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- Mechanics around a rail tank wagon 11 answers
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?