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Show that Newton's second law of motion is the real law of motion. |
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Answer» SOLUTION :From Newton.s 2nd law, the force `vec(f) = (d)/(dt) (m vec(v)),` with proper choice of the UNIT of force. (i) If the external force `vec(F)` = , we have, `(d)/(dt)(m vec(v))` = 0 `therefore""m vec(v)` = CONSTANT, so `vec(v)` = constant This means that a body at rest would remain at rest and body in motion would continue to maintain its uniform velocity. This is Newton.s 1ST law of motion. We consider a system of two bodies, 1 and 2. `vec(F_(21))`= force on body 1, exerted by body 2, and `vec(F_(12))` = force on body 2, exerted by body 1. In the absence of any other external forces, Newton.s 2nd law gives, For body 1 : `vec(F_(21)) = (d)/(dt)(m_(1) vec(v_(1)))` for body 2 : `vec(F_(12)) = (d)/(dt)(m_(2) vec(v_(2)))` Now, if the combination of the two bodies is considered. `vec(F_(21)) and vec(F_(12))` are internal forces only and do not contribute to any external force. If the external force is zero, we have from the 2nd law, 0 = `(d)/(dt)(m_(1) vec(v_(1)) + m_(2) vec(v_(2))) = (d)/(dt)(m_(1)vec(v_(1))) + (d)/(dt)(m_(2) vec(v_(2)))` 0 = `vec(F_(21)) + vec(F_(12))` `therefore""vec(F_(21)) = - vec(F_(12))`. This is Newton.s 3rd law. thus, Newton.s 2nd law of motion is sometimes called the " real" law of motion-it encompasses However, Newton.s wisdom dictated him to propose the 1 st and the 3rd laws separately in order to introduce. respectively, (a) the notion of the inertial frames of reference, and (b) the concept of action-reaction pair of forces. |
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