Question

How does the second law of motion give us a method to measure force?

Answer 1

Newton's second law:

Newton's second law of motion states that the applied force on an object can be given by the product of the mass of the object and the acceleration produced in it.

If $\text{'}m\text{'}$ is the mass of an object, $\text{'}u\text{'}$is the initial velocity,$\text{'}v\text{'}$ is the final velocity, and $\text{'}t\text{'}$is the time taken, then by the statement of the second law of motion, force is given by,

$$\begin{gathered} \Rightarrow Force\propto Rateofchangeofmomentum=\frac{Changeinmomentum}{time} \\ \Rightarrow Force\propto \frac{(FInalmomentum-Initialmomentum)}{time} \\ \Rightarrow F\propto \frac{(mv-mu)}{t} \\ \Rightarrow F\propto \frac{m(v-u)}{t} \\ \Rightarrow F\propto ma \\ \Rightarrow F=kma \\ Theunitofforceischoseninsuchamannerthatthecons\tan tofproportionalitykbecomesone \\ If,k=1 \\ \Rightarrow F=ma \end{gathered}$$

Hence, the second law of motion $F=ma$ gives us a method to measure force.