MOON PUSHES AND PULLS THE EARTH

We know, due to gravity everything falls down. Do you know anything that raises up due to gravity? That is ocean's tide. Moon's gravitation pull is responsible for oceans' low tide and high tide.

The sun is hundred times heavier than earth. But it plays almost no role in causing tides. Why? Look at this formula.

According Newton, the acceleration of a particle on the surface of earth due to a body of mass m at a distance d is,
2GMR/d^3, where G- gravitational constant
R - radius of the earth.

    The formula tells us that acceleration due to gravitational force decreases as the cube of the distance.  The sun is extremely far away.  Hence, it has a negligible effect on earth's waters.  But the moon is very close to us and influence the oceans.
    When a part of the earth is facing the moon (refer figure), the oceans in that part bulges and raises up causing high tides in ocean.
    The oceans in the opposite side of the earth also bulges up due to earth's rotational inertia.  This also the consequence of the moon's gravitational pull.
    The oceans in the other two sides of the earth flattens up causing low tides.
    As the earth rotates; for every 20 hours and 50 minutes, a given place (seashore) experiences two low tides and two high tides.  You can easily figure this out using the diagram.
    When earth, moon and sun face each other in the same straight line.  The joint effect of sun and moon on earth's waters is 'a bit more'.

Falling of leaves, walking, running, oceans tide we see them every day. We are used to them. But they are gravity (natural force) in action.

"Time, tide and gravity wait for no man".

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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

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

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

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