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enter image description here

Suppose the above system moves with a velocity $v$ and collides into a wall.

The spring compresses and stores the energy, so energy is conserved.

However during the collision the spring compresses.

How is momentum conserved as during the compression the speed of the block reduces?

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    $\begingroup$ What about the wall? $\endgroup$ Dec 4, 2017 at 19:35
  • $\begingroup$ Did you ever tried to play with spring? Suppose you compress and decompress it say 20 times quickly. Try! $\endgroup$
    – kakaz
    Dec 4, 2017 at 19:39
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    $\begingroup$ The collision happens in a single instant, and there isn't any time passing to change the elongation of the spring. $\endgroup$ Dec 4, 2017 at 21:22
  • $\begingroup$ What @GregPetersen is getting at is that the wall is attached to the earth. When the collision you describe takes place, the momentum of the wall and earth changes. But, on the scale of the mass of the earth, the associated velocity change of the earth is very slight. $\endgroup$ Dec 5, 2017 at 0:39
  • $\begingroup$ Is the wall on the left or on the right on the diagram? $\endgroup$ Dec 5, 2017 at 0:53

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Momentum is conserved at all times, including during the collision. The apparent violation of conservation of momentum is because the mathematical “wall” has an infinite mass.

Try replacing the wall with a large mass, maybe 100m, and see what happens. Now make it 1000x bigger. And so on. As it gets more massive it has less velocity after the impact but it always has the same momentum, and momentum of the system will always be conserved. The limit as the mass of the wall approaches infinity is a post-collision velocity of zero.

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  • $\begingroup$ +1 Nothing wrong with this succinct answer. The down-vote is not justified. $\endgroup$ Dec 5, 2017 at 12:27

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