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Force of Gravity

posted Dec 15, 2015, 3:57 PM by Upali Salpadoru   [ updated Jul 11, 2016, 7:58 PM ]


Canvas.jpgFig.1. Ali is falling down a cliff.   

The Earth and Ali are under the influence of The Universal Law of Gravity.  According to this law “Every object attracts every other object in the universe. Force increases with the mass and decreases with the displacement.”

Earth attracts Ali and Ali attracts the Earth.

" Don’t laugh now; it is not a joke but a fact".


Now You may ask why the Earth does not move. The change of motion or acceleration depends on the mass. The product of mass and acceleration gives the force.

                             F=ma.

So when the mass is very high as in the case of the earth acceleration is negligible.  

On the other hand the mass of Ali is negligible and so he will experience a very significant acceleration. .

If you are mathematically bent you can follow this;

Earth.jpg

Fig.2  The attraction between two bodies is mutual


Force = Mass x Acceleration

The opposite forces on the two objects earth and moon  are equal.

It is a single force that exist between them.

That means

Force on moon (to right) = Force on earth (to left)

Using the equation F = ma  we get

m(moon) x a (moon) = m(of earth) x a( of earth)    

      As the products m x a are equal, when mass decreases the acceleration has to increase.

You can also drop a coin and a small piece of paper in a similar  way and observe what happens.

 Home Experiment.


 To find out:   Do heavy things fall faster.

 You need:  A coin and a piece of paper.

 Method and Results

EXPERIMENT

1.Dropping a piece of paper and a coin.

2 Dropping the same piece of paper crushed and the coin.

3. Dropping a coin with a small piece of paper on top.

Diagram.

Ex 1.jpg

Ex 2.jpg

Ex 3.jpg

Observation




Explanation





.

Fig. 5   Galileo Galili 1564 – 1642

About 400 years ago, Galileo  proved by experiment and argument that all objects fall down with the same acceleration.

In practice we observe that fluffy matter like feathers and cotton wool come down very slowly. The reason for this is that they are not allowed to fall freely by the molecules of air. When we remove the air in a jar even feathers fall down like cannon balls.


(The legend is that Galileo  dropped objects from the leaning tower of Pisa to convince all objects fall with the same acceleration)





The value of 'g'

The value of ‘g’ varies slightly from place to place even on the surface of the Earth. It also varies as we go away from the Earth. The radius of the Earth is 6400 km. If we double this, that means if we go up 6400km. From the surface , the value of ‘g’ will reduce by 4 times. If we treble the radius, that is if we ascend another 6400 km. ‘g’ will become 1/9th and so on.

A rocket may escape the gravitational field of the Earth by going into deep space, but it will never really escape from the solar system. The suns gravitational field will take over. Reaching the stars is not an easy task..

The Value of ‘g’.

Equator

9.78 m/s2

Tokyo

9.79 m/s2

London

9.81 m/s2

North pole

9.83 m/s2

Sometimes in schools we just take it as 10 ms-2 which is a round number.

We can also consider 'g' as  a force of 10 N on a mass of each kg.



" We understand what gravity is, but then what is Weight?"


In order to understand this one must have a correct idea of these three terms.


MASS.        ACCELERATION      DISPLACEMENT



Do you know them?


They are explained below.


Mass-  This is the amount of matter in an object.

This is what we measure in kilograms. Symbol                m.


Acceleration=  This is the change in motion. It may

be an increase of speed, decrease of speed or even

a change in direction. Symbol                                         a.



Displacement =  The shortest distance between

two points. symbol                                                          d.



The Era  Galileo died, a mathematical genius was born in England that gave us a few formulae that helped us to define and explain what a force is.


The formula relevent for us here is :-    

                       FORCE  =  MASS  x ACCELERATION.


Weight is a force.  IT is the force by which the Earth will attract anything that has mass..

In other words weight is the Force of gravity on that object.



Just as gravity changes from place to place the weight also has to change.


Example.


If a piece of metal has a mass of 10 kg

a.    What will be it weight near the equator?                                        b.    What will be the weight in London?

c.     When taken to the moon?


