论文标题
重新审视的物理漏水车问题
The physical leaky tank car problem, revisited
论文作者
论文摘要
提出了对漏水的坦克汽车问题的详尽分析，指出了其有趣的物理特性，这些物理特性很好地为学生和老师提供了以高度非标准的方式说明牛顿力学的标准力学。有效地需要进行微积分（在领先的本科水平上）才能检查有关运动方程和有趣的限制案例解决方案的一些细节。取而代之的是，我们让任何学生在适当的简单模型及其概括中欣赏问题的所有物理内容，从漏水的坦克汽车的运动到从汽车上以其特殊性流出的水的运动。该问题对一个以上的排水孔（即使有不同的尺寸）以及“二维”几何形状的概括，揭示了进一步的有趣结果，最终导致了无旋转定理及其成果，从而使学生在手中允许学生充分识别身体分析的能力。
An exhaustive analysis of the leaky tank car problem is presented, pointing out its intriguing physical properties, which well serve to students and teachers for illustrating standard Newtonian mechanics in a highly non-standard fashion. Calculus (at a leading undergraduate level) is effectively required only to examine some details concerning the solution of the equation of motion and interesting limiting cases. Instead we let any student to appreciate 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, thus rendering unique the problem at hand for allowing students to fully recognize the power of physical analysis.
