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笔者曾对杆秤的几个问题作过定性的阐述,下面用数学的方法再作定量的讨论,以期对它的认识更清晰些、更深刻些。一根杆秤,A为刻度起点(如图1),当秤钩上挂有质量为m的重物时,秤砣(质量为m_2)放在D点,恰使杆秤平衡,则有: AD=OB/m_2·m (1) 对同一杆秤,刻度比例OB/m_2是一个恒量,因此AD与m成正比,如以m为横坐标,AD为纵坐标,其函数图象如图2所示。下面讨论几种情况: 1.秤杆断去一段:
The writer has made some qualitative explanations on several problems of the steelyard. The following is a quantitative discussion with the mathematical method, in order to understand it more clearly and profoundly. A steelyard scale, A is the starting point of the scale (as shown in Figure 1). When the weight of mass m hangs on the scale hook, scale 砣 (mass m_2) is placed on point D, just balance the steelyard scale, then there is: AD=OB /m_2·m (1) For the same scale, the scale ratio OB/m_2 is a constant, so AD is proportional to m. For example, m is the abscissa and AD is the ordinate. The function image is shown in Figure 2. Several situations are discussed below: 1. The balance bar breaks off: