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有这样一道题,在很多教学资料上出现过,如下:如图1所示,竖直环A半径为R固定在木板上,B的左右两侧各有一挡板固定在地面上,B不能左右运动,在环的最低点静放一小球C,A,B,C的质量均为m的一水平向右的瞬间速度v,小球会在环内侧做圆周运动,为保证小球能通过环的最高点,且不会使环在竖直方向跳起(不计小球和环的摩擦力),瞬时速度必须满足()。A.最小值R4g B.最大值R6g C.最小值R6g D.最大值R7g本题给予的答案是D。解析:若小球在最高点处给予环A的弹力不大于2mg,即R21mv=FN+mg≤3mg,2 211 12 R2 2mv=mv-mg,由这两式得出v≤R7g。
There is such a problem, appeared in a lot of teaching materials, as follows: As shown in Figure 1, the vertical ring A radius R fixed on the board, B on both sides have a baffle fixed to the ground, B can not be around Exercise, at the lowest point of the ring resting a small ball C, A, B, C are the quality of a horizontal right moment of velocity v, the ball will do a circular motion inside the ring, in order to ensure the ball can pass The highest point of the ring, and does not make the ring jump in the vertical direction (excluding ball and ring friction), instantaneous speed must meet (). A. Minimum R4g B. Maximum R6g C. Minimum R6g D. Maximum R7g The answer to this question is D. Analysis: If the ball at the highest point to give the elasticity of the ring A is not greater than 2mg, that is R21mv = FN + mg ≤ 3mg, 2 211 12 R2 2mv = mv-mg, from these two equations derived v ≤ R7g.