Answer


a.     

The weight near the equator =    F = ma.   

When acceleration is due to gravity we write it as    

Weight=  Mass x gravity.

                                                   W = mg.

                                                   W = 10 x 9.78    =  97.8 N.

b.   In London       W = mg.

                             W = 10 x 9.81  = 98.1 N.


c.   On the Moon                                     

                  W = mg                                     

10 x 9.8  / 6  =  16 .3 N

     

Here approximately 6 times less.       


Weightlessness – zero gravity           





Fig.7 An astronaut experiencing 'zero gravity'

“Reporting from Space Centre in orbit  I am  on a weighing machine.  It is not showing weight. I dropped an orange and it seems to be floating.”

This an experience of a weightlessness. What is it due to?


Some students think that the weightlessness is due to the weakening of the gravitational force due to distance, If that is the case Earth would not be able to keep a hpld on the moon. It will fly away  as it is even much further away  than any of the man made satellites.


Weightlessness is due to the falling nature of the satellites.If an object such as a lift falls down freely. a man onside will also come down at the same acceleration. So in relation to the lift the man will seem to be stationery.

Picture shows an astronaut seated on a weighing machine. If the capsule is falling freely man and machine would also be coming down at the same speed. Then there will be no compression on the spring of the balance and it will read zero. The released orange is also coming down, but the person will not be able to see it falling.


This is what happens to astronauts,  once the thrust producing rocket motors have been stopped. When a rocket reaches a certain velocity, called the escape velocity it can enter an orbit. As there will be only a few scattered molecules of air in this region, there will be no fluid friction.


Newton.jpg


Fig. 1. According to legend, Newton saw an apple falling and wondered why?

Sir Isaac Newton explained the Law of Universal Gravity.  He showed that the force that brings an apple down to Earth extends to the moon and beyond.

This paved the way for the Law of Universal Gravity.


The Law of Universal gravity.

The Gravitational attraction between two bodies is directly proportional to the product of the two masses and inversely proportional to the square of the distance between them.

He explained that every thing that has a mass attracts every other object.

The magnitude of the attraction may be determined by the formula below.

g =.jpg

From this we get the formula:


G.jpg


The value of G was derived only seventy years after the death of Newton. As you may have noticed it is a very, very small value.  G= 0.00000000006673 N m2 kg-2.


Let us take the Earth and moon to find out the force of attraction.

Earth.jpg

Mass of Moon = 6.0 x10 24 kg.

Mass of Earth = 7.35 x 10 22 kg.

Gravitational constant = 6.674x 10 -11

Force of Gravity  =  G x m1 xm2 /  (3.844x10 8) 2


 F = 6.674x 10 -11 kg.x6.0 x10 24 kgx 7.35 x 10 22 kg / (6.674x 10 -11 )


F = 1.982x1020 N


Finding the acceleration due to gravity.


There is a formula on motion as:  d = ut + ½ at2.

d= displacement,  u= Initial velocity, t - time, a= acceleration,

If you start from zero velocity you can drop ut.

Then we get  : d= ½  at2

      That is      d= axt2 / 2

Therefore        a- 2d / t2.


So if we can drop something, which will not be affected by air resistance and find the time taken and the distance, we can find the acceleration.

Here is an a circuit diagram for an experiment.

g.jpg

A steel ball is kept attached to an electro magnet. The circuit for this is shown in orange. When the switch is changed to clock , the clock starts working and the megnet gets disconnected. This will drop the steel ball.

When the ball reaches the bottom it will fall on a lever that will disconnect the clock. By this method we can get the time taken for the object to ball accurately. The distance can be measured with a tape or a ruler from the bottom of the object to the lever.

Here is a worked out example;

         Displacement/ m       =     0.75 m    

      Time /s                     = 0.40 s    

      Using the formula

                   Acceleration  = 2 x displacement  / time 2      

             

                      Acceleration =   (2 X0.75)  /  0.4 X 0.4

                                             =9.4 m/s2     

The exact value is a bit higher than this.  9.8 ms-2



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