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### Force of Gravity

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

## 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. 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. From this we get the formula: 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. 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. 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 