December 28, 2015

OUR UNIVERSE

1. THE BIG BANG

We take the world as we see it around us as the given, as if it was always there. But science tells us strange, wondrous and fascinating things about the world. The world as we know it, not just the earth and the solar system – but the whole universe was at a point 1400 crore years back.

Think! What an imagination it needs to visualize that! The whole gigantic universe with its billions (100 curves) of galaxies, each containing billions of stars wasn’t even there as it is now but was concentrated at a point, called by the scientists, the singularity.

Now this is a strange fact, probably the strangest of all facts. So we obviously need to ask: why. Why was the whole universe at a point?

The answer is incredible and it lies in just understanding deeply the reality of an almost omnipotent force that governs the universe. That force is the force of gravity and it is universal. Let us proceed how to get a deep, real understanding of gravity. Since childhood we have observed things falling from a height if left free. We have observed it so many times that we take it for granted. We do not system, it, wonder about it, even feel it.

Yet, think!

Why should things fall? After all, we are not pushing it down and there is no contact between the earth, and the falling body. Isn’t it strange – this action at a distance. You leave a body and it moves towards the earth. The earth is a sphere and all objects get attracted to the centre of the earth and participates in the motion of the earth. Our atmosphere, the air we have, our oceans, everything is held onto the earth along the whole of it’s surface and circumference.

The ancients wondered about this gravity on earth. But later from 13th century onwards people began looking at the heavens too and began wondering and also, additionally, began tracing the motions of the planets the sun and the moon. They collected lot of data and bit by bit they came to understand that it was not the sun that moved around a stationary earth (as the ancients had assumed) but it was the earth (and other planets) that moved around the sun.

This whole inquiry culminated in the Kepler’s laws of motion of planets which describes the regular, uniform behavior of planets round the sun (it was not random or accidental).

Then Newton began a serious, deep inquiry in to this matter. Remember it was very early. Nothing was really clear. The heavenly motions of planets had been traced out. People observed the things falling on earth but no connection was made. It was almost as if, then the heavens were different from the earth. Newton’s incredible daring and genius lay in linking it. As legend has it, he observed an apple falling and suddenly he got this great thought. Are the motions of the apple falling and the moon falling the same? The moon ‘fall’ in the sense that if it did not fall towards the earth it would go off the straight line. It was already understood that the moon’s motion and even the planets motions were a result of two motions – one horizontally and other perpendicular and vertical towards the sun.

These two motions combined to give the almost circular motion of the moon and planets. (All circular motion is a combination of two such motions.)

Well, Newton thought about this and he suddenly got it!

He understood, in a flash of genius, that actually every mass attracts every other mass!

He got the mathematics of it also the power of attraction is directly proportional to both masses and inversely proportional to the square of the distance between them. This simply means the more any, or both of the masses, more the attractive force. Greater the distance, lesser is the attractive force. Also the reduction is as the square of the distance i.e. if distance is doubled the force is reduced 4 times, if the distance is tripled (made 3 times), the force is reduced by (3x3) 9 times!

This equation fitted with Kepler’s equation and Newton made the heavens and the earth one!

Just think! What a law Newton’s universal law of gravitation really is!

Every mass attracts every other mass in the universe and earth is merely one such mass and this law holds true for all the masses of the universe. Even 2 objects on earth actually get attracted. The reason we do not see a visible movement is because the attractive force of gravity is very weak. Unless the masses are of big size, there is not much attraction. This is the reason why things fall slowly on the moon – the mass of moon is 1/6th of the earth and hence the gravitational force (as it is called) is also 1/6the! That is why we see that wondrous (slow motion like) falling of things on the moon.

In space, things do not fall at all! They just ‘hang’ where they are! This is because the object is too far from any big size object to feel any attraction. So it just remains where it is! Isn’t this a wonder!!

Newton had literally swept the space clean and unlocked one of the deepest mysteries of the universe. Now, still a major, in fact, obvious question remained. If every mass attracts every other mass, how can the world as we see it – earth, planets, stars be at all? Should they not actually be together, this whole universe, at one place?

This was seriously asked, in the 1900s and no answer existed. The question, however, remained. Then in the 1900s another strange fact came into light.

Scientists discovered that the universe, as a whole was expanding. Every object was going away from every object. They came to know this by a phenomenon called Doppler effect. Doppler effect is very common with respect to sound. Sound consists of waves and if a body making sound is approaching you, the waves crowd together and the number of waves per second, that is the frequency increases. The opposite happens when the body making the sound is going away from you. Here, the waves are more stretched out and the number of waves per second is less. That is the frequency is decreased. Now the interesting thing is that light too is a wave and the same thing has been tested to happened to light too. A body emitting light, if its going away from you would change its frequency towards the red. This is called the red shift. If the body emitting

light is coming towards you, the n the frequency is increased and the light shifts towards the blue. This is called the blue shift. Now it was observe through countless experiments, that whenever you observe an object in the heavens, a star or a galaxy that is emitting light, it is shifting towards the red! This means that everything is going from away you. This actually means that the whole universe is expanding and everything is going away from each other.

It is then that they understood why the universe is not coming together due to gravity. Actually expansion of the universe was countering gravity. If the universe is expanding, then the whole universe must have been at a point and there must have been a big bang. This is how the scientist came to the conclusion that the whole universe was at a point and then the big bang happened.

After the big bang within moments, hydrogen atoms were created and began filling the whole space from these hydrogen atoms were born the stars, the galaxies and the solar system. How this happened will be understood in the following sections.


2. FORMATION OF GALAXIES


We have learnt that the whole matter of the universe was at one point 14 billion years back and that there was a big bang.

After the big bang what happened?

The simplest atoms of hydrogen gas were formed and they filled the blank space after millions of years. Because of the big bang, the expansion continued in all directions. But in many areas the cloud of hydrogen gas were a little closer and due to gravity formed huge regions of concentrated hydrogen gas. These are the galaxies!

Even in these regions, in some areas hydrogen gas got even further closer and formed stars. When the stars died they burst and again spread out. All the stars in each galaxy also attracted each other and formed systems of stars. The galaxies themselves attracted other galaxies, again due to gravity. Sometimes they push into each other giving various shapes of galaxies and also complicated motions. These motions continue to this day.

So you see its not just all galaxies expanding away from each other. They move themselves too and the motions never stop!

We live in a galaxy called the milky way galaxy. Sometimes in a clear night, we see a white spread in the sky, that is the milky way galaxy. Our milky way galaxy contains our Sun as just one of the billions of stars. So you can imagine how huge just the milky way galaxy is! Now there are billions of such galaxies! So the size of universe is literally unimaginable! We can only feel it.

3. BIRTH OF STARS

We have learnt already that after the big bang, hydrogen gas filled the emptiness of space. We also learnt that in some huge regions galaxies are formed which are nothing but masses of hydrogen gas collecting together. In these galaxies are formed stars.

In some regions a little bit of hydrogen gas comes together in the form of clumps and this begins a process that goes on. The clump starts attractive, due to gravity the surrounding hydrogen gas. It becomes bigger and bigger. The more big it becomes the more powerfully it attracts all the hydrogen gas arrounded towards its centre!

This process goes on and on. The clump becomes bigger and bigger and bigger and attracts more and more powerfully the hydroges gas around it. Now this whole attraction towards it centre creates a very huge pressure. Now pressure is related to temperature, to the producing of heat. If you rub your hands hard, it becomes very hot. Wherever there is pressure there is heat. Heat is nothing more then the internal jiggling and wiggling of atoms/molecules inside matter. More the pressure more the temperature. If the pressure becomes huge the temperature too rises to a very high level. This is what happens inside the clump which becomes very huge. There is a high temperature of lakhs of degrees created inside the star. This removes electrons from the atoms of hydrogen. An atom contains proton and neutrons in its central nucleus and electrons orbit around it. Hydrogen atom contains one proton, one neutron and one electron. When the electrons are removed due to the high heat, a process called nuclear fusion reaction take place.

