperature trends exhibited over the time are 
    quite important. 
    6. Predictive: displays are much more specialized, but increasingly found 
    in complex processes. In the same way that historical data support 
    performance in making a judgment based on the current value, predictive 
    information enables examination of the current value and indicates any 
    likely change in the future.
    Predictor displays enable better control over vehicles, typically at sea or 
    airborne, and enable smoother transitions from one state to another. They 
    are used in slow response systems where it is difficult to see the immediate 
    effect of an action that has been carried out.
    Predictive displays will enable a variable to be plotted into the future. 
    The same graphs that are used as historical displays can also be used as 
    predictive displays. 
    Telecommunication in real life is the transmission of signals and other types 
    of data of any nature by wire, radio, optical or other electromagnetic systems 
    of communication. 
    Telecommunication occurs when the exchange of information between 
    communicating participants includes the use of signs or other technologically 
    based materials such as telephone, TV set, radio receiver, radio emitter, computer, 
    and so on. All can be done either mechanically, electrically or electronically.
    Message: A message is a term standing for information put in an appropriate 
    form for transmission. Each message contains information. A message can be 
    either analog message (a physical time variable quantity usually in smooth 
    and continuous form) or a digital message (an ordered sequence of symbols 
    selected from finite set of elements) 
    - Analog message: a physical time-variable quantity usually in smooth 
    and continuous form. 
    - Digital message: ordered sequence of symbols selected from finite set of 
    elements. 
    A signal is a mathematical function representing the time variation of a physical 
    variable characterizing a physical process and which, by using various models, 

    can be mathematically represented.

    In telecommunication, the message is also known as a signal and the signal is 
    transmitted in an electrical or voltage form.
    8.1.2. Elements of Communication
    Communication is the process of sharing the message through continuous flow 
    of Symbols. It is composed by the following elements:
    Sender 
    The sender is a party that plays the specific role of initiating communication. 
    To communicate effectively, the sender must use effective verbal as well as 
    nonverbal techniques such as:
    - Speaking or writing clearly.
    - Organizing your points to make them easy to follow and understand.
    - Maintaining eye contact.
    - Using proper grammar.
    - Giving accurate information.
    All the above components are essential in the effectiveness of your message. 
    One will lose the audience if it becomes aware of obvious oversights on ones 
    part. The sender should have some understanding of who the receiver is, in 
    order to modify the message to make it more relevant. 
    Receiver 
    The receiver means the party to whom the sender transmits the message. 
    A receiver can be one person or an entire audience of people. In the basic 
    communication model, the receiver is directly connected with the speaker. 
    The receiver can also communicate verbally and nonverbally. The best way to 
    receive a message is:
    - To listen carefully.
    - Sitting up straight. 
    - Making eye contact.
    - Don’t get distracted or try to do something else while you’re listening.
    - Nodding and smiling as you listen.
    - Demonstrate that you understand the message. 
    Message
    The message is the most crucial element of effective communication which 
    includes the content a sender conveys to the receiver. A message can come in
    many different forms, such as an oral presentation, a written document, an 
    advertisement or just a comment. 
    In the basic communication model, the way from one point to another represents 
    the sender’s message travelling to the receiver. The message isn’t necessarily 
    what the receiver perceive it to be. Rather, the message is what the sender 
    intends the message to be. The sender must not only compose the message 
    carefully, but also evaluate the ways in which the message can be interpreted. 
    Channel
    The channel is a medium through which a message travels from the sender to 
    the receiver. The message travels from one point to another via a channel of 
    communication. The channel is a physical medium stands between the sender 
    and receiver. 
    Many channels or types of communication exist, such as 
    - The spoken word.
    - Radio or television.
    - An Internet site.
    - Something written, like a book, letter or magazine. 
    Every channel of communication has its advantages and disadvantages. For 
    example, one disadvantage of the written word, on a computer screen or in 
    a book, is that the receiver cannot evaluate the tone of the message. For this 
    reason, effective communicators should make written word communications 
    clear so receivers don’t rely on a specific tone of voice to convey the message 
    accurately. 
    The advantages of television as a channel for communication include its 
    expansive reach to a wide audience and the sender’s ability to further manipulate 
    the message using editing and special effects. 
    Feedback
    This describes the receiver’s response or reaction to the sender’s message. The 
    receiver can transmit feedback through asking questions, making comments or 
    just supporting the message that was delivered. 
    Feedback helps the sender to determine how the receiver interpreted the 
    message and how it can be improved. The signal normally, must be raised at a 
    level that will permit it to reach its destination. This operation is accomplished 

    by amplifiers.

    8.1.3. Modes of transmission
    1) Simplex transmission
    Simplex transmission is a single one-way base band transmission. Simplex 
    transmission, as the name implies, is simple. It is also called unidirectional 
    transmission because the signal travels in only one direction. An example 
    of simplex transmission is the signal sent from the TV station to the home 
    television. 
    Data in a simplex channel is always one way. Simplex channels are not often 
    used because it is not possible to send back error or control signals to the 
    transmit end.
    2) Half-duplex communications
    Half-duplex transmission is an improvement over simplex transmission 
    because the traffic can travel in both directions. Unfortunately, the road is 
    not wide enough to accommodate bidirectional signals simultaneously. This 
    means that only one side can transmit at a time. Two-way radios, such as 
    police or emergency communications mobile radios, work with half-duplex 
    transmissions. If people at both ends try to talk at the same time, none of the 

    transmissions get through.

