Question

Derive the expression for the expression of force.F=Kma

Answer 1

From Newton’s first law of motion, it is clear that any change in the velocity, or consequently the momentum, is caused by a force. Intuitively, it also makes sense that for a given time interval (say, one second), the greater the force that acts on a particle, the greater is the change in velocity of that particle; and similarly, the more massive a particle, the less change in velocity it undergoes when subjected to the same force for the same duration as a lighter particle. This is expressed mathematically in Newton’s second law of motion by defining the force to be proportional to the rate of change of momentum:

F = Kma.

Up to this point in Physics, there has been no formal definition for a force. Thus, we really have the freedom to choose the value of K as this is the defining equation for the force! In the SI units, we choose K to be 1. If you’re confused as to why we have this freedom, consider the expression for the work done:

Work done = Force*Displacement (note that is a scalar product of the vectors Force and Displacement).

One might as well have defined the work done to be some arbitrary constant K times the expression on the right hand side in the above equation!

Contrast this with the Newton’s law of gravitation where the universal Gravitational constant, G, appears in the expression. Here, since we have already defined what a force is, we no longer have the freedom of fixing the value of the constant G as the quantities that are related by the equation are already well-defined.

In conclusion, the question as to the accuracy of F = ma does not even make sense (in the present context involving the choice of K) as this is how we have defined the force - we have not deduced the value of K from somewhere else.




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Answer 2

$\huge\textbf{Answer}$


» Expression for force


F $\alpha$ dP/dt

F = k dP/dt

F = k d(mv)/dt

F = k m d(v)/dt

F = k ma

Here; k = 1

F = ma