Question

Akhtar, Kiran, and Rahul were riding in a motorcar that was moving with a high velocity on an expressway when an insect hit the windshield and got stuck on the windscreen. Akhtar and Kiran started pondering over the situation. Kiran suggested that the insect suffered a greater change in momentum as compared to the change in momentum of the motorcar (because the change in the velocity of the insect was much more than that of the motorcar). Akhtar said that since the motorcar was moving with larger velocity, it exerted a larger force on the insect. And as a result, the insect died. Rahul while putting an entirely new explanation said that both the motorcar and the insect experience the same force and change in their momentum. Comment on these suggestions.

Answer 1

Hint: In the subject of Physics, there are several quantities that are conserved. Conserved quantity is a function of the dependent variables in a dynamically changing system whose value remains equal along with the entire phase and the path that the system undergoes.
Examples of the conserved quantities are mass, charge, energy, and momentum.

Complete step by step answer:
The momentum is defined as the product of mass and the velocity of the body.
Momentum, $p = mv$
where $m$ = mass and $v$ = velocity.
However, this is only the mathematical definition. The momentum of a body represents the effect or impact that it possesses by the virtue of its mass and the velocity at which it is moving. We can understand that momentum represents the consequence of the body moving.
Since we have seen that the quantity momentum is conserved here, let us understand the law of conservation of momentum.
It states that,
In the collision of two elastic bodies, the total momentum of the system before the collision is equal to the total momentum after the collision after the collision has happened.
Consider 2 bodies – object 1 and object 2 of masses ${m_1}$and ${m_2}$ respectively, moving towards each other at initial velocity of ${v_1}\& {v_2}$ respectively and collide. After collision, their new masses are ${M_1}\& {M_2}$ and their new velocities are ${V_1}\& {V_2}$.
Initial momentum, $p = {m_1}{v_1} + {m_2}{v_2}$
Final momentum after collision, $P = M_1V_1 + M_2V_2$
As per the conservation of momentum,
$ p = P $
$\Rightarrow {m_1}{v_1} + {m_2}{v_2} = {M_1}{V_1} + {M_2}{V_2}$
In the case given in the question, let us consider the insect to be object 1 and the car to be object 2.
We will consider the arguments of each of the three and validate by applying the concepts.

i) Kiran
What Kiran says – the insect suffered a greater change in momentum as compared to the change in momentum of the motorcar
The momentum of insect initially, is ${m_1}{v_1}$ and after collision, the momentum changes to ${M_1}{V_1}$
The change in momentum of the insect is ${M_1}{V_1} - {m_1}{v_1}$.
Since the insect becomes stationary after the collision, the momentum of the insect which was very small due to its tiny mass suffers a massive change in the momentum after colliding with the car since the mass of the car and its velocity is comparatively higher.
So, what Kiran says is true.

ii) Akhtar
What Akhtar says – since the motorcar was moving with larger velocity, it exerted a larger force on the insect.
The force is defined as the rate of change of momentum. When the insect hits the car which is moving at a huge velocity and has a huge mass, there is a tremendous force exerted on the insect since its momentum changes drastically, after colliding with the car wherein it absorbs the momentum of the moving car.
So, what Akhtar says is true.

iii) Rahul
What Rahul says – both the motorcar and the insect experience the same force and change in their momentum.
When the insect collides with the car, the car absorbs the momentum of the insect and similarly, the insect absorbs the momentum of the car. While doing so, each of their momentums rises by the same amount. Hence, a change in their momentums is the same.
Since force depends on the rate of change of the momentum, both of them experience the same amount of force on each other.
So, what Rahul says is true.

Note:
In this case, we have considered the case of an elastic collision. An elastic collision is the type of collision where the total energy of the system before the collision remains the same after the collision. However, it is not practical in real life to have elastic collisions. There is always a loss of energy in the system due to collision which comes out in the form of sound, heat, light, and so on.
This is why one of the most major consequences of a collision is the loud sound that it produces.