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I'm studying a problem involving the scattering of two charged particles, A and B, with a mass ratio of 1:4 and identical charges. The particles move towards each other with equal and opposite velocities.

I'm trying to understand their motion at the point of nearest approach. Specifically, I'm confused about whether the particles would momentarily stop and reverse directions or move with the same velocity toward one of the initial positions, specifically the initial position of the lighter particle.

Could someone help clarify the underlying physics that dictates the behavior of such a system? Does the Coulomb interaction affect the conservation of momentum? I think not because it's an internal force in this case.

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    $\begingroup$ I get the final velocities to be ¹⁄₅v for the 4m mass and ¹¹⁄₅v for the m mass, both towards the initial position of the m mass. i.e. the 4m mass carries on in the same direction but reduces speed from v to ¹⁄₅v while the m mass slows to a halt and bounces back. But they don't have the same final velocity so (c) cannot be true. $\endgroup$
    – John Rennie
    Commented Nov 7, 2023 at 16:36
  • $\begingroup$ @JohnRennie, I gave it some extra thought and convinced myself that a cannot be true. However, if you assume that after the approach they momentarily have the same speed, that would be 3/5 v. How did you arrive at 11/5 v and 1/5 v? $\endgroup$
    – cconsta1
    Commented Nov 7, 2023 at 16:47
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    $\begingroup$ Ah, so (c) just means there is a moment at which their speeds are equal not that the final speeds are equal. Always, always, treat collisions in the centre of momentum frame. This makes it easy to see what happens. $\endgroup$
    – John Rennie
    Commented Nov 7, 2023 at 16:50
  • $\begingroup$ @JohnRennie, thank you! The center of mass motion always gave me headaches. Can you suggest any good references to give it another try? $\endgroup$
    – cconsta1
    Commented Nov 7, 2023 at 16:55

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The initial momentum of the system is directed toward A, the lighter particle. At the time of nearest approach, the two particles are at rest in the center of mass system, so they are moving with the same velocity in the laboratory system. With conservation of momentum, the momentum and common velocity are toward the initial position of particle A.

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