The windshield of a speeding car hits a hovering insect. Consider the time interval from just before the car hits the insect to just after the impact. Which of the following are correct? (Select all that apply.)

Choose the system so that the change of momentum zero. Compare the change of momentum and the change in velocity of the car and the bug, respectively.

The system consists of the bug alone. The system consists of the bug plus the car. The magnitudes of the change of velocity are equal for car and bug. The magnitude of change of momentum of the car is bigger that that of the bug. The magnitude of change of momentum of the bug is bigger than that of the car. The system consists of the car alone. The magnitude of change of velocity of the car is bigger than that of the bug. The magnitudes of the change of momentum are equal for car and bug. The magnitude of change of velocity of the bug is bigger than that of the car.

b) True. The system is the two bodies,

g) True. change of velocity of the car is bigger than that of the bug

h) True. The moment is preserved

Explanation:

This is a problem of collision between two bodies, we are asked to use a reference system where the momentum change is zero, this is the reference system of the center of mass; in this reference system the speeds are measured with respect to the center of mass of the system.

The speed of the expensive

             v’_car = v -

Insect speed

            v’_insect = 0 + v_{cm}

In this system the moment is conserved

            M v’_car + m (-v’_insect) = 0

The negative sign is because the insect approaches the car

          M (v –v_{cm}) - m v_{cm} = 0

          v_{cm} = v  M / (m + M)

In this System after the shock the body does not move with respect to the center of mass

With this analysis let's review the statements:

a) False. The system consists of the two bodies, their speeds

b) True. The system is the two bodies, their speeds

c) False. What is the same is the change of moment

d) False. The moment change is zero by using the center of mass system

e) False are the same

f) False is system are the two bodies

g) True. Yes because it is the body with the greatest mass and must remain immobile after the crash

h) True. The moment is preserved

i) False. The insect must remain immobile after the crash and its speed of the center of more so that it is less than that of the car

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