    3) Full-duplex communications
    Full-duplex transmission operates like a two-way, two-lane street. Traffic can 
    travel in both directions at the same time. A land-based telephone conversation 
    is an example of full-duplex communication. Both parties can talk at the same 
    time, and the person talking on the other end can still be heard by the other 
    party while they are talking. Although when both parties are talking at the 

    same time, it might be difficult to understand what is being said.

    8.2.1. Analog signal system
    Analog signals
    Analog signal is a continuous signal that contains time varying quantities. An 
    analog signal is a continuous wave denoted by a sine wave and may vary in signal 
    strength (amplitude) or frequency (time). The sine wave’s amplitude value can 
    be seen as the higher and lower points of the wave, while the frequency (time) 

    value is measured in the sine wave’s physical length from left to right.

    Analog signal can be used to measure changes in physical phenomenon such as 
    light, sound, pressure, or temperature. For instance, microphone can convert 
    sound waves into analog signal. Even in digital devices, there is typically some 
    analog component that is used to take in information from the external world 
    which will then get translated into digital form –using analog to digital converter.
    A system is a physical set of components that take a signal and produces a 
    signal. In terms of engineering, the input is generally some electrical signal and 
    the output is another electrical signal.
    Analog systems operate with values that vary continuously and have no abrupt 
    transitions between levels. For a long time, almost all electronic systems were 
    analog, as most things we measure in nature are analog. For example, your 
    voice is analogous; it contains an infinite number of levels and frequencies. 
    Therefore, if you wanted a circuit to amplify your voice, an analog circuit seems 
    a likely choice. 
    Example of analog electronic systems
    A public address system
    A public address system (PAS) is an electronic sound amplification and 
    distribution system with a microphone, amplifier and loudspeakers, used to 
    allow a person to address a large public, for example for announcements of 
    movements at large and noisy air and rail terminals or a sports stadium.
    Advantages of analog signals
    - Uses less bandwidth than digital sounds.
    - More accurate representation of sound.
    - It is the natural form of sound.
    - Because of editing limitations, there is little someone can do to tinker 
    with the sound, so what you are hearing is the original sound.
    Disadvantages
    - There are limitations in editing.
    - Recording analog sound on tape is expensive.
    - It is harder to synchronize analogous sound.
    - Quality is easily lost if the tape becomes ruined.
    - A tape must always be wound and rewound in order to listen to specific 
    part of sound which can damage it.
    - Analog is susceptible to clipping where the highest and lowest notes of a 

    sound are cut out during recording.

    In Rwanda recently analog systems were replaced by digital systems that 
    provide greater capacity of data transfer and increased reliability and security.
    8.2.2. Digital Signal system
    A digital signal refers to an electrical signal that is converted into a pattern of 
    bits. Unlike an analog signal, which is a continuous signal that contains timevarying quantities, a digital signal has a discrete value at each sampling point. 
    The precision of the signal is determined by how many samples are recorded 
    per unit of time. For example, the illustration of fig.8.5 below shows an analog 
    pattern (represented as the curve) alongside a digital pattern (represented as 

    the discrete lines).

    A digital signal is easily represented by a computer because each sample can 
    be defined with a series of bits that are either in the state 1 (on) or 0 (off). 
    Digital signals can be compressed and can include additional information for 
    error correction. 
    A radio signal, for example, will be either on or off. Digital signals can be sent 
    for long distances and suffer less interference than analog signals.
    Unlike analog technology which uses continuous signals, digital technology 
    encodes the information into discrete signal states. When only two states are 
    assigned per digital signal, these signals are termed binary signals. One single 

    binary digit is termed a bit - a contraction for binary digit.

    In electronic signal and information processing and transmission, digital 
    technology is increasingly being used because, in various applications, digital 
    signal transmission has many advantages over analog signal transmission. 
    Numerous and very successful applications of digital technology include the 
    continuously growing number of Personal Computers, the communication 
    network ISDN as well as the increasing use of digital control stations (Direct 

    Digital Control: DDC)

    Advantages of digital signals 
    - More capacity from the same number of frequencies; that is, they 
    provide superior Spectral Efficiency. This is a result of the modulation 
    methods used, and the fact that, in many cases more than one ‘conversation’ 
    can be accommodated within a single radio channel.
    - Consistent voice clarity at low received signal levels near the edge 
    of coverage. The general consensus is that digital radios provide better 
    audio quality than analog ones. With analog FM radios, the audio quality 
    steadily declines as the received signal strength gets weaker.
    Digital radios however, will have a consistent audio quality throughout the 
    full service area. The edges of the coverage area in a digital radio system 
    are similar to those experienced with cellular telephones.
    - Data is defined in the standard. This means data implementations are 
    no longer proprietary, there are a wide variety of data mechanisms and 
    inter operability can extend into the data domain. With the accepted 
    increase of efficiency by using data communications over voice, this will 
    further increase the usability and effectiveness of digital radio systems.
    - Secure transmissions: In digital technologies, data and voice can be 
    secured using encryption without impacting voice quality using industry 

    standard encryption techniques.

