Thursday, January 11, 2007

Newton and playing cricket.

Playing cricket is possible because of physics. Newton helped to understand these laws of physics.

But before seeing that, some ideas, which are not so obvious, have to be understood.

How much a person runs in a given time is speed – say 36 kms in one hour, then the speed is 36kmph or (36x1000)/(60x60) metre per sec or 10m/sec.

How much a person runs in a given time and in which direction is velocity. If you run at 10m/sec down the street from your house, turn left into say your friend’s street and run again at 10m/sec then your friend will say your velocity has changed.

When you run at uniform speed in a circle or the moon goes round the earth,
the moon’s velocity is different at every position.

Velocity = how much distance in a given time and in which direction

Speed = how much distance in a given time

The units in which both are given are the same – metre/sec.

Changing velocity requires effort. Changing velocity per given time is called acceleration.

Velocity = (end distance – start distance) / time

Acceleration = (final velocity – start velocity) / time

But how do you subtract directions? Just as adding or subtracting quantities can be done by mathematics. Adding or subtracting quantities with direction can be done by something called ‘vector mathematics’ because quantities with direction are called vectors.

However, one can still find out the change in quantity alone if the directions are same or close to same.

If we look at only the quantities and not the directions

If (end distance – start distance ) = ‘s’ metre

Time = ‘t’ sec

End velocity = ‘v’ metre/sec

Start velocity = ‘u’ metre/sec

Acceleration = ‘a’ (metre/sec)/sec or metre/sec2

Then a = (v-u)/t

at = v-u or v = u + at

average velocity = (v+u)/2

average velocity x time = distance traveled

(v+u)/2 x t = s

½ v x t + ½ u x t = s

as v = u + at , this gives

½ ut + ½ ut + ½ at2 = s

s = ut + ½ at2

So if the bowler standing at the crease throws a ball and the ball has a velocity of 36kmph when it reaches the batsman, how long does it take to reach the batsman if the pitch length is 5m?

u = 0 as the ball and the bowler are not moving initially

v = 10m/sec (= 36kmph)

this gives a = (10 – 0) / t if the ball takes ‘t’ secs to reach the batsman

which means

5 = 0 x t + ½ x (10/t) x t2

5 = ½ x 10 x t

or t = 1 sec

How long will it take if the bowler comes running with a velocity of 36kmph then bowls the ball so that the ball has a velocity of 36kmph when it reaches the batsman?

Now u = 10m/sec

So a = (10-10) /t = 0

Which means 5 = 10 t + ½ x 0 x t2

or t = 0.5 secs

First law:

Inertia means tendency to do nothing or remain unchanged.

Newton made the ‘now obvious discovery’ that things tend to remain in the state of inertia unless acted upon. This became the First law of Newton. Thus for example neglecting air friction and gravity the ball thrown by the bowler would keep on moving until acted upon by the batsman. Similarly, if a body is floating or moving at a uniform speed and in a fixed direction in space then it is moving at a uniform velocity in space. Newton’s first law tells that the body will continue to move so, unless some force pulls or pushes or stops it.

So, that ‘action’ which changes the state of inertia is called as force. Newton ‘discovered’ that the more the amount of matter in a body the more is the force required to change the state of inertia. He also found the more the change in velocity due to the change of state the more is the force required. For example, more force is required to hit the ball if the bowler throws an iron ball rather than a cork ball, even though both may arrive with the same velocity. When the ball is hit, the state of inertia is changed as the velocity (direction and speed) of the ball gets changed. So in cricket, less force is needed to deflect a fast ball than hit it for a four in a completely different direction.

Second law:

Newton’s second law then tells that the force (‘F’) is given by

F = m x a

Where ‘m’ is the mass of a body ( or ‘amount’ of matter in a body) and ‘a’ is the acceleration or change in velocity.

There is another way of saying the same equation. That is by bringing in a quantity called ‘momentum’. Momentum is the quantity of motion in a body given by the product of its mass and velocity. While traveling with the same velocity an iron ball will have more momentum than a cork ball. The cork ball has less mass than an iron ball of the same size. For the same cork ball a fast bowler gives the ball more momentum than a slow bowler. When a fast ball is deflected, the change in direction is small. Therefore the change in velocity is small. This means the change in momentum is small. The force required is small. So, force can be defined as the rate of change of momentum.

Using our symbols

F = (final momentum – initial momentum)/ t = ( mv – mu ) / t = m (v – u) /t = m a

Thus the two definitions of force turn out to be the same. Just different ways of looking at the same quantity.

Imagine a foolish player hits the cricket ball hit vertically up into the air. It goes up for a distance and comes down. Because the direction of movement has changed. The velocity and momentum has changed when it starts coming down. The change of velocity or momentum must happen because of a force. Otherwise the ball should, neglecting air friction, keep on going traveling into space and beyond. Newton as the story goes realized that the apple on the tree does not continue its state of inertia and stay there even if the stem breaks but changes its state of inertia and its momentum because of a force. He reasoned that since the apple comes down and does not go anywhere else, the force is probably due to the earth. This force was termed gravity.

The cricket ball comes down because of gravity.

Newton showed that gravity is the force exerted by one body on another because of the mass or amount of matter in the two bodies. The acceleration due to the gravitational force of the earth is usually termed as ‘g’. When one stands on a weighing machine because of the pull of the earth, the body exerts a force on the weighing machine. This is measured as weight. Weight is therefore a force given by w = m x g , where ‘m’ is the mass of the body and ‘g’ is the acceleration due to gravity. Mass is a quantity measuring the ‘amount’ of matter in a body whereas weight is a measure of the force exerted by the gravitational pull of the earth (since we live on the earth) on the body.

Third law:

Gandhi said ‘ an eye for an eye makes the world go blind’. Newton said ‘ every action has an equal and opposite reaction’. Action here refers to force. Newton’s third law in effect says ‘ a force for a force makes the world go on’.

When we stand on the weighing machine we do not go through the weighing machine as it exerts an equal and opposite force as the weight of our body, which is, the force exerted on the weighing machine by our body.

When the ball hits the bat, the ball exerts a force as it has changed its velocity and momentum. The bat exerts an equal and opposite force on the ball and the ball goes off, not staying in the same place where it hit the bat. The bat is in effect hitting the ball back.

The arm that holds the bat feels the force and if the arm manages to keep the bat steady without moving the bat, the ball flies off.

Thus if the world does not follow the physical laws ‘discovered’ by Newton, it would not be possible to play cricket.

1 comment:

Computational Biology said...

Hello Sir,

Very good demonstration of basics. This can become a book on basic science. Basics are important, as they are the basic connectivities of greater informations. Complex formed by good bonding will get precipitated, and do not get vaporised. Hope I am right.