Derive relation F = ma from Newton 2nd Law of Motion
Let us derive the relation of force F = ma from Newton’s second law:
According to the Newton’s 2nd Law of motion, the rate of change of linear momentum of a body is directly proportional to the applied external force and in the direction of force.
It means that the linear momentum will change faster when a bigger force is applied.
Consider a body of mass ‘m’ moving with velocity v.
The linear momentum of a body is given by:
p = mv
Now According to Newton’s 2nd Law of Motion:
Force is directly proportional to rate of change of momnetum, that is
F α dp/dt
F = k dp/dt
F = k d(mv)/dt
F = k md(v)/dt
F = k ma
Experimentally k =1
F = k ma
Which is the required equation of force.
9 thoughts on “Derive relation F = ma from Newton 2nd Law of Motion”
Hey it’s too good i clearly understood the law
its to good we can easily get 3 marks in examination
it would be clearer if u mentioned p=mv and v/t=a and thus ma arises out,
anyways good work and thanks.
From F=ma, if we derive for acceleration it is, a=F/m…As per this the unit of acceleration would become Newton/Kilogram (N/kg)…
But the actual unit of acceleration is m/s^2…
I am confused…
A Newton is a kgm/s^2. So a kgm/s^2/kg leaves a unit of m/s^2. You just have to break the Newton down into its components to cancel the kg and get the acceleration in typical units.
I have been lurking though the textbook and guides to understand the derivation !
This finally helped me ! Thanks a lot
I cannot understood it properly…….
What is the meaning of-dp & dt??!!!
Take care when you equate Newtonian linear distance d and the circumferential distance which is pi x d (diameter). This holds on knowing that Einstein’s energy is radiated energy and hence involves circular geometry. Otherwise you cannot derive Einstein’s infamous energy formula from Newton’s second law of motion!!!