    8.2.3. Principle of digital signal systems
    Digital systems process digital signals which can take only a limited number 
    of values (discrete steps), usually just two values are used: the positive supply 
    voltage (+Vs) and zero volts (0V).
    Digital systems contain devices such as logic gates, flip-flops, shift registers 
    and counters. A computer is an example of a digital system.
    A logic gate is a building block of a digital circuit. Most logic gates have two 
    inputs and one output and are based on Boolean algebra. At any given moment, 
    every terminal is in one of the two binary conditions false (high) or true (low). 
    False represents 0, and true represents 1. Depending on the type of logic gate 
    being used and the combination of inputs, the binary output will differ. A logic 
    gate can be thought of like a light switch, wherein one position the output is off 
    (0), and in another, it is on (1). Logic gates are commonly used in integrated 

    circuits (IC).

    Boolean functions may be practically implemented by using electronic gates. 
    The following points are important to understand.
    - Electronic gates require a power supply.
    - Gate INPUTS are driven by voltages having two nominal values, e.g. 0 V 
    and 5 V representing logic 0 and logic 1 respectively. 
    - The OUTPUT of a gate provides two nominal values of voltage only, e.g. 0 
    V and 5 V representing logic 0 and logic 1 respectively. In general, there is 
    only one output to a logic gate except in some special cases.
    - There is always a time delay between an input being applied and the 
    output responding. 
    Truth tables are used to help to show the function of a logic gate. Digital systems 
    are said to be constructed by using logic gates. These gates are the AND, OR, 
    NOT, NAND, NOR, EXOR and EXNOR gates. The basic operations are described 
    below with the aid of truth tables.
    AND gate and Truth Tables
    The AND gate is called the “all or nothing” gate. The graph of fig.8.8 shows the 
    idea of the AND gate. The lamp (Y) will light only when both input switches (A 
    and B) are closed. The truth table shows that the output (Y) is enabled (lit) only 

    when both inputs are closed.

    The AND gate is an electronic circuit that gives a high output (1) only if all its 
    inputs are high. A dot (.) is used to show the AND operation i.e. A.B. Bear in 
    mind that this dot is sometimes omitted we write AB.
    OR gate and truth tables
    The OR gate is called the “any or all” gate. The schematic Fig.8.10 shows the 
    idea of the OR gate. The lamp ( Y ) will glow when either switch A or switch B 
    is closed. The lamp will also glow when both switches A and B are closed. The 
    lamp (Y) will not glow when both switches ( Aand B ) are open. The truth table 
    details the OR function of the switch and lamp circuit are shown in fig. 8.10. 
    The output of the OR circuit will be enabled (lamp lit) when any or all input 

    switches are closed.

    The standard logic symbol for an OR gate is drawn in Fig.8.11. Note the different 
    shape of the OR gate. The OR gate has two inputs labeled A and B. The output 
    is labeled Y. The OR gate is an electronic circuit that gives a high output (1) if 

    one or more of its inputs are high. A plus (+) is used to show the OR operation. 

    A NOT gate is also called an inverter. A NOT gate, or inverter, is an unusual gate. 
    The NOT gate has only one input and one output as shwn in fig.8.12. If the input 
    variable is A, the inverted output is known as NOT A. This is also shown as A’, or 

    A with a bar over the top, as shown at the outputs.

    The diagrams below show two ways that the NAND logic gate can be configured 
    to produce a NOT gate. It can not also be done using NOR logic gates in the same 
    way



    This is a NOT-AND gate which is equal to an AND gate followed by a NOT gate.
    The outputs of all NAND gates are high if any of the inputs are low. The symbol 
    is an AND gate with a small circle on the output. The small circle represents 

    inversion.

    The ‘Exclusive-OR’ gate is a circuit which will give a high output if either, but not 
    both, of its two inputs are high. An encircled plus sign egg is used to show the 
    EOR operation.



    The ‘Exclusive-NOR’ gate circuit does the opposite to the EOR gate. It will give 
    a low output if either, but not both, of its two inputs are high. The symbol is 
    an EXOR gate with a small circle on the output. The small circle represents 
    inversion.
    The NAND and NOR gates are called universal functions since with either one 
    the AND and OR functions and NOT can be generated.
    Note:
    A function in sum of products form can be implemented using NAND gates by 
    replacing all AND and OR gates by NAND gates.
    A neither function in product of sums form can be implemented using NOR gates 

    by replacing all AND and OR gates by NOR gates. 


    Table 8.18 is a summary truth table of the input/output combinations for the 
    NOT gate together with all possible input/output combinations for the other 
    gate functions. Also note that a truth table with ‘n’ inputs has 2n
     rows. 

    You can compare the outputs of different gates.

