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1984年在瑞典斯德哥尔摩举行的第十五届国际物理奥林匹克竞赛中,有一道关于求湖震周期的力学题目。这道题设计别致,构思合理。解答首先把实际问题抽象为理想模型,再进行理论求解,最后又通过实验对理论值进行验证和修正。不仅指出了学习物理的基本方法,而且也符合认识事物的一般规律。确是一道有助于学生能力培养的好题。为了开扩学生的思路以及对所给答案的缺点作必要的完善,本文用等效摆长法解答此题。原题及解答参见《物理教学》1984年12期33页。解答图中实线表示水面的平衡位置,虚线表示振荡某瞬间水面的位置。我们选平衡位置的质心为坐标原点。因为水槽宽度相同,均匀对称,用纵切面直角梯形代表。下面分四部求解: 1.质心坐标: 两块三角形的质心分别为(x_1,y_1)、(x_2,y_2),下面矩形的质心坐标为(0,0)
In the fifteenth International Physics Olympiad held in Stockholm, Sweden in 1984, there was a mechanics question about the period of the lake. This question is unique in design and reasonable in design. The solution first abstracts the actual problem into an ideal model, then solves it theoretically, and finally verifies and corrects the theoretical value through experiments. Not only pointed out the basic method of learning physics, but also in line with the general laws of understanding things. It is indeed a good question that helps students develop their abilities. In order to expand students’ thinking and make necessary improvements to the shortcomings of the given answer, this paper uses the equivalent pendulum length method to solve this problem. The original question and answer see “Physics Education” 1984 12 33 pages. The solid line in the solution diagram indicates the equilibrium position of the water surface, and the dashed line indicates the position of the water surface at the moment of oscillation. We choose the center of mass of the equilibrium position as the origin of coordinates. Because the tank width is the same and it is evenly symmetrical, it is represented by a right-angle trapezoid on the longitudinal section. The following four parts are solved: 1. Centroid coordinates: The centroids of the two triangles are (x_1, y_1), (x_2, y_2), and the coordinates of the center of the rectangle below are (0, 0).