sciencecapsules

    One cannot think of  a mathematical step without 'is equal to ' .  It balances right hand side and left hand side.  It aids simplification and manipulation of a mathematical expression. example: 2(A+B)  = C 2A+2B  = C         2A = C-2B           A = C-2B/ 2   In an electronic calculator,  the pressing of ' = " sign executes an asthmatic expression  or simply calculates.       In computer languages, it plays very important role.                                                                 A = B   When a computer looks at this expression, the value stored in the location named B is just transferred to the storage named A .  After execution both A and B will have the same value an...

  What is the solution of X^2 + 1 = 0 ?   X^2 = -1     X = ROOT OF -1 = i    Root of -1 is meaningless and does not have any physical or real attribute.  So we call it imaginary number i.  Now a new number system is born 1i, 2i, 3i,...      Normally, positive numbers are represented in positive X - axis and negative numbers are represented in negative X - axis.  That is, 180 degree opposite to the positive numbers .Since i = (-1)^1/2 , the imaginary number should be represented half way between positive and negative numbers.  That is in Y - axis perpendicular to the X-axis.  So finally i means 90 degree rotation.      Now we take one real example.  Let there be a square table on the floor.  Let us assume that you and your friend push the table at the two sides.  that is, both of you push the table perpendicular to each other.  Commonsense says that table will move i...

  Throw a stone on the sheet of water in a pond.  Circular waves are created and spread throughout the water surface.  The waves travels as crests and troughs.  We are going to model this waves mathematically.       In a right angled triangle, opposite side divided by hypotenuse gives the sine of the angle x   as illustrated in the figure.     Trigonometry says:  As the angle goes from zero degree to 90 degree, the sine value goes from 0 to 1.  When the angle increases to 180 degree, the sine goes down to 0.  As the angle further increases to 270 and to 360 degree,  the sine goes to -1 and then back to 0.  So when the angle makes one rotation, the sine makes one wavy motion as given in the figure.      So sine function is very suitable to represent a wave.   Y = sin x        As the x goes from 0 to 360 degree or in radian 0 to 2 pi, Y oscillat...

        We know, the flow of electrons is electric current.  Electrons are said to be negative charge carriers.        In a molecular structure, if there is a vacancy for an electron,  it is called hole .  When an electron from somewhere in the structure fills-up  this hole, a new  hole will be created where the electron has just left.  Hence a hole can move opposite to the electron .  So the holes are said to be positive charge carriers.     In a germanium crystal, arsenic is infused.  We get electron rich material called N type (negative) material.  When boron is added to germanium, we get holes surplus P type (positive) substance.        A thin P type material is sandwiched between two N type material.  Now a transistor is made.  These three pieces NPN are respectively called emitter, base, and collector.      By co...

     Why the city like ship floats on the water?  For the simple question, the simple answer is ship is less denser than water.  Yes, really.  The ship is designed and shaped so that it average density (mass/unit volume) is less than that of water.  That is why the ship can only have ship-shape .  But the usual explanation is based on Archimedes principle.       In this article, we are going to speak about density, even though it appears to be elementary concept, it has deeper meanings.       Density indicates how much matter is really packed in the unit volume.  Common sense says, cotton package is lighter than a bar of iron.  Physics says, mercury is 13.6 times heavier than water.  That is, 1 cc of water weighs 1 gm.  But 1 cc of mercury weighs 13.6 gm.  Hence mercury is used in pressure-meters, thermometers etc,.      Osnium is the heaviest metal avail...

       We use remote control that triggers TV, AC, etc,. How it works?  How the eye's vision is communicated to the brain? How a bar code reader in a mall works? How the smartphone camera shoots a picture?      "When light waves, infra red rays, ultraviolet falls on certain chemicals like zinc, electrons are ejected out and electric current starts flowing".  This process is known as photoelectric effect .  It is instantaneous .  How can the waves push electron?  Can sound waves push an object?  No.  Can  stream of fire disturb a concrete wall? No. So there must be 'something' in the photoelectric effect.      Einstein investigated and proved that light waves sometimes behave like pockets of energy or particles called photons .  When one photon strike an atom in a material, one electron is ejected out instantly.  It is like throwing a heavy stone on the wall and forcing out ...

      A needle point, we may be able to observe by naked eye.  The bacterium is comparable to the needle point.  It can be observed clearly using microscope.  It"s size ranges from 0.5-5*10^-6 m (micrometer).    There are good and bad bacteria.  The diseases caused by bad bacteria can mostly be treated with the antibiotics.  Also, the bacteria can be filtered out by 'reverse osmosis' etc,.       Next we have virus in the size of 20 to 400 nano meters( 10^-9 m).  They are the smallest life on the planet.  There are no good viruses.  They cause common cold to AIDS.  Their symptoms can only be treated.  The body should have good immunity to survive.       Bacteria and viruses are made up of cells which in turn made up of molecules and atoms .  The molecules are in the order of nano meter.  So the nanotechnology means technology based on molecules....

