HOW THE JUMBO JET LIFTS UP?

When a heavy wind blows over a hut with thatched roof, the roof just blows up. When the air flows fast, the pressure drops. Hence air pressure decreases over the roof; the pressure under the roof becomes greater and it lifts off the roof. This is due to Bernoulli's principle.

Bernoulli's principle says, as the velocity of fluid increases, its pressure decreases. This principle is also used to measure human blood pressure.

When the planes runs very fast, the air flows fast over the wings and it flows slower under the wings. It happens because of the geometry of the wings. Hence there is more pressure under the wings and it lifts up the plane.

There is a formula for the lift of the plane.

L = 0.5*C*D*A*V^2

V- velocity of the plane.
A- area of the wing.
D- density of the air.
C- constant due to wing design.
L- lift

The Boeing 747- jumbo jet requires a lift of 2150000 N(upward force). This lift will cancel out the huge weight of the plane due to gravity and will keep the plane afloat.

Post script: Before the invention of mercury based BP measuring instrument, a capillary tube (very narrow tube) was directly inserted into the veins of the patient; blood rises into the tube to certain height indicating the pressure. This method was used for 200 years. Now we are experiencing non-invasive and painless measurement.

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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

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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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