Fusion means joining together. In normal circumstances a hydrogen nucleus cannot join with another hydrogen nucleus. This is because protons are positively charged and if two nucleus of hydrogen come close together the proton in one hydrogen atom would repel the proton in the other hydrogen atom (two positives charge repel each other).

But when the temperature is extremely high the repulsion is overcome and the two nuclei actually join together, fuse together and becomes another nucleus! This nucleus contains two protons and is the element helium.

So in the star, hydrogen starts becoming helium. In this process a strange thing happens. Mass is lost and converted into huge amounts of energy (by the formula of E=mc2). This creates an outward force from the centre of the star. But there is another force too. Because the star is so huge there is an internal gravitational attraction towards the centre also.

These two forces the constant creation of nuclear energy outwards and the inner sucking force of gravitation balance each other and the star is born!

How long does this last? Obviously till the hydrogen is used up in the Star. What happens when the hydrogen is used up? The star begins the process of death. What is this process?

What are all the things that happen when hydrogen is used up?

We will see that in the next section.


4. DEATH OF STARS


When the hydrogen gas is completely used up to make helium, two things can happen depending on the size of the star.

The process of death of a small sized star (like our Sun):

When the hydrogen is used up in a small sized star, the outward force of nuclear energy created stops. Then what happens is the centre of the star shrinks but the outward covering of the star sort of floats up like a huge flare. So the star suddenly becomes big and redder. This is a red giant. Inside helium now starts a process of nuclear fusion reaction again and becomes lithium. But this does not last long as the helium is used up very quickly. After this again the outward force of nuclear energy stops and the inside of the star shrinks and the outside flares up as a second red giant. For a small size star, this is all. The red giant cools. The star becomes very small, the size of the earth but more dense. This is the white dwarf and a kind of ending of the star. The Sun being a medium sized star will go through all these processes. After 4 to 5 billion years i.e. the Sun would die.

The process of death of a big sized star:

For a large sized star too the hydrogen gets used up and there is an outward flare, this is a huge blast and it is called a Supernova. But here is the difference, inside the star the helium becomes lithium, the lithium becomes the next element and so on and there is a series of red giants. The second difference is what happens when the series ends.

Remember, if the star is huge the inner sucking gravitational force would be very huge. This huge force breaks up matter also and the star instead of becoming a white dwarf becomes a neutron star. The star contains only neutrons.

If the star is even more huge we don’t even get a neutron star it ends up as a black hole where all the matter vanishes due to the huge gravitational force directed towards the centre. Gravity here completely makes the matter vanish and light get sucked into the black hole. So this is the way stars are born and star die continuously in the universe.

In this whole universe we on earth are only a speak and in a way insignificant!


5. FORMATION OF THE SOLAR SYSTEM


There are two main theories that explain the formation of the solar system (the sun, planets and asteroids). But the theory most widely accepted by all scientists today is the nebula theory. Long back, there was a huge mass of gas, dust and ice in the region which is now the solar system. At that time, probably due to a supernova (exploding star), this mass was disturbed. A disturbance in the universe is dangerous because if masses gets close together gravity starts acting and collapses the mass.

This is what happen the mass got closer together due to the explosion and the mass also started spinning. As they got more and more close while spinning the spinning became faster. Slowly over a period of time the whole shapeless spinning gas started becoming orderly, uniform and flat. Now this whole thing exactly like a frisbee or cake spinning very fast round and round. Slowly in certain areas this gas got closer together again due to gravity and slowly formed larger bodies called planetesimals. Even more matter flying around stuck to these planetesimals and slowly over a long period of time the solar system as we know today was formed that is the sun at the centre and the planets Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune.

The question now remains as to how the sun was formed at the centre. At the centre the pressure was very high and temperature rose to lakhs of degrees and the process of formation of star started i.e. hydrogen becoming helium and releasing nuclear energy outward. This nuclear energy balanced the inner gravitation force and our Sun became stable.

There is a big gap between Mars and Jupiter and this gap is filled with numerous smaller particles which is called the asteroid belt. Why was the planet not formed in this gap? This is because Jupiter is a huge mass close to the Sun’s mass. So if any planet tried to form itself was burst into pieces by Jupiter! Thus we have this beautiful solar system with the Sun at its centre and planets around it!


<script type="text/javascript" language="javascript"> var aax_size='728x90'; var aax_pubname = 'wwwvision4all-21'; var aax_src='302'; </script><script type="text/javascript" language="javascript" src="http://c.amazon-adsystem.com/aax2/assoc.js"></script>









ATOMIC STRUCTURE

1. History of Atom

In 460 B.C., a Greek philosopher, Democratism, developed a kind of idea of atoms. He looked at things around him and felt that if you go on breaking any material into parts and further parts, you will have to reach something which can’t be broken further. This he called an atom. It was purely speculation and no experimental evidence was available at that time to prove anything.

More than 2000 years had to pass before people began to consider the idea of atoms seriously. In the 1800’s, an English chemist, John Dalton did lot of experiments with several chemicals and he found a strange thing. Elements always combined with each other in fixed proportions. Any extra amount added would come out as residue. An element A for example would combine with 2 B’s by weight. This will always remain true. How can this be possible unless some fundamental particle in one element is combining with some fundamental particles in another, the number being always the same? Thus he proposed that every element was made up of fundamental particles and he called them by the same name atoms.

Thomsons ‘Rasin in the Pudding’ model of the atom

In 1897, the next great event took place. A negatively charged particle was discovered by J.J.Thomson in his experiments with discharge of gases. He called the negative charge particle electron. He also proposed a model for the atom. Since matter is not negatively charge he felt that there was a positive charge that balanced the negative charge and the electrons were put like raisins on a lump of pudding that was the positive charge.

(Picture-1)

Berlin proved that when the energy is released when heated until it glows, this energy always comes out as discrete units, that is it takes only multiples of certain basic values. The energy was not continuous. He called these energy packets quanta.

At that time light was considered to be a wave but Albert Einstein thought otherwise. He felt that light was made up of quanta and he called this quantum of light Photon. Einstein also discovered the photo electric effect, the phenomenon by which a material gives out electrons when light is put on it and absorb. By this time people wondered about light. What was it really? A wave or a particle? Finally they came to the conclusion that light sometimes behaves as a wave and at other times behaves as a particle (but never both). The behavior which actually comes out depends upon the set up of the experiment. During the same time, alpha particles were discovered which had a positive charge. Scientists felt that this was the positive charge in the atom. In 1911, a land mark experiment was performed by Earnest Rutherford. He felt that it would be interesting to bombard atoms with alpha rays. He just wanted to see what would happen. He used radium to generate the alpha particles and shown them on to atoms in a thin gold foil. Behind the foil sat a fluorescent screen for which he could observe the alpha particles impact.

A strange thing happened. Most of the alpha particles passed through but occasionally some were hit back as if striking something hard! The only explanation of this was that most of the atoms had empty space in between and with hard points here and there.

Rutherford proposed his planetary model of the atom. He said that the positive charge was concentrated at the centre called the nucleus and the electrons moved round it like planets. But there was one terrible problem with this model. By the time a lot had been discovered about electricity and magnetism in general. A negative charge moving around the nucleus should lose energy by generating electro magnetic waves. Bohr used the principle energy comes in dissect packets of energy called Quanta to come with his model of the atom. He proposed that only some special orbits are allowed for electrons to move around. These orbits are called energy level. When electron gains energy it jumps from lower to higher orbit. When it looses energy, it jumps from higher to lower. Electron can’t have an intermediary between two levels. The energy difference between two levels is the quanta.

In 1932, J. Chadwick another sub atomic partial called the neutron. The neutron has mass nearly equal to the proton and has no charge. The mass of the nucleus is equal to the sum of the masses of the protons and the neutrons.