     In our daily life, we usually measure mass.  What is mass exactly?  Put a small child on a swing and push it.  You can easily do it.  Seat a 80 kg man on the swing.  It is difficult to push him.  Hence,  mass is the measure of resistance given by the body to change its state or for its acceleration(inertia).   Mass can also be termed as a 'measure of inertia'.       But a weight is force on the body due to earth's gravity.  A body of 1 kg mass experiences 9.8 newton gravitational force. f = mg f = 1*9.8 newton Hence its weight is 9.8 newton. 1. A mass remains the same everywhere but the weight depends on gravity.  A man weighs less on the moon but very heavy on the Jupiter due to gravity. 2. When gravity zero, weight is also zero.  That is why astronauts feel weightlessness and float in the space.  But still they carry mass and inertia. 3. When a thing moves in very hig...

    Let us assume that you and your enemy belongs to the same town.(hope you do not have an enemy. Even if you have one, make sure he does not know about prime numbers).  Both of you have left the town for greener pastures and you both visit the home town periodically.  You do not want to meet or face your foe even accidentally.  How to choose the timings cleverly?  This is just an example with a  smile to understand the nature of prime numbers.        Suppose you choose to visit the town at every 17th day (prime number).  And your 'friend' select to visit every 10th day.  The visits will not mostly coincide because 10 is not the factor of 17.  For that matter, 17  is not divisible by any other whole number. Suppose you unwisely choose every 2nd day, 5th day,  20th day.  You are more likely to meet your foe face to face sooner or later.  It is because 2, 5, and 20 are mutual factors ...

       Think of old radio sets made of tube valves.  Transistors replaced valves and the radio shrunk to pocket size.  Then electronic circuits were replaced by silicon chips.  Hence the radio set shrunk further and embedded in smart phone today.        The miniaturization is more pronounced and visible in electronics.  but the phenomena happens in all the fields.        Fans, lamps,(CFL, LED), motor pumps, grinders, car engines, fordable umbrella, contact lenses, button cells, phones, speakers(ear phone), clocks, machines and tools and what not.  Everything has shrunk. ADVANTAGES OF MINIATURIZATION 1. It is affordable. 2. Space saving , raw material saving 3. less energy, less pollution. 4. It is portable  5. highly efficient. MOORE'S LAW "The law is the observation that the number of electronic components in a silicon chip (integrated circuits) doubles approxima...

         For want of shoe nail, shoe is lost.      For want of shoe, the horse is lost.    For want of horse , the messenger is lost.    For want of messenger, the message is lost.    For want of message, the war is lost.      Because of one small piece of nail, war is lost.  The communication was so difficult in those days.  The communication progressed from messenger, pigeon, telegram, telephone, radio, mobile phone, smart phone, through time.  So the time has solved and revolutionized the communication.      Similarly, we have progressed from oil lamps, to led lamps via candles, petromax, incandescent bulbs, fluorescent lamp, CFL etc,.      In transport;  Horses, horse driven carriages, bicycles, automobiles, trains, bullet trains, air planes, jets, supersonic planes, luxury ships, spaceships and so on.   In future:...

       Next time when you get a drug injection, look at the syringe.  It is a simple cylinder and piston mechanism .  This device can push or draw  fluids.  OR the piston can get pushed or drawn in by the pressurized fluids.  The 'piston and cylinder' have wide applications from pressure air pumps to car engines.        We know, in a steam engine this apparatus  plays a crucial role.  And the steam engine fueled the industrial revolution.  The railway system used this engine for many decades.      Piston and the cylinder rules the automobile industry even today.  It is the heart of any fossil fuel engine.  The power of any auto vehicle is determined and measured by volume of the cylinder and the number of the cylinders.(110 cc ,800cc, ... 2 stroke, 4 stroke).  The subject thermodynamics is mostly built around this engines.      We can define eng...

       Suppose a circle grows, along with it, its diameter also grows.  We can say, circumference of a circle is proportional to its diameter. C proportional to 2r There must be a number or constant which bridges the two. C = 3.14.....*2r 3.14....... = π = C/2r That number is 3.14..  and it is famously known as pi. Why this particular number?  We have to ask the creator only.  This is a irrational or a never ending number.  A circle having circumference of 22 units will have the diameter of 7 units.  So sometimes pi is denoted by 22/7.  A circle having unit radius will have the circumference 2pi. That is,        C = π*2r        C = 2π      since  r= 1    We know, a full circle( C ) is having a total angle of  360 degrees.   Hence 2*π = C = 360 degrees.      π = 180 degrees      π/2 = 3.14/2 = 90...

     The moon appears to grow and decay.  What really happens?  It is just an interplay of light and shadow.       Like earth, half of the moon's surface is illuminated by sun light always.  The moon circles the earth every 28 days.  when it shows fully illuminated face, we say it is full moon day .  When it shows night side(dark side), it is new moon day .  If it shows partly night side and day side, it must be either in waxing or waning phase.  The figure illustrate the concept beautifully.      When we see exactly half moon, the earth, the sun and the moon must form a right angled triangle as shown in the diagram.  The angle suspended at the earth is 89.85 degrees. The trigonometry says : COS(89.85) = distance between the moon and the earth / distance between sun and the earth = .002617 Reversing both sides, distance between sun and the earth / distance between the moon and t...