    Who invented the idea?
    This logical way of comparing numbers to make decisions that produce either 
    a yes or no, 1 or 0, true or false is called Boolean algebra after its discoverer, 
    English mathematician George Boole (1815–1864), who set out the idea in 
    an 1854 book titled An Investigation of the Laws of Thought, on Which Are 
    Founded the Mathematical Theories of Logic and Probabilities. His objective 
    was to show how complex human reasoning could be represented in a logical, 

    mathematical form.





    The figure above shows how network for a certain telecommunications 
    company in Rwanda. Study it carefully and answer the following 
    questions.
    a) How many cells are shown on the figure above? Give their 

    respective names.


    b) Id8.3.1. Structure of cellular network
    An overall cellular network contains a number of different elements from the 
    base transceiver station (BTS) itself with its antenna back through a base 
    station controller (BSC), and a mobile switching centre(MSC) to the location 
    registers (HLR and VLR) and the link to the public switched telephone network 
    (PSTN). 
    Of the units within the cellular network, the BTS provides the direct 
    communication with the mobile phones. There may be a small number of base 
    stations linked to a base station controller. This unit acts as a small centre to 
    route calls to the required base station, and it also makes some decisions about 
    which base station is the best suited for a particular call. 
    The links between the BTS and the BSC may use either land lines of even 
    microwave links. Often the BTS antenna towers also support a small microwave 
    dish antenna used for the link to the BSC. The BSC is often co-located with a 
    BTS. 
    The BSC interfaces with the mobile switching centre. This makes more 

    widespread choices about the routing of calls and interfaces to the land line 

    based PSTN as well as the location registers. entify different masts shown on the figure.
    c) In regard to the figure, what is the importance of masts in those 
    different cells?
    d) Why do you think in transmission of network, the targeted area is 
    divided into small portions?
    e) Compare the number of cells that should be allocated for urban 

    areas to those for rural areas.

    8.3.1. Structure of cellular network
    An overall cellular network contains a number of different elements from the 
    base transceiver station (BTS) itself with its antenna back through a base 
    station controller (BSC), and a mobile switching centre(MSC) to the location 
    registers (HLR and VLR) and the link to the public switched telephone network 
    (PSTN). 
    Of the units within the cellular network, the BTS provides the direct 
    communication with the mobile phones. There may be a small number of base 
    stations linked to a base station controller. This unit acts as a small centre to 
    route calls to the required base station, and it also makes some decisions about 
    which base station is the best suited for a particular call. 
    The links between the BTS and the BSC may use either land lines of even 
    microwave links. Often the BTS antenna towers also support a small microwave 
    dish antenna used for the link to the BSC. The BSC is often co-located with a 
    BTS. 
    The BSC interfaces with the mobile switching centre. This makes more 
    widespread choices about the routing of calls and interfaces to the land line 
    based PSTN as well as the location registers. 


    8.3.2. Principle of cellular network
    The increase in demand and the poor quality of existing service led mobile 
    service providers to research ways to improve the quality of service and 
    to support more users in their systems. Because the amount of frequency 
    spectrum available for mobile cellular use was limited, efficient use of the 
    required frequencies was needed for mobile cellular coverage.
    In modern cellular telephony, rural and urban regions are divided into areas 
    according to specific provisioning guidelines.
    Deployment parameters, such as amount of cell-splitting and cell sizes, 
    are determined by engineers experienced in cellular system architecture. 
    Provisioning for each region is planned according to an engineering plan that 
    includes cells, clusters, frequency reuse, and handovers.
    Cells
    A cell is the basic geographic unit of a cellular system. The term cellular comes 
    from the honeycomb shape of the areas into which a coverage region is divided. 
    Cells are base stations transmitting over small geographic areas that are 
    represented as hexagons. Each cell size varies depending on the landscape. 
    Because of constraints imposed by natural terrain and man-made structures, 
    the true shape of cells is not a perfect hexagon. 
    Clusters 
    A cluster is a group of cells. No channels are reused within a cluster. 
    Fig. 8.23 illustrates a seven-cell cluster. In clustering, all the available frequencies 
    are used once and only once. As shown on fig.8.24, each cell has a base station 
    and any mobile user moving remains connected due to hand-offs between the 

    stations.

    Frequency Reuse 
    Because only a small number of radio channel frequencies were available 
    for mobile systems, engineers had to find a way to reuse radio channels in 
    order to carry more than one conversation at a time. The solution was called 
    frequency planning or frequency reuse. Frequency reuse was implemented 
    by restructuring the mobile telephone system architecture into the cellular 
    concept. 
    The concept of frequency reuse is based on assigning to each cell a group of 
    radio channels used within a small geographic area. Cells are assigned a group 
    of channels that is completely different from neighboring cells.
     The coverage areas of cells are called the footprint. This footprint is limited by 
    a boundary so that the same group of channels can be used in different cells that 

    are far enough away from each other so that their frequencies do not interfere.


    Cells with the same number have the same set of frequencies. Here, because the 
    number of available frequencies is 7, the frequency reuse factor is 1/7. That is, 
    each cell is using 1/7 of available cellular channels.
    Cell Splitting
    Unfortunately, economic considerations made the concept of creating full 
    systems with many small areas impractical. To overcome this difficulty, system 
    operators developed the idea of cell splitting.
    