2. How are the electrons distributed in the difference orbits


To keep an atom electrically stable, it has the same number of negatively charged electrons in orbit around the nucleus as there are positively charged protons in the nucleus. In situations where there are either more or less electrons in orbit than there are protons in the nucleus, the atom is called an ion. This happens in static electricity and in some chemical solutions.

Electron shells

Electrons are arranged in shells or orbits around the nucleus.

Maximum number

There is a definite arrangement of the electrons in these shells and a maximum number of electrons possible in each shell.

Shell or Orbit Number 1 2 3 4 5

2 8 18 32 50

The most electrons possible in the first shell are 2. After the first shell is filled, the second shell starts filling up, according to the number of positive charges in the nucleus. The most allowed in the second shell is 8 electrons. Then the third shell starts to fill.

Electron shells for a Sodium atom (atomic number 11, with 11 electrons)

(Picture-2)

Filling order complicated

After the second orbit or shell is filled, things start to get complicated. The third shell fills until it gets to 8, and then the fourth shell starts adding electrons until it too has 8 electrons. Then the third shell fills until it gets to 18.

Outer shell basis of Chemistry or valency

The number of electrons in each shell is the basis of chemical combinations.

Energy levels

Electrons have potential energy, depending on their shell or orbit. Each orbit has it’s own energy level. The each energy levels are further broken into sub orbits. There are some situations when an electron will jump from one orbit—or energy level—to another. When that happens, the electron gives off electromagnetic energy of one wave length or colour of light.

Since each element has its own electron shell or energy level configuration, it has own set of colours called its spectrum. This is used to identify any element.

The power of the Atomic theory :

What a reality, the atomic structure is! It is a deep fact about the whole physical world and explains so much! As we already saw in the earlier chapters, it explains sound (propagation of waves due to spring like disturbances of medium.) It explains heat. Heat is nothing but the jiggling and wiggling of atoms. It explains the giving off of light of a certain colour. This happens when electrons jump from one orbit to another.

Electric current is nothing but free electrons moving in metals due to a potential difference. Magnetism in magnets is the result of the molecular atoms in matter that are aligned. All the macroscopic properties can be explained by the atomic theory. Examples are state (solid, liquid or gas), pressure of gases, strength of materials (more bounding of the atoms inside, more the strength), temperature (average energy of movement of atoms in a body), density (more packed the atoms, more the density) etc. The whole of chemistry that is chemical combination depends upon valency as mentioned earlier. Hence chemistry fundamentally is based on atomic theory. The foundation of biology is chemistry and hence even biology depends upon atomic theory (the formation of complex molecules).

ELECTROMAGNETISN

1. Charges and force between charges

Electricity is related to charges. What is charge? Charge is a strange thing given in nature. It is not seen or felt ordinarily. For example if you touch a table you feel no effect due to charge.

(Picture-1)

Around 200 years back, charges were discovered to be in matter by the simplest process of rubbing two substances. Much later they came to understand the fundamental essence of charges. This happened when they discovered that all matter is made up of atoms and molecules (molecules are only atoms joined together).

In an inch of any material, there are crores and crores of atoms / molecules ! ( see the next chapter for the details) Now electricity is a property of electrons and protons. Electrons and protons are in atoms. Electrons are negatively charged, protons are positively charged and there is a third type of particle called neutrons. Neutrons have no charge. The negative and positive are only names to say that there are two kinds of charges. The protons and neutrons reside in a central nucleus. The electrons orbit around the nucleus. Now, the property of these two kind of charges (positive and negative) is that positive and positive repel (go away from each other), negative and negative repel and negative and positive attract! This is given in nature !

When two substances are rubbed with each other, electrons from one substance (Say A) escape into another (Say B). B has now more electrons than protons so it has negative charge. B has lost electrons, so it has more protons than electrons.

So it has positive charge. Thus A and B attract each other since there are unlike charges. If A is taken to similar negatively charge body C, A and C repel. If B is taken close to a similar positively charged body D then B and D also repel. Repulsion happens because like charges repel. The force between charges (the repulsion or attraction) is called electrical force. The closer the charges are, greater the force. More the charges, more the force. This is expressed in the equation f = k q1 q2 / r2 , where q1 and q2 are the charges of the two bodies and r is the distance between them. This is called Coulomb’s Law.

(Picture-2)


2. Currents, Ohm’s Law and Batteries


Currents are flow of charges in a conducting wire. How can such a flow of charges be created. Currents can be created using batteries. It was Volta created the first battery.

Working of a battery :

A battery has three main parts: a positive electrode (terminal), a negative electrode, and a liquid or solid separating them called the electrolyte. The positive and negative electrodes are separated by the chemical electrolyte. It can be a liquid, but in an ordinary battery it is more likely to be a dry powder. When you connect the battery to a lamp and switch on, chemical reactions start happening. One of the reactions generates positive ions and electrons at the negative electrode. The positive ions flow through the electrolyte to the positive electrode. Meanwhile, the electrons flow around the outside circuit to the positive electrode and make the lamp light up on the way.

(Picture-3)

parts of a battery

(Picture-4)

Principle of a battery

understand the mathematics of current. The current in a wire is directly proportional to what is called a potential difference between two points. Potential difference is defined as the work done to carry a unit positive charge from one place to another.

The more the potential difference, more the amount of current. V a directly proportional to i. So V = i x R Where R is the resistance in the wire to the flow of current. Current is measured in amperes and potential is measured in volts. Resistance is measured in Ohms. This relationship between potential and current is called Ohm’s Law.

(Picture-5)


3. Magnetic effect of current


We have learnt about charged particles. There are positive and negative charges. We know that like charges repel and unlike charges attract. We have also seen that a current can be created through a battery and we have also understood Ohm’s Law.

It was first observed by Oersted that a magnetic needle is affected near a current carrying wire. He accidentally discovered this phenomenon while giving a lecture. It was one of the greatest turning points in the history of science !

Current in a wire brings about a magnetic effect in the space around it. To put it simply current in a wire behaves like a magnet. What is the direction of the magnetic field created by current carrying wire. This is given by the right hand thumb rule. If you imagine holding the current carrying wire in your right hand and with your thumb pointing in the direct of the current, then the curl of your fingers gives the direction of the magnetic field. See figure.

(Picture-6)


4. Electro magnetic induction


We have seen that a current carrying wire produces a magnetic effect. Is the reverse true ? Is there a relationship between magnets and currents ? Michael Faraday wondered about it and tried many experiments and finally discovered that if you move a magnet near a wire, current is induced in it. This is called electro magnetic induction and this was used to make a generator.

So in effect we have two principles. The current carrying wire brings about a magnetic effect and moving magnet induces current ! These are the fundamental laws of electricity and magnetism !

Electromagnetic induction

(Picture-7)


5. The working of motors


Motor work on the principle that a current in a wire creates a magnetic field. What we do is we take a coil bent it into a loop and place this coil between two magnets. The right hand side and left hand side will experience opposite forces of repulsion. Thus they will be turning motion. A turning motion is a called a torque. In practical motors many loops are taken and magnets are replaced by electromagnets.

(Picture-8)


6. The working of generators


Generators work on exactly the opposite principle. Here the loop is given a motion so that electric current is induced in it.

(Picture-9)


7. Electromagnetic waves (Spectrum)


We have two principles till now. Firstly we saw that when a current flows in a wire it becomes like a magnet creating a magnetic field around it. When such a wire in the form of a loop is kept between two magnets, we have a motor.

Secondly we saw that if there is relative motion between a magnet and a wire a current is induced in the wire. This principle is used to make generators.

Now, the current in a wire is steady. What if the current oscillates ? In other words, what if the current is not steady. A wondrous thing happens ! The changing current creates a changing magnetic field. But according to Faraday’s Law this changing magnetic field should create in turn electric field. But the changing electric field again creates a changing magnetic field and so on.

