题目内容
表演“水流星”节目,如图所示,拴杯子的绳子长为
,绳子能够承受的最大拉力是杯子和杯内水重力的8倍.要使绳子不断,节目获得成功,重力加速度为g,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241254194975028.png)
小题1:杯子通过最高点时速度的最小值为多大?
小题2:通过最低点时速度的最大值为多大?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125419154285.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241254194975028.png)
小题1:杯子通过最高点时速度的最小值为多大?
小题2:通过最低点时速度的最大值为多大?
小题1:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125419809419.png)
小题2:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125419871489.png)
本题考查曲线运动
小题1:当杯子通过最高点时,节目获得成功,则杯子的重力完全充当向心力,绳子对杯子的弹力为零.设此时最小速度为
,则有
,解得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125419934491.png)
即杯子通过最高点时速度的最小值为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125419934491.png)
小题2:当杯子通过最低点时,绳子除要提供向心力之外,还要克服杯子及水自身的重力,即绳子的拉力包括重力
及向心力
;要使节目获得成功,杯子的重力
及向心力
应不大于绳子的最大拉力
,
设杯子通过最低点时速度时最速度为
,则有
,解得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125420636596.png)
通过最低点时速度的最大值为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125420667565.png)
小题1:当杯子通过最高点时,节目获得成功,则杯子的重力完全充当向心力,绳子对杯子的弹力为零.设此时最小速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125419903280.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125419918637.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125419934491.png)
即杯子通过最高点时速度的最小值为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125419934491.png)
小题2:当杯子通过最低点时,绳子除要提供向心力之外,还要克服杯子及水自身的重力,即绳子的拉力包括重力
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125419981392.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125420012349.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125419981392.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125420012349.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125420105480.png)
设杯子通过最低点时速度时最速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125420121312.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125420464791.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125420636596.png)
通过最低点时速度的最大值为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824125420667565.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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