Nine Standard >> Second law of motion

Newton's second law of motion

The rate of change of motion is directly proportional to the applied force and the change takes place in the direction in which the force acts.

From this law, we will obtain the measurement of force. 

F=m \(\times\) a

Where F= force
           m=mass of the body
           a=accleation

 force \(\propto\) rate of change of momentum

Implications of Newton's Second Law :
Understanding Newton's Second Law of Motion and its implications is essential for comprehending the dynamics of objects in motion and analyzing various real-world scenarios. Let's explore some of the key implications of this law:

Relationship between Force, Mass, and Acceleration:
Newton's Second Law establishes a precise quantitative relationship between force, mass, and acceleration. It shows that the acceleration of an object is directly proportional to the force applied and inversely proportional to the object's mass. This means that a larger force will result in a greater acceleration, while a larger mass will lead to a smaller acceleration for the same force.

Take a body that is moving with initial velocity u and after time t the final velocity is v. Mass of the body is m and its acceleration is f.

initial velocity= u
time= t
final velocity= v
mass of the body= m

Initial momentum= mass \(\times\) initial velocity
                          =m \(\times\) u
                          =mu

final momentum= mass \(\times\) final velocity
                          =m \(\times\) v
                          =mv

Time is taken for change the momentum is t.

Change of momentum is=mv-mu

Rate of change of momentum=\(\frac{mv-mu}{t}\)
                                            =\(\frac{m(v-u)}{t}\)
                                            =\(m\frac{(v-u)}{t}\)
                                             =ma [ \(\because\) \(\frac{(v-u)}{t}=a\)]

Initially, we started from the second law of motion that

        F \(\propto\) ma

   or, F =kma [where k is a constant]

Therefore we obtained F=kma  -------  (i)

If unit force is defined as the quantity of force acting on a mass of unit that is unit mass will generate unit acceleration.

i.e F=1, m=1, a=1

then from equation (i) we get

    1=k.1.1
or, k=1 

if k=1 then
F=ma

Applications in Real Life:
The applications of Newton's Second Law are widespread in our daily lives and various scientific fields. For example, in automotive engineering, this law is critical for designing efficient engines, optimizing fuel consumption, and developing safety features such as airbags. In sports, it helps athletes understand how to enhance their performance by applying force effectively. The law also plays a crucial role in space exploration, robotics, and the study of celestial bodies' motion.