So when a current is not steady, electric and magnetic fields are created and they propagate outwards as waves. And these waves are called electro - magnetic waves. Maxwell found out the velocity of such waves and it was exactly equal to the velocity of light. Thus they discovered that light waves actually are electro magnetic waves. Electro magnetic waves have various frequencies and wave lengths and the whole range is called the electro magnetic spectrum.

(Picture-10)



LIGHT



1. WHAT IS LIGHT AND WHAT ARE ITS PROPERTIES?


Light is one of the most mysterious things on the world. We don’t see light, we in fact, see because of it. Anything heated becomes luminous, is itself glowing, and enables us suddenly to see things around it. If you are sitting in a dark room, by an can’t see anything. When you switch on the light, the bulb glows and other objects are seen! How, what is happening? Clearly the bulb is the source of light and if we close our eyes, we can’t see, obviously. Something mysteriously is happening between the source of light (here bulb) and our eyes.

What is it?

Something is travelling between the source and our eyes. And this something seems to travel on straight lines. Otherwise why would there be shadows if anything obstructs that something coming from the source of light. (here bulb) Then, there are colours. It is as if light comes in a variety of colours. A red short is red, may be, because that mysterious something is a type that causes the sensation of red.

Red is red. We can’t question it. It is that particular quality. What we are doing here is trying to ask what causes red. That which causes on us the sensation of red is “red light”. In the same way violet light, yellow light, blue light, green light, indigo light, orange light.

What about black colour and white colour. White is a mixture of all colours and black is that which gives off no colour. When light, that invisible thing, falls on a particular object, the object absorbs some colours and gives off a colour. The colour given off, if red, will make us see red. Similarly with other colours. If the object gives off all colours, we see white. If the object absorbs all colour and gives off no colour, we see black.

If the object lets the light pars through completely the object is not seen eg: glass, water. What if the object does not take anything and reflects the light from an object completely. Then it becomes a mirror!

(Picture-I)

See the figure. The light from object A travels on straight line and hits the mirror. The mirror doesn’t take anything and simply reflects it and then it reaches our eye. Now comes the catch!

What do we see! Since all the light from A has reached us, we see A but where do we see A?

From childhood our brain knows only to ‘see’ objects in straight lines. So it sees the object at A as shown on the figure!

(Picture-2)

See figure(2) the object itself has the eye. Then we see ourselves at a obstance which the same distance ‘d’ but ‘inside’ the mirror! In a way the objects that we see is a hallucinatism but it is a hallucination due to physics and it’s reality not due to a ghost! Let us now consider another and last strange phenomenon that we see with our naked eye.

Why does the win in a glass of water appear to be above than it’s normal bottom? Why does a stick seem to bend in water? The answer is that light bends when travelling from one medium to another. (Here from water to air). So what? What if it bends?

If we take two rays - ray 1 and ray 2 and if it bends and reaches our eyes, our eyes don’t know that. It sees on straight lines only and that means that it hallucrates and sees the object above than the normal. Even the bottom comes up.

A spom bends and bulges from the same reason.

(Picture-3)

So these facts give us some ideas about light which are fairly obvious. But it is a wonder, isn’t it?

Its strange - this thing that travels in straight lines, bends when travelling from one medium to another, is composed of various components which cause various sensations of colours in us!

Light travels in straight lines

Light consists of various colours

Light is reflected from norms

Light is refracted (as it is called, the act of bending) when from one met to another.

When Light strikes one face of a prism, the different colours of light refract by different amounts! Thus they emerge from the other face with the colours separated. Rainbows are formed that way (the raindrop acts as prism)

(Picture-4)

The principle of refraction is used in lenses to make things bigger.

HEAT

1. WHAT IS HEAT REALLY AND WHAT ARE ITS PROPERTIES ?


Heat is a sensation that we feel, but what is that sensation and how is it caused? Heat in the earlier times was thought to be a kind of fluid that goes from one body to another. But later they understood that heat is nothing but the jiggling and wiggling of atoms and molecules. Matter is not all one piece. Inside it is made up of crores and crores of atoms. These atoms move randomly and more the movement of the atoms, more the heat. Our skins have evolved to precise heat with a sensation of hot and cold! In a cold night, why do we feel cold? It is because the molecules of air move about at less average energy( called kinetic energy). When we rub our hands - hard lot of heat is automatically produced. Why? Again it is because when you rub your hands together, the atoms inside jiggle more and more and that gives us a sensation of heat! So when pressure is increased then heat is produced. The pressure can be due to friction, electricity. Then there is another thing that heat does , it can change the state from solid to (picture)


Change of State


liquid and liquid to gas! Why does this happen? It happens because in a solid the atoms are fixed in their places. They cannot move about and when heat is given to such a solid, the bonds etween the atoms that keep them fixed weaken and they move about though the link between them does not break. This is a liquid. On further heating, the links that is the bonds are broken completely and that is a gas obviously!

Heat also expands solids, liquids and gases. This is because the bonds between the atoms inside get loosened and the body as a whole expands. (Picture)


Expansion of Solid


Heat is also transmitted in 3 ways - conduction, convection, radiation. When one part of a solid body is heated, the atoms inside that part starts jiggling and wiggling. These in turn moves the atoms beside them and so on. Thus heat is transmitted from one end to the other. This is conduction(see Picture)

Convection is very interesting. Suppose we take a bucket full of water and heat it for sometime. The lower part which is closer to the heat gets heated up. The bonds inside loosen up and the distance between the atoms become greater. When the distance becomes greater it is like the weight is reduced as less is now in the space occupied earlier. The gravitational attraction hence reduces and the water goes up. The colder heavier water pushes into its place (the lower part of the water). Thus heat gets transmitted by actual movement of water. This is called convection. Exactly to the same thing happens causing winds. The air closer to the earth is heated up, becomes lighter due to the atoms going further apart and hence rising due to less gravitational attraction. The colder heavier gas pushes into its place and winds are caused!

There is a third way in which heat is transmitted. They are through waves. There are waves called heat waves or infrared waves. They are part of the electromagnetic spectrum (to be covered in a later section). These waves do not need any medium. The sun’s heat is actually heat waves which travel through space and come to earth !

GASES

1. BERNOULLI’S PRINCIPLE

Statement:

The pressure of a liquid is decreased if the velocity with which it is moving is increased. Why is this so? This is because a flowing liquid (or even a gas) is made up of molecules. When these molecules hit the surface it is a pressure. When the molecules are going fast, the number of hits are less and hence the pressure is less.

This principle is used to make airplanes fly. What we do is we make the wings of the airplane in such a way that air needs to travel a longer distance on the top surface when compared to the bottom surface. Since the air is moving smoothly on both the surfaces, it takes a longer time for the air moving on the top surface to cover the wing as compare to the air that is moving along the bottom surface.

This means that the velocity of the air moving on the top surface is less when compare to the velocity of air moving along the bottom surface. Hence the pressure on the top surface is lesser when compared to the pressure on the bottom surface. So there is a net upward pressure on the bottom surface and airplane flies! (see figure)

2. WHAT ARE THE PROPERTIES AND LAWS OF GASES?

2.1 What is a Gas ?

A gas is a substance that can compressed easily. Gases fill the container in which they are put. Actually the atoms and molecules in a gas are free to move about. There are spaces in between molecules ! That’s why it is a gas ! There are three fundamental variables that define the state of a gas. They are pressure, temperature and volume. These three variables are connected deeply in the form of laws. The first law is Boyles law. This gives the connection between pressure and volume. Pressure is the force per unit area on the wall of container. Volume is the space occupied by the gas. How are these two related and why ?

2.2 Gas Laws

Boyle’s law

If you increase the volume keeping temperature constant, there will be less molecules per unit volume. Hence the hitting of the molecules of the container will be less. Hence the volume is inversely proportional to pressure. This is called Boyle’s law. The next law is Charle’s law. Charle’s law states that the volume of a gas is directly proportional to its temperature provided the pressure is held constant. It is because if you increase the temperature and pressure is kept constant, then the body will increase in volume due to increased movement of molecules.

