HOW NOT TO SLIP AND FALL IN BATHROOM

We mainly talk about electric, magnetic, gravitational and nuclear forces. But the frictional force also plays important role in our daily life.
How the frictional force arises? When one body moves over another body, a opposing force called friction arises. When liquid flows, it flows in layers and here the frictional force is called viscous force. Irregularities in the contacting surfaces, adhesive force between the surfaces and gravity also contribute to the frictional force. Friction is responsible for everyday activities like eating, drinking, writing, walking etc. Without friction "there will be many slips between the cup and the lip"

MEASURE OF FRICTION

'Co-efficient of friction" is used to measure the friction. It is the ratio between the force which is just enough to move the body' and the weight of the body (in simple terms). It normally falls between 0 and 1. The bathroom tiles should have this value from 0.4 to 0.7. Higher the value, more safe we are.
Gravity facilitate friction. Because the gravity brings objects together. In space, no gravity hence no friction.
Friction creates heat. That is why match box works. In the microwave oven, microwave agitate water molecules in the food and friction arises and warms up the food.
Rail road reduces the friction greatly. Hence the train is able to carry lot of people and load with less energy. But still, the ticket is costly because of overhead charges and maintenance.
All the automobiles and machines require oil and ball-bearings to reduce friction. Without oil, they will consume lot of energy and wear out quickly.
Hence, the friction is "the necessary evil" . Give the devil its due.
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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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