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物理变换是研究物理学的一种重要思维方法。在解题的教学中,教师如能引导学生掌握一定的变换规律进行分析和推理,就能更好地收到启迪学生思维,开拓学生思路,提高解题技能的效果。下面准备通过几个具体例题的分析谈谈变换在解题时所起的重要作用,以及探讨几种变换的途径。[例1]将三个电阻 R_1=13Ω,R_2=6.5Ω,R_3=1.3Ω并联,求并联后的总电阻。解析:此题所给模型非常简单,只有三个电阻并联。按照习惯的思维,求总电阻时利用公式1/R=1/R_1+1/R_2+1/R_3,亦并不算繁琐。但,如果我们注意三个电阻的阻值特征,冲破常规的思维指向,就可以将“三个电阻并联”的模型变换成“十三个 R_1的并联”模型,迅速得出 R=1Ω的结论。[例2]质量为 m,电量为 q 的带电粒子,垂直磁场方向从 A 点射入磁场口中,途经 P 点,AP 连线与入射方向夹角为θ,粒子从 A 到 P 经历的时间是:
Physical transformation is an important way of thinking in studying physics. In the problem-solving teaching, if teachers can guide students to master certain transformation laws for analysis and reasoning, they can better receive enlightenment on students’ thinking, open up students’ thinking, and improve the effect of solving problems. The following preparations will be used to discuss the important role of transformation in solving problems through the analysis of several concrete examples, and to explore several ways of transformation. [Example 1] Three resistors R_1 = 13Ω, R_2 = 6.5Ω, and R_3 = 1.3Ω are connected in parallel to obtain the total resistance after the parallel connection. Analysis: This model gives a very simple model with only three resistors in parallel. According to the customary thinking, using the formula 1/R=1/R_1+1/R_2+1/R_3 when calculating the total resistance is not too much trouble. However, if we pay attention to the resistance characteristics of the three resistors and break through the conventional way of thinking, we can transform the “three resistors in parallel” model into “13 R_1 parallel” models and quickly obtain R. =1 Ω conclusion. [Example 2] Charged particles with mass m and electric charge q. The direction of the vertical magnetic field is injected from the point A into the magnetic field port, passing through the point P, the angle between the line connecting the AP and the incident direction is θ, and the time from A to P is elapsed for the particle. :