COTTON CANDY AND WATER PUMP

Is there any connection between your house water pump and the cotton candy you eat at the carnival? yes, there is.

The centripetal force is always responsible for the rotations of a body. This force acts from the body to the center always. To every force, there is a reaction force. Here,it is known as centrifugal force which acts from the center towards the circling body radially.

Cotton candy machine:
A sugar reserve with added flavor and color is placed at the center of the rotating bowl. The sugar reserve is surrounded by an extruder- a metal cylinder with holes along its sides.
The sugar is heated and melted by an electric filament. The sugar liquid is thrown out radially through the holes in the extruder because of Centrifugal force. The thrown liquid solidifies as fibers in the rotating bowl. Then the sugar strands are collected by the stick. Your cotton candy is ready.

Centrifugal water pump:

In the water pump, a device called impeller is rotated by an electric motor. It has eye (a hole) at the center. The eye is connected to the upward going pipe. The impeller also has radial path carved on it.

First, we have to surround the impeller by the water- priming. When the impeller rotates, the water is thrown radially outwards from the eye because of centrifugal force. A vacuum or negative pressure is created at the eye. Hence water is sucked through the eye and moves upwards through the pipe. Centrifugal pump is the most preferred pump world wide.
There are many devices working on the principle of centrifugal force. It is just two of them.

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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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