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conservation of linar momentum - variable mass

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If a railroad car traveling down a straight, frictionless track encounters vertical rain that fills it with additional mass, will the velocity decrease in order for the momentum to be conserved? Will the opposite happen if the water is let out from a hole in the bottom?

I cannot see any external forces to affect the system, but the fact that velocity is changing calls for acceleration, which calls for a force - I am having a hard time wrapping my mind around it. How can the velocity of the car change without any work being done?

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