Question

State newton's 2nd law of motion and prove that F = ma

In Easy words!​

Answer 1

it will help you in understanding Newton's second law of motion

Answer 2

$\underline {\Huge \mathfrak {Answer :}}$

$\underline {\bold{Statement :}}$

The second law of motion states that the rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of force.

$\underline {\bold {Proof:}}$

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

℘ mv - mu

℘ m (v - u)

∴ The rate of change of momentum

℘ m (v - u) /t

Or, the applied force,

F ℘ m (v - u) /t

=> F = K. m (v - u)/t

=> F = K. ma [∵ a = (v - u)/t]

One unit of force is defined as the amount that produces an acceleration of 1 m/s^2 in an object of mass 1 kg.

That is,

1 unit of Force = K × 1kg × 1m/s^2

Thus, the value of K = 1

Hence, F = 1 ma

=> $\boxed {\Huge\bold{ F = ma}}$