How did Newton come up with the second law?
Most of the Laws in physics are propounded based on experimental data. Certain experiments are carried out and observations are made. Then these observations are generalized, and subjected to gruelling tests. If they pass each test, it becomes a Law. Now Newton noticed that if a force is applied to a body, the more the magnitude of force, the more is the rate of change of momentum, i.e., if a harder force is applied, the momentum changes faster with time. So he wrote F proportional to change in momentum. Then he realized that the mass of the body also affects the magnitude of force. So he then came to know that it is also proportional to mass. He then wrote the very famous equation, F=kma, where k is a constant of proportionality, which HAPPENED to be unity. So he got F=ma. Voila.
Let us start by stating Newton’s second law of motion. It states that the rate of change of momentum is directly proportional to the force applied and takes place in the direction of the force. F=force, M= momentum, m=mass, v=final velocity, u=initial velocity, t=time and k=proportionality constant. F is directly proportional to the change in momentun M=m*v change in momentum is M=m[v-u] Impulse is force*time. I=f*t impulse=momentum. Therefore,f*t=m[v-u] making f the subject of the formula f=m[v-u]/t remember that f is directly proportional to the rate of change of momentum. Introducing the proportionality constant, f=k*m[v-u]/t acceleration=change in velocity divided by time a=[v-u]/t substituting a into the first formula f=k*m*a if f=1,m=1 and a=1 1=k*1*1,therefore k=1 if k=1, f=1*m*a f=ma.