    As a service area becomes full of users, this approach is used to split a single area 
    into smaller ones. In this way, urban centers can be split into as many areas as 
    necessary in order to provide acceptable service levels in heavy-traffic regions, 
    while larger, less expensive cells can be used to cover remote rural regions. 
    Handoff 
    The final obstacle in the development of the cellular network involved the 
    problem created when a mobile subscriber travelled from one cell to another 
    during a call. As adjacent areas do not use the same radio channels, a call must 
    either be dropped or transferred from one radio channel to another when a 
    user crosses the line between adjacent cells. 

    Because dropping the call is unacceptable, the process of handoff was created. 
    Handoff occurs when the mobile telephone network automatically transfers a 

    call from radio channel to radio channel as mobile crosses adjacent cells.



    During a call, two parties are on one voice channel. When the mobile unit moves 
    out of the coverage area of a given cell site, the reception becomes weak. At 
    this point, the cell site in use requests a handoff. The system switches the call 
    to a stronger-frequency channel in a new site without interrupting the call or 
    alerting the user. The call continues as long as the user is talking, and the user 
    does not notice the handoff at all.
    Conclusion
    We can say that mobile communication system is a high capacity communication 
    system arranged to establish and maintain continuity of communication paths 
    to mobile stations passing from the coverage of one radio transmitter into the 
    coverage of another radio transmitter.
    A control center determines mobile station locations and enables a switching 
    center to control dual access trunk circuitry to transfer an existing mobile 
    station communication path from a formerly occupied cell to a new cell location. 
    The switching center subsequently enables the dual access trunk to release the 

    call connection to the formerly occupied cell.


    While listening to radio on one of the evening, Mukamisha heard that the 
    tuned channel was on FM at 100.7 MHz But her radio works efficiently 
    when she pulls up the antenna.
    a) What do you think is the significance of the antenna on her radio?
    b) Hoping you has ever used/played a radio. Where do you think the 
    information/sound from the radio come from?
    c) Explain the mode of transmission of information as suggested in b) 
    above to the receiving radio.
    d) While going to sleep, her radio fell down and the speaker got 
    problems. Do you think she was able to listen to late night programs 
    on the same channel?

    e) As indicated on the radio, what does FM, MW, and SW mean?

    8.4.1. Simple radio transmitter
    A radio transmitter consists of several elements that work together to generate 
    radio waves that contain useful information such as audio, video, or digital 
    data. The process by which a radio station transmits information is outlined in 

    Fig. 8.29.

    - Power supply: Provides the necessary electrical power to operate the 
    transmitter.
    - The audio (sound) information is changed into an electrical signal of the 
    same frequencies by, say, a microphone, a laser, or a magnetic read write 
    head. This electrical signal is called an audio frequency (AF) signal, 
    because the frequencies are in the audio range (20 Hz to 20,000Hz). 
    - The signal is amplified electronically in AF amplifier and is then mixed 
    with a radio-frequency (RF) signal called its carrier frequency, which 
    represents that station. AM radio stations have carrier frequencies from 
    about 530 kHz to 1700 kHz. Today’s digital broadcasting uses the same 
    frequencies as the pre-2009 analog transmission.
    - The Modulator or Mixer adds useful information to the carrier wave. 
    The mixing of the audio and carrier frequencies is done in two ways. 
    In amplitude modulation (AM), the amplitude of the high-frequency carrier 
    wave is made to vary in proportion to the amplitude of the audio signal, as 
    shown in Fig.8.30. It is called “amplitude modulation” because the amplitude of 

    the carrier is altered (“modulate” means to change or alter).


    In frequency modulation (FM), the frequency of the carrier wave is made 
    to change in proportion to the audio signal’s amplitude, as shown in Fig.8.31. 
    The mixed signal is amplified further and sent to the transmitting antenna of 
    fig.8.29 where the complex mixture of frequencies is sent out in the form of 

    electromagnetic waves.

    Phase modulation (PM) 
    Phase modulation is a form of modulation that encodes information as 
    variations in the instantaneous phase of the carrier wave. It is widely used for 
    transmitting radio waves and is an integral part of many digital transmission 
    coding schemes that underlie a wide range of technologies like Wi-Fi, GSM and 
    satellite television. In this type of modulation, the amplitude and frequency of 

    the carrier signal remains unchanged after P

    The modulating signal is mapped to the carrier signal in the form of variations 
    in the instantaneous phase of the carrier signal. Phase modulation is closely 
    related to frequency modulation and is often used as intermediate step to 
    achieve FM.
    Amplifier: Amplifies the modulated carrier wave to increase its power. The 
    more powerful the amplifier, the more powerful the broadcast.
    In digital communication, the signal is put into digital form which modulates the 
    carrier. A television transmitter works in a similar way, using FM for audio and 
    AM for video; both audio and video signals are mixed with carrier frequencies.
    8.4.2. Simple radio receiver
    A radio receiver is the opposite of a radio transmitter. It uses an antenna to 
    capture radio waves, processes those waves to extract only those waves that are 
    vibrating at the desired frequency, extracts the audio signals that were added 
    to those waves, amplifies the audio signals, and finally plays them on a speaker.
    Now let us look at the other end of the process, the reception of radio and TV 
    programs at home. A simple radio receiver is graphed in Fig. 8.30. The EM 

    waves sent out by all stations are received by the antenna. 

