SCIENCE CAPSULES

         Today, around 700 million cars  speed along our roads.      A tiny amount of high energy fuel, (petrol), trapped in a small, enclosed space (engine cylinder) and ignited will release an enormous amount of energy as the gas expands.  If this is done hundreds of times a minute, this energy can be harnessed to move a piston up and down.  Attaching what is known as a 'crank shaft' converts this motion to rotation.      American inventor ford recognised that the car was so expensive because it took so long to build.  With the advent of the industrial revolution, engineers realised the potential for speeding up the manufacturing process by getting different workers each to repeat their tasks over and over again.  Ford spotted that this so called 'assembly line' could be applied to car manufacturing.  The framework of the car moved along a line of workers, who each added a new part.  As th...

         Dubai has trade and tourism based economy.  They go for world's top and best.  Hence there is no wonder in their attempt to build world's tallest building. FACTS AND FIGURES      It has 163 floors.  The total height is 829.8 m, nearly one kilometer .  It took 6 years for construction.  Each floor was completed in just three days time.  It can shelter 35000 people.  At any moment there are 10000 people in it.  It is the tallest free standing structure in the world.  It is constructed mainly using vertical concrete pumping.  1000 pieces of art will  adorn the interiors.  The exterior temperature at the top of the building is said to be 6 degree c cooler than its base.  A 304 - room Armani hotel occupies 15 lower floors.  It has 900 private residential apartments which according to the developer sold out within eight hours of being on the market.  The building...

         We know the conservation of energy, mass, and momentum are cornerstones of science.  We have studied the 'Law of conservation of angular momentum' in school physics.  It also holds some surprising facts.  We will see them now.      Momentum is the product of mass and velocity.  Angular momentum is the product of the 'moment of inertia' and angular velocity.  The moment of inertia plays the role of mass in a circular motion.  It is roughly the product of rotating mass and its distance from the axis of rotation. Hence Angular momentum = Moment of inertia* angular velocity = constant or Mass * distance from axis*angular velocity = constant   In the above formula, if one quantity increases, another quantity must decrease to keep the product constant.     A dancer on an ordinary floor or ice floor sometimes spins herself.  If she out-stretches her arms, she will spin slowly....

         How they measure chance? what are the basic operations in probability? Let us find out.       In tossing of a coin, there are two events-- head and tail.  The chance one event occurring = one/total number of events.  That is 1/2.  You have 50% chance of getting head or tail for each toss.  If you toss a coin, one time you should get head and next time you should get tail, so the formula says.  But both the times, you may get head or tail.  If you toss the coin 100 times, roughly 50 times you will get head and tail.  On the long run, the formula proves correct.     On throwing dice, there are six events (1,2,3,4,5,6).  Hence chance of getting an 'event' for a throw is 1/6.  There are three important logical operations in probability.  Let us go for it.   OR operation:     What is the chance or probability getting 1 or 6 in a roll.  Here, either 1 or 6...

1. Add two numbers        2+2 = 4 2. Add the number repeatedly      4+4 +4 = 12   3*4 = 12 That is multiplication 3. Now multiply repeatedly       12*12*12 = 1728  12ˆ3 = 1728     That is taking power     Let us go backwards. 1. Take cube root of 1728, we get 12                      (dividing repeatedly) 2. Divide 12 by 3, we get 4                         (subtracting repeatedly) 3. Subtract 2 from 4, we get 2  Addition is the basic operation, in moving forward.  But subtraction is the basic operation when moving backward.      Using addition and subtraction, we can move to and fro in mathematical process and get the desired answers. Calculus designed in similar fashion.     As an example consider a freely falling body.  We kno...

         Whenever we wait for the city buses, they do not turn up for a long time or they come in groups of 3 or 4.  Why this happens?   Say, buses in a particular route are scheduled to arrive at a 'stop' for every 12 minutes.  That is, 5 buses are expected in a bus-stop in an hour.  But they are bunched up or scattered away due to heavy traffic or other odd reasons.  But there is a statistical formula (exponential distribution) using which, we can calculate our 'chance' of getting  a bus in an interval of time.       P = 1-eˆ(-rk) P- probability or chance of occurrence of event in the interval of time 0 sec to k second.     e- 2.71 ... Euler's constant.     r - rate of occurrence of events  In our case;  k = 5 minutes  r = 1/12:   one bus arrives for every 12 minutes. or 1/12 of a bus arrives at every minute. Now p = 1- 2.71 ˆ[-5(1/12)]     ...

          If you toss a coin 5 times, 4 times you may get head and one time you may get tail.  Toss it 10 times, it may be head 7 times or 3 times tail.  Toss it 100 times. Roughly 50 times you will get head or tail.  If you do 10000 times, Most likely 5000 times we get head or tail.  A computer can easily simulate this process.  As the 'number' increases, we reach the fifty percent probability. 7/10 is not 50%  But 5007/10000 is.      Let us roll the dice three times, it may be 2,4,6.  The average is 2+4+6/3 =4.  But, if we roll the dice many, many times and find the average, it will settle down exactly at 3.5.   1,1,2,3,5,8,13....144,233....      The above is the Fibonacci series, Adding the previous two numbers, you get the next number.  Now take successive numbers one by one and find their ratio.     2/1 = 2     3/2 = 1.5     5/3 = 1.666 ...