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Showing posts from February, 2019

ALUMINIUM BEVERAGE CAN -AN ENGINEERING MARVEL

         The aluminium cans that you use to drink not only contains juices and coke but so much science      15000 cans are manufactured in one-second worldwide.  A light and strong container.      We can have spherical containers like fruits.  It requires the least raw material.  (Sphere is the only shape which has maximum volume and minimum surface area).  But it is difficult to manufacture spheres.  And it has only 74% packing efficiency.  That means 26% of space in a box goes waste.      Next, we can think of the cuboid (rectangle area).  Here edges are sharp and weak.  And the packing efficiency is also not good.      Finally, we come to cylindrical containers.  We can rapidly manufacture them.  The packing efficiency is 91%.  The cylinders have a curved surface.  The curved surfaces always have more strength than flat surfaces.      The bottom of the can is always "domed".  Because of 1. The arched surface gives strength.  2. The semi-spherical surface requ

GREED IS GOOD, IS IT?

         Thomasalwa Edison was trying to make an electric light source.  He tried a thousand materials to act as a filament in the bulb.  He tried Aluminium, gold, carbon fibre and even hair.  On sending Electric current, the filament should be instantly heated up and emit light somewhat similar to day-light and should not melt.  At last, he found 'Tungsten'.  So he invented the world's first incandescent (Non-smoking) lamp.  It lighted up our nights for 100 years.  But now we have moved to LED lights.      Why Edison struggled to invent the electric bulb, for fame, for money, or for soul-satisfaction.      Whatever may be the selfish or selfless motive, it has benefited humanity for a number of years.      Today, New smartphones arrive every now then.  The companies or corporates want to get a big share of the market and mint money.  But, we get phones that are cheaper, smarter.  We get benefits and goodies because of their Greed.      Why the "food-deliv

HOW TO TAKE DECISIONS?

        Tom has to decide whether to go to a college or take up a job. SCENARIO I      If Tom belongs to a middle-class family, going to a good college and earning a degree will help his family and his career.  Going to a job straight away will put him in a low-level job.  And he may stick with it for his entire life.  Here education yields more than a job. SCENARIO II      Say, Tom belongs to a rich family.  His father is running an industry employing hundreds of persons.  His father is also ailing at present.  So, for Tom education is not essential.  It is only an ornament.  If he takes up a job in the family business, he will earn valuable experience and move up the ladder in the company management quickly.  He can study through distance education.  Or he can go to part-time classes.  He is not going to lose anything for want of higher education.  Here work-experience yields more than education.      "The cost of what you do is what you miss or lose".      T

HOW TO THINK OUT OF BOX

     Here is a job interview question which forces you to think out of the box.      "It is an ancient invention.  It helps us to see through walls.  It is widely used throughout the world.  What is it?"      The answer is W O D N I W (spelling reversed)      The word "invention" makes us think about "scientific devices".  But sometimes think "out of usual".   How to cultivate the habit of lateral thinking?  Here, I will try to present one procedure.      First, let us take one problem.  You employ a painter to paint the irregular shape of a wall for artistic purpose. How to calculate the surface area of the wall?  How much to pay to the painter?  How much paint to buy? Now, the procedure,       Take six hats in different colours.  White, black, red, green, yellow, and blue.  STEPS:      1. Put on a white hat.  Think about facts and available info.      If we have standard shapes, like rectangle and circle, we can use stan

WHY NIGHT SKY IS DARK? DAY SKY IS BLUE AND TWILIGHT SKY IS RED?

       Even in open ground, if you erect light bulbs in all the four corners, the ground will be flooded with light.  But universal space has lots and lots of stars (actually suns).  Then, why the night sky is pitch dark?      To answer this question, we have to go billions of years back.  That is the birth time of the universe.  Long, long back, the matter for the entire universe was contained in a tiny atom.  The tiny dot has zero size, large mass, infinite density.  There was 'big bang', an astronomical explosion.  The entire matter was thrown out.  The universe was born.  The time started to tick.  Explosion temperature begins to cool down.  Galaxies, star systems formed.  They all continue to move and expand like a balloon[due to explosion].  Even today, all celestial bodies continue to move away from us.  The expansion of the universe is the greatest discovery of the century.      Next, we have to understand 'Doppler effect'.  When a train approaches us,

WILL YOUR APARTMENT SWAY WITH WIND?

       Yes, if you happen to live on the hundredth floor.  Tall buildings oscillate up to few meters due to wind and earth-quack.  It may be uncomfortable for dwellers.  It may even be dangerous.  There is a physics technique to prevent this vibration.      Tall towers can be considered as an inverted pendulum. It will oscillate with its own natural frequency due to natural forces.  Now select a pendulum of the same frequency and attach a suitable weight.  Hang this pendulum in the top portion of the tower.  When the tower swings in one direction, the pendulum will swing in the opposite direction.  That is, tower and pendulum will execute opposite oscillations.  Hence the building's energy will be dissipated through the pendulum and the swings of the building will come to a stop (damped) quickly.  Hence this pendulum is called 'Tuned mass damper" (TMD). [Matching the frequencies is called tuning].      In Taiwan, there is a skyscraper by name Taipei-101.  It has

HOW MANY SECURITY CAMERAS YOU REQUIRE?

