Physics, asked by Ashwin770, 1 year ago

give derivation of Newton's second law of motion

Answers

Answered by abhi178
1
Newton's second law of motion :- Newton said " if body changes momentum with respect to time, force must be experienced by body and that force is the rate of change of momentum per unit time."

Let mass of body m is moving with velocity \vec{u} and after t times , velocity of it became \vec{v}.
then, initial momentum = m\vec{u}
final momentum = m\vec{v}
change in momentum = m\vec{v}-m\vec{u}

according to Newton's law, force = \frac{\Delta{P}}{\Delta{t}}

= \frac{m\vec{v}-m\vec{u}}{t}

=m\frac{\vec{v}-\vec{u}}{t}

we know, from 1st kinematics equation.
\vec{a}=\frac{\vec{v}-\vec{u}}{t}

so, F=m\vec{a}

hence, \boxed{F=ma} is the formula generated with help of 2nd law of motion
Answered by Anonymous
0

Newton's 2nd law of motion states that ;

" The rate of change of momentum is directly proportional to the unbalance force in the direction of force "

\sf \: Force  \propto  \dfrac{Change  \: in  \: momentum}{Time  \: taken}

Consider a body of Mass m having an initial velocity u. The initial momentum of this body will be mu. Suppose a force F acts on this body for time t & causes the final velocity to become v. The final momentum of this body will be mv. Now,the change in momentum of this body is mv - mu & the time taken for this change is t. So, According to Newton's First Law of Motion :

\large \: \sf \: F  \propto  \dfrac{ mv \:  -  \: mu}{t}

\implies\large \: \sf \: F  \propto  \dfrac{ m(v - u)}{t}

Recall the first equation of motion  

v = u + at

\implies\tt{a=\dfrac{v-u}{t}}

Substitute this value in above one

Hence,

\tt{ F \propto ma }

But we need to remove the proportionality symbol ,

In order to remove it we need to add an proportionality constant.

So,

\tt{ F =k* ma }

k = 1

So,

\tt{F=m*a}

Derived.

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