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| Newton's Third Law of Motion and Force of Gravitation |
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| Let us now see how Newton's third law of motion is applicable to the gravitational force existing between the various objects in the universe. |
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| According to Newton's third law of motion “to every action, there is an equal and opposite reaction”. That is, if a body A exerts a force on another body B, then the body 'B' also exerts an equal and opposite force on the body 'A'. |
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| Two Bodies A and B Exerts an Equal and Opposite |
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| Force on Each Other |
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| Let us consider the gravitational force existing between a stone and the Earth. When a stone is dropped from a height it falls towards the Earth. This is because the Earth exerts a force on the stone and according to the universal law of gravitation, the stone also exerts an equal force on the Earth. Now the question is why we do not see the Earth moving towards the stone. Newton's second law of motion gives an explanation for this. |
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| According to the second law of motion, whenever a force is acting on an object, it produces acceleration in it. The gravitational force of attraction produces acceleration both in the Earth and in the stone. |
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| Gravitational Force of Attraction Between the Earth and the Stone |
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| According to Newton's second law of motion, |
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| Force acting on an object = mass of the object x acceleration produced in the object |
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| It is the gravitational force, which produces acceleration in both Earth and the stone. The above relation tells us that the acceleration produced due to the gravitational force is more in the case of the stone as its mass is very small whereas the acceleration produced in the Earth will be negligible as the Earth is massive. The acceleration produced in the Earth being very small, the displacement of the Earth is negligible whereas in the case of the stone, the acceleration produced is very large and hence we see the stone moving towards the Earth. This example shows that Newton's third law is applicable to the gravitational force. |
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| By actual calculation, let us find out the acceleration produced in the stone and in the Earth and the displacement due to their force. |
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| Consider an object of mass 1 kg falling from a height of 1m. According to Newton's law of gravitation, the force of attraction between the Earth and the object is given by the equation |
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| Where F is the force, |
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| G = gravitational constant = 6.6734 x 10-11 Nm2/kg2 |
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| m1 = Mass of the Earth = 6 x 1024 kg |
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| m2 = Mass of the object = 1 kg |
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| d = distance between the object and the Earth = height from the ground + radius of the Earth |
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| Radius of the Earth = 6.4x106 m = 6400000 m. |
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| d = 1 + 6400000 m |
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| = 6400001 m |
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| F = 9.775 N |
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| = 9.8 N |
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| i.e., the gravitational force between an object of mass 1kg and the Earth is 9.8 N. |
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| Acceleration produced in the Earth is negligible when compared to acceleration produced in the object. |
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| Using the II equation of motion, we calculate the distance moved by the stone and the Earth in one second. The initial velocity of the stone is zero. |
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| = 4.9 m |
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| Again, the distance covered by the Earth is negligible. Thus from the above calculations, it is very clear, why we do not see the Earth rising towards the object. |
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