           We have a museum housing valuable antiques.  We have a gallery of highly priced or priceless paintings.  We have a mall of many showrooms.  How to guard them all?  How many guards we require?  How many CCTV cameras required?  A bit of math will help here.     Suppose an exhibition has triangular stalls.  Each stall can be guarded by one man because he can easily have a look at the three walls.  Hence the formula is, No. Of guards =  whole number part of  No. of walls / 3      We know a square hall or rectangular hall with four walls can also be looked after by a single man.  Many art galleries and museums have many corners turning at right angles (90 degrees).  These galleries can be divided into rectangular halls.   Hence No. of cameras required = whole number part of (1/4 * no. of corners)      Suppose, a mall is made up of a number of rooms.  And two rooms have a common door.  Then a man standing at the door can watch two rooms at a time.  For example, a t

HOW YOUR LUXURY CAR GLIDES?

             Everywhere we see the 'ball bearings'.  What is this device for?  Let us explore.      Imagine a big drum filled with water standing erect.  Try to move it.  Only with great difficulty, you can start moving it.  That is what is called static friction.  Once it starts moving, it is slightly easy to maintain the motion-called sliding friction.  But if you roll the drum, it is very easy.  Hence rolling friction is less than all the other frictions. That is why car rolls instead of sliding.  Also, in every movable object, wheels are used.  Examples, suitcase, executive chair, hospital beds etc.      In a ball bearing, there are two steel rings-inner ring and outer ring-called races.  Between them, steel balls are placed in special enclosures. 1. The balls between the rings are free to roll.  And the rolling friction is always less. 2. The balls touch the rings at small points.  The area of contact is less and the friction is less.  Recollect, the area of co

DO NOT THINK STRAIGHT

         Think Sideways.  Lateral thinking. What is it?   Example 1. We know about aeroplane carrying ships. In the middle of the nineteenth century, aircraft carriers were designed.  People wanted to land and to take-off air-crafts from the ships.  Hence they put straight run-ways on the top deck.  Here, a plane could either land or take-off at a time.  It was difficult to stop the running plane at the correct moment.  They used strong nets, hooks etc.  There was also not enough space for standing air-crafts.  Search for a solution was on.      On 7th August 1951, Rear Admiral Dennis Campbell was waiting for a meeting.  He thought laterally-literally.  An idea flashed to him.  "why do not we tilt the runway by an angle?" (say 9 degrees-exactly)      When the runway was laid-down at 9 degrees to the straight line, many problems were solved.  They got more space.  Simultaneous taking off and landing was possible.  Free air-crafts could be put on one side away from th

THE IMORTAL ART

         Street-acts, theatre drama, silent movie, talkies(talking movies), TV digital projection, RGB (red, green, blue) laser projection, 4k (4000 pixels) cinema, 3D movie, smart TV, on-demand video.  Thus the drama evolved.  It will continue to evolve.  Today, many can afford a good quality home-theatre system. But still cinema house, Broadway theatre thrives.  Because each medium gives a different experience and people go for it.      Drawing, painting, photo, colour photo, 3D picture, 360-degree view.      The progress has gone like this in the case of a picture.  High quality and high colour digital photo can be taken and transmitted easily today.  But still, art and painting materials are selling well.  Drawing tutorials and painting video (bob rose in youtube) are more popular.  Paintings are being sold for high prices.  Because painting gives a different appeal than a digital photograph.  Also, painting work gives soul-satisfying experience.      Solo singing, orch

A TASTE OF RAMANUJAN'S MATH

         Ramanujan, an expert in number theory.  We will see, one of his works.           3= 3           3 = 2+1           3 = 1+1+1      Here 3 is written in three ways.  A natural number is expressed as sum of natural numbers.       4= 4       4 = 3+1       4 = 2 + 2       4 = 2+1+1       4 = 1+1+1+1      Here 4 is expressed in 5 different ways.      We define "partition number" p(n) as the number of ways a given natural number 'n' can be written as a sum of natural numbers.      Hence p(3)=3                  p(4)=5      It seems easy to find out the partition number.  But as the number gets larger, everything goes out of hand.  Partition number for 1 to 10 is given below. n    p(n)        n     p(n) 1     1           6       11 2     2            7       15 3     3            8       22 4     5           9        30 5     7          10       42    p(n) goes on increasing exponentially.  Is there a procedure or a formula to find the part

A PROBLEM THAT BAFFLES MATHEMATICIANS

        We will produce a sequence of numbers following some rules.      1. Take any positive natural integer.      2. If it is even, next term will be half of it.      3. If it is odd, multiply it by three and add one to get next term.      4. Apply the rule no.2 or 3 to the next term and go on produce the sequence.      Let us take an example; consider the number 12.  It is even; hence next term is 6, again even; next term is 3.  Now it is odd; next term is 3+3+1 = 10.  Just proceed like this, we get, 12, 6,3,10,5,16,8,4,2,1      Now let us take 19; 19,58,29,88,44,22,11,34,17,52,26,13,40,20,10,5,16,8,4,2,1      It seems, we always end up with 8,4,2,1 .  In fact, all the numbers tested so far (even using the computer) always end up with 8,4,2,1...   In other words, this sequence ultimately reaches one.      We know, it is impossible to test the infinite numbers.  Is there any mathematical proof that the sequence will always reach one?  No, not so far.  This problem i