题目内容

(8分)如图所示,在竖直平面内固定着光滑的圆弧槽,它的末端切线水平,上端离地面H, 一个质量为m的小球从上端无初速滑下,若使小球的水平射程出现最大值,则圆弧槽的半径为多大?此情况下,小球达圆弧末端时对槽的压力多大?

解析:

(1)设圆弧半径为R

从释放到恰抛出,由机械能守恒

                                                               (1分)

                                                             (1分)

从抛出到落地为平抛

                                                                   (1分)

                                                        (1分)

                                                    (1分)

当R=H-R时,X有最大质

时,                                        (1分)

(2)对圆槽未端:                                      (2分)

                                                (1分)

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