Force

Force

Force is the external agent which changes or tries to change the state of rest or motion of a body. It is also called pull or push. Its SI unit is Newton (N). It is derived physical quantity. Since it has both magnitude and direction it is a vector quantity.

Force can produce the following effects on a body:

• It can change the direction of motion.
• It can change the speed of a body.
• It can change the state of rest or motion of a body.
• It can change the shape and the size of a body.

Examples of forces are frictional force, gravitational force, magnetic force, centripetal and centrifugal force, nuclear force etc.
The mutual force of attraction between any two heavenly bodies in the universe is called force of gravitation or simply gravitation. Due to this force earth revolve around the sun. Before 1542 AD it was believed that the earth is the center of the solar system and all other plants and sun revolve around the earth which is called geocentric model, proposed by ancient Greek. Later Nicholas Copernicus introduced new model called a heliocentric model in which sun is the center of the solar system and earth revolve around the sun including remaining plants.

Consequences of gravitational force:

• Existence of atmosphere
• Existence of solar system.
• Revolution of satellites around the planets.
• Revolution of artificial satellites around the earth
• Revolution of planets around the planets.

Newton’s Universal law of gravitation:

Newton’s law of gravitation states that “The force of gravitation between two masses or bodies anywhere in the universe is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers”.

It is called universal law because this law holds true for all the bodies, whether it is massive or microscopic placed anywhere in the universe. The effect of gravitation is more in liquid than in solid because inter-molecular force of attraction is less in liquid and it is weaker than in solid.

Consider, two bodes with mass m₁ and m₂ which are 'd' distance apart from their centers.

According to Newton’s law of gravitation,

$F\alpha {{m}_{1}}{{m}_{2}}$..............................1

$F\alpha \frac{1}{{{d}^{2}}}$...............................2

Combining equation 1 and 2 we get,

Or, $F\alpha \frac{{{m}_{1}}{{m}_{2}}}{{{d}^{2}}}$.....................3

Therefore, $F= \frac{G{{m}_{1}}{{m}_{2}}}{{{d}^{2}}}$......................................4

Where, G is a proportionality constant which is commonly known as universal gravitational constant and its value is 6.67×10 -11 Nm²kg ^{– 2} .

From equation (4) it is found that there exists a force of attraction between any two bodies in the universe separated by some distance. The force acting between the bodies has the following features:

• This force is attractive in nature
• The direction of force is along the line joining their centers.

Definition of G:

According to Newton’s law of gravitation,

$F=\ \frac{G{{m}_{1}}{{m}_{2}}}{{{d}^{2}}}$

If we put the value of m₁ =1kg and m₂ = 2 kg and d = 1m in above expression, we get

F = G ……………………5

From equation (iv) we can define gravitational constant as ‘The force of attraction between two bodies, each with a mass of 1kg kept at a distance of 1 meter apart.

Value of G = 6.67×10 -11 Nm²kg ^{– 2} was found experimentally by Henry Cavendish. This value of G shows that gravitational force is very weak force. The value of G is independent of the nature and composition of masses and medium in which they remain. It cannot be noticed if the two masses are small but becomes noticeable when the two bodies are extremely large.

G is called a universal gravitational constant because it exist everywhere in the universe and it is applicable to all the objects in the universe whether the objects are terrestrial or celestial or of space.

Gravity:
Gravity of a planet or satellite is defined as 'The gravitational force between a planet or satellite and a body on or near to ifs surface.' It is always directed towards the centere of the object. Due to gravity an object acquires weight. 

Let us consider the mass of earth be 'M' and an object is place on the surface of  the earth. The distance between their centers be 'R' which is nearly equal to the radius of the earth.

According to Newton's law of gravitation;

 $F=\ \frac{G{{m}_{1}}{{m}_{2}}}{{{R}^{2}}}$  .........i

or, $mg=\frac{GMm}{{{R}^{2}}}$                      [$\because $F=W=mg]

Where, 
            M=mass of earth
            R=Radius of earth
            W=Weight of the object
            G=Gravitational constant= 6.67×10 -11 Nm²kg ^{– 2}

or, $g=\frac{GM}{{{R}^{2}}}$

or, $g\alpha \frac{GM}{{{R}^{2}}}$...................ii

Here, equation (ii) shows that gravity of a planet is directly proportional to the Mass of the planet or satellite (M) that means if the radius of the planet is increased keeping mass M constant, the gravity will be less and if the radius is decreased, the gravity will increase. 
Equation (ii) also shows that acceleration due to gravity is independent of mass of and object.

Differences between gravity and gravitation:

Sn	Gravity	Gravitation
1	Gravity is the force between a planet or a satellite and a body on or near to the surface	Gravitation is the mutual force of attraction between two heavenly bodies in the universe
2	It is not universal force.	It is universal force.
3	It is expressed as $F=\frac{GMm}{{{R}^{2}}}$	It is expressed as $F=\frac{G{{M}_{1}}{{M}_{2}}}{{{d}^{2}}}$
4	Due to gravity all the objects fall towards the earth or planet.	Due to gravitation, the earth and other planets revolve around the sun.