    The signal antenna detects and sends the radio waves, to the receiver is very 
    small and contains frequencies from many different stations. The receiver uses 
    a resonant LC circuit to select out a particular RF frequency (actually a narrow 
    range of frequencies) corresponding to a particular station. 
    A simple way of tuning a station is shown in Fig.8.31. When the wire of antenna 
    is exposed to radio waves, the waves induce a very small alternating current in 

    the antenna.

    A particular station is “tuned in” by adjusting the capacitance C and/or 
    inductance L so that the resonant frequency of the circuit equals that of the 
    station’s carrier frequency.
    R.F. Amplifier: A sensitive amplifier that amplifies the very weak radio 
    frequency (RF) signal from the antenna so that the signal can be processed by 
    the tuner.
    R.F. Tuner: A circuit that can extract signals of a particular frequency from a 
    mix of signals of different frequencies. On its own, the antenna captures radio 
    waves of all frequencies and sends them to the RF amplifier, which dutifully 
    amplifies them all. Unless you want to listen to every radio channel at the same 
    time, you need a circuit that can pick out just the signals for the channel you 

    want to hear. That’s the role of the tuner.

    The tuner usually employs the combination of an inductor (for example, a coil) 
    and a capacitor to form a circuit that resonates at a particular frequency. This 
    frequency, called the resonant frequency, is determined by the values chosen 
    for the coil and the capacitor. This type of circuit tends to block any AC signals 
    at a frequency above or below the resonant frequency.The fig.8.35 shows a 
    combination of a radio transmitter and aradio receiver.
    You can adjust the resonant frequency by varying the amount of inductance 
    in the coil or the capacitance of the capacitor. In simple radio receiver circuits, 
    the tuning is adjusted by varying the number of turns of wire in the coil. More 
    sophisticated tuners use a variable capacitor (also called a tuning capacitor) to 

    vary the frequency. 

    The tuner usually employs the combination of an inductor (for example, a coil) 
    and a capacitor to form a circuit that resonates at a particular frequency. This 
    frequency, called the resonant frequency, is determined by the values chosen 
    for the coil and the capacitor. This type of circuit tends to block any AC signals 
    at a frequency above or below the resonant frequency.The fig.8.35 shows a 
    combination of a radio transmitter and aradio receiver.
    You can adjust the resonant frequency by varying the amount of inductance 
    in the coil or the capacitance of the capacitor. In simple radio receiver circuits, 
    the tuning is adjusted by varying the number of turns of wire in the coil. More 
    sophisticated tuners use a variable capacitor (also called a tuning capacitor) to 

    vary the frequency. 

    8.4.3. Wireless Radio Communication
    Let us now discuss the basic principles of wireless radio communications. 
    We shall mainly concentrate on the principle of amplitude modulation and 
    demodulation.
    The simplest scheme of wireless communication would be to convert the speech 
    or music to be transmitted to electric signals using a microphone, boost up the 
    power of the signal using amplifiers and radiate the signal in space with the aid 
    of an antenna. This would constitute the transmitter. At the receiver end, one 
    could have a pick-up antenna feeding the speech or music signal to an amplifier 

    and a loud speaker.

    The above scheme suffers from the following drawbacks:

    i) Electromagnetic waves in the frequency range of 20 Hz to 20 kHz (audiofrequency range) cannot be efficiently radiated and do not propagate well 
    in space.
    ii) Simultaneous transmission of different signals by different transmitters 
    would lead to confusion at the receiver.
    In order to solve these problems; we need to devise methods to convert or 
    translate the audio signals to the radio-frequency range before transmission and 
    recover the audio-frequency signals back at the receiver. Different transmitting 
    stations can then be allotted slots in the radio-frequency range and a single 
    receiver can then tune into these transmitters without confusion. 
    The frequency range 500 kHz to 20 MHz is reserved for amplitude-modulated 
    broadcast, which is the range covered by most three band transistor radios. The 
    process of frequency translation at the transmitter is called modulation. The 
    process of recovering the audio-signal at the receiver is called demodulation. 

    A simplified block diagram of such a system is shown in the below figure.

            

           

           

        

           

        

         

  • UNIT 9: RELATIVITY CONCEPTS AND POSTULATES OF SPECIAL RELATIVITY

    Yves, a student teacher in year two once was moving in a pick up as shown in 
    the figure above. She had a small ball that she projected upwards when the 
    car was moving at a speed of 60km/h.
    Basing on the statement above and figure 9.1, answer the following questions.
    a) Do you think Yves was able to catch the ball 3 seconds later after projection 
    assuming the car continued at a steady speed of 60 km/h?
    b) What do you think was the shape of the path described by the ball as 
    observed by Yves while in the car?
    c) Yves a stationary observer at the banks of the road observes the projected 
    ball right at a time when Yves projected it.Do you think the path of the ball as 
    observed by Yves was similar to that of Diana? If not, can you describe what 
    you think would be the observed path by him.
    d) While still in the moving car, Yves moves at 5 km/h with respect to the car. 
    Do you think as observed by Diana, Yves was moving at 5 km/h? If not, what 

    is the estimation of speed of Yves as observed by Diana?

