Question

Give the quantitative expression of force.

Answer 1

Step1: Newton's second law

1. Newton's second law describes the relationship between the three quantities, as given below.
2. The rate of change of momentum of a body is equal to the force exerted on the body in a given direction, according to Newton's second law of motion.

Step2: Formula used

Consider a body with mass$‘m’$ that moves at velocity $‘v’$. As a result, the body's momentum $‘p’$ is given by,

$p=mv$

Step3: Relation between acceleration, mass, and force

We now know that the rate of change in momentum of a body is equal to the force applied to the body thanks to Newton's second law of motion. As a result, the force F equals, $F=\frac{dp}{dt}=\frac{d\left(mv\right)}{dt}[Asp=mv]$

$F=v\frac{dm}{dt}+m\frac{dv}{dt}...........equtaion\left(i\right)$

The acceleration $‘a’$ of a body is defined as the rate of change of velocity i.e. $\frac{dv}{dt}$

Since mass does not change with the time equation (i) can be written as,

$$\begin{gathered} F=v\frac{dm}{dt}+m\frac{dv}{dt} \\ F=v\left(0\right)+ma \\ F=ma \end{gathered}$$

Hence the quantitative expression of force is $F=ma$