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在编制和解答高中物理习题时,都会考虑和应用高中阶段所学的数学知识。解有些习题时,表面看是“山穷水尽疑无路”,可是用上相关的数学知识后,会感到“柳暗花明又一村”。下面举例分析圆的知识在解答物理题中的应用。例1.从一个坚直圆的顶点A,沿不同方向有许多光滑轨道,如图1所示。求证小球分别山A点由静止沿不同轨道滑至圆周的B、C、E、D各点。所需的时间相等。(设直径AE为d) 解:设任一轨道与直径AE的夹角为θ,位移为s.根据运动学和动力学的知识,可知:s=gcosθ·t~2/2,t=(2s/gcosθ)~(1/2)。表面看,
When preparing and answering high school physics exercises, all the mathematics knowledge learned in high school will be considered and applied. Solving some problems, the surface is “the mountains and the rivers are utterly ignorant.” However, after using the relevant mathematical knowledge, they will feel that “there is no such thing as another village.” The following example analyzes the application of circle knowledge in solving physical problems. Example 1. From a perfectly rounded vertex A, there are many smooth tracks in different directions, as shown in Figure 1. Prove the small ball respectively, point A, point B, C, E, and D, which slide along the different orbits to the circumference. The required time is equal. (Set the diameter AE to d) Solution: Let the angle between any orbit and the diameter AE be θ and the displacement be s. According to kinematics and dynamics knowledge, it can be known that: s=gcosθ·t~2/2, t=( 2s/gcosθ)~(1/2). On the surface,