题目内容
一个半径为R=0.5m的水平转盘可以绕竖直轴O’O’’转动,水平转盘中心O’处有一个光滑小孔,用一根长L=1m细线穿过小孔将质量分别为200g和500g小球A和小物块B连接,小物块B 放在水平转盘的边缘且与转盘保持相对静止,如图所示。现让小球A在水平面做角速度ωA=" 5" rad/s的匀速圆周运动,小物块B与水平转盘间的动摩擦因素μ="0.3" (取g="10" m/s2),求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241331514084493.jpg)
(1)细线与竖直方向的夹角θ;
(2)小物块B与水平转盘间要保持相对静止,水平转盘角速度ωB的取值范围;
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241331514084493.jpg)
(1)细线与竖直方向的夹角θ;
(2)小物块B与水平转盘间要保持相对静止,水平转盘角速度ωB的取值范围;
(1)小球A的重力和绳子的拉力合力提供向心力,
,
,
,![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133151595491.png)
(2)
,所以取值范围是![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133151657929.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133151455833.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133151501615.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133151564602.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133151595491.png)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241331516261240.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133151657929.png)
(1)小球A的重力和绳子的拉力合力提供向心力,
,
,
,![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133151595491.png)
(2)绳子的拉力为
,当转盘转速较大时,B有向外运动的趋势,静摩擦力指向圆心,有
,当转盘转速较小时,B有向里运动趋势,静摩擦力指向外,
,所以取值范围是![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133151657929.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133151455833.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133151501615.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133151564602.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133151595491.png)
(2)绳子的拉力为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133151938928.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241331519851262.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241331516261240.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824133151657929.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目