Question

Derive the relationship between force and momentum.

Answer 1

Step 1: Deriving the relationship between force and momentum

1. According to the second law of Newton, the rate of change of momentum of an object is directly proportional to the resultant force applied and is in the direction of the resultant force.
2. Consider $m$ is the mass of an object, moving with the initial velocity $u$ and the velocity changes to$v$ in time interval t.
3. From Newton's second law

$$\begin{gathered} F\propto \frac{Changeinlinearmomentum}{timeinterval} \\ F\propto \frac{mv-mu}{t} \end{gathered}$$

Here $mv$ is the final momentum and $mu$ is the initial momentum

$F=k\times \frac{m(v-u)}{t}$ Where k is the constant of proportionality.

Experimentally the values of $k=1$

$F=m\left(\frac{v-u}{t}\right)$ or $F=\frac{dp}{dt}$

Hence derived.