How does Newtons second law give the concept of force and derive the same.State conservation of momentum of two bodies.
Newton's second law of motion states that the force applied on an object is directly proportional to the rate of change of momentum of the object.
Momentum is defined as the product of mass and velocity, thus, for an object of mass m and velocity v, momentum p = m * v
If the initial velocity of an object of mass m is u and its final velocity is v, then the change in momentum,
p2 â p1 = mv â mu = m(v â u)
Thus, the rate in change in momentum is the change in momentum divided by the time taken to do so:-
Rate of change in momentum = m(v â u)/t
In the above expression it is notable that since acceleration is a = (v â u)/t, therefore
Rate of change in momentum = m * a
Since force = rate of change of momentum, thus
F = ma
This is how Newton's second law gives the concept of force as the product of mass and acceleration.
Hope this clarifies your doubt.