HOW YOUR LUXURY CAR GLIDES?

Everywhere we see the 'ball bearings'. What is this device for? Let us explore.

Imagine a big drum filled with water standing erect. Try to move it. Only with great difficulty, you can start moving it. That is what is called static friction. Once it starts moving, it is slightly easy to maintain the motion-called sliding friction. But if you roll the drum, it is very easy. Hence rolling friction is less than all the other frictions. That is why car rolls instead of sliding. Also, in every movable object, wheels are used. Examples, suitcase, executive chair, hospital beds etc.

In a ball bearing, there are two steel rings-inner ring and outer ring-called races. Between them, steel balls are placed in special enclosures.

1. The balls between the rings are free to roll. And the rolling friction is always less.
2. The balls touch the rings at small points. The area of contact is less and the friction is less. Recollect, the area of contact is large in a vertically standing drum.
3. Suppose, no balls between the rings, the rings will slide against each other, creating a lot of friction and heat energy resulting in loss of fuel and efficiency.
The latest toy 'fidget spinner' is a good example of the ball bearing.

4. In a car, the 'ball bearing' is mounted between the shaft and the wheel. Now the wheel can rotate with less friction.
It is because:
The work-load passes from the outer ring to the inner ring through the steel balls. The balls mainly bear the load. Hence the name 'ball bearing'. It can be compared to the car tyre which bears the load.
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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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