Question

derive the methamatical relation of Newton's second law of motion..


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Answer 1

Answer:

Derive the mathematical relation of Newton's second law of motion. Answer: Consider an object of mass m moving along a straight line with an initial velocity u (say). ... Thus, the second law of motion gives a method to measure the force acting on an object as a product of its mass and acceleration.

Step-by-step explanation:

Newton’s Second Law of Motion

Newton’s second law of motion can be formally stated as follows: The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

Second Law of Motion Formula

Let us consider an object of mass m, moving along a straight line with an initial velocity u. Let us say, after a certain time t, with a constant acceleration, the final velocity becomes v. Here we see that, the initial momentumLaw Of Motion

The final momentum

Law Of Motion

The change in momentum can be written as

Law Of Motion

As we know, the rate of change of momentum with respect to time is proportional to the applied force. The applied force

Law Of Motion

Or,

Law Of Motion

as acceleration (a) = rate of change of velocity with respect to time.

Law Of Motion

Above is the second law of motion formula.

Notations Used In The Formula

F is the force

k is the constant of proportionality

a is the acceleration

The SI units of mass and acceleration are kg and m.s-2 respectively.

So,

Law Of Motion

The second law of motion gives us a method to measure the force acting on an object as a product of the mass of the object and the acceleration of the object which is the change in velocity with respect to time.

Answer 2

Newton's Second law of motion :- The rate of change of momentum is directly proportional to the force applied on the system.

Force applied is directly proportional to the product of mass and acceleration .

Let be the initial and final momentums respectively.

According to newton's second law :-

pf - pi / t ∝ F

We know that, Momentum ( P) = mv .

Let v be the final and u be the initial velocity .

Now,

mv - mu / t ∝ F

F ∝ m ( v-u) /t

F ∝ ma.

F = kma.

Here, K is the proportionality constant. It's value is 1 .

Units of Force are given by the units of mass and acceleration. Units of force is Kgm/s² .

In accordance to honour the contributions of Newton, 1 kgm/s² is termed as 1 Newton.