Problem in law of conservation of linear momentum

Question

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?

Did you ever tried to play with spring? Suppose you compress and decompress it say 20 times quickly. Try! — kakaz, Dec 04 '17 at 19:39
The collision happens in a single instant, and there isn't any time passing to change the elongation of the spring. — John Alexiou, Dec 04 '17 at 21:22
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. — Chet Miller, Dec 05 '17 at 00:39
Possible duplicate of Contradiction between law of conservation of energy and law of conservation of momentum? — sammy gerbil, Dec 05 '17 at 12:22

JohnV2 · Answer 1 · 2017-12-05T19:23:59.650

1

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.

edited Dec 05 '17 at 19:23

answered Dec 05 '17 at 03:43

JohnV2

37

+1 Nothing wrong with this succinct answer. The down-vote is not justified. – sammy gerbil Dec 05 '17 at 12:27

Problem in law of conservation of linear momentum

1 Answers1