    9.1.1. Introduction to special relativity
    Physics as it was known at the end of the nineteenth century is referred to as 
    classical physics:
    - Newtonian mechanics beautifully explained the motion of objects on 
    Earth and in the heavens. Furthermore, it formed the basis for successful 
    treatments of fluids, wave motion, and sound. 
    - Kinetictheory explained the behavior of gases and other materials. 
    - Maxwell’s theory of electromagnetismdeveloped in 1873 by James 
    Clerk Maxwell, a Scottish physicist embodied all of electric and magnetic 
    phenomena,
    Soon, however, scientists began to look more closely at a few inconvenient 
    phenomena that could not be explained by the theories available at the time. 
    This led to birth of the new Physics that grew out of the great revolution at the 
    turn of the twentieth century and is now called Modern Physics (the Theory 
    of Relativity and Quantum Theory).
    Most of our everyday experiences and observations have to do with objects 
    that move at speeds much less than the speed of light. Newtonian mechanics 
    was formulated to describe the motion of such objects, and this formalism is 
    still very successful in describing a wide range of phenomena that occur at low 
    speeds. It fails, however, when applied to particles whose speeds approach that 
    of light.
    Experimentally, the predictions of Newtonian theory can be tested at high 
    speeds by accelerating electrons or other charged particles through a large 
    electric potential difference. For example, it is possible to accelerate an electron 
    to a speed of 0.99 c (where c is the speed of light) by using a potential difference 
    of several million volts. 
    According to Newtonian mechanics, if the potential difference is increased by 
    a factor of 4, the electron’s kinetic energy is four times greater and its speed 
    should double to 1.98 c. However, experiments show that the speed of the 
    electron—as well as the speed of any other particle in the Universe—always 
    remains less than the speed of light, regardless of the size of the accelerating 
    voltage. Because it places no upper limit on speed, Newtonian mechanics is 
    contrary to modern experimental results and is clearly a limited theory.
    In 1905, at the age of only 26, Einstein published three papers of extraordinary 
    importance:
    - One was an analysis of Brownianmotion; 
    - A second (for which he was awarded the Nobel Prize) was on the 
    photoelectriceffect. 
    - In the third, Einstein introduced his special theory of relativity.
    Although Einstein made many other important contributions to Science, the 
    special theory of relativity alone represents one of the greatest intellectual 

    achievements of all time. 

    With this theory, experimental observations can be correctly predicted over the 
    range of speeds from to speeds approaching the speed of light. At low speeds, 
    Einstein’s theory reduces to Newtonian mechanics as a limiting situation 
    (principle of correspondence). 
    It is important to recognize that Einstein was working on Electromagnetism 
    when he developed the special theory of relativity. He was convinced that 
    Maxwell’s equations were correct, and in order to reconcile them with one of 
    his postulates, he was forced into the bizarre notion of assuming that space
    and timeare not absolute.
    In addition to its well-known and essential role in theoretical Physics, the 
    Special Theory of Relativity has practical applications, including the design of 
    nuclear power plants and modern global positioning system (GPS) units. These 

    devices do not work if designed in accordance with non-relativistic principles.

    9.1.2. Galilean transformation equation
    (a) Principle of Galilean relativity
    You’ve no doubt observed how a car that is moving slowly forward appears 
    to be moving backward when you pass it. In general, when two observers 
    measure the velocity of a moving body, they get different results if one observer 
    is moving relative to the other. The velocity seen by a particular observer is 
    called the velocity relativeto that observer, or simply relative velocity.
    To describe a physical event, it is necessary to establish a frame of reference. 
    You should recall from Mechanics that Newton’s laws are valid in all inertial 
    frames of reference. Because an inertialframe frame is defined as one in which 
    Newton’s first law is valid, we can say that an inertial frame of reference is one 
    in which an object is observed to have no acceleration when no forces act on 
    it. Furthermore, any system moving with constant velocity with respect to an 
    inertial system must also be an inertial system. 
    There is no preferred inertial reference frame. This means that the results 
    of an experiment performed in a vehicle moving with uniform velocity will 
    be identical to the results of the same experiment performed in a stationary 
    vehicle. The formal statement of this result is called the principle of Galilean 
    relativity: “The laws of Physics must be the same in all inertial frames of 
    reference.”
    Let us consider an observation that illustrates the equivalence of the laws of 
    Mechanics in different inertial frames. A pickup truck moves with a constant 

    velocity, as shown in Fig. 9.2a. 

