A car of mass 2045 kg moving in the x direction at a speed of 29 m/s strikes a h

Question

A car of mass 2045 kg moving in the x direction at a speed of 29 m/s strikes a hovering mosquito of mass 2.5 mg, and the mosquito is smashed against a windshield. The interaction between the mosquito and the windshield is an electric interaction between the electrons and protons in the mosquito and those in the windshield. a) What is the approximate momentum change of the mosquito? Give magnitude and direction. b) At a particular instant during the impact, when the force exerted on the mosquito by the car is F, what is the magnitude of the force exerted on the car by the mosquito? c) What is the approximate momentum change of the car? Give magnitude and direction. Explain any assumptions you make. d) Qualitatively, why is the collision much more damagin to the mosquito than to the car?

Explanation / Answer

Here,

mass of car ,M = 2045 Kg

speed of car , u1 = 29 m/s

mass of mosquito , m = 2.5 *10^-3 gm

a) as the final velocity is equal to car .

change in momentum of mosquito = m * u1

change in momentum of mosquito = 2.5 *10^-6 * 29 Kg.m/s

change in momentum of mosquito = 7.25 *10^-5 Kg.m/s

direction of change in momentum is positive x direction

b)

According to Newton's third law

magnitude of force exterted on car by mosquito = magnitude of force exerted by car on mosquito

magnitude of force exterted on car by mosquito = F

c) as the mass of car is very large than mosquito

the approximate momentum change of the car is 0.

d) as a very small force acts on both ,

due to mass of car, the motio of car is not changed a lot.

that's why it is more damaging to the mosquito than car.

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