Acceleration due to gravity: 

Before the Galileo's idea of falling bodies, Greek philosopher, Aristotle believed that when heavy body and light body fall form the same height, the heavier one falls faster on the earth than the lighter one which which was prove to be wrong after Galileo's experiment. According to Galileo the heavier and the lighter objects fall simultaneously on the earth surface. In other words, the acceleration produced on freely falling objects does not depend on the mass.
When Galileo performed the experiment with feather and coin, he found that feather fall more slowly than the coin. It was found that feather fell slowly due to the air resistance when Newton performed the experiment in both in vacuum and air. In vacuum where there is no air resistance both the coin and feather fell simultaneously.

Feather and coin experiment in air

Every object thrown upward falls towards the center of the earth with increase in velocity and hits the ground. The increase in the velocity of an object with produces acceleration on it. The acceleration produced on a freely falling body due to the force of gravity is called acceleration due to gravity. It is denoted by 'g' and its unit is m/s².

Feather and coin experiment in vacuum

Variation of acceleration due to gravity: 
i. Variation of acceleration due to gravity due to the shape of earth:
Earth is not perfectly spherical in shape. It is bulged out in the equatorial region and flattened in the polar regions. So, the radius towards the pole is smaller than the radius towards the equatorial region i.e R_e>R_p. Hence the value of acceleration due to gravity varies from place to place on earth. The value of acceleration due to gravity is 9.78 m/s² at equator and 9.83 m/s² at poles.

ii. Variation of acceleration due to gravity with altitude: 
If we consider the radius of the earth be 'R' at the surface 'h' be the distance at certain height above the surface of the earth. Then the total distance between the center of the earth and the point at certain height 'h' be (R+h). Then,

Acceleration at surface of the earth is $g=\frac{GM}{{{R}^{2}}}$  ........................a

Acceleration at certain height 'h' is ${{g}^{'}}=\frac{GM}{{{(R+h)}^{2}}}$......................b
Putting the value of GM=gR2 from equation (a) in equation (b) we get,

$g={{g}^{'}}\frac{{{R}^{2}}}{{{(R+h)}^{2}}}$

iii) Variation of acceleration due to gravity with depth: 

If we consider the earth to be a perfect sphere of mass M and radius R. Let 'P' be any point 'x' under the surface of the earth.Then acceleration due to gravity at point 'p' will be,

$g=\frac{GM}{{{(R-x)}^{2}}}$

Here, R-x is less than R, so the value of 'g' under the surface is less than at the surface.

Differences between Acceleration due to gravity (g) and Gravitational constant (G):

S.no	Acceleration due to gravity (g)	Gravitational constant (G)
1	It is acceleration produced on a freely falling body due to gravity.	It is the mutual force of attraction between two bodies with unit mass kept at 1m distance.
2	It is vector quantity.	It is scalar quantity.
3	It differs from place to place.	It remains constant everywhere.
4	It unit is m/s2	Its unit is Nm2/Kg2.

Differences between Acceleration due to gravity and gravity: 

S.no	Acceleration due to gravity (g)	Gravity
1	It is acceleration produced on a freely falling body due to gravity.	It is the force of attraction between planet or satellite and an object on or near to the surface.
2	It is the effect of gravity.	It is the cause of the acceleration due to gravity.
3	It unit is m/s2	Its unit is N.

Free fall:
 The falling of an object towards the center of another object without any external resistance is called free fall. In other words, the falling of an object with an acceleration equal to the acceleration produced by the pull of the earth is called free fall. E.g. The falling of an object on the surface of the moon.
Weightlessness: 
The condition in which the weight of an object seems to be zero is called weightlessness. It is also called as the apparent loss of weight of an object. The state of weightlessness can be observed in the following conditions:

• A body at the centere of the earth.
• A body in a freely falling elevator or lift.
• A body in the neutral point in space.
• A body inside the satellite orbiting a planet. 

Differences between free fall and weightlessness:

S.no	Free fall	Weightlessness
1	The motion possessed by a body without any external resistance is called free fall.	The condition in which the weight of an object seems to be zero.
2	It is cause of weightlessness.	It is the effect of free fall.

Differences between Weightlessness during free fall and Weightlessness in space: 

S.no	Weightlessness in free fall	Weightlessness in space
1	It occurs during free fall of an object.	It occurs when acceleration due to gravity is zero.
2	In this condition, a = g.	In this condition, g = 0.
3	It occurs due to gravity	It does not occur under the influence of gravity.
4	It occurs within the gravitational field.	It occurs in the outer space.
5	It is apparent weightlessness	It is true weightlessness.

Mass: The quantity of matter contained in a body is called mass of that object. Its SI unit is 'Kg'. It  is scalar quantity and measured by beam balance. It is a constant quantity. It can be zero.

Weight: It is the measurement of force of gravity acts on a body. It is a vector quantity with SI unit 'N'. It is measured by spring balance. Weight of an object will be zero, at the centere of the earth or at the place where R = 0.  
Differences between Mass and Weight: 

S.no	Mass	Weight
1	It is the quantity of matter contained in a body.	It is the amount of force of gravity acted on a body.
2	Mass of an object does not vary from place to place	Weight of an object varies from place to place.
3	Mass is scalar quantity	Wight is the vector quantity.
4	Mass is measured by beam balance.	It is measured by spring balance.
5	There is no place or condition under which mass of an object be zero.	Weight of an object will be zero, at the centere of the earth or at the place where R = 0.
6	The SI unit of mass is kilogram(Kg).	The SI unit of weight is Newton(N).

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