ARTIFICIAL GRAVITY

Why your washing machine spins rapidly to dry your clothes? Let us find out

Think a rotating body. A force called centripetal force must act to keep the body in rotation. That is a constant force but its direction keeps-on changing circularly. So the acceleration is always present in a rotatory motion. More speed means more acceleration and more force[F = ma].

We know, ' acceleration' due to gravity is 9.8m/s^2. A force which give rise to 9.8 m/s^2 acceleration is called one 'g' force.

Centripetal force acts from the body towards the centre. An equal reaction force[centrifugal force] acts from the centre towards the body and tries to push the body away. Hence by spinning a body at the right speed, one can create the centrifugal force of any 'g' value.

The spinning earth gives rise to centrifugal force. That force pushes the earth from inside and makes it bulging. Hence earth looks more like an apple then like an orange.

The medical centrifuge is a very important invention next to the microscope. Here, test tubes containing solutions are spun fast to separate heavy and light particles. In this centrifuge, the centrifugal force of thousands of g comes into play. It pushes dense particles to the bottom of the tube (precipitation).

For example viruses, milk cream is separated in this way.
the human centrifuge is a cabin connected to a long arm and rotated vigorously in the circular hall. Here, pilots and astronauts are trained to experience 'g' force up to 20g for a brief time.

The washing machine dryer contains a drum with a lot of holes in the wall. The wet clothes carrying drum is spun fast. Due to high g centrifugal force, the clothes are pushed towards the wall of the drum. That is, squeezed, and the water escapes through the holes.

This is the story of 'how high-g is created on the surface of the earth.
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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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