Mathematical formulation of second law — lesson. Science CBSE, Class 9.

PDF chapter test TRY NOW

Consider an object of mass,

$m$ with an initial velocity,

$u$ is moving along a straight line. It is in uniform acceleration with velocity,

$v$ in time,

$t$ by a constant force,

$F$ .

Initial momentum of the object,

$p_1$

$=$

$m\ u$
Final momentum of the object,

$p_2$

$=$

$m\ v$

$\begin{array}{l} Change in momentum α p_{2} - p_{1} \\ α mv - mu \\ α m \times (v - u) \\ Rate of change of momentum α \frac{m \times (v - u)}{t} \end{array}$

$\begin{array}{l} F α \frac{m \times (v - u)}{t} \\ F = \frac{km \times (v - u)}{t} \end{array}$

Where

$k$ is the constant of proportionality.

$F = k m a$

Here,

$a = \frac{(v - u)}{t}$

The above equation, which implies the rate of change of velocity, is known as acceleration.

Unit of force:

We know that the SI units of mass is

$kg$ and acceleration is

$m\ s^{ –2}$ . The unit of force is selected in such a way that the value of the proportionality constant,

$k$ is one.

A unit of force is known as the amount of force that causes an acceleration of

$1\ m\ s^{ –2}$ in an object having

$1\ kg$ mass.

$1 unit of force = k \times (1 kg) \times (1 {ms}^{- 2})$

Hence, the value of

$k$ becomes one and makes

$F = m a$ .

The SI unit of force is

$kg\ m\ s^{ –2}$ or newton (

$N$ ). The value of one newton is written as,

$1\ N$

$=$

$1\ kg\ m\ s^{ –2}$

The second law of motion implies that the force (

$F$ ) acting on an object is a product of its mass (

$m$ ) and acceleration (

$a$ ).

$F = m a$

Previous theory

Exit to the topic

Next theory

Send feedback

Did you find an error?

Send it to us!

8. Mathematical formulation of second law

Theory: