Question

Explain newton's law .

Ex- 1st law , 2nd law , 3rd law .

Note : Don't copy , Don't spam .

Answer 1

Newton's law of motion:

☀ Newton's law of motion - Newton is the father of physics and he established the laws of motion in his book named Principia in the year 1667. There are three Newton's law of motion.

Newton's first law of motion:

☀ Every body maintain it's initial state of rest or motion with uniform speed on straight line unless an external force act on it. In short, an object continuous to be in a state of rest or of uniform motion along a straight line unless acted upon by an unbalanced force.

◆ It's also known to be law of Galileo or law of inertia.

♛ Law of inertia = It is the property of a body by virtue of which the body opposes change in it's initial state of rest or motion with uniform speed on a straight line.

There are 2 types of inertia:

⑴ Inertia of rest

⑵ Inertia of motion

Some examples of inertia:

⑴ When a coat /blanket is beaten by a stick the dust particles are removed.

⑵ When a car start suddenly the passenger bends backwards.

Newton's 2nd law of motion:

☀ The rate of change in momentum of a body is directly proportional to the applied force on the body and take place in the direction of force.

If F = force applied ; a = acceleration produced and m = mass of body then Force = Mass × Acceleration

◆ Newton's second law gives the magnitude of force.

◆ Newton's first law is contained in the second law.

♛ Force - It is that external cause which when acts on a body changes or tries to change the initial state of the body.

♛ Momentum - It is that property of a moving body and is defined of mass and velocity of the body. It's a vector quantity. SI unit is kg m/s.

$\: \: \: \: \: \: \:{\bf{Momentum = \: Mass \times Velocity}} \: \: \: \: \green\star$

F = ma that is Newton's second law of motion, where F is the force exert on a body, m is the mass and a is the acceleration.

Let us derive this formula!

According to the statement, let us assume that an object of mass m is moving in a straight line with an initial velocity u. Afterwards it is accelerated(uniformly) to the final velocity v and take time t. Now the constant force F is applied through the time t. The initial and final momentum of the object will be ${\sf{p_1}}$ as ${\sf{mu}}$ and the ${\sf{p_2}}$ as ${\sf{mv}}$

Knowledge required: p = m × v i.e., Momentum = Mass × Velocity

The change in momentum

⠀⠀⠀⠀⠀⠀∝ ${\sf{p_2 \: - p_1}}$

⠀⠀⠀⠀⠀⠀∝ ${\sf{mv \: - mu}}$

⠀⠀⠀⠀⠀⠀∝ ${\sf{m(v-u)}}$

The rate of change of momentum

⠀⠀⠀⠀⠀⠀∝ ${\sf{\dfrac{m(v-u)}{t}}}$

Or when the force applied

⠀⠀⠀⠀⠀F ∝ ${\sf{\dfrac{m(v-u)}{t}}}$

⠀⠀⠀⠀⠀F = ${\sf{\dfrac{km(v-u)}{t}}}$

⠀⠀⠀⠀⠀⠀= kma

We write a at the place of ${\sf{\dfrac{(v-u)}{t}}}$ because of the formula of acceleration. Here, k is constant proportional.

⠀⠀⠀⠀⠀We already know that mass and acceleration have SI units as kg and m/s² respectively. So we can make the SI unit of force by using there two SI units.

⠀⠀⠀⠀⠀⠀⠀⠀⠀The unit of force is so chosen then k became one.

⠀⠀⠀⠀Knowledge required: The one unit of the force is defined as the the amount that produces an acceleration of 1 m/s² in an object of 1 kg mass. Therefore,

↪️ 1 unit of force = k(1 kg)(1 m/s²)

↪️ 1 unit of force = 1(1 kg)(1 m/s²)

↪️ F = kma

↪️ F = 1ma

↪️ F = ma Henceforth, proved!

Newton's 3rd law of motion:

☀ Every action is equal to every reaction but in opposite direction. In short, To every action, there is an equal and opposite reaction and they act on the two different bodies.

Some examples -

⑴ Motion of the rocket.

⑵ Recoil of the gun.

Answer 2

NEWTON'S LAW OF MOTION :

Let a body is moving with a velocity 'u'. When a force is applied its velocity becomes 'v' in time 't'

Initial Velocity → u

Final Velocity → v

1st Law :

$\sf \therefore \small Change \: in \: velocity \: = Final \: Velocity – Initial \: Velocity$

= v – u

$\sf \small Acceleration = \frac{change \: in \: velocity}{time}$

$\boxed{ \purple{\rarr \sf \small a = \frac{v - u}{t} }}$

at = v – u

$\sf \small v = u + at$

$\boxed{ \purple{ \sf \small v = u + at }} \rarr \mathfrak{Newton's \: 1st \: Law \: of \: Motion}$

2nd Law :

Distance(S) = average velocity × time

$\sf \small S = (\frac{v + u}{t} ) \times t$

$\sf \small S = ( \frac{u + at + u}{2} ) \times t$

$\sf \small S = ( \frac{2u + at}{2} ) \times t$

$\boxed{ \blue{\sf \small\: S = ut + \frac{1}{2} a {t}^{2} }} \rarr \mathfrak{Newton's \: 2nd \: Law \: of \: Motion}$

3rd Law :

Again,

$\sf \small S = ( \frac{v + u}{2} ) \times t$

$\sf \small S = \frac{v + u}{2} \times \frac{v - u}{a}$

$\sf \small 2aS = {v}^{2} - {u}^{2}$

$\boxed{ \green{ \sf \small {v}^{2} = {u}^{2} + 2aS}} \rarr \mathfrak{Newton's \: {3}^{rd} \: Law \: of \: Motion}$

More Information :

• The average velocity of an object is its total displacement divided by the total time taken.

• In other words, it is the rate at which an object changes its position from one place to another.

• Average velocity is a vector quantity.