The physical leaky tank car problem, revisited

An exhaustive analysis of the leaky tank car problem is presented, pointing out its intriguing physical properties, which also well serve to students and teachers for illustrating standard Newtonian mechanics in a highly nonstandard fashion. Calculus is effectively required only to examine some details concerning the solution of the equation of motion and interesting limiting cases, while we unveil all the physical content of the problem, within a proper simple model and its generalization, ranging from the motion of the leaky tank car to that of the water flowing from the car with their peculiarities. Generalizations of the problem to more than one draining hole (even with different sizes), as well as to “two-dimensional” geometries, reveal further intriguing results, culminating into a no-rotation theorem and its corollaries.