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A cistern rail car is standing on infinitely slippery ice. The cistern is filled with water and it has an outlet in the form of a thin vertical pipe (spout) at the left end, so when the valve is open the water can escape vertically downward (in the car frame of reference). Initially the system is at rest, the valve closed. Then we open the valve and the cistern starts moving (presumably to the right). However the water dropping out must be moving (slipping on the ice) in the same direction as the cistern, according to the spout geometry. So we end up with everything moving in the same direction (say, to the right) in spite of initially having zero momentum. How to resolve this paradox? What will be the motion of the cistern in the process of water leaking out? How will the water on the ground and the cistern be moving after all water leaks out?

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Maxim Umansky
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    Done before: http://physics.stackexchange.com/questions/1683/mechanics-around-a-rail-tank-wagon. – dmckee --- ex-moderator kitten Jul 11 '13 at 20:43
  • Oops! That's the same question indeed, did not know it was there. But it is a good one. – Maxim Umansky Jul 11 '13 at 21:29
  • It is a good question and understanding it completely means you know something about classical mechanics. Unfortunately the Stack Exchange engine doesn't have a time ordered or threaded presentation for all the content so it is hard to see how things evolved, but there is a lot of good commentary under the old version. – dmckee --- ex-moderator kitten Jul 11 '13 at 21:38

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In this example, as the center of mass of the water moved to the left, you would develop a current in the water that would have to be stopped by the walls of the car. This would produce a net force on the car, which would move it so that the center of mass of the car-water system would not move. In reality, dissipative effects would probably prevent net motion.

Zo the Relativist
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