Question

Which law gives a quantitative measurement of the force?

Answer 1

Newton's second law of motion:

1. Force is equal to the rate of change of momentum. For a constant mass, force equals mass times acceleration.
2. Suppose an object is moving in a straight line, let $\mathrm{m}$ be the mass of an object moving with initial velocity $\mathrm{u}$ and reachs final velocity of $\mathrm{v}$. If an external force $\mathrm{F}$ is applied for time $\left(\mathrm{t}\right)$ creating an acceleration of $\mathrm{a}$. Then,

$$\begin{gathered} \mathrm{Force}\propto \frac{\mathrm{final}\mathrm{momentum}-\mathrm{initial}\mathrm{momentum}}{\mathrm{time}} \\ \mathrm{Force}\propto \frac{\mathrm{mv}-\mathrm{mu}}{\mathrm{t}} \\ \mathrm{Force}\propto \frac{\mathrm{m}(\mathrm{v}-\mathrm{u})}{\mathrm{t}} \\ \Rightarrow \mathrm{F}=\mathrm{kma} \end{gathered}$$

Here, $\mathrm{k}$ is proportionality constant.

3. If 1 unit force is applied on the mass of $1\mathrm{kg}$ and the acceleration created is$1\mathrm{m}/{\mathrm{s}}^2$.

then,$\mathrm{k}=1$

$\Rightarrow \mathrm{F}=\mathrm{ma}$

Hence, Newton's second law of motion gives a quantitative measure of force.