State Newtons 2nd law of motion and prove F = MA, where the symbol have their usual meaning.
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Answers
Answer:
Newton's second law is the rate of change in momentum is directly proportional to the force applied.
According to Newton’s second law of motion, “The rate of change of momentum of a body is directly proportional to the force applied on it”. If, p⃗ is the momentum of the body, m is the mass of the body and v⃗ is the velocity of the body then momentum is given below.
p⃗ =mv
Now let us write Newton’s second law of motion.
F⃗ ∝dp⃗ /dt
Where F is the force
Now, let us substitute the value of p⃗ and we get the following.
F⃗ ∝ d(mv)/dt
Now, as we know mass m is constant then we can write the expression as following.
F⃗ ∝md(v⃗ )/dt
Again, we can rewrite the above expression as below.
F⃗ ∝ma (Rate of change of velocity is acceleration: dv⃗ /dt=a )
We can replace the proportionality sign introducing a constant k.
F⃗ =kma
If the proportionality constant k=1, then the above equation becomes
F⃗ =ma
Where F is the force and has the unit of newton, m is the mass of unit kg and a is the acceleration of unit m/s2
Hence, equation (1) is exactly Newton’s second law in mathematical form and equation (2) is the derived from (1) where we assumed that mass of the object to be constant and proportionality constant to be zero.
Note:
*To derive F=ma, we consider mass to be constant and proportionality constant to be unity.
*To derive F=ma, we consider mass to be constant and proportionality constant to be unity.*When we study relativistic mechanics where the speed of an object is nearly equal to speed of light (v ~ c) then F=ma does not apply. As at the higher speed nearly equal to speed of light mass no longer remains constant it becomes variable.