    If a passenger in the truck throws a ball straight up, and if air effects are 
    neglected, the passenger observes that the ball moves in a vertical path. The 
    motion of the ball appears to be precisely the same as if the ball were thrown 
    by a person at rest on the Earth. The law of gravity and the equations of motion 
    under constant acceleration are obeyed whether the truck is at rest or in 
    uniform motion.
    Now consider the same situation viewed by an observer at rest on the Earth. 
    This stationary observer sees the path of the ball as a parabola, as illustrated 
    in Fig. 9.2b. Furthermore, according to this observer, the ball has a horizontal 
    component of velocity equal to the velocity of the truck. 
    Although the two observers disagree on certain aspects of the situation, they 
    agree on the validity of Newton’s laws and on such classical principles as 
    conservation of energy and conservation of linear momentum. This agreement 
    implies that no mechanical experiment can detect any difference between the 
    two inertial frames.
     The only thing that can be detected is the relative motion of one frame with 
    respect to the other. That is, the notion of absolute motion through space is 

    meaningless, as is the notion of a preferred reference frame.

    (b) Galilean space–time transformation equations
    Suppose that some physical phenomenon, which we call an event, occurs in an 
    inertial system. The event’s location and time of occurrence can be specified 
    by the four coordinates (x, y, z, t). We would like to be able to transform these 
    coordinates from one inertial system to another one moving with uniform 
    relative velocity. 
    Consider two inertial systems S and S’ (Fig. 9.4). The system S’ moves with a 
    constant velocity v along the xx’ axes, where v is measured relative to S. 
    We assume that an event occurs at the point P and that the origins of S and S’ 

    coincide at t = 0

    An observer in S describes the event with space–time coordinates (x, y, z, t), 
    whereas an observer in S’ uses the coordinates (x’, y’, z’, t’) to describe the same 
    event. 
    As we see from Fig. 9.4, the relationships between these various coordinates 

    can be written

    These equations are the Galilean space–time transformation equations. 
    Note that time is assumed to be the same in both inertial systems. That is, within 
    the framework of classical mechanics, all clocks run at the same rate, regardless 
    of their velocity, so that the time at which an event occurs for an observer in S 
    is the same as the time for the same event in S’. Consequently, the time interval 
    between two successive events should be the same for both observers. 
    Although this assumption may seem obvious, it turns out to be incorrect in 
    situations where v is comparable to the speed of light.
    Length and time intervals are absolute
    Galilean–Newtonian relativity assumed that the lengths of objects are the same 
    in one reference frame as in another, and that time passes at the same rate in 

    different reference frames. 

    In classical mechanics, then, space and time intervals are considered to be 
    absolute: their measurement does not change from one reference frame to 
    another. The mass of an object, as well as all forces, are assumed to be unchanged 
    by a change in inertial reference frame. 
    (c) Galilean-Newton Relative velocity
    Now suppose that a particle moves a distance dx in a time interval dt as 
    measured by an observer in S. It follows that the corresponding distance dx’ 

    measured by an observer in S’ is

    9.1.3. Einstein’s principle of relativity
    The special theory of relativity has made wide-ranging changes in our 
    understanding of nature, but Einstein based his special theory of relativity on 

    two postulates:

    1. The principle of relativity: The laws of Physics must be the same in all 
    inertial reference frames. The first postulate can also be stated as: there is 
    no experiment you can do in an inertial reference frame to determine if you 
    are at rest or moving uniformly at constant velocity.
    2. The constancy of the speed of light: The speed of light in vacuum has the 
    same value 8 c ms = × 3.0 10 / , in all inertial frames, regardless of the velocity 
    of the observer or the velocity of the source emitting the light.
    3. Uniform motion is invariant: A particle at rest or with constant velocity in 
    one inertial reference frame will be at rest or have constant velocity in all 
    inertial reference frames.
    The first postulate asserts that all the laws of Physics dealing with Mechanics, 
    Electromagnetism, Optics, Thermodynamics, and are the same in all reference 
    frames moving with constant velocity relative to one another. This postulate is 
    a sweeping generalization of the principle of Galilean relativity, which refers 
    only to the laws of mechanics.
    Einstein’s second postulate immediately implies the following result: It is 
    impossible for an inertial observer to travel at c, the speed of light in 

    vacuum.

    Note that postulate 2 is required by postulate 1: If the speed of light were not 
    the same in all inertial frames, measurements of different speeds would make it 
    possible to distinguish between inertial frames; as a result, a preferred, absolute 
    frame could be identified, in contradiction to postulate 1.
    These innocent-sounding propositions have far-reaching implications. Here 
    are three: 
    1. Events that are simultaneous for one observer may not be simultaneous 
    for another. 
    Two events occurring at different points in space which are simultaneous 
    to one observer are not necessarily simultaneous to a second observer. The 
    central point of relativity is this: Any inertial frame of reference can be used 
    to describe events and do Physics. There is no preferred inertial frame of 
    reference. However, observers in different inertial frames always measure 
    different time intervals with their clocks and different distances with their 

    meter sticks. A light flash goes off in the center of a moving train (Fig.9.5).




         


    9.2.1. Time dilation: Moving clocks run slowly
    We can illustrate the fact that observers in different inertial frames always 
    measure different time intervals between a pair of events by considering a 

    vehicle moving to the right with a speed v, as shown in Fig.9.6. 

             

              

  • UNIT 10:STELLAR DISTANCE AND RADIATION

             

         

            

          

     

  • Topic 11

  • Topic 12

  • Topic 13