题目内容
如图所示,一光滑斜面的直角点A处固定一带电荷量为+q、质量为m的绝缘小球,另一同样小球置于斜面顶点B处,已知斜面长为L,现把上部小球从B点由静止自由释放,球能沿斜面从B点运动到斜面底端C处,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241409359701127.png)
(1)小球从B处开始运动到斜面中点D处时的速度;
(2)小球运动到斜面底端C处时,球对斜面的压力是多大?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241409359701127.png)
(1)小球从B处开始运动到斜面中点D处时的速度;
(2)小球运动到斜面底端C处时,球对斜面的压力是多大?
(1)
(2)
mg-![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140936126634.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140936033543.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140936079425.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140936126634.png)
由于小球沿斜面下滑过程中所受电场力为变力,因此不能用功的定义来求解,只能用动能定理求解
(1)由题意知:小球运动到D点时,由于AD=AB,所以有电势φD=φB,即UDB=φD-φB=0①
则由动能定理得:mg
sin30°=
mv
-0②
联立①②解得:vD=
③
(2)当小球运动至C点时,对球受力分析如图所示,则由平衡条件得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241409365941938.png)
FN+F库sin30°=mgcos30°④
由库仑定律得:
F库=
⑤
联立④⑤得:
FN=
mg-![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140936126634.png)
由牛顿第三定律得:FN′=FN=
mg-
.
(1)由题意知:小球运动到D点时,由于AD=AB,所以有电势φD=φB,即UDB=φD-φB=0①
则由动能定理得:mg
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140936204372.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140936267319.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140936376307.png)
联立①②解得:vD=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140936033543.png)
(2)当小球运动至C点时,对球受力分析如图所示,则由平衡条件得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241409365941938.png)
FN+F库sin30°=mgcos30°④
由库仑定律得:
F库=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140936657893.png)
联立④⑤得:
FN=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140936079425.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140936126634.png)
由牛顿第三定律得:FN′=FN=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140936079425.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140936126634.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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