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A 100g toy car moving at 3m/s hits a wall at right angles and rebounds at 2.8m/s. The collision with the wall takes 0.25s.

a) Calculate the impulse applied to the wall by the car

b) Calculate the impulse applied to the car by the wall.

The answers for these 2 questions say that the impulse would be 0.58Ns away from the wall and 0.58Ns onto the wall, respectively. However, I am still confused at the notion of "applied impulse". For question a), I interpret it as how the car changes the walls momentum, which, since the wall doesn't have momentum to begin with, shouldn't the correct answer be 0Ns?

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Two bodies that collide exchange momentum. If not fully, then partially. Some amount of momentum is transferred from one body to the other. This is why total momentum is conserved. The amount exchanges is called the impulse, and due to Newton's 3rd law it is applied in equal and opposite measure to the two colliding bodies. In fact is applied through the same point, and the two impulse vectors lie on the same infinite line.

The reason this might be confusing when a ball hits a wall is that after the impact the wall still has zero momentum. Or so it seems. Since the wall is attached to the earth, when a ball impacts a wall, the impulse-momentum does get transferred to the earth but because the mass of the earth is 26 orders of magnitude greater than the ball, it is not noticed.

But go to space and throw a heavy ball against a spaceship and you will see the exchange in momentum where the lighter faster ball will transfer some of its momentum and the heaver spacecraft is going to slowly start moving.

If you do become an astronaut one day and are stationed in space, I do recommend doing this experiment.

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I interpret it as how the car changes the walls momentum, which, since the wall doesn't have momentum to begin with, shouldn't the correct answer be 0Ns?

No. It is true that net change of momentum of the wall is 0 but the impulse by the car is non zero. There are other external forces on the wall by ground such as friction and other constraint forces due to which the total net impulse of the wall is 0.

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  • $\begingroup$ But the impulse on the wall and the Earth to which it is attached is 0.58N $\endgroup$
    – Adrian Howard
    Commented May 8, 2021 at 4:43
  • $\begingroup$ @AdrianHoward I am not following what you are trying to imply. Can you elaborate it please ? $\endgroup$
    – Bhavay
    Commented May 8, 2021 at 4:53

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