题目内容
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115601924978.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241156019403299.jpg)
(1) 小球滑过乙轨道,设恰好能做完整圆周运动不脱离轨道在最高点时
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115601955742.jpg)
……………………(1分)
…………………(1分)
设CD长为
,从开始到乙轨道的最高点,对小球根据动能定理
……………………(2分)
解得:
………………………………(1分)
(2)小球不能滑过乙轨道,且不脱离轨道,则在乙轨道内上升的最大高度为r。设CD的长度为s2,则
…………………… (2分)
解得:
……………………(1分)
又小物块至少滑过D点,
…………(1分)
…………(1分)
所以CD段可取长度为
﹥
或
…………………(2分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115601955742.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115601971494.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115602189292.gif)
设CD长为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115602205199.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115602220763.gif)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115602236550.gif)
(2)小球不能滑过乙轨道,且不脱离轨道,则在乙轨道内上升的最大高度为r。设CD的长度为s2,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115602252667.gif)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115602267504.gif)
又小物块至少滑过D点,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115602283594.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115602298390.gif)
所以CD段可取长度为
﹥
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115602314568.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824115602314627.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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