BLACK LIGHT     Can you see things with invisible light?  Yes, you can.. The ultraviolet rays are invisible.  When it is shone on an object quoted with florescent chemicals, they emit back light and appear bright.  For example, the security thread of a dollar bill glows green under black light, a safe guard against counterfeiting .  So light can be invisible and black.   SOLID GAS OR DRY ICE.      Under high pressure  and cold temperature, carbon-di-oxide gas directly becomes solid called dry ice.  It is widely used in fire extinguishers which emit them as white powder.   DYNAMIC EQUILIBRIUM:      How can a thing be at rest and moving at the same time?  Imagine a queue is moving through a room.  At a time, the room can accommodate only 10 persons.  So the room always have 10 people, yet the people keep moving.  This is dynamic equilibrium. HOT ICE      Using ...

    Wheel is an important invention and it is one of the 6 simple machines.  It is heavily used in transportation since it greatly reduces friction.  We have ship's wheel, steering wheel, potter's wheel, gyroscope and fly wheel.      When you ride a motorbike and switch off the engine abruptly, it continue to run for a long distance on a smooth road because of the special design of the wheel.  Here, the wheel is large and number of spokes are connected to the heavy rim from the axle. The rim carries heavy mass since air filled Tyre is mounted on it.  This is called fly wheel design.  In this design, the moment of inertia is high or rotational mass is heavy.  So it carries a lot of energy and stopping it will be difficult.  So the fly wheel seems to have a storage of mechanical energy.      The man made forces cannot disturb the earth's rotations even slightly because it is so heavy and carries enor...

Hang a uniform chain from a two fixed points, it naturally forms a shape called catenary .  In this shape, tension force in the chain and the gravitational force balances.  It is not parabolic shape, even though it looks like one.  People found the equation for this curve with great difficulty. y = a*(e^(x/2)+e(-x/2))/2      Here e is the famous constant 2.71.., a is the constant of chain.  X and Y are graph axes.     Diamond necklace hanging from a girl's neck; freely hanging electric cables; the silk thread on a spider's web; the suspension bridge across the river; all take catenary form.      Invert the catenary, you get an arch.   It is the most stable form, an arch can have .  It does not bend or buckle.  It will freely stand under its own weight and minimal amount of material is required for construction.  Hence it is widely used in architecture.      The catenary has ...

A severe earthquake is many many times stronger than a shake of the table.  How to measure both of them in a scale from 1 to 10?  The sound of a bomb blast is many times highly intense than a whisper.  How to measure them in a scale of 1 to 100 ?  Here logarithms comes to our help. we know,     10^2 = 100     log 100 = 2.0000        (base 10) 2.0000 is the logarithm of 100 to the base of 10 similarly,      log 10000000000 = 10.0000           (base 10) Hence using the idea of logarithm, we can represent any number lying between 100 and 10000 crores in the scale of 2 to 10. example:       log 102456 = 5.010537              (base 10)  Long range of numbers can be compressed using logarithms.   In the case of earthquake, the formula is,        R = log (A/A0) A0- the intensity of smal...

Take any four digit number.  But one condition, all digits should not be the same like 1111 or 3333.  But 2 or 3 digits can be same.  Let us consider the number 2017. STEPS 1.Arrange the digits of the number in descending order. that is , make biggest number out of four digits.  We get 7210. 2. Next, arrange the digit in ascending order, making smallest number out of the same four digits.  It is 0127 or 127. 3. Subtract the small number from the big one. 7210 - 127 = 7083. Now repeat the above three steps with 7083. 1.  8730 2.  0378 3.  8730-378 = 8352 Repeat the process few more times.           2017 1. 7210-0127 = 7083 2. 8730-0378 = 8352 3. 8532-2358 = 6174 4. 7641-1467 = 6174   within 3 iterations, the result stuck at 6174.  It does not change further.  6174 is called kaprekar's constant or kernel of the 4 digit numbers.  The process is known as keprekar's operation. ...

      We use formula widely in science.  All the physics phenomenon are represented by mathematical formula.   They pack lot of information in a nut shell .  They can be easily written, manipulated and easy to remember.  Also they make calculation easy.  Let us take one simple example- a three symbol formula.   F= ma force = mass X acceleration. 1. When one kick a ball, the force is transfered from the leg to the ball. To carry a mechanical force a body of some mass is required.  Without a mass, force is 0.  If m= 0 then f=0. 2. When the force is increased, mass cannot increase and hence acceleration increases. That is what a accelerator does in a motor vehicle. 3. Both the mass and acceleration contribute to the force.  A light bullet with high acceleration requires large force.  A heavy truck with a little acceleration also requires a huge force.   4. A body moving steadily with zero acceleration is unde...