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Akhtar, Kiran and Rahul were riding in a motorcar that was mov... - Science
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 a 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 experienced the same force and a change in their momentum. Comment on these suggestions.
The comment on each suggestion based on the laws of motion:
Kiran's suggestion: "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)."
Comment: Kiran's reasoning about the change in velocity is correct, but her conclusion about the change in momentum is incorrect. According to Newton's Third Law and the Law of Conservation of Momentum, during a collision, the change in momentum for both colliding objects is equal in magnitude and opposite in direction. While the insect experiences a much larger change in velocity due to its small mass, the total change in momentum for the insect will be equal in magnitude to the change in momentum for the car.
Akhtar's suggestion: "Since the motorcar was moving with a larger velocity, it exerted a larger force on the insect. And as a result the insect died."
Comment: Akhtar's suggestion is incorrect. According to Newton's Third Law, the force exerted by the motorcar on the insect is equal in magnitude to the force exerted by the insect on the motorcar. The reason the insect dies is not because the car exerts a larger force, but because the insect's tiny mass cannot withstand even an equal force when it causes such a drastic and rapid change in its momentum (and thus, very high deceleration).
Rahul's suggestion: "Both the motorcar and the insect experienced the same force and a change in their momentum."
Comment: Rahul's suggestion is correct.
Same force: By Newton's Third Law, the force exerted by the car on the insect is equal in magnitude and opposite in direction to the force exerted by the insect on the car.
Same change in momentum: By the Law of Conservation of Momentum, the total momentum of the car-insect system is conserved. This means that the change in momentum of the insect is equal in magnitude and opposite in direction to the change in momentum of the car. The insect experiences a much larger change in velocity due to its small mass (Δp = mΔv), but the Δp itself is the same for both.