These are the two fundamental laws that govern all gases.

LIQUIDS

1. Introduction:

When we look around the world we see actually 3 different kinds of things – Solids, Liquids and Gases.

What is the difference between solids, liquids and gases?

Solids have a definite shape, are reasonably rigid i.e. don’t change shape too easily.

Liquids do not have a definite shape and takes the shape of the container.

Gases are even more free. They fill the container fully.

Why do solids, liquids and gases have their nature.

If we keep ice in open air, it melts and becomes a liquid! After some more time, it becomes vapour and vanishes! Surely a solid is not all one piece. If it is becoming a liquid, there is an internal nature it has that gets changed. The same thing with liquid becoming gas.

Yes!

There is an internal nature to everything.

During the 19th century an extraordinary fact came to light.

Everything, an inch of any material, is made up of crores and crores of small particles called atoms or combinations of atoms called molecules.

The first indication came from experiments in chemistry and later many many experiments gave a detailed account of the inner working of atoms.

The story of the atomic structure is explained fully in the section of “understanding atomic structure”. In a solid the atoms are bonded tightly and hence outwardly, it is solid!

In a liquid the atoms are not in one place but are bonded!

In a gas the atoms are free!

This is the reason why a solid is a solid, a liquid is a liquid and a gas, a gas! When heated, the bonds between the atoms in a solid become weak and becomes a liquid outwardly. On further heating, the bonds become completely broken and a gas is formed. We discuss change of state in the section of “understanding heat”.

In this section we try to gain a deeper understanding into liquids. Liquids and solids together are called fluids.

Pascal’s law, Archimedie’s Principle, and Bernoullis principle explain the deeper working of liquids. Bernoulli’s principle applies to gases also and will be considered in the next section on, Fluids (2) – gases.


2. Pascal’s Law


Pascal’s Law states that if you apply a pressure at one point in a liquid, it spreads equally in all directions.

What does this mean?

A liquid is a liquid. This means that it does not resist. If you apply a pressure at one point, obviously it will get transmitted to all points in the container and in all directions. It is because a liquid does not resist a force that this happens.

Pressure is force per unit area.

Why do we need a concept like pressure for liquids (gases too) and not just force? Liquids do not have a definite shape. It takes the shape of the container. So we cannot use the concept of force. The effect of the force depends on the largeness of the surface on which force acts.

If the area of the surface is large the effect of force would be less. If the area is small, the effect of force would be more.

Thus both force and area are important and this is pressure, the force per unit area does give the pressure.

If the force is 8 Newton and the area in which the force is acting is 4m2, then the effect of force i.e.


Pressure = 8/4 = 2N/m2

If the force is halved (4 Newton) and the area is halved (2m2)


Pressure = 4/2 = 2N/m2


Both factors force and area of contact comes in to play to determine pressure.

Now, Pascal’s law can be used in a dramatic way in a hydraulic press.

Consider the figure below…

If a force is applied at A, a small force, for a long distance l, it gets transmitted to B, a great force for a shorter distance D,


So f x d = F x D (Pressure is the same on both the surfaces)


Thus a small force for a greater distance causes us to lift heavy objects by giving a greater force with a smaller distance.






3. Archimedes Principle





Archimedes was a Greek and he is famous for having discovered a principle that governs all liquids – the Archimedes principle. Let us proceed how to understand his principle.

It is a common observation that when you push a body into a bucket of water, you experience a force in the opposite upward direction. This means that the water exerts a force on you when you immerse a body in water.

If you just put the body in water, it either floats or sinks.

Now why does a body thrust into water or every liquid experience an upward, resistant force?

Why do some bodies float and some bodies sink?

These questions are answered by the Archimedes Principle. When you put a body in water, that body displaces water. The l….. of the water rises. How much water is displaced?

Obviously the volume that the body has occupied in the water, that much of volume of water is displaced. See the figure 2 below.

Now, the displaced amount of water tries to get back into its on final position and thus gives an upward force to the body. This is called the Buoyant force as it is trying to keep the body up.

Obviously this buoyant force is equal to the weight of water displaced.

This is the Archimedes principle.

Now, when does a body sink?

When the weight of the body is greater than the upward force which is nothing but the weight of water displaced, the body obviously sinks.

When the weight of the body is less than the upward force, the body obviously floats.

So clearly 2 things are important here.
The weight of the body itself.
The amount of water (or liquid) the body displaces.

If ‘2’ > ‘1’, the body floats. When ‘2’ < ‘1’ the body sinks. A work floats on water because its weight is less than the amount of water displaced (which gives an upward thrust).

An iron nail sinks on water because its weight is more than the water it displaces i.e., the upward thrust given to the nails greater than the weight of the nail. But what about an iron ship? Why does an iron ship float and not sink in water?




The ship is heavy but it is big in terms of volume also. When it enters water, the amount and hence weight of water it displaces is also huge and the upward thrust is huge!

The upward thrust in the ship is actually more than the weight of the ship! Thus the ship floats!

Thus we see both the factors acting always when we consider floating / sinking
Weight of displaced water that determines the upward thrust on the body.
Weight of the body itself.

‘1’ > ‘2’ – body floats.

‘1’ < ‘2’ – body sinks.

All bodies whether they are floating or into water experiences thrust upward thrust. This is equvalent to weight loss.

The weight acting downward is contracted by a buoyant force upwards.

Apparent weight loss = weight of body – upward thrust (buoyant force)

Thus we clearly see how (and why) bodies behave the way then do when immersed in liquids.



SOUND

1. Introduction - What is Sound?

Sound is a sensation that is always all around us. We hear sounds when objects strike or any disturbance suddenly happens in air. But if we close our ears, we cannot hear any sound. Sounds are of different kinds. Some sounds are loud, other sounds are low or soft. Some sounds have a higher pitch. A scream is at a high pitch. Girls have a higher pitch of sound than boys. We know and understand pitch directly by our sensation of it i.e. we can directly know what is at a higher pitch and what is at a lower pitch. Gradation of pitch is after all the musical notes – “Sa”, “re”, “ga”, “ma”, “pa”, “dha”, “nee”.

Sounds coming from far are heard faintly and those coming from near are heard more clearly. There is also a quality of a sound. We can recognize our friend’s voice by the quality of his voice.

Now these facts seem straight forward but they are actually wondrous facts – in nature. They actually raise many questions. We normally do not ask these questions because we take these facts for granted having got used to them from childhood. We feel they are like that because they are like that.

But these facts suggest many deep questions.

What is sound? This question means that, what is happening really between the source of sound and our ear? When we clap our hands (for example), we hear a distinct sound but the real question is, what happened quickly between the point of clapping and our ear? It is a wnder that something happens, isn’t it? What is it? To put the question in another way, what is the physical basis of our sensation of sound.

The next deep question that can be asked about the facts given before is, when is a sound heard loudly and when softly?

The third question that can be asked is when is the pitch high and when is the pitch low.

You see, something invisible is happening between the source of the sound and our ear.

What is it?

Let us now proceed to answer this question.

The ancients asked these same questions and suspected that air has something to do with propogation of sound.

There is the famous bell jar experiment that can be done.


Take a jar and put a bell with connection in it. When the top is not sealed and the switch is on, the bell rings and we can hear the ringing of the bell.

Now, remove the air inside the jar using a vacuum pump and seal the top. Again put the switch on, we see the bell shaking i.e. ringing but we don’t hear anything.

Yes! Air is part of the process of transmission of sound to the ear.

But the question still remains, what is the role that air is playing? What happens to the air?

In the 10th century a remarkable fact came into light that an inch of any material – solid, liquid or gas is made up of crores & crores of atoms or combination of atoms called molecules.

Keeping this in mind, it is obvious that something internal is happening that causes the disturbance that reaches our ear and causes in us the sensation of sound.

