Question

Explain Newton's second law of motion with the help of an example.

Answer 1

Hint: To answer this question, we need to focus on the basic statement of the second law. Using that, we have to take a suitable example from day to day life.

Complete step-by-step solution
Newton's second law of motion states that the force applied on a body is directly proportional to its rate of change of momentum.
\[F \propto \dfrac{{dp}}{{dt}}\] (1)
To explain this law, we take the example of a bullet of mass \[m\] fired on a wooden block. Let the speed of the bullet be \[v\]. After passing through the wooden block the bullet will finally come to rest. Hence the final velocity of the bullet will be zero.
\[\therefore \]change in momentum \[ = \] Final momentum-Initial momentum
\[\Delta p = m(0) - mv\]
\[\Delta p = - mv\] (2)
So, a momentum change of \[mv\] is there.
The following two cases are considered.
Case I –
When the bullet is high enough, it will pierce the wooden block, before coming to the rest.
Case II –
When the speed of the bullet is moderate, it will not cause much damage to the wooden block.
In the first case, the bullet has a higher speed than in the second case.
From (2), this means that the change in momentum is greater in the first case than in the second case in the given amount of time. Thus, the rate of change of momentum is greater in the first case.
Also, the wooden block is pierced completely in the first case. But it is not much affected in the second case. This means that a greater force is applied by the bullet on the wooden block in the first case.
Thus, a greater change in momentum implied a greater amount of force applied. This is Newton's second law of motion.

Note: The Newton’s second law of motion can be also be explained by the given examples:
A cricketer catching a ball draws in the hands in the backward direction to prevent from getting hurt.
A person falling from a height on a flat surface gets serious injuries. But the same person falling from the same height on the sand gets only slightly hurt.
Buffers are provided in the vehicles to prevent shocks.