SCIENCE CAPSULES

     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...