One can understand this by realizing that sound propogation is invisible and something must be happening inside and in the air..

Now the gases in a region, or liquid or a solid contains atoms / molecules in close proximity. Of course they are closer in solids than in liquids and closer in liquids than in gases but atoms are close.

Now atoms when brought together have the property of elasticity. They are like a balls with springs attached in the middle. When we shout, (lets say) or 2 things strike, the molecules immediately beside the source get disturbed and get compressed. But since the molecules are connected like springs and are elastic, they snap back but in going back to their original position, they do not come back exactly to the original position but go an extra distance. This pushes the next immediate air that gets compressed and that too tries to come back to the original position and goes an extra distance and compresses the next immediate air and so on. A wave of compressions (more pressure) and what is called rarefactions (less pressure, molecules more apart) occur.

The above is only for one hit of the source. But the source is continuously giving pressure, so a series of waves is sent out as long as the source is vibrated.

The wave travels out and it is energy and due to the pressure increase loses ultimately it’s energy due to getting converted to heat. Hence we cannot hear sounds (or only very faintly) at a distance.





2. Pitch and loudness depends on frequency and amplitude


Let us try to fully grasp the above point and what it implies.

There are 2 things that are important properties of sound as mentioned earlier – loudness and pitch.

Let us now understand both these facts with our deeper understanding of sound as a series of compressions and rarefactions.

Lets take loudness first. When we speak softly, we are putting less pressure an air so the (maximum) compression (or rarefaction) is less.

When we speak loudly, we are putting more pressure on air so the (max) compression or rarefaction is more. So, the greater the compression from normal state, greater is the volume or loudness!

Take a spoon and bang on the table lightly, the sound is low! Bang it hard, the sound is louder. Again the same principle applies. If the pressure is more, compression is more and hence loudness is more.

A tyre or balloon bursts i.e. gives a loud sound because the air suddenly shoots out, the pressure is more and hence the compression (max) is more and hence the ear grasps that as a loud sound and gives us a loud sensation.

Wherever there is a loud sound there is high pressure i.e. high (max) compression and hence high volume.

The maximum compression is called by the technical word amplitude.

So more amplitude – distance from mean position, the greater is the loudness of the sound.

The next question is with respect to pitch. What about pitch? What determines pitch? How do we relate the deeper nature of sound (as having compressions and rarefactions) with the pitch.

Why do girls have high pitch and boys lower pitch. Why does “Nee” note have higher pitch than “re” note.

The answer is that when there are more vibrations per second i.e., the number of successive compression and rarefaction in one second is more, the pitch is more.

This number of successive compressions and rarefactions per second is called by the name frequency.

Hence if frequency is more, the pitch is high.

MECHANICS

1. Introduction – The origin of our understanding of motion or mechanics

Motion in Physics means movement of bodies. Here in this section we will look at motion or movement of solid bodies.

When does a body move?

Let us start with our own observations of things, when they move.

The first kind of motion and the one that strikes us first is when one body hits another or there is a push or a pull given to bodies.

Kicking a football, opening a door, striking a carrom coin, throwing a ball, etc. etc. These can be called contact forces in gross terms became one body when striking another through actual contact does move the other body. Of course the body to move must be light enough and / or the contact force applied must be strong enough.

For example a large rock cannot be moved by a man but can be moved by a crane. But a small rock can be moved by a man. These are the things that we observe.

We also observe things falling from a height when left free. Of course birds and airplanes seem to go contrary to this but that is a phenomenon involving air and we won’t go into that now as in this section we are dealing with specifically motion involving solid bodies.

And then we see the heavenly bodies moving – the Sun, rising in the East, moving across the sky and setting in the West, the moon also moves across the sky but most people do not observe the moon moving as we sleep during that time! But we do see the moon at different places in the sky at different times when we do happen to observe it during late nights and very early in the morning.

We also see the countless stars and among these are the planets that also look like stars but are planets really. Usually people cannot distinguish between planets and stars but the interesting thing is that to us, the planets move during the year ( if you locate it and observe it the whole year) but the stars don’t seem to move.

Then we also see certain objects like magnets that move other objects like iron when brought near it. Travellers know another phenomenon that if you hang a magnet or a compass needle is left free, it moves and points in a specific (N-S) direction.

These are our observations and these same observations led the ancients to wonder and ask questions about all these motions.

Since we happen to see these things from childhood, we take them for granted we tend to feel that it is like that because it is like that!

Yet, there is a wonder to the observations just made. Setting aside contact forces for the moment, let us consider bodies falling when left free from a height.

Why should bodies fall at all? After all, nobody is pushing it. See the phenomenon as if you are seeing it for the first time. It is a wonder. Invariably, always, without fail, bodies fall on earth, if left free from a height.

The apparent motion of the Sun is even move wondrous and raises many questions.

What is the Sun? Why is there night and day? How far is it? Is the earth moving or the Sun moving? Why does it seem to move across the sky? Why is its apparent motion so regular?

Why do the moon and the planets too move as seen by us?

These questions were asked by the ancients. But some, the real seekers of knowledge, the more passionate of them did not only ask questions, they located the positions with the passage of time. It is equal to measuring the motion.

They found no irregularities with respect to the Sun and the moon. The Sun and the Moon went across the sky rising from the east and setting in the west as seen by us from Earth.

But when it came to the planets, they found a strange behavior of planets.


Let us take Mars. When they observed Mars the whole year, they found Mars to go in one direction till June and then it went backward for 3 months and then went forward again. This is how Mars looks to us.

The same is true of all the planets. This is called retrograde motion.

Now the central question is the following. Is the earth at the centre and all planets, Sun, Moon are moving round it or Is the Sun the centre and the planets move around it?

If the earth is at the centre, the planets should move across the sky, why is there backward or retrograde motion of the planets?

The ancient thinkers especially Ptolemy gave a system of Earth as the center and gave complicated motions to the planets.

But in the 16th century, it was Copernicus who got the real idea.

He proposed that the Sun is at the centre and the planets are moving round the Sun. He did this by explaining backward or retrograde motion of the planets.

If the Sun is at the centre and let us take 2 planets Earth & Mars are going round the Sun, then how will Mars look to people on Earth? This was the question that Copernicus asked.


When earth and Mars are side by side (Point A) and if Earth goes faster than Mars, then how will Mars look to people on Earth?

It will seem to go backward!

When earth and Mars are as shown in and Mars is at point B i.e. at opposite ends, Mars would seem to go forward!

So at some period Mars goes forward and during some period, it goes backward. Putting the Sun at the centre and the planets going around it explains the backward motion of all Planets as seen from earth.

The planets are not going backward and forward. They are simply going around the sun. it seems to go like that only because earth also is moving!

Now this was a great turning point in understanding motion.

Once we understood that Sun is at the centre, the next step was to state exactly, with measurement, as to how planets go around the sun.

Kepler did that work and came up with 3 Kepler’s laws.

Another great thinker Galileo came next and he measured free fall of bodies.

His interest was not just observing free fall but to measure how much distance it travelled while falling as time passed (on successive seconds).

He got the value of the acceleration as 9.8m/s2.

Now let us see how the picture looked at that time concerning motion.

The sun was at the centre and all the planets moved around it. (including earth). Things fell on earth with an acceleration of 9.8m/s2. The planets moved according to Kepler’s laws.

But the questions still remained. Why did the planets move like that? Why did the acceleration on earth of freely falling bodies have that value?

It was then that Newton came on the scene. He thought intensely and deeply over the problem, One day, the legend says, he was walking in an apple orchard and he saw an apple falling and it suddenly occurred to him that the moon falling or being pulled to earth by earth is the same pull that earth puts on the apple!

He further reasoned that the force is due to the product of masses & inversely proportional to the distance between the masses.

i.e. the earth pulls on the apple and the moon also. The force in the apple is

directly proportional to mass of apple x mass of earth.

