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第二届全国中学生力学竞赛中有这样一道题:一质点自倾角为α的斜面上方的定点O沿光滑斜槽OP从静止开始下滑,如图1所示。为使质点在最短时间内从O点到达斜面,则斜槽与竖直方向的夹角β等于__。这道题摘自周衍柏编的《理论力学教程》,可见其难度是比较大的。 [错解]根据平面几何可知,直线外一点到直线的距离最短,故过O作OP垂直斜面,如图2所示,那么由直角三角形O_1BA与直角三角形OPA相似可得β=α,即斜槽与竖直方向夹角β=α时,质点能用最短时间从O到达斜面。上述结果是错误的。其原因是这部分考生错误地把质点沿斜糟的匀变速直线运动当作匀速直线运动处理了。
The second session of the National Middle School Student Mechanics Contest has such a question: A fixed point O above the slope of a particle with a self-dip angle of inclination along the smooth slope OP starts to slide from the standstill, as shown in Figure 1. In order for the particle to reach the slope from point O in the shortest time, the angle β between the slope and the vertical direction is equal to __. This question was taken from Zhou Yanbo’s “Theory of Theoretical Mechanics” and it shows that the difficulty is relatively large. [False Solution] According to the plane geometry, the distance from the straight line to the straight line is the shortest, so O is used as the OP vertical slope, as shown in Figure 2, then the right angle triangle O_1BA is similar to the right angle triangle OPA and β=α, that is, oblique When the angle between the groove and the vertical direction β=α, the particle can reach the slope from O in the shortest time. The above result is wrong. The reason for this is that this part of the examinee mistakenly treated the particle as a uniform linear motion along a diagonal uniform linear motion.