State Newton's second law of motion. Derive the mathematical expression for Newton's second law of motion!
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Newton's Second law of motion :- The rate of change of momentum is directly proportional to the force applied on the system. Force applied is directly proportional to the product of mass and acceleration
Suppose an object of mass, m is moving along a straight line with an initial velocity, u. It is uniformly accelerated to velocity, v in time, t by the application of a constant force, F throughout the time, t. The initial and final momentum of the object will be, p1 = mu and p2 = mv respectively. The change in momentum ∝ p2 – p1 The change in momentum∝ mv – mu The change in momentum∝ m × (v – u). The rate of change of momentum ∝ m × (v −u)/t Or, the applied force, F ∝m × (v −u)/t F = km (v - u)/t F = kma Here a [a = (v – u)/t ] is the acceleration, which is the rate of change of velocity. The quantity, k is a constant of proportionality.The SI units of mass and acceleration are kg and m s-2 respectively. The unit of force is so chosen that the value of the constant, k becomes one. For this, one unit of force is defined as the amount that produces an acceleration of 1 m s-2 in an object of 1 kg mass. That is, 1 unit of force = k × (1 kg) × (1 m s-2). Thus, the value of k becomes 1. and F = ma which is the mathematical expression on the Newton's second law of motion.
Suppose an object of mass, m is moving along a straight line with an initial velocity, u. It is uniformly accelerated to velocity, v in time, t by the application of a constant force, F throughout the time, t. The initial and final momentum of the object will be, p1 = mu and p2 = mv respectively. The change in momentum ∝ p2 – p1 The change in momentum∝ mv – mu The change in momentum∝ m × (v – u). The rate of change of momentum ∝ m × (v −u)/t Or, the applied force, F ∝m × (v −u)/t F = km (v - u)/t F = kma Here a [a = (v – u)/t ] is the acceleration, which is the rate of change of velocity. The quantity, k is a constant of proportionality.The SI units of mass and acceleration are kg and m s-2 respectively. The unit of force is so chosen that the value of the constant, k becomes one. For this, one unit of force is defined as the amount that produces an acceleration of 1 m s-2 in an object of 1 kg mass. That is, 1 unit of force = k × (1 kg) × (1 m s-2). Thus, the value of k becomes 1. and F = ma which is the mathematical expression on the Newton's second law of motion.
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