Grade 12th passMechanics

State and explain Newton`s second law of motion with appropriate example

Biplob Mondol

8 Years agoGrade 12th pass

1 Answer

Arun

8 Years ago

Newton’s Second Law

Force `F` Applied by a Man on a Body Having Mass `M`.

The rate of change of momentum of a body is directly proportional to the impressed force and takes place in the direction of the force.

Newton’s first law provides a qualitative definition of the force while second law provides a quantitative definition of the force.

Let $\vec{v}$ be the instantaneous velocity of the body. Momentum $\vec{p}$ of the body is given by,

$\vec{p} = m\vec{v}$

According to second law,

$\vec{F}$ ∝ (rate of change of momentum)

Or,

$\vec{F}\alpha \frac{d\vec{p}}{dt}$

Or,

$\vec{F}\alpha \frac{d(m\vec{v})}{dt}$

Or,

$\vec{F}\ =k \frac{d(m\vec{v})}{dt}$

Here ‘k’ is the constant of proportionality. Mass ‘m’ of a body is considered to be a constant quantity.

$\vec{F}\ =k m\frac{d(\vec{v})}{dt}$

or,

$\vec{F}\ =k m\vec{a}$

The units of force are also selected that ‘k’ becomes one.

Thus, if a unit force is chosen to be the force which produces a unit acceleration in a unit mass,

i.e., F = 1, m = 1 and a = 1.

Then, k = 1

So, Newton’s second law can be written , in mathematical form, as

$\vec{F}\ =m\vec{a}$

i.e., Force = (mass) (acceleration)

This provides us a measure of the force.

Here, if F = 0 then we find a = 0. This reminds us of first law of motion. That is, if net external force is absent, then there will be no change in state of motion, that means its acceleration is zero.

Further we can extend second law of motion, (in fact its decomposition) to three mutually perpendicular directions as per our coordinate system.

If components in x, y and z direction are Fx, Fy & Fz respectively, the three acceleration produced when Fx, Fy & Fz act simultaneously) in the body are, Now,

three-forces