Question

State Newton’s second law of motion.

Answer 1

Hint: Try to understand the concept of Newton’s second law of motion. Write the equation of force in terms of rate of change of momentum. Simplify the second law of motion in terms of the equation of force from in terms of mass and acceleration.

Complete step-by-step answer:
Newton's second law of motion can be expressed as the rate of change of momentum of an object is directly proportional to the applied force on the object and the change in momentum takes place in the direction of the applied force.
If an external force F acts on a body of mass m for time t the body will accelerate and let the velocity of the object will change from $v$ to $v+\mathrm{\Delta }v$.
The initial momentum of the object will be $p=mv$
The final momentum will be $p+\mathrm{\Delta }p=mv+m\mathrm{\Delta }v$
Change in momentum will be, $\mathrm{\Delta }p=m\mathrm{\Delta }v$
According to the second law of motion,
$\begin{array}{rl}& F\propto {\displaystyle \frac{\mathrm{\Delta }p}{\mathrm{\Delta }t}}\\ & F=k{\displaystyle \frac{\mathrm{\Delta }p}{\mathrm{\Delta }t}}\end{array}$
Where k is the proportionality constant.
Taking the limit $\mathrm{\Delta }t\to 0$ , we can write,
$F=k{\displaystyle \frac{dp}{dt}}$
Now, if we consider the object has fixed mass m, then
${\displaystyle \frac{dp}{dt}}={\displaystyle \frac{d\left(mv\right)}{dt}}=m{\displaystyle \frac{dv}{dt}}=ma$
Where a is the acceleration of the object.
i.e. we can write the second law as
$F=kma$
We can define unit force from the above equation. So, we can take the value of k as 1.
So, we can write,
$F=ma$
From the second law of motion we can get this equation for force.
The SI unit for force in Newton.

Note: Newton’s laws of motion are built on the concept of Galileo’s laws of motion. Newton’s second law of motion is also known as the law of force and acceleration as an applied force on an object causes the object to accelerate.