Inversely proportional to square of distance (i.e.radius of the earth)

The force on the moon is

directly proportional to mass of moon x mass of earth

& inversely proportional to square of distance (i.e. distance between earth and moon)

Newton could, with this insight derive Kepler’s laws and at one stroke Newton made earth & heavens one!

He put all motion in the form of 3 laws of motion & called the pull of gravity between masses the universal law of gravitation.

Let us learn these laws systematically and mathematically. But before we go into it we must understand certain concepts of motion in one dimension. That will make our understanding of Newton’s laws complete.

The next section is on motion in one dimension. After that we cover Newton’s laws of motion and Universal law of Gravitation.


2. Motion in one dimension


2.1. Distance and Displacement

Look at the figure.

Suresh begins, at point A, from his house and travels on the road and takes turns crossing many houses and reading point B, his friend, Ramdas’s house.

A bird from a terrace also moves in the air from the terrace of Suresh’s house and goes to Ramdas’s terrace in a straight line.

The total distance travelled by Suresh is is called Distance. It has no direction.

The straight line distance from the initial point A towards the final point B (of the bird) is called Displacement. It has direction also. The direction is from A to B.

The figures-3&4 below illustrate this point further.

Units of both distance and displacement are the same. It is the unit of Length.

10 mm = 1 cm 100 cm = 1 m 1000 m = 1 km

1 feet = 12 inches 3 feet = 1 yard


2.2. Speed :


We know what is speed when we look at two objects moving; we can tell which is going faster. But what is involved in speed? How can we measure speed exactly?

Suppose two men come to you and the first man says, “I have travelled 100 metres”. The second man says “I have travelled 100 metres”. Just with this information, will we know who travelled faster? What else is required to know the faster of the two men?

Yes, the men must specify the time also. So the first man says “I travelled 100 metres in 50 seconds”. The second man says “I travelled 100 metres in 20 seconds”.

First man : 100 metres in 50 seconds.

Second man : 100 metres in 20 seconds.

So, in one second,

First man travelled = 100/50 = 2 m/seconds

Second man travelled =100/20 = 5 m/seconds

So second man is faster. In general if someone or something travels ‘d’ metres in ‘t’ seconds then in 1 second, i.e.

Speed=distance/time

The unit is m/sec or feet/sec or time/hr etc.


2.3. Velocity


Velocity too is speed but velocity talks about the displacement (not distance) in one second.

so, Velocity=Displacement/Time

So velocity measures how much final (net) straight line distance the body travelled (from initial to final point) in one second i.e. displacement divided by time.

eg. if the displacement was 10 metres in 20 seconds


in one second displacement = 10/20=1/2m/s


In general Velocity=displacement/time




2.4. Uniform Speed


Uniform speed is simply constant speed i.e. the body is covering equal distances in equal intervals of time.

eg: A man is going on a scooter. His hand on the accelerator is steady. He is neither raising the accelerator not lowering it. His speedometer shows 30 km/hr (8.3 m/s)

Now what does this mean?

It means that at every second he travelled 8.3 metres only.


1 sec 1 sec 1 sec 1 sec 1 sec 1 sec

8.3 m 8.3 m 8.3 m 8.3 m 8.3 m 8.3 m

This is the meaning of covering equal distances in equal intervals of time.


2.5. Average Speed


Usually bodies do not go at uniform or constant speed, at least on bikes!

See the figure below:


A caterpillar moving


1 sec 1 sec 1 sec 1 sec 1 sec 1 sec 1 sec

1 c m 2 cm 0 cm 1 cm 1 cm

A caterpillar moved 1 cm in 1st second,

2 cm in 2nd second,

again 0 cm in 3rd second, (it stopped for a second)

1 cm in 4th second,

1 cm in 5th second,

3 cm in 6th second,

2 cm in 7th second.

Now what is it’s speed? We will have to give seven speeds here, isn’t it?

That is difficult. But I still want how ffast the caterpillar travelled.

So we can take how much total distance it travelled in the total time.


10 cm in 7 seconds


so speed = 10/7 cm/sec

In general average speed = Total distance travelled/total time taken


2.6. Uniform velocity, Average velocity


Uniform velocity means that equal displacements take equal ........ls of time.


To find the Average velocity we use the formula

Average velocity = Total displacement/total time taken


2.7. SIGN NOTATION


Displacement and velocity being a vectors have two signs (for straight line motion). If we take a right side motion as positive, then the left side motion is (-)

V-------------------------------------------V

If we take upside motion as (+)ve then down side motion is (-)ve.


|

Let us see why

A man moves ahead (for displacement in a straight line) 4 metres and then moves back in the same straight line 3 metres. See figure...

--------------------------------------------->C A--------------------------------->C

A-------------------------------------------->-------- --------------------------------------


B-------------------------------------4mts B-------------------------------

This displacement from A to C is +4 metres

This displacement from A t o B is -3 metres (opposite direction)

So total displacement is 4 - 3 = 1 m.

If we had not put the signs.

We would have got 4 + 3 = 7 x

It would have been a wrong answer! So clearly displacement has (+)ve and (-)ve signs.

Since velocity is only displacement (in one second) velocity too has (+)ve and (-)ve signs.


2.8. Acceleration - Non-Uniform and Uniform Acceleration


In real life, usually, a body changes it’s velocity. It may go faster, slower or come to a stop. This is clear enough. This is called acceleration.

But how do we measure this?

Usually, bodies do not go at a constant speed (as we saw in the caterpillar example). Suppose I am going on my bike. How do I go? I am at 20 km/hr now, I accelerate and reach 40 km/hr in one second. Then I stop at a red light. Then again I came to 20 in one second. I raise......

So here we have to give values and numbers at every moments. This is called non-uniform acceleration.

There can be also uniform acceleration.

Look at the following example

A body moves in the following way...

1sec 1sec 1sec 1sec 1sec 1sec 1sec 1sec Time

-----------------------------------------------------------------------

2m 4m 6m 8m 10m 12m 14m 16m Distance





What do you observe?

In 1st second it moves - 2 m

2nd second it moves - 4 m, an increase of 2m

3rd second it moves - 6 m, a further increase of 2m

4th second it moves - 8 m, an increase of 2m

10 m, an increase of 2m

12 m, an increase of 2m

14 m, an increase of 2m

16 m, an increase of 2m

With each second the distance moved is 2 m move per second.

The change in velocity per second is 2 m/s.

If a body starts with a velocity of 2 m/s and after 10 second reaches a velocity of 10 m/s. then, change in velocity is (10 - 2) m/s in 10 seconds = 8 m/s in 10 seconds.

Hence in one second, the change in velocity is 8/10 = 0.8 m/s/s

In general if a body starts with a velocity ‘U’ and reaches a velocity of ‘V’ in ‘t’ seconds. The change in velocity = V - U in ‘t’ seconds.


in one second,


change in velocity =V-U/T


a = V-U/t m/8/s or m/s


Note that the above is true in Uniform Acceleration only.


i.e. change in velocity is same through out the motion. Now, Average velocity is U+V/2


Displacement = Average Velocity x time


=(U+V/2)t


=(U+U+at/2)t


(S=Ut+1/2 at2)-2


V=U+at S=ut+1/2at2


t=(V-U/a)


t2 = U2=V2-2UV/a


S=U(V-U/a)+1/2a(V2+U2-2UV/a)


= 2UV-2U2+V2+U2-2UVa-2UV/2a


S=V2-U2/2a


V2 - U2 = 2as ——— 3


3. Newton’s Laws and universal law of gravitation





Newton was the central figure in the history of physics. He was the person who made Mechanics into a ‘whole’, comprehesive science. He gave the fundamental statement to it.

What is it that Newton said?

Lets begin with his famous 3 laws of motion


3.1. Newton’s First Law (statement)


“Every body remains at rest or of uniform motion in a straight line unless influenced by an external force”.

