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As a matter of fact, we will prove this theorem, employing gravitational field concept for a spherical mass like that of Earth. For the time being, we consider Earth and apple as particles, based on the Newton’s shell theory. In that case, the distance between Apple and center of Earth is equal to the radius of Earth i.e 6400 km.

Magnitude of force

The magnitude of gravitational force between terrestrial objects is too small to experience. A general question that arises in the mind of a beginner is “why do not we experience this force between, say, a book and pencil?” The underlying fact is that gravitational force is indeed a very small force for masses that we deal with in our immediate surrounding - except Earth.

We can appreciate this fact by calculating force of gravitation between two particle masses of 1 kg each, which are 1 m apart :

F = 6.67 X 10 - 11 X 1 X 1 1 2 = 6.67 X 10 - 11 N

This is too insignificant a force to manifest against bigger forces like force of gravitation due to Earth, friction, force due to atmospheric pressure, wind etc.

Evidently, this is the small value of “G”, which renders force of gravitation so small for terrestrial objects. Gravitation plays visible and significant role, where masses are significant like that of planets including our Earth, stars and such other massive aggregation, including “black holes” with extraordinary gravitational force to hold back even light. This is the reason, we experience gravitational force of Earth, but we do not experience gravitational force due to a building or any such structures on Earth.

Gravitational force vector

Newton’s law of gravitation provides with expression of gravitational force between two bodies. Here, gravitational force is a vector. However, force vector is expressed in terms of quantities, which are not vectors. The linear distance between two masses, appearing in the denominator of the expression, can have either of two directions from one to another point mass.

Even if, we refer the linear distance between two particles to a reference direction, the vector appears in the denominator and is, then, squared also. In order to express gravitational force in vector form, therefore, we shall consider a unit vector in the reference direction and use the same to denote the direction of force as:

Direction of gravitational force

Force between two particles placed at a distance

F 12 = G m 1 m 2 r r 2

F 21 = - G m 1 m 2 r r 2

Note that we need to put a negative sign before the second expression to make the direction consistent with the direction of gravitational force of attraction. We can easily infer that sign in the expression actually depends on the choice of reference direction.

Net gravitational force

Gravitation force is a vector quantity. The net force of gravitation on a particle is equal to resultant of forces due to all other particles. This is also known as “superposition principle”, according to which net effect is sum of individual effects. Mathematically,

F = Σ F i

Here, F is the net force due to other particles 1, 2, 3, and so on.

Questions & Answers

how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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what is energy?
James Reply
can anyone tell who founded equations of motion !?
Ztechy Reply
n=a+b/T² find the linear express
Donsmart Reply
Quiklyyy
Sultan Reply
Moment of inertia of a bar in terms of perpendicular axis theorem
Sultan Reply
How should i know when to add/subtract the velocities and when to use the Pythagoras theorem?
Yara Reply
Centre of mass of two uniform rods of same length but made of different materials and kept at L-shape meeting point is origin of coordinate
Rama Reply
A balloon is released from the ground which rises vertically up with acceleration 1.4m/sec^2.a ball is released from the balloon 20 second after the balloon has left the ground. The maximum height reached by the ball from the ground is
Lucky Reply
work done by frictional force formula
Sudeer Reply
Torque
Misthu Reply
Why are we takingspherical surface area in case of solid sphere
Saswat Reply
In all situatuons, what can I generalize?
Cart Reply
the body travels the distance of d=( 14+- 0.2)m in t=( 4.0 +- 0.3) s calculate it's velocity with error limit find Percentage error
Clinton Reply
Explain it ?Fy=?sN?mg=0?N=mg?s
Admire Reply

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Source:  OpenStax, Physics for k-12. OpenStax CNX. Sep 07, 2009 Download for free at http://cnx.org/content/col10322/1.175
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