Skip to main content

HOW THE NATURAL LAWS WORK?

     


      A is proportional B.  C is inversely proportional to square of D.  This kind of laws are common in physics.  If one quantity depends on another, there must be some number bridge connecting both .

 That is;
A "is proportional to" B
     How to make to A "is equal to" B
    Here we put a "constant" K , A fixed value, a unchanging number between them.
    A=K*B
If we find K, the problem is solved.  We get a accurate relationship between A and B.

     One way to get K is; K = A/B
Make number of trials (experiments), find A  and B for each trial; divide them and get the average value of K.  The "K" will be mostly correct, if the law holds good.
Another way, if B is equal one, then K will be equal to A.
 Third way, you can find K using trial and error method.  That is 'guessing'. 

  Let us go for some examples . Draw a circle.  Let it grow.  As the circumference C grows, its diameter 2 r  also grows.  Let r be its radius. Now we can write
C is proportional to 2r
or
C= K.2r
K = C/2r=22/7=3.14....=pi

    Here the "constant of proportionality" is pi=3.14... It is found using many trial and error methods down the ages.  A circle having circumference of 22 units, has approximately 7 units of diameter.  Here the constant is not sharp and accurate.  It is an irrational number.  A never ending number.  People still find the digits of pi using super computers.

     Newtons second laws says that force is proportional to the product of mass and acceleration.  Here the constant of proportionality is just 'one'.  Hence we can write,
F=ma

     Another Newton's law says that gravitational force between planets is proportional to the product of their masses and inversely proportional to the square of the distance between them.
So, F=G m1 m2/d^2
    Here G is constant.  If m1,m2,d all are equal to unity, then F=G.  That is, gravitational force between two bodies each weighing one kg and separated by a distance of one meter is the constant G.  That force will be very weak and feeble.  But Cavendish successfully measured G using carefully designed experiment, G = 6.74*10^-11.

     Energy of electromagnetic wave is proportional to its frequency.
E= h*freq ; h = 6.626*10^-34.
Here the constant is Planck's constant h and it is discovered by Max Planck.  It is an highly important constant in physics.

      The famous Ohm's law states that current is proportional to voltage.  Here the constant is the simply the 'Resistance '(R) in the path of current.
    V= RI

     The constant occupies even our cosmos.  We know our universe is expanding rapidly.  The speed at which the galaxy is moving is governed by Hubble's constant.
    Try to frame your own law and find the constant. 
--------------------------------------------------------------------------------------------------

Comments

Post a Comment

Popular posts from this blog

LISSAJOUS FIGURES

  Definition:  "When a particle is subjected to two sine wave motion or two oscillatory motion at right angles, the particle describes lissajous figures".      We know sine wave motion and circular motion is basically same.  Hence we draw two circles A and B perpendicular to each other.  The circle B rotates twice faster than circle A.  That is, frequency of circle B is two times than that of A.        A particle at the intersection of two circles is subjected to two sine wave motion   A and B at 90 degree simultaneously.  The particle will describe figures depending on the frequency and phase of A and B .  In our case, the ratio of frequency is  1:2 and the two waves are in phase.        To draw lissajous figures :  A moving point in both the circles are chosen.   Here we should remember; during the time taken by the circle A to complete one rotation, circle B completes two.  Hence the points are marked on the circles according to their speed.  Then straight lines
Post a Comment
Read more

THE PARABOLA

          A jet of water shooting from a hose pipe will follow a parabolic path.  What is the so special about parabola.    Y= x^2 Draw a graph for the above equation.  It will result in a parabola.  This parabola is also called unit parabola.  Any equation involving square will yield a parabola. Example:  Y = 2x^2 +3x+3 (also called quadratic equation)    X= 2 and -2, both  satisfies the equation 4 = X^2.  Parabolic equations always have two solutions.     Any motion taking place freely under gravity follows parabolic path. Examples:   An object dropped from a moving train,   A bomb dropped from flying plane,  A ball kicked upwards.      If a beam of light rays fall on the parabolic shaped mirror, they will be reflected and brought to focus on a point.  This fact is made use of in Dish Antenna, Telescope mirrors, etc.      Inverted parabola shape is used in the construction of buildings and bridges.  Because the shape is able to bear more weight.      A plane
Post a Comment
Read more

CASINO'S GAME

           Let us find out how the casino survives with mathematics.      Say, your friend invite you for a game of dice.  You must bet (wager) 2 dollars.  If you roll 'six' you will get back 8 dollars.  The game will go on for 30 rounds.  All sounds good.      The probability of rolling 'six' is 1/6.  Since the game will be played for 30 times, the 'expected win' is 30*1/6 = 5.  That is, you are expected to win 5 rounds out of 30.  Hence your gain will be 5 * 8 =40 dollars.  ok.  This also implies that you will loose 25 rounds.  Hence your loss will be 25*2 =50 dollars.  Your net gain will be gain-less = 40-50 = -10 dollars. For 30 rounds, the loss is -10 dollars, Hence, for one round =-10/30 = -1/3 dollars.  There will be a loss of -1/3 or 0.33 dollars per round.  It is not a fair game.     Let us make a simple formula to calculate  'Pay out per round\. The probability for a win = p The pay-out in case of win = V No. of rounds = n The expect
4 comments
Read more