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| Newton's Second Law of Motion |
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| The rate of change of momentum of a body is proportional to the applied force and takes place in the direction in which the force is applied. |
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| For a constant mass system |
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We have already learnt that the rate of
change of velocity is called acceleration
 
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| where k is the constant of proportionality and the units of k are Ns2/kg/m |
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| For m in kg |
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| F in Newton |
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| The value of k = 1 |
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 -----------Newton's II law |
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| i.e., for the units of all quantities taken in SI units or CGS units, the value of k = 1. |
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| Newton's II law can also be written in component form and it holds good for each component. |
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| If two or more forces act on the same body, then the acceleration of the body can be written as the vector sum of the individual accelerations produced by each force. |
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| The acceleration of the body can be better expressed as the acceleration caused by the resultant force. |
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| Through both the methods, we get the same result. The student must understand that these two methods are essentially the same. |
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| Without units, force could only be expressed as a weak, strong, not so weak or strong force. But these expressions give a very vague and incomparable idea of the magnitude of force. Therefore, a clearly defined and easily understandable unit is essential. The SI unit of force is Newton. |
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| One newton |
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| One newton is the force that produces an acceleration of 1m/s2 in a body of mass 1kg. |
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| 1 newton = 1 kg x 1m/s2 |
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| Another such unit for force in the CGS system, is the dyne. |
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| One dyne |
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| One dyne is the force which produces an acceleration of 1cm/s2 in a body of mass 1gram. |
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| 1 dyne = 1 gm x 1cm/s2 |
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| The relation between one dyne and one Newton is |
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| 1 N = 105 Dyne |
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| or 1 Dyne = 10-5 N |
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| Another unit of force by which the magnitude of force can be understood and gauged, is the gravitational unit of force. |
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| A gravitational unit of force is that force with which the Earth attracts a body of unit mass towards its centre. |
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| A gravitational unit of force may also be defined as that force which produces an acceleration of one g in a body of unit mass. |
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| The gravitational unit of force in the CGS system is the gram weight of force and in the SI system, it is the kg weight of force. |
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| One gram weight of force is the force with which a body of mass 1 g is attracted towards the centre of the Earth. |
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| 1 gm wt = 981g /cms2 |
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| = 1 x 'g' dyne [g is acceleration due to gravity in CGS units]. |
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| One kilogram weight of force is the force with which a body of mass 1kg is attracted towards the centre of the Earth. |
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| 1 kg wt = 1 kg x 9.8m /s2 |
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| = 9.8N |
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| The gravitational system is easier to comprehend and visualise than the absolute system, but the only flaw is that the value of 'g' is not a constant in all places on the Earth. It is different at the equator and at the poles. It is different in Bangalore and different in Chennai. It is different on the mountain peaks and different at the bottom of the sea. |
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| The second law of motion improves our understanding of most types of motion involving a force. |
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| We get to understand that if a body is pushed with a stronger force, it accelerates at a faster rate and vice versa. |
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| We understand that if two different bodies are pushed with an equal force, the product of their mass and acceleration, are equal. |
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| F = m1a1 ; F = m2a2 |
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| i.e., larger the mass, smaller is the acceleration produced by a given force. Thus, the mass 'm' measures the resistance or the inertia offered by the object to the change in its velocity, induced by the force. This is why mass 'm' is called the inertial mass of the object. The net inertial mass of the body is the sum of all the inertial masses of the constituent bodies joined to make the single body i.e. m = m1 + m2 + m3……….. |
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| We also understand that in circular motion, there has to be a force. This is because the velocity has constant magnitude but the direction of the velocity is constantly changing i.e., there is an acceleration because velocity vector is changing. Hence, we can conclude that a force is required for this acceleration. |
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