Mathematical formulation of second law of motion.
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Mathematical Formulation of Second Law of Motion
The initial and final momentum of the object will be, p1 = mu and p2 = mv respectively. ∝ m × (v – u). ... The second law of motion gives us a method to measure the force acting on an object as a product of its mass and acceleration.
Answer:
Suppose, the velocity of a body of mass, m changes from u to v in time, t.
The initial momentum (P1) = mu
and, final momentum (P2) = mv
Now, according to Newton's second law of motion, the magnitude of the force F, is
F ∝ (P2 - P1) /t
or, F = K (P2 - P1) /t
or, F = K(mv - mu) /t
or, F = K m(v - u) /t
Or, F = K ma
The unit of force is so chosen that the value of constant becomes one.
Thus, F = ma
i.e, Force = mass × acceleration.
Explanation:
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