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Force Fields - Part I |
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When Newton sat under an apple tree and an apple fell on his head, he wondered what made the apple fall towards the ground. Why did it not fly towards the sky or in any other direction ? Galileo had noted that Jupiter had moons and they were revolving around Jupiter just as the moon around the earth. Kepler had nearly a century earlier derived mathematically how the planets revolve around the sun. It was Newton’s genius to put all these supposedly unrelated observations together and say that the force between bodies is the force of gravitation. Whether it is between the apple and the earth, the earth and the sun or the earth and the moon, the force that each of these bodies is responding to is the same.
In a similar manner, a force of attraction is found between a positive charge and a negative charge. A force of repulsion is seen between two like charges. A piece of iron can be seen to be attracted to a magnet. Thus “invisible” forces are under effect in different situations. In this chapter we will try and understand the nature of these forces and how bodies or particles under the influence of these forces behave. 1.
Newton’s Law of Gravitation 1.
Newton’s Law of Gravitation To establish an interaction between the masses m1 and m2, Newton proposed that the force of attraction between them is directly proportional to the masses and inversely proportional to the square of the distance between them. The force acts along the line joining the two masses. The force is always attractive. To write the same in terms of an equation, we have the following F
or
F
= -G
(m1 m2) The equation above is the Newton’s law of gravitation. It is also known as the inverse square law. Thus, Newton’s law of gravitation states that the gravitational force between masses is directly proportional to the product of the masses and inversely proportional to the square of their distance. G is the gravitational
constant. Value
of G is 6.673 x 10-11
N.m2/kg2. The
gravitational force is always attractive which is indicated by the negative
sign. It has become some sort of a convention to show attractive forces by
negative sign and repulsive forces as positive sign. This follows neatly
from the fact that if one has to remove either of the masses, one will have
to supply energy. Since force is a vector, the above equation can be written in a vector form as
Both
the masses m1 and m2 are pulling each other. The sun
is pulling the earth and the earth is pulling the sun with the same force.
If the earth is attracting the apple towards it, the apple is also
attracting the earth towards itself; but because the mass of the apple is
very small as compared to the earth, the movement of the earth is
negligible.
Conventionally the masses are also known as gravitational charges. Thus gravitational charge of a body is the (gravitational) mass[1] of the body. You
will wonder how the gravitational force acts when there is no contact
between the two masses or bodies. The existence of a force is very difficult
to visualize. To simplify the problem it can be assumed that when a
gravitational charge M is placed at a certain point A, the
properties of the surrounding space is changed. This is known as the force
field, and in this case, it is the gravitational force field. The mass M
influences every other mass that comes under its force field. The
strength of the force field reduces by 1/ r2 as one moves away
from M. The figure shows a typical gravitational force field around a mass M placed at a point A.
[1] There is a distinction between gravitational mass and inertial mass. Gravitational mass is the mass under uniform gravitational field. Inertial mass is the mass that is equal to force/acceleration.
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