Mathematical derivation of Newton 2nd law of motion of class 9th
Answers
Newton's second law of Motion is that, The acceleration of an object is dependent upon two factors Net force and Mass of object.
F = ma
The second law of motion state that "Acceleration of an object produced by net force is directly proportional to the magnitude of that net force and inversely proportional to the mass of the object if it is in the same direction of the net force".
Mathematical derivation of Newton 2nd law of motion:
Let the mass of moving object is m.
Let it's initial velocity be u and final velocity be v.
As we know that, Momentum = Mass × Velocity
p = m × v
Therefore,
Initial momentum of object = mu
Final momentum of object = mv
Change in momentum = mv-mu
Now, Force is directly proportional to change in momentum according to newton's second law of motion.
∴ F ∝ mv-mu/t ∝ m(v-u)/t
But we know that, v-u/t = a.
Therefore, F ∝ ma
Hence, Force is directly proportional to the product of mass and acceleration.
The second law of motion is related to the behaviour of the objects to which there is Not balanced force. Writing this law in the form of equation, then it can be written as:
a = F / m
In simple terms, The same equation is written as:
F = m * a
"The most important thing to be remember in the 2nd equation of Motion is NET FORCE"
The direction of the Net force is in the same direction of acceleration. Hence, The direction of Acceleration and Net force is always same. So, if the net force is given or known, then indirectly we know about the acceleration also.
Problems based on Second Law of Motion:
- Net Force and Mass is given; we have to find acceleration.
Acceleration = Net force / Mass
- Mass and Acceleration is given; we have to find net force.
Net force = Mass * Acceleration
- Acceleration and Net force is given; we have to find Mass.
Mass = Force / Acceleration