Can Momentum Be Conserved in Different Collision Scenarios?

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The discussion focuses on the conservation of momentum in various collision scenarios involving two objects, A and B. It explores situations where A is moving and collides with stationary B, considering outcomes where they move in the same direction, opposite directions, or where one is stationary. Key points include that A can move B if A's mass is significantly smaller, and that both objects must move post-collision to conserve momentum. The conversation highlights that if both are stationary, momentum conservation is violated, as energy would convert to other forms. Overall, the analysis emphasizes the necessity of movement in all collision scenarios to uphold the principle of momentum conservation.
Meowzers
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So, I am trying to grasp the concept of conservation of momentum. I need someone to just look over my reasonings (and correct me for any errors) for the following situation.

Let's say there are two objects, A and B. A is moving and then it has a head-on collision with object B, which is stationary. There are no external forces acting upon the objects. So, I'm trying to figure out which of the following situations are possible.

-A and B move in the same direction - I say this is possible if object A has a mass that is much greater than B. This way, when the objects collide, object A's velocity barely gets changed after colliding with B.

-A and B move in opposite directions - This is possible - I saw a lot of demonstrations showing this result.

-A moves and B is stationary - I think this is possible. It's like the reverse of the first situation. The mass of A is a lot smaller than B so that it just bounces off B.

-A is stationary and B moves - I think this is possible. Elastic collision? It's like that toy where you pull back one ball, and the one on the opposite end flies off at the same veleocity.

-A and B are both stationary - This one I'm not sure about. Isn't it possible that the KE turns into other forms of energy. But then, the conservation of energy formula wouldn't work.

m1v1 + m2(0) = m1(0) + m2(0)
m1v1 = 0. That means the ball either has no mass or no velocity, which wouldn't work for the problem.
 
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Your thinking is not bad when you say B could be stationary when A is much less massive than B, but in fact B has to move some. Even the Earth moves under you feet when you jump up and down.

The last one would violate conservation of momentum. The masses could stick together, with almost all the energy being lost, but even if they stick they both have to move.
 
Thank you very much for your help!
 
Meowzers said:
-A moves and B is stationary - I think this is possible. It's like the reverse of the first situation. The mass of A is a lot smaller than B so that it just bounces off B.

If A has momentum moving towards the right, hits B, and moves towards the left, what happened to its momentum?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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