A body remains at rest if it is at rest. Ok that’s fine. That goes with common sense and is pretty plain and obvious.

But what about the 2nd part - (A body) remains in 1. Uniform motion, 2. In a straight line, 3.Unless disturbed by an external force.

Is this true?

On Earth, we see bodies stopping even when nothing is stopping it. A ball rolled on a floor does come to a stop after moving some distance by itself.

Actually on Earth, the bodies are not free. Either the surfaces or air opposes any motion. When a body rolls on the floor, it is not really free because the roughness of the floor is showing it down. It is opposing the motion. This opposing force is called Frictm.

But think of what would happen if there were no force opposing a moving body. A region like space where there are no bodies and no air would be a frictionless area. What if a body is given a small push and then left alone. You will actually see the body moving with the same speed and NEVER STOPPING, unless something stops it, NEVER GOING FASTER or SLOWER unless something makes it go faster or slower. If a push is given in the same direction of its motion it’ll go faster. If a push is given in the opposite direction, it will go slower. If it is given at an angle only then it’s direction will change.

A body remains at rest or

in uniform motion

in a straight line

unless it is influenced by some external force.

You understand? In the universe, as such, the first law is true.

A body by itself cannot change it’s state of rest and also of motion.

It’s a wondrous thing, isn’t it? Since childhood, we are used to thinking that a body in motion will come to a stop ultimately. But now, I hope, you understand that it comes to a stop on Earth only because of an opposing force called Friction.

That’s why if the Friction is less, say on a smooth floor, the body takes longer to come to a stop. Making Friction zero and leaving the moving body totally undisturbed will make the body continue to move forever and ever....

You see motion too is natural like rest.

A body at rest will remain at rest.

A body in motion will remain in motion!

This is the principle of satellities and the motion of planets and moon etc. Once a particular motion was given, there was nothing to stop it! The Earth once was given rotation around itself and revolution around Sun and it is doing the same thing and will do the same forever and ever and ever!

Give any motion to a body it will be in that motion forever in the universe. We don’t see it happening on Earth because of surface friction.


3.2. Newton’s Second Law


“A force acting on a body accelerates it; greater the force, greater the acceleration. Greater the mass of the object, the lesser the acceleration FOR THE SAME FORCE.”

Putting it another way

The acceleration of a body is directly proportional to the force and inversely proportional to mass.

(Directly proportional means if one is increased the other increases proportionately i.e. if one is doubled the second is doubled. If one is tripled, the second is tripled and so on.

Inversely proportional means if one is increased the other is decreased proportionately. If one is doubled, the other is halved, when one is tripled, the other becomes one third)

Let us try to understand the 2nd Law

A marble is at rest on a floor.

If I push it, it moves.

A marble is moving slowly on a floor.

If I push it in the direction of motion of the body, it goes faster.

If I push it in the opposing direction, it goes slower.

If I push it at an angle to it’s motion it changes direction.

So 4 things can happen to a body when a force is applied to it.

(1) It already on motion it can go from rest to motion.

(2) go faster

(3) go slower

(4) change direction

depending on the direction of the force.

Same direction to the direction of motion - faster

Opposite direction to the direction of motion - slower

at an angle to the direction of motion - changes direction.

Going faster or slower is called acceleration. But an interesting question arises here. Ok A body goes faster but how fast does it go faster?! This is not a silly question. A hard kick given to a football will make the ball go faster fast (at once)

But if I continue to give a force slowly to the same ball for a long time ultimately it will achieve a high speed but it will have taken a longer time.

A greater force makes a body go faster, faster!

A lesser force makes a body go faster but slower when compared to a greater force!

Hence acceleration is not just change of speed but the rate at which the speed is changing i.e. how fast it is changing.

More force, faster (more quickly) the speed will change.

Lesser force, slower (more slowly) the speed will change.

You understand?

Acceleration is a key concept in Physics. So one part of Newton’s 2nd Law simply says that greater the force, greater the acceleration, lesser the force, lesser the acceleration, no force - no acceleration i.e. rest or uniform motion (Newton’s first law)!

So, in a way, Newton’s 1st law is contained in Newton’s 2nd law in an obvious way.

Now, let us come to the 2nd part of Newton’s 2nd Law.

Greater the mass, lesser the acceleration for the same force.

i.e. if certain force is applied to body A and the same force is applied to body B and if A is heavier than B.

Then which body accelerates more?

Obviously B.

In plain language, it is more difficult to change the speed of a heavier body than a lighter one. Greater force is needed to change the speed of a heavier body as compared to a lighter body.

This is plain enough.

So 2 things simultaneously determine the rate of change of speed i.e. acceleration -

1.Force, 2. Mass.


3.3. Newton’s Thrid Law


Every action (force) has an equal, opposite reaction (force) and in the same straight line.

In other words, if;

Body A gives a force to body B,

Body B gives (at once) an equal opposite force to A in the same direction.

If you push the wall, the wall pushes you back. It will be quite funny if it doesn’t! If you kick a stone, the stone will get the force but you too will get it, you’ll be hurt! Force come in pairs, there cannot be only a single force. An action force will get a reaction force at the same time. Also the reation force is opposite and exactly in a straight (opposite) line.


3.4. Fundamental forces - Gravitational, Electrical, Magnetic and Nuclear (weak and strong)





Introduction

We have said that force causes acceleration and greater the force, greater the accleration proportionately and lesser the force, lesser the acceleration. We also understand that for the same force, greater the mass, lesser the acceleration.

But a great, fundamental question still remains. Where do these forces come from? What is the origin?

Forces cannot come from nothing. There has to be something that is the cause of force, that is responsible for accelerations on masses.

Forces can come due to mass of a body (gravitational forces) - charge of a body (electrical forces) - charges in motion (magnetic forces) can originate on the nucleus of atoms (strong and weak nuclear forces)

These forces are fundamental forces. At other forces - like friction, pushes and pulls, tension on springs & strings, wind forces, muscular forces ARE AT ROOT these fundamental forces!

In the universe at large, basically, 4 forces cause all motions, cause all accelerations on masses.

These 4 forces, Gravitational, Electric, Magnetic, Nuclear forces are caused, exist due to mass, charge, charge in motion and originate in the nucleus respectively.

We will discuss electrical, magnetic and nuclear force in later sections now we will consider gravitational force.


3.5. Gravitational force or the universal law of gravitation


This force is due plainly to masses of bodies. The very mass of a body on the universe has a power - a power to attract another mass! Every mass attracts every other mass in the universe!

Greater the masses greater the force between them (and it is attractive, the masses come closer). Greater the distance, lesser the force between them. In fact it is inversely proportional to the square of the distance. If the distance is doubled, the force reduces 4 times. If the distance is tripled, the force reduces 3x3=9 times and so on..!






Gravitational force is a very weak force (compared to electrical or magnetic force). Masses attract, surely, but one of the mass atleast should be big enough for a visible acceleration.

Two chairs near each other do not attract but if one chair becomes Earth, the other chair ‘falls’ on it.

On the moon too an object falls but since the mass of the moon is 1/6 th of the Earth, the force and hence the acceleration due to gravity is 1/6 th of Earth. It falls slowly like in slow motion!

In space, if a body is left alone, nothing happens as it is very far away from any big object and negligible acceleration is observed because of negligible force. So a body in space left alone remains there! Nothing happens. It remains at rest because no force is acting on it! It simply hangs there!

Gravitational law discovered by Newton is a tremendously simple and a powerful fundamental fact in the universe. Masses attract!

The whole of space science is explained, almost all phenomena on a macroscopic level can be understood exactly, completely, beautifully by this law and it’s simple and yet the implications and application of this law staggers the mind, makes one’s breath stop!

It blows the mind to use a common phrase!



December 23, 2015

THE TIGER BY WILLIAM BLAKE

December 19, 2015

VOCATION - CBSE - VI

WHEN EARTH'S LAST PICUTRE IS PAINTED