Understanding Newton's Law of Gravitation

By M Khomeitomba Meetei *

Note (i):- "Sir Issac Newton demonstrated that weight depends on the distance from the centre of the earth. Things weigh less on mountain tops." Through his finding we come to know that weight depends on the distance from the centre of the earth.

This means that weight of an object increase towards the centre of gravity of the earth and decrease, away from the centre of gravity of the earth. Due to this reason, when an object falls towards the earth's surface or towards the centre of gravity there is acceleration (increase in motion) due to the gravitational attractive force of the earth.

Here, I express that the means and method to find out the value of gravitational attractive force of the earth in weight (gm/sec) to 1 gm (on the surface of the earth) which occurred the acceleration due to the gravitational force of the earth.

Topic (Aim):- To find out the value of the gravitational attractive force of the earth in weight (gm/sec) to 19m (on the surface of the earth) which occured acceleration.

PROCESS NO. 1
Materials required and to be done:- (a) Weight 2kg (2000gm) (b) Weight 4kg weight (4000gm). These 2kg and 4kg weight should be made of same matter. The weight 2kg should be made in the form of solid cube shape and the weight 4kg should be made elongated in the shape of weight 2kg (solid cuboid). These 2kg and 4kg weights should be of same density. (c) One time recorder.

PROCESS NO. 2
The place of experiments and required conditions:- The two weight mentioned above should be dropped from the highest place where having the gravitational attractive force of the earth. Air is taken as the common medium in every experiments. Air should be maximum normal state. Here, we know the gravitational attractive force of the earth is constant.

PROCESS NO. 3
Should be done:- The time taken by the two weights in every experiments/observations; should be recorded when dropped from the highest place to reach the earth's surface.

IDEA (A)
Let us consider that the 2kg weight take 90 seconds to reach the earth's surface from the highest place then 4kg weight win be taken 45 seconds in the same air resistance force. Now, we know that it is inversely proportional.

IDEA (B)
The value of the gravitational attractive force of the earth (desire of the topic) should be treated as the true value when to find from the reasonable difference which we find when we do experiments according to the conditions in the process No.1, No.2 and process No.3 without considering the air resistance force (Here, gravitational attractive force of the earth is constant).

PROCESS NO. 5

Experiments No. 1

Let us drop the 2 Kg weight mentioned in process No. 1 from the highest place having the fig. 1.1—to be contd

From the figure 1.1 we know that the possible weight of the 2kg weight will be found to the surface ABCD which faced directly perpendicular to the centre of gravity of the earth. According to Sir Issac Newton's experiment the weight of the 2kg will be decreased on the top. Let us take the possible weight of the 2kg on the top is as 1875 gm. Let us drop the 1875 gm weight. By the gravitational attractive force of the earth there should be occured acceleration nearer to the earth's surface or C.G. of the earth. The weight 1875 gm confront the air resistance force (a1). Let us consider the time taken by the 1875 gm weight to reach the earth's surface is as 90 sec. And when to reach the earth's surface the weight of the 1875 gm will be found 2 kg exactly.

Experiment No. 2

experiment let us drop the weight 4kg as shown in the figure 1.2 from the highest place wherehaving the gravitational attractive force of the earth (place done in experiment No.1). On that height place the possible weight of the 4kg win be found (acted) on the face EFGH which directly perpendicular to the centre of gravity of the earth. According to the possible weight of the experiment No. 1 the possible weight of 4 kg on the top will be 3750 gm. while the fall down by the 3750 gm. weight it confront the air resistence force (at); same air resistence force Df experiment No. l.

But in experiment No. 2 the weight 3750 gm is more half than the weight 1875 gm of the experiment No. 1. Therefore, the time taken by the 3750 gm weight in experiment No. 2 will be 45 sec. compared to experiment No. 1 . On the surface the weight will be found 4 kg exactly. From experiment No. 1 and experiment No. 2; we know that "It is an inversely proportion".

Experiment No. 3

As in the above figure 1.3 let us drop the 4kg (3750 gm on the top) weight from the highest place where having the gravitational attractive force of the earth. The possible weight of 4kg = 3750 gm will be found on the surface CDEF which directly perpendicular to the centre of gravity.

When compared to the experiment No. 2, in experiment No. 3 increases air resistence force (a2). Therefore the time taken by the weight 3750 gm in experiment No. 3 will be greater than experiment No. 2. Let us; consider the time taken by the weight 3750 gm in expt. No. 3 as 48 sees. From this we know that air resistence force (a2) make increase 3 secs(late/delay).

NOTE (II):- It is the real and true value of the gravitational attractive force of the earth which found ITom without considering the air resistence force.

(I) In experiment No.3 the air resistence force (a2) produces, 3 secs late (delay). Therefore the airresistence force (a1) also produces 3 secs late (delay). This implies tht in experiment No.3 the air resistence forces al and a2 produce 6 secs (1ate/delay). Therefore in experiment No.2 we can say (we know) the air resistence force qt produces 3 secs late (delay).

(II) Now; let us consider that without air resistence force in experiment No.2;the time taken by the weight 3750gm of the distence will be 42 secs. (Mathematically, imaginary, experimentally considerable in the condition of gravitational attractjve force/natural condition ).And total weight on the surface of the earth will be 3750 gm + 250 gm = 4000 gm.

NOTE (III):- Let as the primary weight; the 3750 gm (on the top) in experiment no. 2 and let as the secondary weight the value added 250 gm (the weight of the gravitational attractjve force of the earth). By the inversely proportion; the proportion time of secondary weight 250 gm (gravitational attractive force of the earth) is vanished (fast/hastened) i.e no included in the 42 sess. Therefore, 42 sec is the proportion tjme of the primary weight 3750gm of the distance (in the condition of gravitational attractive force/natural condition).

CALCULATION

(A) From experiment No. 2 the weight of 4000 gm (4 kg) will be 3750 gm on the top. Therefore, the gravitational attractive force of the earth (in weight) within 42 secs. to 3750 gm = 4000 gm - 3750 gm - 250 gm.

(B) The weight of gravitational attractjve fQrce of the earth(250 gm) is the total weight within 42 secs to the 3750 gm (primary weight). Therefore; the weight of the gravitational attractive force of the earth in 1 sec to 3750 gm 250 gm / 42 secs = 5.952381 gm/sec

(C) The above value 5.952381gm/sec is t03750gm. Therefore, in 19m of 3750gm per sec is =(5.952381/3750)gm/sec=0.0015873 gm/sec.

D) The proportion weight of 4000 gm (on the surface of the earth) is 3750 gm on the top (highest place where having the attractive force of the earth). Therefore, the proportion weight of 1 gm (on the surface of the earth) will be 0.9375gm on the top. Therefore the gravitational attractive force of the earth to 0.9375 gm/ sec=(0.0015873gm X 0.9375gm)in a sec=0.0014881 gm2 in a sec = 0.014881 gm2/sec.

Thus we can find out the gravitational attractive force (in weight) to 19m (on the surface of the earth).

NOTE (IV):- The above value (0.0014881gm2/sec) of the gravitational attractive force of the earth to the 1 gm (on the surface of the earth) is not real value. It is the value which get from the means and method of how to find the gravitational attractive force of the earth (in weight) to the 1 gm (on the surface of the earth) per sec.

NOTE (V):- In experiment No. 2 the weight 3750 gm take 45 sec to reach earth'8 surface throughout the air resistance force (a1). But in experiment No.3 the weight 3750gm take 48 sec to reach the earth's surface throughout the air resistance forces a1 and a2. From this we know that the time taken by the weight (time of fall down) from a high place is directly proportion to the air resistance forces.