PHYSICS OF AN ACCIDENT

Stopping a car running at 60 kmph all of a sudden is equal to elephant falling from a third floor and hitting the ground. Lot of energy has to be dissipated. Engine is constructed in front portion of the car so that it can absorb the impact in case of the crash. The front of the car should not be rigid. It should absorb and dissipate the energy by crumbling and deforming. The bumper is also used to absorb energy during the crash. Besides, there are air bags in front of the passengers.

During an impact, there is a large deceleration (negative acceleration). The loose and soft organs in the body cannot withstand such a force and energy. Hence so many safety measures are built in a car.

Engine is at the front and the boot is at the back in every car to withstand the unexpected collision. Wash rooms are kept at the two ends of every compartment of a passenger train for the same reason.

The lunar module of the Apollo landed safely on the moon. The acceleration by the lunar gravity was reduced by firing small rockets. But when the Apollo reached the earth from the moon, it just crashed into the ocean. The energy of crash was dissipated into the waters. The module came above the waters by deflating the balloons.

We have developed sophisticated cars with so many safety measures. Still the accidents are on the rise. Now, Tesla company is developing self driving cars. Will it be completely eliminate human errors? Will it reduce the accidents greatly? We have to wait and see.

But, We have to do everything in our control, everything humanly possible to reduce the road accidents world wide.
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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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