题目内容
(12分)如图所示,粗糙水平轨道AB与竖直平面内的光滑半圆轨道BDC在B处平滑连接,B、C分别为半圆轨道的最低点和最高点,D为半圆轨道的最右端。一个质量m的小物体P被一根细线拴住放在水平轨道上,细线的左端固定在竖直墙壁上。在墙壁和P之间夹一根被压缩的轻弹簧,此时P到B点的距离为x0。物体P与水平轨道间的动摩擦因数为μ,半圆轨道半径为R。现将细线剪断,P被弹簧向右弹出后滑上半圆轨道,恰好能通过C点。试求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250036163732654.jpg)
(1)物体经过B点时的速度的大小?
(2)细线未剪断时弹簧的弹性势能的大小?
(3)物体经过D点时合力的大小?
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250036163732654.jpg)
(1)物体经过B点时的速度的大小?
(2)细线未剪断时弹簧的弹性势能的大小?
(3)物体经过D点时合力的大小?
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003616420747.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003616389629.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003616404904.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003616420747.png)
试题分析:(1)由于小球恰好能通过最高点C,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003616435767.png)
B到C机械能守恒,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250036164511083.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003616389629.png)
(2)P到B过程弹力、摩擦力做功,动能定理:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250036164671176.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250036164821177.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003616404904.png)
(3)B到D机械能守恒,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250036165131038.png)
D点轨道对物块的支持力
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003616529937.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003616545629.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003616420747.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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